From b0d970cfc76de81024808516fb5540ca5fc1a3b5 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Tue, 23 Jul 2024 02:15:54 +0200 Subject: [PATCH 001/124] Update README.md Moved Janelle from developer group to previous contributors --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index fef06dae..8555a64b 100644 --- a/README.md +++ b/README.md @@ -79,13 +79,13 @@ Read our [Contribution Guidelines](CONTRIBUTING.md) to know how you can help to - [Christa van IJzendoorn](mailto:C.O.vanIJzendoorn@tudelft.nl) at Delft University of Technology - [Caroline Hallin](mailto:E.C.Hallin@tudelft.nl) at Delft University of Technology - [Glenn Strypsteen](mailto:glenn.strypsteen@kuleuven.be) at Katholieke Universiteit Leuven -- [Janelle Skaden](mailto:Janelle.E.Skaden@usace.army.mil) at U.S. Army Engineer Research and Development Center (ERDC) **Previous Members & Contributors:** - [Bas Hoonhout](mailto:bas@hoonhout.com) (founder) - Tom Pak - Pieter Rauwoens - Lisa Meijer +- Janelle Skaden ## Citation From 649f716f8dfbf318209406052074bbac9ecbee7c Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Tue, 23 Jul 2024 02:25:05 +0200 Subject: [PATCH 002/124] Update model.rst added vegetation heading --- docs/user/model.rst | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/docs/user/model.rst b/docs/user/model.rst index 47e3a783..d8a83b92 100644 --- a/docs/user/model.rst +++ b/docs/user/model.rst @@ -257,6 +257,10 @@ grain size dependency is implemented through :math:`u_{\mathrm{th}}`. :math:`u_{\mathrm{th}}` typically varies between 1 and 6 m/s for sand. +Vegetation +------------------------------------- + + Simulation of Sediment Sorting and Beach Armoring ------------------------------------------------- From b1a791fcfcbb2eeac1d5a1961664348e92e2cbf0 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Tue, 23 Jul 2024 02:34:45 +0200 Subject: [PATCH 003/124] Update index.rst --- docs/index.rst | 19 +++++-------------- 1 file changed, 5 insertions(+), 14 deletions(-) diff --git a/docs/index.rst b/docs/index.rst index 1c5eab26..d00dfd3d 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -27,22 +27,13 @@ Contents :caption: User Documentation :maxdepth: 2 + user/introduction user/installation - user/whatsnew - user/model - user/implementation - user/defaults - user/inputfiles - user/output + user/model_description + user/model_setup + user/tutorials_and_examples user/sourcecode - user/bibliography - -.. toctree:: - :caption: Tutorials - :maxdepth: 2 - - tutorials/sandmotor - tutorials/2D-parabolic + user/references .. toctree:: :caption: Developer Documentation From 4919b642ebf3f7cf419a1c53cd532fd58d8eda12 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Tue, 23 Jul 2024 02:51:41 +0200 Subject: [PATCH 004/124] Update and rename bibliography.rst to references.rst --- docs/user/{bibliography.rst => references.rst} | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) rename docs/user/{bibliography.rst => references.rst} (75%) diff --git a/docs/user/bibliography.rst b/docs/user/references.rst similarity index 75% rename from docs/user/bibliography.rst rename to docs/user/references.rst index 1109f3f3..ebe4af17 100644 --- a/docs/user/bibliography.rst +++ b/docs/user/references.rst @@ -1,8 +1,8 @@ -Bibliography +References ============= .. rubric:: References in this documentation .. bibliography:: :cited: - :style: plain \ No newline at end of file + :style: plain From 2ba3ada6bfbf6a823ca93fbed613e99c1d5d97de Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Tue, 23 Jul 2024 02:52:37 +0200 Subject: [PATCH 005/124] Create introduction.rst --- docs/user/introduction.rst | 1 + 1 file changed, 1 insertion(+) create mode 100644 docs/user/introduction.rst diff --git a/docs/user/introduction.rst b/docs/user/introduction.rst new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/docs/user/introduction.rst @@ -0,0 +1 @@ + From 4ceb967efc2427cddb2ac456b04f72cc33ca5f00 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Tue, 23 Jul 2024 02:53:32 +0200 Subject: [PATCH 006/124] Rename model.rst to model_description.rst --- docs/user/{model.rst => model_description.rst} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename docs/user/{model.rst => model_description.rst} (100%) diff --git a/docs/user/model.rst b/docs/user/model_description.rst similarity index 100% rename from docs/user/model.rst rename to docs/user/model_description.rst From c7b624651f20466db027912866fdedf4b84a6b7c Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Tue, 23 Jul 2024 02:54:12 +0200 Subject: [PATCH 007/124] Rename inputfiles.rst to model_setup.rst --- docs/user/{inputfiles.rst => model_setup.rst} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename docs/user/{inputfiles.rst => model_setup.rst} (100%) diff --git a/docs/user/inputfiles.rst b/docs/user/model_setup.rst similarity index 100% rename from docs/user/inputfiles.rst rename to docs/user/model_setup.rst From e770473ebf275d3b3c36a8e1cce2ef4f0dcbbd60 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Tue, 23 Jul 2024 02:54:47 +0200 Subject: [PATCH 008/124] Update model_setup.rst --- docs/user/model_setup.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index 1421d384..bf55327b 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -1,4 +1,4 @@ -Input files +Model setup ================= The computational grid and boundary conditions for AeoLiS are specified through external From cc21034238f55647323b83db3d92f051f1092912 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Tue, 23 Jul 2024 02:56:55 +0200 Subject: [PATCH 009/124] Create tutorials_and_examples.rst --- docs/user/tutorials_and_examples.rst | 1 + 1 file changed, 1 insertion(+) create mode 100644 docs/user/tutorials_and_examples.rst diff --git a/docs/user/tutorials_and_examples.rst b/docs/user/tutorials_and_examples.rst new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/docs/user/tutorials_and_examples.rst @@ -0,0 +1 @@ + From b2e4f16dd9cf8225e54dc33ccee9bdaa15381d5a Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 19:52:40 +0200 Subject: [PATCH 010/124] Update index.rst --- docs/index.rst | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/index.rst b/docs/index.rst index d00dfd3d..e728f1b6 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -31,6 +31,7 @@ Contents user/installation user/model_description user/model_setup + user/model_interaction user/tutorials_and_examples user/sourcecode user/references From 8fd581a1e56becdbdbd7a97cf56596b7ce1f9728 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 19:54:56 +0200 Subject: [PATCH 011/124] Create model_interaction.rst --- docs/user/model_interaction.rst | 1 + 1 file changed, 1 insertion(+) create mode 100644 docs/user/model_interaction.rst diff --git a/docs/user/model_interaction.rst b/docs/user/model_interaction.rst new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/docs/user/model_interaction.rst @@ -0,0 +1 @@ + From 5dd798a4aaa87ee0f79853a6c1dd2763ab658158 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 19:58:39 +0200 Subject: [PATCH 012/124] Update model_interaction.rst --- docs/user/model_interaction.rst | 14 ++++++++++++++ 1 file changed, 14 insertions(+) diff --git a/docs/user/model_interaction.rst b/docs/user/model_interaction.rst index 8b137891..bfddd4d6 100644 --- a/docs/user/model_interaction.rst +++ b/docs/user/model_interaction.rst @@ -1 +1,15 @@ +Model interaction +================= +ADD INTRODUCTION TO MODEL INTRODUCTION - WHY, HOW + +Callback function +----------------- + + +Hotstart +-------- + + +BMI +--- From b42acc90555ff5361c5ffd70aa130520543365bb Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 20:16:09 +0200 Subject: [PATCH 013/124] Update model_interaction.rst --- docs/user/model_interaction.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/user/model_interaction.rst b/docs/user/model_interaction.rst index bfddd4d6..5eabf9dc 100644 --- a/docs/user/model_interaction.rst +++ b/docs/user/model_interaction.rst @@ -11,5 +11,5 @@ Hotstart -------- -BMI ---- +BMI (Basic Model Interface) +--------------------------- From 20f4b32c2e95a496311b9d5e201938f0c52eab7f Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 22:34:16 +0200 Subject: [PATCH 014/124] Update implementation.rst --- docs/user/implementation.rst | 28 ---------------------------- 1 file changed, 28 deletions(-) diff --git a/docs/user/implementation.rst b/docs/user/implementation.rst index 532b560d..f8693298 100644 --- a/docs/user/implementation.rst +++ b/docs/user/implementation.rst @@ -700,34 +700,6 @@ If the groundwater elevation is larger than the bed elevation, there is a seepag and the groundwater elevation is set equal to the bed elevation. On the landward boundary, a no-flow condition, :math:`\frac{{\partial \eta }}{{\partial t}} = 0` (Neumann condition), or constant head, :math:`\eta = constant` (Dirichlet condition), is prescribed. - -Basic Model Interface (BMI) ---------------------------- - -A Basic Model Interface (BMI, :cite:`Peckham2013`) is implemented -that allows interaction with the model during run time. The model can -be implemented as a library within a larger framework as the interface -exposes the initialization, finalization and time stepping -routines. As a convenience functionality the current implementation -supports the specification of a callback function. The callback -function is called at the start of each time step and can be used to -exchange data with the model, e.g. update the topography from -measurements. - -An example of a callback function, that is referenced in the model -input file or through the model command-line options as -``callback.py:update``, is: - -.. code:: - - import numpy as np - - def update(model): - val = model.get_var('zb') - val_new = val.copy() - val_new[:,:] = np.loadtxt('measured_topography.txt') - model.set_var('zb', val_new) - .. .. rubric:: Bibliography .. .. bibliography:: From fb55ab135ed92b4102cf8ce6975996df90a1925e Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 22:34:35 +0200 Subject: [PATCH 015/124] Update model_interaction.rst --- docs/user/model_interaction.rst | 27 ++++++++++++++++++++++++++- 1 file changed, 26 insertions(+), 1 deletion(-) diff --git a/docs/user/model_interaction.rst b/docs/user/model_interaction.rst index 5eabf9dc..c4d6e3e9 100644 --- a/docs/user/model_interaction.rst +++ b/docs/user/model_interaction.rst @@ -11,5 +11,30 @@ Hotstart -------- -BMI (Basic Model Interface) +Basic Model Interface (BMI) --------------------------- + +A Basic Model Interface (BMI, :cite:`Peckham2013`) is implemented +that allows interaction with the model during run time. The model can +be implemented as a library within a larger framework as the interface +exposes the initialization, finalization and time stepping +routines. As a convenience functionality the current implementation +supports the specification of a callback function. The callback +function is called at the start of each time step and can be used to +exchange data with the model, e.g. update the topography from +measurements. + +An example of a callback function, that is referenced in the model +input file or through the model command-line options as +``callback.py:update``, is: + +.. code:: + + import numpy as np + + def update(model): + val = model.get_var('zb') + val_new = val.copy() + val_new[:,:] = np.loadtxt('measured_topography.txt') + model.set_var('zb', val_new) + From 4e90a305552ff516e9882e18005b0773dbdc8b09 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 22:58:26 +0200 Subject: [PATCH 016/124] Update introduction.rst --- docs/user/introduction.rst | 3 +++ 1 file changed, 3 insertions(+) diff --git a/docs/user/introduction.rst b/docs/user/introduction.rst index 8b137891..f7ae24be 100644 --- a/docs/user/introduction.rst +++ b/docs/user/introduction.rst @@ -1 +1,4 @@ +.. _introduction: +Introduction +============ From 8f8d72f8e220ab7d4008a1ff6bc84c9f09305919 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:07:38 +0200 Subject: [PATCH 017/124] Update model_setup.rst --- docs/user/model_setup.rst | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index bf55327b..8eeae38d 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -1,5 +1,9 @@ Model setup ================= +INTRODUCTORY TEXT + +Model input +----------- The computational grid and boundary conditions for AeoLiS are specified through external input files called by the model parameter file aeolis.txt. The computational grid is defined From dd0cfcd48eb26bf4292de176ea5eaca48a1afa4f Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:11:59 +0200 Subject: [PATCH 018/124] Update model_setup.rst --- docs/user/model_setup.rst | 30 ++++++++++++++++++++---------- 1 file changed, 20 insertions(+), 10 deletions(-) diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index 8eeae38d..30cbf193 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -39,7 +39,7 @@ files can be found in the table below. Each file is further defined below. - File containing meteorological time series data aeolis.txt ----------- +^^^^^^^^^^ This is the parameter file for AeoLiS that defines the model processes and boundary conditions. Parameters in the file are specified by various keywords; each keyword has a pre-defined @@ -52,7 +52,7 @@ process keywords in aeolis.txt to T (True) and F (False). Example aeolis.txt pa found in the examples folder on the AeoLiS GitHub. x.grd ------ +^^^^^ The x.grd file defines the computational grid in the cross-shore direction defined in meters. In a 1-dimensional (1D) case, the file contains a single column of cross-shore locations @@ -62,7 +62,7 @@ where each value corresponds to a specific location in the 2D grid. The file ca and is referenced from the parameters file with the xgrid_file keyword. y.grd ------ +^^^^^ This file defines the computational grid in the alongshore direction. In a 1D case, y.grd will contain a single column of zeros. In a 2D case, similar to the x.grd file, @@ -73,7 +73,7 @@ As with the x.grd file, this file can be renamed and is referenced from the para keyword: ygrid_file. z.grd ------ +^^^^^ The z.grd file provides the model with the elevation information for the computational grid defined in x.grd and y.grd. Similar to x.grd and y.grd, when running @@ -84,7 +84,7 @@ positive is up and negative is down. The file can be renamed and is referenced parameters file with the keyword: bed_file. veg.grd -------- +^^^^^^^ The veg.grd file is an optional grid providing initial vegetation coverage (density) at each position in the model domain defined in x.grd and y.grd. Similar to the grid files, if simulations are in @@ -102,7 +102,7 @@ where each red dots represent vegetation cover at each cross-shore position. File format for a 1D AeoLis vegetation grid. Each red dot is the vegetation density at a specific location in the computational grid. mass.txt --------- +^^^^^^^^ The mass.txt file allows users to specify variations in grain size distribution in both horizontal and vertical directions. If the grain size distribution is constant throughout @@ -147,7 +147,7 @@ file for AeoLis can be seen below. at each location in the computational grid (x, y, bed layer). wind.txt --------- +^^^^^^^^ The wind.txt file provides the model with wind boundary conditions and is formatted similar to the tide.txt and wave.txt files. The first column is time in seconds from @@ -167,7 +167,7 @@ importance. File format for wind boundary conditions file for AeoLis input. tide.txt --------- +^^^^^^^^ The tide.txt file contains the water elevation data for the duration of the simulation. It is formatted such that the first column is time in seconds and @@ -185,7 +185,7 @@ time or water elevation. File format for the water elevation conditions file for AeoLis input. wave.txt --------- +^^^^^^^^ The wave.txt file provides the model with wave data used in AeoLiS for runup calculations. The file is formatted similar to tide.txt but has three columns instead of two. @@ -204,7 +204,7 @@ a data value. File format for the wave conditions file for AeoLis input. meteo.txt ---------- +^^^^^^^^^ The meteo.txt file contains meteorological data used to simulate surface moisture in the model domain (see Simulation of surface moisture in Model description on for surface moisture implementation in AeoLiS). This file is formatted similar to the other environmental boundary @@ -223,3 +223,13 @@ column is air pressure (kPa). :align: center File format for meteorological data used to simulate surface moisture in AeoLiS where each red dot represents a time series value. + + +Model state/output +------------------ + +Activate/deactivate processes +----------------------------- + +Solver selection +---------------- From ec35c39fc9f21a1c443056d23819b0b6665fb802 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:12:59 +0200 Subject: [PATCH 019/124] Update model_setup.rst --- docs/user/model_setup.rst | 14 ++++++++++++++ 1 file changed, 14 insertions(+) diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index 30cbf193..66412359 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -228,6 +228,20 @@ column is air pressure (kPa). Model state/output ------------------ +The AeoLiS model state is described by a collection of spatial grid +variables with at least one value per horizontal grid cell. Specific +model state variables can also be subdivided over bed composition +layers and/or grain size fractions. All model state variables can be +part of the model netCDF4 output. The current model state variables +are listed below. + +.. literalinclude:: ../../aeolis/constants.py + :language: python + :start-after: #: Aeolis model state variables + :end-before: #: AeoLiS model default configuration + + + Activate/deactivate processes ----------------------------- From 413304838edda095c46e9ca24fca334768efb30d Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:13:27 +0200 Subject: [PATCH 020/124] Delete docs/user/output.rst --- docs/user/output.rst | 14 -------------- 1 file changed, 14 deletions(-) delete mode 100644 docs/user/output.rst diff --git a/docs/user/output.rst b/docs/user/output.rst deleted file mode 100644 index 7acd5ec7..00000000 --- a/docs/user/output.rst +++ /dev/null @@ -1,14 +0,0 @@ -Model state/output -================== - -The AeoLiS model state is described by a collection of spatial grid -variables with at least one value per horizontal grid cell. Specific -model state variables can also be subdivided over bed composition -layers and/or grain size fractions. All model state variables can be -part of the model netCDF4 output. The current model state variables -are listed below. - -.. literalinclude:: ../../aeolis/constants.py - :language: python - :start-after: #: Aeolis model state variables - :end-before: #: AeoLiS model default configuration From d293024f5a33af55ad0b3d26e63bb4cb1fe69af7 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:16:08 +0200 Subject: [PATCH 021/124] Update model_setup.rst --- docs/user/model_setup.rst | 22 ++++++++++++++++++---- 1 file changed, 18 insertions(+), 4 deletions(-) diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index 66412359..8cb286df 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -224,6 +224,24 @@ column is air pressure (kPa). File format for meteorological data used to simulate surface moisture in AeoLiS where each red dot represents a time series value. +Default settings +---------------- + +The AeoLiS model can be configured using a model configuration +file. For any configuration parameters not defined in the model +configuration file, or in case the model configuration file is absent, +the default model configuration is used. The default model +configuration is listed below. + +.. literalinclude:: ../../aeolis/constants.py + :language: python + :start-after: #: AeoLiS model default configuration + :end-before: #: Merge initial and model state + + +Activate/deactivate processes +----------------------------- + Model state/output ------------------ @@ -241,9 +259,5 @@ are listed below. :end-before: #: AeoLiS model default configuration - -Activate/deactivate processes ------------------------------ - Solver selection ---------------- From 4aad034b137ecd34306e6f08d9e5a86676242004 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:16:50 +0200 Subject: [PATCH 022/124] Delete docs/user/defaults.rst --- docs/user/defaults.rst | 16 ---------------- 1 file changed, 16 deletions(-) delete mode 100644 docs/user/defaults.rst diff --git a/docs/user/defaults.rst b/docs/user/defaults.rst deleted file mode 100644 index 504cfc26..00000000 --- a/docs/user/defaults.rst +++ /dev/null @@ -1,16 +0,0 @@ - -.. _default settings: - -Default settings -================ - -The AeoLiS model can be configured using a model configuration -file. For any configuration parameters not defined in the model -configuration file, or in case the model configuration file is absent, -the default model configuration is used. The default model -configuration is listed below. - -.. literalinclude:: ../../aeolis/constants.py - :language: python - :start-after: #: AeoLiS model default configuration - :end-before: #: Merge initial and model state From 75993e296a4701b2af2d905e6cc1c15adcd019a3 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:21:15 +0200 Subject: [PATCH 023/124] Update index.rst --- docs/index.rst | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/index.rst b/docs/index.rst index e728f1b6..343beaa1 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -25,7 +25,7 @@ Contents .. toctree:: :caption: User Documentation - :maxdepth: 2 + :maxdepth: 3 user/introduction user/installation @@ -38,7 +38,7 @@ Contents .. toctree:: :caption: Developer Documentation - :maxdepth: 2 + :maxdepth: 3 developer/quickstart developer/testing-introduction @@ -46,7 +46,7 @@ Contents .. toctree:: :caption: Current Development - :maxdepth: 2 + :maxdepth: 3 developer/modularity developer/domain-decomposition From 0a2a86bc375d9c132efaa634045175c9d001e6da Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:25:31 +0200 Subject: [PATCH 024/124] Update model_description.rst --- docs/user/model_description.rst | 693 ++++++++++++++++++++++++++++++++ 1 file changed, 693 insertions(+) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index d8a83b92..3b453e7c 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -103,6 +103,659 @@ simulation. The model is initially intended to provide accurate sediment fluxes from the beach to the dunes rather than to simulate subsequent dune formation. +Numerical implementation of the advection equation +-------------------------------------------------- + +The advection equation is implemented in two-dimensional form +following: + +.. math:: + :label: apx-advection + + \frac{\partial c}{\partial t} + + u_{z,\mathrm{x}} \frac{\partial c}{\partial x} + + u_{z,\mathrm{y}} \frac{\partial c}{\partial y} = + \frac{c_{\mathrm{sat}} - c}{T} + +in which :math:`c` [:math:`\mathrm{kg/m^2}`] is the sediment mass per +unit area in the air, :math:`c_{\mathrm{sat}}` [:math:`\mathrm{kg/m^2}`] is the +maximum sediment mass in the air that is reached in case of +saturation, :math:`u_{z,\mathrm{x}}` and :math:`u_{z,\mathrm{y}}` are the x- and +y-component of the wind velocity at height :math:`z` [m], :math:`T` [s] is an +adaptation time scale, :math:`t` [s] denotes time and :math:`x` [m] and :math:`y` [m] +denote cross-shore and alongshore distances respectively. + +The formulation is discretized in different ways to allow for different types of simulations balancing accuracy vs. computational resources. The conservative method combined with an euler backward scheme (written by Prof. Rauwoens) is the current default for most simulations. Non-conservative methods end explicit Euler forward schemes are also available. + +Default scheme -- Conservative Euler Backward Implicit +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The default numerical method assumes the advection scheme in a conservative form in combination with an euler backward scheme. This scheme is prepared to use a TVD method but this is not implemented yet (add footnote{Total Variance Diminishing, this is explained in the lecture notes by Zijlema p94}) + +The fluxes at the interface of the cells are defined used in the advection terms: + +.. math:: + :label: conservative1 + + \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t} + \\ + \frac{u_{\text{x},i+1/2,j} \cdot c^{n+1}_{i+1/2,j,k} - u_{\text{x},i-1/2,j} \cdot c^{n+1}_{i-1/2,j,k}}{\Delta x} + \\ + \frac{u_{\text{y},i,j+1/2} \cdot c^{n+1}_{i,j+1/2,k} - u_{\text{y},i,j-1/2} \cdot c^{n+1}_{i,j-1/2,k}}{\Delta y} + + \\ = \\ + \frac{\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i.j.k} + c^{n+1}_{i,j,k} ) - c^{n+1}_{i,j,k}}{T} + +In which :math:`n` is the time step index, :math:`i` and :math:`j` are the cross-shore and alongshore spatial grid cell indices and :math:`k` is the grain size fraction index. :math:`w` [-] is the weighting factor used for the weighted addition of the saturated sediment concentrations over all grain size fractions. Note that u is spatially varying but has no temporal index. This is because u is a result of a separate wind solver and considered temporally invariant in the advection solver. + +Now we use a correction algorithm where: + +.. math:: + :label: conservative2 + + c^{n+1}_{i,j,k} = c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} + +where :math:`\delta c_{i,j,k}` is solved for and :math:`*` denotes the previous iteration. + +When now assuming an upwind scheme in space, we can derive 4 concentrations at the cell faces which are dependent on the velocity at the cell faces. + +We assume in x direction: + +.. math:: + + c^{n+1}_{i+1/2,j,k} = + \begin{cases} + c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{x},i+1/2,j} > 0$,}\\ + c^{n+1 *}_{i+1,j,k} + \delta c_{i+1,j,k} & \text{if $u_{\text{x},i+1/2,j} < 0$.} + \end{cases} + +.. math:: + + c^{n+1}_{i-1/2,j,k} = + \begin{cases} + c^{n+1 *}_{i-1,j,k} + \delta c_{i-1,j,k} & \text{if $u_{\text{x},i-1/2,j} > 0$,}\\ + c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{x},i-1/2,j} < 0$.} + \end{cases} + +and in y-direction: + +.. math:: + + c^{n+1}_{i,j+1/2,k} = + \begin{cases} + c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{y},i,j+1/2} > 0$,}\\ + c^{n+1 *}_{i,j+1,k} + \delta c_{i,j+1,k} & \text{if $u_{\text{y},i,j+1/2} < 0$.} + \end{cases} + +.. math:: + + c^{n+1}_{i,j-1/2,k} = + \begin{cases} + c^{n+1 *}_{i,j-1,k} + \delta c_{i,j-1,k} & \text{if $u_{\text{y},i,j-1/2} > 0$,}\\ + c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{y},i,j-1/2} < 0$.} + \end{cases} + +Now we assume: + +- :math:`\Gamma_x = 1` if :math:`u_{\text{x},i+1/2,j,k} > 0` and :math:`\Gamma_x = 0` if :math:`u_{\text{x},i+1/2,j,k} \leq 0` +- :math:`\Gamma_y = 1` if :math:`u_{\text{y},i,j+1/2,k} > 0` and :math:`\Gamma_x = 0` if :math:`u_{\text{y},i,j+1/2,k} \leq 0` + +(We did not test if this works well with diverging and converging flows. We may need another term that describes the conditions at the negative cell faces if they are of opposite direction than the positive cell faces and vice versa) + +Let's continue for the moment so that + +.. math:: + + \begin{gathered} + \frac{c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} - c^n_{i,j,k}}{\Delta t} + \\ + \Gamma_x \cdot \frac{u_{\text{x},i+1/2,j} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}) - u_{\text{x},i-1/2,j} \cdot (c^{n+1 *}_{i-1,j,k} + \delta c_{i-1,j,k})}{\Delta x} + \\ + (1-\Gamma_x) \cdot \frac{u_{\text{x},i+1/2,j} \cdot (c^{n+1 *}_{i+1,j,k} + \delta c_{i+1,j,k}) - u_{\text{x},i-1/2,j} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k})}{\Delta x} + \\ + \Gamma_y \cdot \frac{u_{\text{y},i,j+1/2} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}) - u_{\text{y},i,j-1/2} \cdot (c^{n+1 *}_{i,j-1,k} + \delta c_{i,j-1,k})}{\Delta y} + \\ + (1-\Gamma_y) \cdot \frac{u_{\text{y},i,j+1/2} \cdot (c^{n+1 *}_{i,j+1,k} + \delta c_{i,j+1,k}) - u_{\text{y},i,j-1/2} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k})}{\Delta y} + + \\ = \\ + \frac{\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i,j,k}+c^{n+1 *}_{i,j,k} + \xcancel{\delta c_{i,j,k}}) - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}}{T} + \end{gathered} + +(note that the above does not take converging and diverging flows into account, also :math:`\delta c_{i,j,k}` at the right hand side in the "min" brackets is difficult to solve for. In the code, this term is neglected which may cause some inaccuracy when calculating pickup. Although mass continuity is corrected for in the implicit scheme when calculating pickup using equation ???) + +Now we simplify: + +.. math:: + + \begin{gathered} + (\frac{\Delta x \Delta y}{\Delta t} + \Gamma_x\Delta y \cdot u_{\text{x},i+1/2,j} - (1-\Gamma_x)\Delta y \cdot u_{\text{x},i-1/2,j} + \Gamma_y\Delta x \cdot u_{\text{y},i,j+1/2}\\ - (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j-1/2}+\frac{\Delta x \Delta y}{T_s})\cdot \delta c_{i,j,k}\\ + -(\Gamma_x\Delta y \cdot u_{\text{x},i-1/2,j})\cdot \delta c_{i-1,j,k}\\ + +((1-\Gamma_x)\Delta y \cdot u_{\text{x},i+1/2,j})\cdot \delta c_{i+1,j,k}\\ + -(\Gamma_y\Delta x \cdot u_{\text{y},i,j-1/2})\cdot \delta c_{i,j-1,k}\\ + + ((1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j+1/2})\cdot \delta c_{i,j+1,k}\\ + \end{gathered} + +or + +.. math:: + + \begin{gathered} + A0 \cdot \delta c_{i,j,k} + + A\text{m1} \cdot \delta c_{i-1,j,k} + + A\text{p1} \cdot \delta c_{i+1,j,k}\\ + + A\text{mx} \cdot \delta c_{i,j-1,k} + + A\text{px} \cdot \delta c_{i,j+1,k} = y_{i,j,k} + \label{eq:lin} + \end{gathered} + +or the linear system of equations in general form: + +.. math:: + :label: conservative_general + + A \cdot \delta c_{i,j,k} = y_{i,j,k} + +Where :math:`A` is a 3-dimensional sparse matrix that is compiled using the matrix diagonals (:math:`A0, Am1, Ap1, Amx, Apx`) which are defined as: + +.. math:: + + \begin{aligned} + A0 = & +\frac{\Delta x \Delta y}{\Delta t} \\ + & +\frac{\Delta x \Delta y}{T_s} \\ + & - (1-\Gamma_x)\Delta y \cdot u_{\text{x},i-1/2,j} \\ + & + \Gamma_x\Delta y \cdot u_{\text{x},i+1/2,j} \\ + & - (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j-1/2} \\ + & + \Gamma_y\Delta x \cdot u_{\text{y},i,j+1/2} \\ + \end{aligned} + +and + +.. math:: + + A\text{m}1 = -\Gamma_x\Delta y \cdot u_{\text{x},i-1/2,j} + +and + +.. math:: + + A\text{p}1 = (1-\Gamma_x)\Delta y \cdot u_{\text{x},i+1/2,j} + +and + +.. math:: + A\text{mx} = -\Gamma_y\Delta x \cdot u_{\text{y},i,j-1/2} + +and + +.. math:: + + A\text{px} = (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j+1/2} + +Let's go towards the RHS + +.. math:: + + \begin{aligned} + y_{i,j,k} = & - \frac{\Delta x \Delta y}{\Delta t}(c^{n+1 *}_{i,j,k}-c^{n}_{i,j,k}) \\ + & + \frac{\Delta x \Delta y}{T_s}(\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i,j,k} + c^{n+1 *}_{i,j,k}) - c^{n+1 *}_{i,j,k}) \\ + & + \Delta y \cdot u_{\text{x},i-1/2,j} \cdot + (\Gamma_x \cdot c^{n+1 *}_{i-1,j,k} + (1-\Gamma_x) c^{n+1 *}_{i,j,k})\\ + & - \Delta y \cdot u_{\text{x},i+1/2,j} \cdot (\Gamma_x \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_x) c^{n+1 *}_{i+1,j,k})\\ + & + \Delta x \cdot u_{\text{y},i,j-1/2} \cdot (\Gamma_y \cdot c^{n+1 *}_{i,j-1,k} + (1-\Gamma_y) c^{n+1 *}_{i,j,k})\\ + & - \Delta x \cdot u_{\text{y},i,j+1/2} \cdot (\Gamma_y \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_y) c^{n+1 *}_{i,j+1,k})\\ + \end{aligned} + +in the python code some intermediate variable is defined to make it easier to shift indexes + +.. math:: + + \text{Ctxfs} =(\Gamma_x \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_x) c^{n+1 *}_{i+1,j,k}) + +and + +.. math:: + + \text{Ctxfn} =(\Gamma_y \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_y) c^{n+1 *}_{i,j+1,k}) + +also Erosion and deposition are defined using seperate variables. + +.. math:: + D_{i,j,k}= \frac{\Delta x \Delta y}{T_s}c^{n+1 *}_{i,j,k} + +and + +.. math:: + + A_{i,j,k}= \frac{\Delta x \Delta y}{T_s}m_{i,j,k} + D_{i,j,k} + +and + +.. math:: + U_{i,j,k}= \frac{\Delta x \Delta y}{T_s}\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} + +and + +.. math:: + E_{i,j,k} = \min(U_{i,j,k},A_{i,j,k}) + +After solving equation :math:`\delta c_{i,j,k}` using :eq:`conservative_general`, :math:`c^{n+1}_{i,j,k}` can be calculated using equation :eq:`conservative2`. + +Also, the pickup per grid cell can be calculated using: + +.. math:: + + \text{pickup} = \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k}- c^{n+1}_{i,j,k}}{T_s}\Delta t + \label{eq:pickup} + +note that this is only valid when using an Euler backward scheme. + +Solving the Linear System of Equations +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The linear system of equations can be elaborated : + +.. math:: + :label: apx-system + + \left[ + \begin{array}{cccccc} + A^0_1 & A^{1}_1 & \textbf{0} & \cdots & \textbf{0} & A^{n_{\mathrm{y}}+1}_1 \\ + A^{-1}_2 & A^0_2 & \ddots & \ddots & & \textbf{0} \\ + \textbf{0} & \ddots & \ddots & \ddots & \ddots & \vdots \\ + \vdots & \ddots & \ddots & \ddots & \ddots & \textbf{0} \\ + \textbf{0} & & \ddots & \ddots & A^0_{n_{\mathrm{y}}} & A^1_{n_{\mathrm{y}}} \\ + A^{-n_{\mathrm{y}}-1}_{n_{\mathrm{y}}+1} & \textbf{0} & \cdots & \textbf{0} & A^{-1}_{n_{\mathrm{y}}+1} & A^0_{n_{\mathrm{y}}+1} \\ + \end{array} + \right] \left[ + \begin{array}{c} + \vec{\delta c}_1 \\ \vec{\delta c}_2 \\ \vdots \\ \vdots \\ \vec{\delta c}_{n_{\mathrm{y}}} \\ \vec{\delta c}_{n_{\mathrm{y}}+1} \\ + \end{array} + \right] = \left[ + \begin{array}{c} + \vec{y}_1 \\ \vec{y}_2 \\ \vdots \\ \vdots \\ \vec{y}_{n_{\mathrm{y}}} \\ \vec{y}_{n_{\mathrm{y}}+1} \\ + \end{array} + \right] + +where each item in the matrix is again a matrix :math:`A^l_j` and +each item in the vectors is again a vector :math:`\vec{\delta c}_j` and +:math:`\vec{y}_j` respectively. The form of the matrix :math:`A^l_j` depends on +the diagonal index :math:`l` and reads: + +.. math:: + :label: apx-diagonal + + A^0_j = + \left[ + \begin{array}{ccccccc} + 0 & 0 & 0 & 0 + & \cdots & \cdots & 0 \\ + a^{0,-1}_{2,j} & a^{0,0}_{2,j} & a^{0,1}_{2,j} & \ddots + & & & \vdots \\ + 0 & a^{0,-1}_{3,j} & a^{0,0}_{3,j} & a^{0,1}_{3,j} + & \ddots & & \vdots \\ + \vdots & \ddots & \ddots & \ddots + & \ddots & \ddots & \vdots \\ + \vdots & & \ddots & a^{0,-1}_{n_{\mathrm{x}}-1,j} + & a^{0,0}_{n_{\mathrm{x}}-1,j} & a^{0,1}_{n_{\mathrm{x}}-1,j} & 0 \\ + \vdots & & & 0 + & a^{0,-1}_{n_{\mathrm{x}},j} & a^{0,0}_{n_{\mathrm{x}},j} & a^{0,1}_{n_{\mathrm{x}},j} \\ + 0 & \cdots & \cdots & 0 + & 1 & -2 & 1 \\ + \end{array} + \right] + +for :math:`l = 0` and + +.. math:: + :label: apx-offdiagonal + + A^l_j = + \left[ + \begin{array}{ccccccc} + 1 & 0 & \cdots & \cdots + & \cdots & \cdots & 0 \\ + 0 & a^{l,0}_{2,j} & \ddots & + & & & \vdots \\ + \vdots & \ddots & a^{l,0}_{3,j} & \ddots + & & & \vdots \\ + \vdots & & \ddots & \ddots + & \ddots & & \vdots \\ + \vdots & & & \ddots + & a^{l,0}_{n_{\mathrm{x}}-1,j} & \ddots & \vdots \\ + \vdots & & & + & \ddots & a^{l,0}_{n_{\mathrm{x}},j} & 0 \\ + 0 & \cdots & \cdots & \cdots + & \cdots & 0 & 1 \\ + \end{array} + \right] + +for :math:`l \neq 0`. The vectors :math:`\vec{\delta c}_{j,k}` and :math:`\vec{y}_{j,k}` +read: + +.. math:: + :label: c-array + + \begin{array}{rclrcl} + \vec{\delta c}_{j,k} &=& \left[ + \begin{array}{c} + \delta c^{n+1}_{1,j,k} \\ + \delta c^{n+1}_{2,j,k} \\ + \delta c^{n+1}_{3,j,k} \\ + \vdots \\ + \delta c^{n+1}_{n_{\mathrm{x}}-1,j,k} \\ + \delta c^{n+1}_{n_{\mathrm{x}},j,k} \\ + \delta c^{n+1}_{n_{\mathrm{x}}+1,j,k} \\ + \end{array} + \right] & ~ \mathrm{and} ~ + \vec{y}_{j,k} &=& \left[ + \begin{array}{c} + 0 \\ + y^n_{2,j,k} \\ + y^n_{3,j,k} \\ + \vdots \\ + y^n_{n_{\mathrm{x}}-1,j,k} \\ + y^n_{n_{\mathrm{x}},j,k} \\ + 0 \\ + \end{array} + \right] \\ + \end{array} + +:math:`n_{\mathrm{x}}` and :math:`n_{\mathrm{y}}` denote the number of +spatial grid cells in x- and y-direction. + +Iterations to solve for multiple fractions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The linear system defined in Equation :eq:`apx-system` is solved by a +sparse matrix solver for each sediment fraction separately in +ascending order of grain size. Initially, the weights +:math:`\hat{w}^{n+1}_{i,j,k}` are chosen according to the grain size +distribution in the bed and the air. The sediment availability +constraint is checked after each solve: + +.. math:: + :label: solve + + m_{\mathrm{a}} \geq \frac{\hat{w}^{n+1}_{i,j,k} c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \Delta t^n + +If the constraint if violated, a new estimate for the weights +is back-calculated following: + +.. math:: + :label: solve-weights + + \hat{w}^{n+1}_{i,j,k} = \frac{ c^{n+1}_{i,j,k} + m_{\mathrm{a}} \frac{T}{\Delta t^n} }{c^{n+1}_{\mathrm{sat},i,j,k}} + +The system is solved again using the new weights. This +procedure is repeated until a weight is found that does not violate +the sediment availability constraint. If the time step is not too +large, the procedure typically converges in only a few +iterations. Finally, the weights of the larger grains are increased +proportionally as to ensure that the sum of all weights remains +unity. If no larger grains are defined, not enough sediment is +available for transport and the grid cell is truly +availability-limited. This situation should only occur occasionally as +the weights in the next time step are computed based on the new bed +composition and thus will be skewed towards the large fractions. If +the situation occurs regularly, the time step is chosen too large +compared to the rate of armoring. + +Euler Schemes in non-conservative form +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Early model results relied on Euler schemes in a non conservative form. This allowed for a relatively easy implementation but did not guarantee mass conservation. In version 2 of AEOLIS the conservative form became the default. However, some users still use the older scheme. + +The formulation is discretized following a first order upwind scheme +assuming that the wind velocity :math:`u_z` is positive in both +x-direction and y-direction: + +.. math:: + :label: apx-explicit + + \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + + u^n_{z,\mathrm{x}} \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x_{i,j}} + + u^n_{z,\mathrm{y}} \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y_{i,j}} \\ = + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} + +in which :math:`n` is the time step index, :math:`i` and :math:`j` are +the cross-shore and alongshore spatial grid cell indices and :math:`k` +is the grain size fraction index. :math:`w` [-] is the weighting +factor used for the weighted addition of the saturated sediment +concentrations over all grain size fractions. + +The discretization can be generalized for any wind direction as: + +.. math:: + :label: apx-explicit-generalized + + \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + + u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + + u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \\ + + u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + + u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} = + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} + +in which: + +.. math:: + :label: apx-upwind1 + + \begin{array}{rclcrcl} + u^n_{z,\mathrm{x+}} &=& \max( 0, u^n_{z,\mathrm{x}} ) &;& u^n_{z,\mathrm{y+}} &=& \max( 0, u^n_{z,\mathrm{y}} ) \\ + u^n_{z,\mathrm{x-}} &=& \min( 0, u^n_{z,\mathrm{x}} ) &;& u^n_{z,\mathrm{y-}} &=& \min( 0, u^n_{z,\mathrm{y}} ) \\ + \end{array} + +and + +.. math:: + :label: apx-upwind2 + + \begin{array}{rclcrcl} + c^n_{i,j,k,\mathrm{x+}} &=& \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x} &;& + c^n_{i,j,k,\mathrm{y+}} &=& \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y} \\ + c^n_{i,j,k,\mathrm{x-}} &=& \frac{c^n_{i,j,k} - c^n_{i-1,j,k}}{\Delta x} &;& + c^n_{i,j,k,\mathrm{y-}} &=& \frac{c^n_{i,j,k} - c^n_{i,j-1,k}}{\Delta y} \\ + \end{array} + +Equation :eq:`apx-explicit-generalized` is explicit in +time and adheres to the Courant-Friedrich-Lewis (CFL) condition for +numerical stability. Alternatively, the advection equation can be +discretized implicitly in time for unconditional stability: + +.. math:: + :label: apx-implicit-generalized + + \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + + u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + + u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \\ + + u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + + u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} = + \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} + +Equation :eq:`apx-explicit-generalized` and +:eq:apx-implicit-generalized` can be rewritten as: + +.. math:: + :label: apx-explicit-rewritten + + c^{n+1}_{i,j,k} = c^n_{i,j,k} - \Delta t^n \left[ + u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + + u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \phantom{\frac{c^n_{i,j,k}}{T}} \right. \\ + \left. + u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + + u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} + + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] + +and + +.. math:: + :label: apx-implicit-rewritten + + c^{n+1}_{i,j,k} + \Delta t^n \left[ + u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + + u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \phantom{\frac{c^{n+1}_{i,j,k}}{T}} \right. \\ + \left. + u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + + u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} + + \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] = c^n_{i,j,k} + +and combined using a weighted average: + +.. math:: + :label: apx-combined + + c^{n+1}_{i,j,k} + \Gamma \Delta t^n \left[ + u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + + u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \phantom{\frac{c^{n+1}_{i,j,k}}{T}} \right. \\ + \left. + u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + + u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} + + \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] \\ = + c^n_{i,j,k} - (1 - \Gamma) \Delta t^n \left[ + u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + + u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \phantom{\frac{c^n_{i,j,k}}{T}} \right. \\ + \left. + u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + + u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} + + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] + +in which :math:`\Gamma` is a weight that ranges from 0 -- 1 and +determines the implicitness of the scheme. The scheme is implicit with +:math:`\Gamma = 0`, explicit with :math:`\Gamma = 1` and semi-implicit +otherwise. :math:`\Gamma = 0.5` results in the semi-implicit Crank-Nicolson +scheme. + +Equation :eq:`apx-upwind2` is back-substituted in Equation +:eq:`apx-combined`: + +.. math:: + :label: apx-combined-substituted + + c^{n+1}_{i,j,k} + \Gamma \Delta t^n \left[ + u^{n+1}_{z,\mathrm{x+}} \frac{c^{n+1}_{i+1,j,k} - c^{n+1}_{i,j,k}}{\Delta x} + + u^{n+1}_{z,\mathrm{y+}} \frac{c^{n+1}_{i,j+1,k} - c^{n+1}_{i,j,k}}{\Delta y} \right. \\ + \left. + u^{n+1}_{z,\mathrm{x-}} \frac{c^{n+1}_{i,j,k} - c^{n+1}_{i-1,j,k}}{\Delta x} + + u^{n+1}_{z,\mathrm{y-}} \frac{c^{n+1}_{i,j,k} - c^{n+1}_{i,j-1,k}}{\Delta y} + + \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] \\ = + c^n_{i,j,k} - (1 - \Gamma) \Delta t^n \left[ + u^n_{z,\mathrm{x+}} \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x} + + u^n_{z,\mathrm{y+}} \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y} \right. \\ + \left. + u^n_{z,\mathrm{x-}} \frac{c^n_{i,j,k} - c^n_{i-1,j,k}}{\Delta x} + + u^n_{z,\mathrm{y-}} \frac{c^n_{i,j,k} - c^n_{i,j-1,k}}{\Delta y} + + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] + +and rewritten: + +.. math:: + :label: apx-combined-rewritten + + \left[ 1 - \Gamma \left( + u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + + u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - + u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - + u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + + \frac{\Delta t^n}{T} + \right) + \right] c^{n+1}_{i,j,k} \\ + + \Gamma \left( + u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^{n+1}_{i+1,j,k} + + u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^{n+1}_{i,j+1,k} - %\right. \\ - \left. + u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^{n+1}_{i-1,j,k} - + u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^{n+1}_{i,j-1,k} + \right) \\ = + \left[ 1 + (1 - \Gamma) \left( + u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + + u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - + u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - + u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + + \frac{\Delta t^n}{T} + \right) + \right] c^n_{i,j,k} \\ + + (1 - \Gamma) \left( + u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^n_{i+1,j,k} + + u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^n_{i,j+1,k} - %\right. \\ - \left. + u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^n_{i-1,j,k} - + u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^n_{i,j-1,k} + \right) \\ - + \Gamma \hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - + (1 - \Gamma) \hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} + +and simplified: + +.. math:: + :label: apx-combined-simplified + + a^{0,0}_{i,j} c^{n+1}_{i,j,k} + + a^{1,0}_{i,j} c^{n+1}_{i+1,j,k} + + a^{0,1}_{i,j} c^{n+1}_{i,j+1,k} - + a^{-1,0}_{i,j} c^{n+1}_{i-1,j,k} - + a^{0,-1}_{i,j} c^{n+1}_{i,j-1,k} = y_{i,j,k} + +where the implicit coefficients are defined as: + +.. math:: + :label: apx-implicitcoef + + \begin{array}{rclcrcl} + a^{0,0}_{i,j} &=& \left[1 - \Gamma \left( + u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + + u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - + u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - + u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + + \frac{\Delta t^n}{T} + \right) \right] \\ + a^{1,0}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} \\ + a^{0,1}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} \\ + a^{-1,0}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} \\ + a^{0,-1}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} \\ + \end{array} + +and the explicit right-hand side as: + +.. math:: + :label: apx-explicitrhs + + y^n_{i,j,k} = \left[ 1 + (1 - \Gamma) \left( + u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + + u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - + u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - + u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + + \frac{\Delta t^n}{T} + \right) + \right] c^n_{i,j,k} \\ + + (1 - \Gamma) \left( + u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^n_{i+1,j,k} + + u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^n_{i,j+1,k} - + u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^n_{i-1,j,k} - + u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^n_{i,j-1,k} + \right) \\ - + \Gamma \hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - + (1 - \Gamma) \hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} + +The offshore boundary is defined to be zero-flux, the +onshore boundary has a constant transport gradient and the lateral +boundaries are circular: + +.. math:: + :label: apx-boundaryconditions + + \begin{array}{rclcrcl} + c^{n+1}_{1,j,k} &=& 0 \\ + c^{n+1}_{n_{\mathrm{x}}+1,j,k} &=& 2 c^{n+1}_{n_{\mathrm{x}},j,k} - c^{n+1}_{n_{\mathrm{x}}-1,j,k} \\ + c^{n+1}_{i,1,k} &=& c^{n+1}_{i,n_{\mathrm{y}}+1,k} \\ + c^{n+1}_{i,n_{\mathrm{y}}+1,k} &=& c^{n+1}_{i,1,k} \\ + \end{array} + +Shear stress perturbation for non-perpendicular wind directions +--------------------------------------------------------------- + +The shear stress perturbation π›Ώπœ is estimated following the analytical description of the influence of alow and smooth hill in the wind profile by Weng et al. (1991). The perturbation is given by the Fouriertransformed components of the shear stress perturbation in the unperturbed wind direction which are the functions π›Ώπœπ‘₯(π‘˜) and π›Ώπœπ‘¦(π‘˜). The x-direction is defined by the direction of the wind velocity 𝑣0 on a flat bed, while the y direction is then the transverse. + +As a result, the perturbation theory can only estimate the shear stress induced by the morphology-wind interaction in parallel direction of wind. Therefore, model simulations were, up to now, limited to input wind directions parallel to the crossΒ­shore axis of the grid. + +To overcome this limitation and to allow for modelling directional winds, an overlaying computational grid is introduced in AeoLiS, which rotates with the changing wind direction per time step. By doing this, the shear stresses are always estimated in the positive x-direction of the computational grid. The following steps are executed for each time step: + +1. Create a computational grid alligned with the wind direction (set_computational_grid) +2. Add and fill buffer around the original grid +3. Populate computation grid by rotating it to the current wind direction and interpolate the original topography on it. Additionally, edges around +4. Compute the morphology-wind induced shear stress by using the perturbation theory +5. Add the only wind induced wind shear stresses to the computational grid +6. Rotate both the grids and the total shear stress results in opposite direction +7. Interpolate the total shear stress results from the computational grid to the original grid +8. Rotate the wind shear stress results and the original grid back to the original orientation + +.. note:: + The extra rotations in the last two steps are necessary as a simplified, but faster in terms of computational time, interpolation method is used. + + Multi-fraction Erosion and Deposition ------------------------------------- @@ -530,6 +1183,46 @@ Substitution of :math:`u` (Equation :eq:`gw-discharge`) in the continuity equati \frac{{\partial \eta }}{{\partial t}} = \frac{K}{{{n_e}}}\frac{\partial }{{\partial x}}\left( {(D + \eta )\frac{{\partial \eta }}{{\partial x}}} \right) + \frac{{{U_l}}}{{{n_e}}} +Numerical solution of the Boussinesq groundwater equation +--------------------------------------------------------- +The Boussinesq equation is solved numerically with a central finite difference +method in space and a fourth-order Runge-Kutta integration technique in time: + +.. math:: + :label: solve-boussinesq + + f(\eta ) = \frac{K}{{{n_e}}}\left[ {D\underbrace {\frac{{{\partial ^2}\eta }}{{\partial {x^2}}}}_a + \underbrace {\frac{\partial }{{\partial x}}\underbrace {\left\{ {\eta \frac{{\partial \eta }}{{\partial x}}} \right\}}_b}_c} \right] + +The Runge-Kutta time-stepping, where :math:`\Delta t` is the length of the timestep, is defined as, + +.. math:: + :label: runge-kutta + + \begin{gathered} + \eta _i^{t + 1} = \eta _i^t + \frac{{\Delta t}}{6}\left( {{f_1} + 2{f_2} + 2{f_3} + {f_4}} \right) \hfill \\ + {f_1} = f(\eta _i^t) \hfill \\ + {f_2} = f\left( {\eta _i^t + \frac{{\Delta t}}{2}{f_1}} \right) \hfill \\ + {f_3} = f\left( {\eta _i^t + \frac{{\Delta t}}{2}{f_2}} \right) \hfill \\ + {f_4} = f\left( {\eta _i^t + \Delta t{f_3}} \right) \hfill \\ + \end{gathered} + +where, :math:`i` is the grid cell in x-direction and :math:`t` is the timestep. The central difference solution to :math:`f(\eta)` is obtained through discretisation of the Boussinesq equation, + +.. math:: + :label: a-solve + + {a_i} = \frac{{\eta _{i + 1}^{} - 2\eta _i^{} + \eta _{i - 1}^{}}}{{{{(\Delta x)}^2}}} + +.. math:: + {b_i} = \frac{{\eta _i^{}\left( {\eta _{i + 1}^{} - \eta _{i - 1}^{}} \right)}}{{\Delta x}} + +.. math:: + {c_i} = \frac{{\left( {b_{i + 1}^{} - b_{i - 1}^{}} \right)}}{{\Delta x}} + +The seaward boundary condition is defined as the still water level plus the wave setup . +If the groundwater elevation is larger than the bed elevation, there is a seepage face, +and the groundwater elevation is set equal to the bed elevation. On the landward boundary, +a no-flow condition, :math:`\frac{{\partial \eta }}{{\partial t}} = 0` (Neumann condition), or constant head, :math:`\eta = constant` (Dirichlet condition), is prescribed. Capillary rise ^^^^^^^^^^^^^^ From a466d7a45957d5bd97a59b1f58937d60d063c019 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:25:58 +0200 Subject: [PATCH 025/124] Delete docs/user/implementation.rst --- docs/user/implementation.rst | 708 ----------------------------------- 1 file changed, 708 deletions(-) delete mode 100644 docs/user/implementation.rst diff --git a/docs/user/implementation.rst b/docs/user/implementation.rst deleted file mode 100644 index f8693298..00000000 --- a/docs/user/implementation.rst +++ /dev/null @@ -1,708 +0,0 @@ -Numerical implementation -======================== - -The numerical implementation of the equations presented in -:ref:`model` is explained here. The implementation is available as -Python package through the OpenEarth GitHub repository at: -http://www.github.com/openearth/aeolis-python/ - -Advection equation ------------------- - -The advection equation is implemented in two-dimensional form -following: - -.. math:: - :label: apx-advection - - \frac{\partial c}{\partial t} + - u_{z,\mathrm{x}} \frac{\partial c}{\partial x} + - u_{z,\mathrm{y}} \frac{\partial c}{\partial y} = - \frac{c_{\mathrm{sat}} - c}{T} - -in which :math:`c` [:math:`\mathrm{kg/m^2}`] is the sediment mass per -unit area in the air, :math:`c_{\mathrm{sat}}` [:math:`\mathrm{kg/m^2}`] is the -maximum sediment mass in the air that is reached in case of -saturation, :math:`u_{z,\mathrm{x}}` and :math:`u_{z,\mathrm{y}}` are the x- and -y-component of the wind velocity at height :math:`z` [m], :math:`T` [s] is an -adaptation time scale, :math:`t` [s] denotes time and :math:`x` [m] and :math:`y` [m] -denote cross-shore and alongshore distances respectively. - -The formulation is discretized in different ways to allow for different types of simulations balancing accuracy vs. computational resources. The conservative method combined with an euler backward scheme (written by Prof. Rauwoens) is the current default for most simulations. Non-conservative methods end explicit Euler forward schemes are also available. - -Default scheme -- Conservative Euler Backward Implicit -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -The default numerical method assumes the advection scheme in a conservative form in combination with an euler backward scheme. This scheme is prepared to use a TVD method but this is not implemented yet (add footnote{Total Variance Diminishing, this is explained in the lecture notes by Zijlema p94}) - -The fluxes at the interface of the cells are defined used in the advection terms: - -.. math:: - :label: conservative1 - - \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t} + \\ - \frac{u_{\text{x},i+1/2,j} \cdot c^{n+1}_{i+1/2,j,k} - u_{\text{x},i-1/2,j} \cdot c^{n+1}_{i-1/2,j,k}}{\Delta x} + \\ - \frac{u_{\text{y},i,j+1/2} \cdot c^{n+1}_{i,j+1/2,k} - u_{\text{y},i,j-1/2} \cdot c^{n+1}_{i,j-1/2,k}}{\Delta y} + - \\ = \\ - \frac{\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i.j.k} + c^{n+1}_{i,j,k} ) - c^{n+1}_{i,j,k}}{T} - -In which :math:`n` is the time step index, :math:`i` and :math:`j` are the cross-shore and alongshore spatial grid cell indices and :math:`k` is the grain size fraction index. :math:`w` [-] is the weighting factor used for the weighted addition of the saturated sediment concentrations over all grain size fractions. Note that u is spatially varying but has no temporal index. This is because u is a result of a separate wind solver and considered temporally invariant in the advection solver. - -Now we use a correction algorithm where: - -.. math:: - :label: conservative2 - - c^{n+1}_{i,j,k} = c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} - -where :math:`\delta c_{i,j,k}` is solved for and :math:`*` denotes the previous iteration. - -When now assuming an upwind scheme in space, we can derive 4 concentrations at the cell faces which are dependent on the velocity at the cell faces. - -We assume in x direction: - -.. math:: - - c^{n+1}_{i+1/2,j,k} = - \begin{cases} - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{x},i+1/2,j} > 0$,}\\ - c^{n+1 *}_{i+1,j,k} + \delta c_{i+1,j,k} & \text{if $u_{\text{x},i+1/2,j} < 0$.} - \end{cases} - -.. math:: - - c^{n+1}_{i-1/2,j,k} = - \begin{cases} - c^{n+1 *}_{i-1,j,k} + \delta c_{i-1,j,k} & \text{if $u_{\text{x},i-1/2,j} > 0$,}\\ - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{x},i-1/2,j} < 0$.} - \end{cases} - -and in y-direction: - -.. math:: - - c^{n+1}_{i,j+1/2,k} = - \begin{cases} - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{y},i,j+1/2} > 0$,}\\ - c^{n+1 *}_{i,j+1,k} + \delta c_{i,j+1,k} & \text{if $u_{\text{y},i,j+1/2} < 0$.} - \end{cases} - -.. math:: - - c^{n+1}_{i,j-1/2,k} = - \begin{cases} - c^{n+1 *}_{i,j-1,k} + \delta c_{i,j-1,k} & \text{if $u_{\text{y},i,j-1/2} > 0$,}\\ - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{y},i,j-1/2} < 0$.} - \end{cases} - -Now we assume: - -- :math:`\Gamma_x = 1` if :math:`u_{\text{x},i+1/2,j,k} > 0` and :math:`\Gamma_x = 0` if :math:`u_{\text{x},i+1/2,j,k} \leq 0` -- :math:`\Gamma_y = 1` if :math:`u_{\text{y},i,j+1/2,k} > 0` and :math:`\Gamma_x = 0` if :math:`u_{\text{y},i,j+1/2,k} \leq 0` - -(We did not test if this works well with diverging and converging flows. We may need another term that describes the conditions at the negative cell faces if they are of opposite direction than the positive cell faces and vice versa) - -Let's continue for the moment so that - -.. math:: - - \begin{gathered} - \frac{c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} - c^n_{i,j,k}}{\Delta t} + \\ - \Gamma_x \cdot \frac{u_{\text{x},i+1/2,j} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}) - u_{\text{x},i-1/2,j} \cdot (c^{n+1 *}_{i-1,j,k} + \delta c_{i-1,j,k})}{\Delta x} + \\ - (1-\Gamma_x) \cdot \frac{u_{\text{x},i+1/2,j} \cdot (c^{n+1 *}_{i+1,j,k} + \delta c_{i+1,j,k}) - u_{\text{x},i-1/2,j} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k})}{\Delta x} + \\ - \Gamma_y \cdot \frac{u_{\text{y},i,j+1/2} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}) - u_{\text{y},i,j-1/2} \cdot (c^{n+1 *}_{i,j-1,k} + \delta c_{i,j-1,k})}{\Delta y} + \\ - (1-\Gamma_y) \cdot \frac{u_{\text{y},i,j+1/2} \cdot (c^{n+1 *}_{i,j+1,k} + \delta c_{i,j+1,k}) - u_{\text{y},i,j-1/2} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k})}{\Delta y} + - \\ = \\ - \frac{\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i,j,k}+c^{n+1 *}_{i,j,k} + \xcancel{\delta c_{i,j,k}}) - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}}{T} - \end{gathered} - -(note that the above does not take converging and diverging flows into account, also :math:`\delta c_{i,j,k}` at the right hand side in the "min" brackets is difficult to solve for. In the code, this term is neglected which may cause some inaccuracy when calculating pickup. Although mass continuity is corrected for in the implicit scheme when calculating pickup using equation ???) - -Now we simplify: - -.. math:: - - \begin{gathered} - (\frac{\Delta x \Delta y}{\Delta t} + \Gamma_x\Delta y \cdot u_{\text{x},i+1/2,j} - (1-\Gamma_x)\Delta y \cdot u_{\text{x},i-1/2,j} + \Gamma_y\Delta x \cdot u_{\text{y},i,j+1/2}\\ - (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j-1/2}+\frac{\Delta x \Delta y}{T_s})\cdot \delta c_{i,j,k}\\ - -(\Gamma_x\Delta y \cdot u_{\text{x},i-1/2,j})\cdot \delta c_{i-1,j,k}\\ - +((1-\Gamma_x)\Delta y \cdot u_{\text{x},i+1/2,j})\cdot \delta c_{i+1,j,k}\\ - -(\Gamma_y\Delta x \cdot u_{\text{y},i,j-1/2})\cdot \delta c_{i,j-1,k}\\ - + ((1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j+1/2})\cdot \delta c_{i,j+1,k}\\ - \end{gathered} - -or - -.. math:: - - \begin{gathered} - A0 \cdot \delta c_{i,j,k} - + A\text{m1} \cdot \delta c_{i-1,j,k} - + A\text{p1} \cdot \delta c_{i+1,j,k}\\ - + A\text{mx} \cdot \delta c_{i,j-1,k} - + A\text{px} \cdot \delta c_{i,j+1,k} = y_{i,j,k} - \label{eq:lin} - \end{gathered} - -or the linear system of equations in general form: - -.. math:: - :label: conservative_general - - A \cdot \delta c_{i,j,k} = y_{i,j,k} - -Where :math:`A` is a 3-dimensional sparse matrix that is compiled using the matrix diagonals (:math:`A0, Am1, Ap1, Amx, Apx`) which are defined as: - -.. math:: - - \begin{aligned} - A0 = & +\frac{\Delta x \Delta y}{\Delta t} \\ - & +\frac{\Delta x \Delta y}{T_s} \\ - & - (1-\Gamma_x)\Delta y \cdot u_{\text{x},i-1/2,j} \\ - & + \Gamma_x\Delta y \cdot u_{\text{x},i+1/2,j} \\ - & - (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j-1/2} \\ - & + \Gamma_y\Delta x \cdot u_{\text{y},i,j+1/2} \\ - \end{aligned} - -and - -.. math:: - - A\text{m}1 = -\Gamma_x\Delta y \cdot u_{\text{x},i-1/2,j} - -and - -.. math:: - - A\text{p}1 = (1-\Gamma_x)\Delta y \cdot u_{\text{x},i+1/2,j} - -and - -.. math:: - A\text{mx} = -\Gamma_y\Delta x \cdot u_{\text{y},i,j-1/2} - -and - -.. math:: - - A\text{px} = (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j+1/2} - -Let's go towards the RHS - -.. math:: - - \begin{aligned} - y_{i,j,k} = & - \frac{\Delta x \Delta y}{\Delta t}(c^{n+1 *}_{i,j,k}-c^{n}_{i,j,k}) \\ - & + \frac{\Delta x \Delta y}{T_s}(\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i,j,k} + c^{n+1 *}_{i,j,k}) - c^{n+1 *}_{i,j,k}) \\ - & + \Delta y \cdot u_{\text{x},i-1/2,j} \cdot - (\Gamma_x \cdot c^{n+1 *}_{i-1,j,k} + (1-\Gamma_x) c^{n+1 *}_{i,j,k})\\ - & - \Delta y \cdot u_{\text{x},i+1/2,j} \cdot (\Gamma_x \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_x) c^{n+1 *}_{i+1,j,k})\\ - & + \Delta x \cdot u_{\text{y},i,j-1/2} \cdot (\Gamma_y \cdot c^{n+1 *}_{i,j-1,k} + (1-\Gamma_y) c^{n+1 *}_{i,j,k})\\ - & - \Delta x \cdot u_{\text{y},i,j+1/2} \cdot (\Gamma_y \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_y) c^{n+1 *}_{i,j+1,k})\\ - \end{aligned} - -in the python code some intermediate variable is defined to make it easier to shift indexes - -.. math:: - - \text{Ctxfs} =(\Gamma_x \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_x) c^{n+1 *}_{i+1,j,k}) - -and - -.. math:: - - \text{Ctxfn} =(\Gamma_y \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_y) c^{n+1 *}_{i,j+1,k}) - -also Erosion and deposition are defined using seperate variables. - -.. math:: - D_{i,j,k}= \frac{\Delta x \Delta y}{T_s}c^{n+1 *}_{i,j,k} - -and - -.. math:: - - A_{i,j,k}= \frac{\Delta x \Delta y}{T_s}m_{i,j,k} + D_{i,j,k} - -and - -.. math:: - U_{i,j,k}= \frac{\Delta x \Delta y}{T_s}\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - -and - -.. math:: - E_{i,j,k} = \min(U_{i,j,k},A_{i,j,k}) - -After solving equation :math:`\delta c_{i,j,k}` using :eq:`conservative_general`, :math:`c^{n+1}_{i,j,k}` can be calculated using equation :eq:`conservative2`. - -Also, the pickup per grid cell can be calculated using: - -.. math:: - - \text{pickup} = \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k}- c^{n+1}_{i,j,k}}{T_s}\Delta t - \label{eq:pickup} - -note that this is only valid when using an Euler backward scheme. - -Solving the Linear System of Equations -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -The linear system of equations can be elaborated : - -.. math:: - :label: apx-system - - \left[ - \begin{array}{cccccc} - A^0_1 & A^{1}_1 & \textbf{0} & \cdots & \textbf{0} & A^{n_{\mathrm{y}}+1}_1 \\ - A^{-1}_2 & A^0_2 & \ddots & \ddots & & \textbf{0} \\ - \textbf{0} & \ddots & \ddots & \ddots & \ddots & \vdots \\ - \vdots & \ddots & \ddots & \ddots & \ddots & \textbf{0} \\ - \textbf{0} & & \ddots & \ddots & A^0_{n_{\mathrm{y}}} & A^1_{n_{\mathrm{y}}} \\ - A^{-n_{\mathrm{y}}-1}_{n_{\mathrm{y}}+1} & \textbf{0} & \cdots & \textbf{0} & A^{-1}_{n_{\mathrm{y}}+1} & A^0_{n_{\mathrm{y}}+1} \\ - \end{array} - \right] \left[ - \begin{array}{c} - \vec{\delta c}_1 \\ \vec{\delta c}_2 \\ \vdots \\ \vdots \\ \vec{\delta c}_{n_{\mathrm{y}}} \\ \vec{\delta c}_{n_{\mathrm{y}}+1} \\ - \end{array} - \right] = \left[ - \begin{array}{c} - \vec{y}_1 \\ \vec{y}_2 \\ \vdots \\ \vdots \\ \vec{y}_{n_{\mathrm{y}}} \\ \vec{y}_{n_{\mathrm{y}}+1} \\ - \end{array} - \right] - -where each item in the matrix is again a matrix :math:`A^l_j` and -each item in the vectors is again a vector :math:`\vec{\delta c}_j` and -:math:`\vec{y}_j` respectively. The form of the matrix :math:`A^l_j` depends on -the diagonal index :math:`l` and reads: - -.. math:: - :label: apx-diagonal - - A^0_j = - \left[ - \begin{array}{ccccccc} - 0 & 0 & 0 & 0 - & \cdots & \cdots & 0 \\ - a^{0,-1}_{2,j} & a^{0,0}_{2,j} & a^{0,1}_{2,j} & \ddots - & & & \vdots \\ - 0 & a^{0,-1}_{3,j} & a^{0,0}_{3,j} & a^{0,1}_{3,j} - & \ddots & & \vdots \\ - \vdots & \ddots & \ddots & \ddots - & \ddots & \ddots & \vdots \\ - \vdots & & \ddots & a^{0,-1}_{n_{\mathrm{x}}-1,j} - & a^{0,0}_{n_{\mathrm{x}}-1,j} & a^{0,1}_{n_{\mathrm{x}}-1,j} & 0 \\ - \vdots & & & 0 - & a^{0,-1}_{n_{\mathrm{x}},j} & a^{0,0}_{n_{\mathrm{x}},j} & a^{0,1}_{n_{\mathrm{x}},j} \\ - 0 & \cdots & \cdots & 0 - & 1 & -2 & 1 \\ - \end{array} - \right] - -for :math:`l = 0` and - -.. math:: - :label: apx-offdiagonal - - A^l_j = - \left[ - \begin{array}{ccccccc} - 1 & 0 & \cdots & \cdots - & \cdots & \cdots & 0 \\ - 0 & a^{l,0}_{2,j} & \ddots & - & & & \vdots \\ - \vdots & \ddots & a^{l,0}_{3,j} & \ddots - & & & \vdots \\ - \vdots & & \ddots & \ddots - & \ddots & & \vdots \\ - \vdots & & & \ddots - & a^{l,0}_{n_{\mathrm{x}}-1,j} & \ddots & \vdots \\ - \vdots & & & - & \ddots & a^{l,0}_{n_{\mathrm{x}},j} & 0 \\ - 0 & \cdots & \cdots & \cdots - & \cdots & 0 & 1 \\ - \end{array} - \right] - -for :math:`l \neq 0`. The vectors :math:`\vec{\delta c}_{j,k}` and :math:`\vec{y}_{j,k}` -read: - -.. math:: - :label: c-array - - \begin{array}{rclrcl} - \vec{\delta c}_{j,k} &=& \left[ - \begin{array}{c} - \delta c^{n+1}_{1,j,k} \\ - \delta c^{n+1}_{2,j,k} \\ - \delta c^{n+1}_{3,j,k} \\ - \vdots \\ - \delta c^{n+1}_{n_{\mathrm{x}}-1,j,k} \\ - \delta c^{n+1}_{n_{\mathrm{x}},j,k} \\ - \delta c^{n+1}_{n_{\mathrm{x}}+1,j,k} \\ - \end{array} - \right] & ~ \mathrm{and} ~ - \vec{y}_{j,k} &=& \left[ - \begin{array}{c} - 0 \\ - y^n_{2,j,k} \\ - y^n_{3,j,k} \\ - \vdots \\ - y^n_{n_{\mathrm{x}}-1,j,k} \\ - y^n_{n_{\mathrm{x}},j,k} \\ - 0 \\ - \end{array} - \right] \\ - \end{array} - -:math:`n_{\mathrm{x}}` and :math:`n_{\mathrm{y}}` denote the number of -spatial grid cells in x- and y-direction. - -Iterations to solve for multiple fractions -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -The linear system defined in Equation :eq:`apx-system` is solved by a -sparse matrix solver for each sediment fraction separately in -ascending order of grain size. Initially, the weights -:math:`\hat{w}^{n+1}_{i,j,k}` are chosen according to the grain size -distribution in the bed and the air. The sediment availability -constraint is checked after each solve: - -.. math:: - :label: solve - - m_{\mathrm{a}} \geq \frac{\hat{w}^{n+1}_{i,j,k} c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \Delta t^n - -If the constraint if violated, a new estimate for the weights -is back-calculated following: - -.. math:: - :label: solve-weights - - \hat{w}^{n+1}_{i,j,k} = \frac{ c^{n+1}_{i,j,k} + m_{\mathrm{a}} \frac{T}{\Delta t^n} }{c^{n+1}_{\mathrm{sat},i,j,k}} - -The system is solved again using the new weights. This -procedure is repeated until a weight is found that does not violate -the sediment availability constraint. If the time step is not too -large, the procedure typically converges in only a few -iterations. Finally, the weights of the larger grains are increased -proportionally as to ensure that the sum of all weights remains -unity. If no larger grains are defined, not enough sediment is -available for transport and the grid cell is truly -availability-limited. This situation should only occur occasionally as -the weights in the next time step are computed based on the new bed -composition and thus will be skewed towards the large fractions. If -the situation occurs regularly, the time step is chosen too large -compared to the rate of armoring. - -Euler Schemes in non-conservative form -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -Early model results relied on Euler schemes in a non conservative form. This allowed for a relatively easy implementation but did not guarantee mass conservation. In version 2 of AEOLIS the conservative form became the default. However, some users still use the older scheme. - -The formulation is discretized following a first order upwind scheme -assuming that the wind velocity :math:`u_z` is positive in both -x-direction and y-direction: - -.. math:: - :label: apx-explicit - - \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + - u^n_{z,\mathrm{x}} \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x_{i,j}} + - u^n_{z,\mathrm{y}} \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y_{i,j}} \\ = - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} - -in which :math:`n` is the time step index, :math:`i` and :math:`j` are -the cross-shore and alongshore spatial grid cell indices and :math:`k` -is the grain size fraction index. :math:`w` [-] is the weighting -factor used for the weighted addition of the saturated sediment -concentrations over all grain size fractions. - -The discretization can be generalized for any wind direction as: - -.. math:: - :label: apx-explicit-generalized - - \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + - u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + - u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \\ + - u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + - u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} = - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} - -in which: - -.. math:: - :label: apx-upwind1 - - \begin{array}{rclcrcl} - u^n_{z,\mathrm{x+}} &=& \max( 0, u^n_{z,\mathrm{x}} ) &;& u^n_{z,\mathrm{y+}} &=& \max( 0, u^n_{z,\mathrm{y}} ) \\ - u^n_{z,\mathrm{x-}} &=& \min( 0, u^n_{z,\mathrm{x}} ) &;& u^n_{z,\mathrm{y-}} &=& \min( 0, u^n_{z,\mathrm{y}} ) \\ - \end{array} - -and - -.. math:: - :label: apx-upwind2 - - \begin{array}{rclcrcl} - c^n_{i,j,k,\mathrm{x+}} &=& \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x} &;& - c^n_{i,j,k,\mathrm{y+}} &=& \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y} \\ - c^n_{i,j,k,\mathrm{x-}} &=& \frac{c^n_{i,j,k} - c^n_{i-1,j,k}}{\Delta x} &;& - c^n_{i,j,k,\mathrm{y-}} &=& \frac{c^n_{i,j,k} - c^n_{i,j-1,k}}{\Delta y} \\ - \end{array} - -Equation :eq:`apx-explicit-generalized` is explicit in -time and adheres to the Courant-Friedrich-Lewis (CFL) condition for -numerical stability. Alternatively, the advection equation can be -discretized implicitly in time for unconditional stability: - -.. math:: - :label: apx-implicit-generalized - - \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + - u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + - u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \\ + - u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + - u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} = - \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} - -Equation :eq:`apx-explicit-generalized` and -:eq:apx-implicit-generalized` can be rewritten as: - -.. math:: - :label: apx-explicit-rewritten - - c^{n+1}_{i,j,k} = c^n_{i,j,k} - \Delta t^n \left[ - u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + - u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \phantom{\frac{c^n_{i,j,k}}{T}} \right. \\ + \left. - u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + - u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} + - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] - -and - -.. math:: - :label: apx-implicit-rewritten - - c^{n+1}_{i,j,k} + \Delta t^n \left[ - u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + - u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \phantom{\frac{c^{n+1}_{i,j,k}}{T}} \right. \\ + \left. - u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + - u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} + - \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] = c^n_{i,j,k} - -and combined using a weighted average: - -.. math:: - :label: apx-combined - - c^{n+1}_{i,j,k} + \Gamma \Delta t^n \left[ - u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + - u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \phantom{\frac{c^{n+1}_{i,j,k}}{T}} \right. \\ + \left. - u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + - u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} + - \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] \\ = - c^n_{i,j,k} - (1 - \Gamma) \Delta t^n \left[ - u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + - u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \phantom{\frac{c^n_{i,j,k}}{T}} \right. \\ + \left. - u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + - u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} + - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] - -in which :math:`\Gamma` is a weight that ranges from 0 -- 1 and -determines the implicitness of the scheme. The scheme is implicit with -:math:`\Gamma = 0`, explicit with :math:`\Gamma = 1` and semi-implicit -otherwise. :math:`\Gamma = 0.5` results in the semi-implicit Crank-Nicolson -scheme. - -Equation :eq:`apx-upwind2` is back-substituted in Equation -:eq:`apx-combined`: - -.. math:: - :label: apx-combined-substituted - - c^{n+1}_{i,j,k} + \Gamma \Delta t^n \left[ - u^{n+1}_{z,\mathrm{x+}} \frac{c^{n+1}_{i+1,j,k} - c^{n+1}_{i,j,k}}{\Delta x} + - u^{n+1}_{z,\mathrm{y+}} \frac{c^{n+1}_{i,j+1,k} - c^{n+1}_{i,j,k}}{\Delta y} \right. \\ + \left. - u^{n+1}_{z,\mathrm{x-}} \frac{c^{n+1}_{i,j,k} - c^{n+1}_{i-1,j,k}}{\Delta x} + - u^{n+1}_{z,\mathrm{y-}} \frac{c^{n+1}_{i,j,k} - c^{n+1}_{i,j-1,k}}{\Delta y} + - \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] \\ = - c^n_{i,j,k} - (1 - \Gamma) \Delta t^n \left[ - u^n_{z,\mathrm{x+}} \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x} + - u^n_{z,\mathrm{y+}} \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y} \right. \\ + \left. - u^n_{z,\mathrm{x-}} \frac{c^n_{i,j,k} - c^n_{i-1,j,k}}{\Delta x} + - u^n_{z,\mathrm{y-}} \frac{c^n_{i,j,k} - c^n_{i,j-1,k}}{\Delta y} + - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] - -and rewritten: - -.. math:: - :label: apx-combined-rewritten - - \left[ 1 - \Gamma \left( - u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + - u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - - u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - - u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + - \frac{\Delta t^n}{T} - \right) - \right] c^{n+1}_{i,j,k} \\ + - \Gamma \left( - u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^{n+1}_{i+1,j,k} + - u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^{n+1}_{i,j+1,k} - %\right. \\ - \left. - u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^{n+1}_{i-1,j,k} - - u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^{n+1}_{i,j-1,k} - \right) \\ = - \left[ 1 + (1 - \Gamma) \left( - u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + - u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - - u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - - u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + - \frac{\Delta t^n}{T} - \right) - \right] c^n_{i,j,k} \\ + - (1 - \Gamma) \left( - u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^n_{i+1,j,k} + - u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^n_{i,j+1,k} - %\right. \\ - \left. - u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^n_{i-1,j,k} - - u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^n_{i,j-1,k} - \right) \\ - - \Gamma \hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - - (1 - \Gamma) \hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - -and simplified: - -.. math:: - :label: apx-combined-simplified - - a^{0,0}_{i,j} c^{n+1}_{i,j,k} + - a^{1,0}_{i,j} c^{n+1}_{i+1,j,k} + - a^{0,1}_{i,j} c^{n+1}_{i,j+1,k} - - a^{-1,0}_{i,j} c^{n+1}_{i-1,j,k} - - a^{0,-1}_{i,j} c^{n+1}_{i,j-1,k} = y_{i,j,k} - -where the implicit coefficients are defined as: - -.. math:: - :label: apx-implicitcoef - - \begin{array}{rclcrcl} - a^{0,0}_{i,j} &=& \left[1 - \Gamma \left( - u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + - u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - - u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - - u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + - \frac{\Delta t^n}{T} - \right) \right] \\ - a^{1,0}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} \\ - a^{0,1}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} \\ - a^{-1,0}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} \\ - a^{0,-1}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} \\ - \end{array} - -and the explicit right-hand side as: - -.. math:: - :label: apx-explicitrhs - - y^n_{i,j,k} = \left[ 1 + (1 - \Gamma) \left( - u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + - u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - - u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - - u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + - \frac{\Delta t^n}{T} - \right) - \right] c^n_{i,j,k} \\ + - (1 - \Gamma) \left( - u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^n_{i+1,j,k} + - u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^n_{i,j+1,k} - - u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^n_{i-1,j,k} - - u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^n_{i,j-1,k} - \right) \\ - - \Gamma \hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - - (1 - \Gamma) \hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - -The offshore boundary is defined to be zero-flux, the -onshore boundary has a constant transport gradient and the lateral -boundaries are circular: - -.. math:: - :label: apx-boundaryconditions - - \begin{array}{rclcrcl} - c^{n+1}_{1,j,k} &=& 0 \\ - c^{n+1}_{n_{\mathrm{x}}+1,j,k} &=& 2 c^{n+1}_{n_{\mathrm{x}},j,k} - c^{n+1}_{n_{\mathrm{x}}-1,j,k} \\ - c^{n+1}_{i,1,k} &=& c^{n+1}_{i,n_{\mathrm{y}}+1,k} \\ - c^{n+1}_{i,n_{\mathrm{y}}+1,k} &=& c^{n+1}_{i,1,k} \\ - \end{array} - -Shear stress perturbation for non-perpendicular wind directions ---------------------------------------------------------------- - -The shear stress perturbation π›Ώπœ is estimated following the analytical description of the influence of alow and smooth hill in the wind profile by Weng et al. (1991). The perturbation is given by the Fouriertransformed components of the shear stress perturbation in the unperturbed wind direction which are the functions π›Ώπœπ‘₯(π‘˜) and π›Ώπœπ‘¦(π‘˜). The x-direction is defined by the direction of the wind velocity 𝑣0 on a flat bed, while the y direction is then the transverse. - -As a result, the perturbation theory can only estimate the shear stress induced by the morphology-wind interaction in parallel direction of wind. Therefore, model simulations were, up to now, limited to input wind directions parallel to the crossΒ­shore axis of the grid. - -To overcome this limitation and to allow for modelling directional winds, an overlaying computational grid is introduced in AeoLiS, which rotates with the changing wind direction per time step. By doing this, the shear stresses are always estimated in the positive x-direction of the computational grid. The following steps are executed for each time step: - -1. Create a computational grid alligned with the wind direction (set_computational_grid) -2. Add and fill buffer around the original grid -3. Populate computation grid by rotating it to the current wind direction and interpolate the original topography on it. Additionally, edges around -4. Compute the morphology-wind induced shear stress by using the perturbation theory -5. Add the only wind induced wind shear stresses to the computational grid -6. Rotate both the grids and the total shear stress results in opposite direction -7. Interpolate the total shear stress results from the computational grid to the original grid -8. Rotate the wind shear stress results and the original grid back to the original orientation - -.. note:: - The extra rotations in the last two steps are necessary as a simplified, but faster in terms of computational time, interpolation method is used. - - -Boussinesq groundwater equation -------------------------------- -The Boussinesq equation is solved numerically with a central finite difference -method in space and a fourth-order Runge-Kutta integration technique in time: - -.. math:: - :label: solve-boussinesq - - f(\eta ) = \frac{K}{{{n_e}}}\left[ {D\underbrace {\frac{{{\partial ^2}\eta }}{{\partial {x^2}}}}_a + \underbrace {\frac{\partial }{{\partial x}}\underbrace {\left\{ {\eta \frac{{\partial \eta }}{{\partial x}}} \right\}}_b}_c} \right] - -The Runge-Kutta time-stepping, where :math:`\Delta t` is the length of the timestep, is defined as, - -.. math:: - :label: runge-kutta - - \begin{gathered} - \eta _i^{t + 1} = \eta _i^t + \frac{{\Delta t}}{6}\left( {{f_1} + 2{f_2} + 2{f_3} + {f_4}} \right) \hfill \\ - {f_1} = f(\eta _i^t) \hfill \\ - {f_2} = f\left( {\eta _i^t + \frac{{\Delta t}}{2}{f_1}} \right) \hfill \\ - {f_3} = f\left( {\eta _i^t + \frac{{\Delta t}}{2}{f_2}} \right) \hfill \\ - {f_4} = f\left( {\eta _i^t + \Delta t{f_3}} \right) \hfill \\ - \end{gathered} - -where, :math:`i` is the grid cell in x-direction and :math:`t` is the timestep. The central difference solution to :math:`f(\eta)` is obtained through discretisation of the Boussinesq equation, - -.. math:: - :label: a-solve - - {a_i} = \frac{{\eta _{i + 1}^{} - 2\eta _i^{} + \eta _{i - 1}^{}}}{{{{(\Delta x)}^2}}} - -.. math:: - {b_i} = \frac{{\eta _i^{}\left( {\eta _{i + 1}^{} - \eta _{i - 1}^{}} \right)}}{{\Delta x}} - -.. math:: - {c_i} = \frac{{\left( {b_{i + 1}^{} - b_{i - 1}^{}} \right)}}{{\Delta x}} - -The seaward boundary condition is defined as the still water level plus the wave setup . -If the groundwater elevation is larger than the bed elevation, there is a seepage face, -and the groundwater elevation is set equal to the bed elevation. On the landward boundary, -a no-flow condition, :math:`\frac{{\partial \eta }}{{\partial t}} = 0` (Neumann condition), or constant head, :math:`\eta = constant` (Dirichlet condition), is prescribed. - -.. .. rubric:: Bibliography - -.. .. bibliography:: -.. :labelprefix: A -.. :keyprefix: a- - From 6910e88af502a43b378f6c9b77dc52cf5fef4420 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:32:32 +0200 Subject: [PATCH 026/124] Update installation.rst --- docs/user/installation.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/user/installation.rst b/docs/user/installation.rst index c12fe309..d209598a 100644 --- a/docs/user/installation.rst +++ b/docs/user/installation.rst @@ -59,8 +59,8 @@ Example from command line: .. code:: shell - aeolis params.txt + aeolis run params.txt .. note:: - Model parameters and other configuration is passed in a `params.txt`. See the :ref:`default settings` for more details. \ No newline at end of file + Model parameters and other configuration is passed in a `params.txt`. See the :ref:`default settings` for more details. From e5af1a72bd89c82cb2b1676a1faf6869a298d493 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:39:57 +0200 Subject: [PATCH 027/124] Add files via upload --- docs/developer/whatsnew.rst | 280 ++++++++++++++++++++++++++++++++++++ 1 file changed, 280 insertions(+) create mode 100644 docs/developer/whatsnew.rst diff --git a/docs/developer/whatsnew.rst b/docs/developer/whatsnew.rst new file mode 100644 index 00000000..0ab79da9 --- /dev/null +++ b/docs/developer/whatsnew.rst @@ -0,0 +1,280 @@ +.. + [Categories] + Breaking changes + Improvements + New functions/methods + Bug fixes + Tests + +What's New +========== + +v2.1.2 (July 2023) +------------------ + +Improvements +^^^^^^^^^^^^ +* New unit test and integration tests procedures (Nike Agrawal, Manuel Garcia) + +Bug fixes +^^^^^^^^^ +* Updated DOI for referencing (Sierd de Vries) + +Documentation +^^^^^^^^^^^^^ +* Updated citation file (Manuel Garcia) +* Advanced description on steps to create release (Manuel Garcia) + +What's Changed +^^^^^^^^^^^^^^ +* Add Github action for running tests automatically by @niketagrawal in https://github.com/openearth/aeolis-python/pull/111 +* Integration test to verify the model's expected result for 1D and 2D base cases by @niketagrawal in https://github.com/openearth/aeolis-python/pull/105 +* add release guidelines by @manuGil in https://github.com/openearth/aeolis-python/pull/109 +* Unit-Tests for Model.py by @manuGil in https://github.com/openearth/aeolis-python/pull/112 +* Update citation by @manuGil in https://github.com/openearth/aeolis-python/pull/117 +* Moisture bug fix by @CarolineHalllin in https://github.com/openearth/aeolis-python/pull/116 +* Implementation grain size dependent Bagnold equation by @christavanijzendoorn in https://github.com/openearth/aeolis-python/pull/122 +* Implementing TOML file for packaging by @manuGil in https://github.com/openearth/aeolis-python/pull/125 +* Patch/deprications by @manuGil in https://github.com/openearth/aeolis-python/pull/128 +* loop over fractions replaced by numba enhanced function by @Sierd in https://github.com/openearth/aeolis-python/pull/119 +* Docs: Add developer documentation and fix bugs by @niketagrawal in https://github.com/openearth/aeolis-python/pull/134 + +**Full Changelog**: https://github.com/openearth/aeolis-python/compare/v2.1.1...v2.1.2 + +v2.1.1 (March 2023) +------------------- + +Improvements +^^^^^^^^^^^^ +* New variable to simulate fences `fence_height` (Glenn Strypsteen) + +Bug fixes +^^^^^^^^^ +* Issue with checking the size of `y` in input file for 1D cases (Glenn Strypsteen) + +Documentation +^^^^^^^^^^^^^ +* Update references to default branch in contributing guide + + +v2.1.0 (February 2023) +----------------------- + +Breaking changes +^^^^^^^^^^^^^^^^ +* Solve unrealistic behaviour for large tidal ranges and mildly sloping beaches +* Reduce computational time when using Numba + +Improvements +^^^^^^^^^^^^ +* Better documentation on numerical solvers + +Bug fixes +^^^^^^^^^ +* Solve conflict between versions of Numpy and Numba +* Solve incompatibility with Scipy 1.10 + +Tests +^^^^^^^ +* Adopt Pytest as a testing framework + + +v2.0.0 (April 2022) +------------------- + +Breaking changes +^^^^^^^^^^^^^^^^ +* New vegetation growth/expansion capabilities (Bart Van Westen) +* Addition of groundwater module and new moisture routines (Caroline Hallin) +* Incorporation of Okin (2008) vegetation shear coupler (Nick Cohn) +* Addition of Palmsten and Holman (2012) dune erosion module (Nick Cohn) +* Approach to add sand fences into model (Nick Cohn) + +Improvements +^^^^^^^^^^^^ +* Replacement of wave runup driver with Stockdon et al. (2006) (Nick Cohn) +* Non-FFT 1D based topographic shear coupler added for computational speed up (Nick Cohn) + + +v1.2.2 (18 April 2020) +----------------------- + +Breaking changes +^^^^^^^^^^^^^^^^ + +* Removed support for statistical variable names with dot-notation + (e.g. `.avg` and `.sum`) (Bas Hoonhout) + + + +Improvements +^^^^^^^^^^^^ +* Logger shows minute by minute updates (Tom Pak) + +New functions/methods +^^^^^^^^^^^^^^^^^^^^^ + +* Avalanching process included in bed.py (Tom Pak) +* Implementation of non-erodible layers (Tom Pak) + +Bug fixes +^^^^^^^^^ + +* boundary condition definition updated (Tom Pak) +* compatiblity with new NETCDF4 version restored (Sierd de Vries) +* compatiblity with 1D domains (Sierd de Vries) + +Tests +^^^^^ + +None. + +v1.1.5 (unreleased) +------------------- + +Breaking changes +^^^^^^^^^^^^^^^^ + +None. + +Improvements +^^^^^^^^^^^^ + +* Also enable inundation if process_tide is True, but tide_file not + specified. In this case the water level is constant zero. + +* Changed class attributes into instance attributes to support + parallel independent model instances. + +New functions/methods +^^^^^^^^^^^^^^^^^^^^^ + +None. + +Bug fixes +^^^^^^^^^ + +* Fixed double definition of statistics variables in netCDF file in + case both `output_types` is specified and individual statistics + variables are specified in `output_vars`. + +Tests +^^^^^ + +None. + +v1.1.4 (15 February 2018) +------------------------- + +Improvements +^^^^^^^^^^^^ + +* Route all log messages and exceptions through the logging + module. Consequently, all information, warnings, and exceptions, + including tracebacks can be logged to file. + +* Added model version number and Git hash to log files and model + output. + +v1.1.3 (9 February 2018) +------------------------ + +Bug fixes +^^^^^^^^^ + +* Apply precipitation/eaporation only in top bed layer to prevent + mismatching matrix shapes in the multiplication. In the future, + precipitation might be distributed over multiple layers depending on + the porosity. + +v1.1.2 (21 December 2017) +------------------------- + +Breaking changes +^^^^^^^^^^^^^^^^ + +* Changed name of statistics variables that describe the average, + minimum, maximum, cumulative values, or variance of a model state + variable. The variables names that used to end with `.avg`, `.sum`, + etc. now end with `_avg`, `_sum`, etc. The new naming convention was + already adopted in the netCDF output in order to be compatible with + the CF-1.6 convention, but is now also adopted in, for example, the + Basic Model Interface (BMI). Old notation is deprecated but still + supported. + +Improvements +^^^^^^^^^^^^ + +* Prepared for continuous integration through CircleCI. +* Prepared for code coverage checking through codecov. + +Bug fixes +^^^^^^^^^ + +* Use percentages (0-100) rather than fractions (0-1) in the + formulation of Belly and Johnson that describes the effect of soil + moisture on the shear velocity threshold. Thanks to Dano Roelvink + and Susana Costas (b3d992b). + +Tests +^^^^^ + +* Reduced required accuracy for mass conservation tests from + 0.00000000000001% to 1%. + +v1.1.1 (15 November 2017) +------------------------- + +Improvements +^^^^^^^^^^^^ + +* Made code compatible with Python 3.x. +* Prepared and uploaded package to PyPI. +* Switch back to original working directory after finishing + simulation. +* Removed double definition of model state. Now only defined in + `constants.MODEL_STATE`. +* Also write initial model state to output. +* Made netCDF output compatible with CF-1.6 convention. + +New functions/methods +^^^^^^^^^^^^^^^^^^^^^ + +* Added support to run a default model for testing purposes by setting + the configuration file as "DEFAULT". +* Added generic framework for reading and applying spatial + masks. Implemented support for wave, tide and threshold masks + specifically. +* Added option to include a reference date in netCDF output. +* Added experimental option for constant boundary conditions. +* Added support for reading and writing hotstart files to load a + (partial) model state upon initialisation. +* Added preliminary wind shear perturbation module. Untested. +* Added support to switch on or off specific processes. +* Added support for immutable model state variables. This + functionality can be combined with BMI or hotstart files to prevent + external process results to be overwritten by the model. +* Added option to specify wind direction convention (nautical or + cartesian). + +Bug fixes +^^^^^^^^^ + +* Fixed conversion from volume to mass using porosity and density (fe9aa52). +* Update water level with bed updates to prevent loss of water due to + bed level change (fe9aa52). +* Fixed mass bug in base layer that drained sediment from bottom + layers, resulting in empty layers (f612760). +* Made removal of negative concentrations mass conserving by scraping + the concentrations from all other grid cells (03de813). + +Tests +^^^^^ + +* Added tests to check mass conservation in bed mixing routines. +* Added integration tests. + +v1.1.0 (27 July 2016) +--------------------- + +Initial release From 2f0e09ed3e62adf19e07aef3244abea585090904 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:40:34 +0200 Subject: [PATCH 028/124] Delete docs/user/whatsnew.rst --- docs/user/whatsnew.rst | 280 ----------------------------------------- 1 file changed, 280 deletions(-) delete mode 100644 docs/user/whatsnew.rst diff --git a/docs/user/whatsnew.rst b/docs/user/whatsnew.rst deleted file mode 100644 index 237d3d56..00000000 --- a/docs/user/whatsnew.rst +++ /dev/null @@ -1,280 +0,0 @@ -.. - [Categories] - Breaking changes - Improvements - New functions/methods - Bug fixes - Tests - -What's New -========== - -v2.1.2 (July 2023) ------------------- - -Improvements -^^^^^^^^^^^^ -* New unit test and integration tests procedures (Nike Agrawal, Manuel Garcia) - -Bug fixes -^^^^^^^^^ -* Updated DOI for referencing (Sierd de Vries) - -Documentation -^^^^^^^^^^^^^ -* Updated citation file (Manuel Garcia) -* Advanced description on steps to create release (Manuel Garcia) - -What's Changed -^^^^^^^^^^^^^^ -* Add Github action for running tests automatically by @niketagrawal in https://github.com/openearth/aeolis-python/pull/111 -* Integration test to verify the model's expected result for 1D and 2D base cases by @niketagrawal in https://github.com/openearth/aeolis-python/pull/105 -* add release guidelines by @manuGil in https://github.com/openearth/aeolis-python/pull/109 -* Unit-Tests for Model.py by @manuGil in https://github.com/openearth/aeolis-python/pull/112 -* Update citation by @manuGil in https://github.com/openearth/aeolis-python/pull/117 -* Moisture bug fix by @CarolineHalllin in https://github.com/openearth/aeolis-python/pull/116 -* Implementation grain size dependent Bagnold equation by @christavanijzendoorn in https://github.com/openearth/aeolis-python/pull/122 -* Implementing TOML file for packaging by @manuGil in https://github.com/openearth/aeolis-python/pull/125 -* Patch/deprications by @manuGil in https://github.com/openearth/aeolis-python/pull/128 -* loop over fractions replaced by numba enhanced function by @Sierd in https://github.com/openearth/aeolis-python/pull/119 -* Docs: Add developer documentation and fix bugs by @niketagrawal in https://github.com/openearth/aeolis-python/pull/134 - -**Full Changelog**: https://github.com/openearth/aeolis-python/compare/v2.1.1...v2.1.2 - -v2.1.1 (March 2023) -------------------- - -Improvements -^^^^^^^^^^^^ -* New variable to simulate fences `fence_height` (Glenn Strypsteen) - -Bug fixes -^^^^^^^^^ -* Issue with checking the size of `y` in input file for 1D cases (Glenn Strypsteen) - -Documentation -^^^^^^^^^^^^^ -* Update references to default branch in contributing guide - - -v2.1.0 (February 2023) ------------------------ - -Breaking changes -^^^^^^^^^^^^^^^^ -* Solve unrealistic behaviour for large tidal ranges and mildly sloping beaches -* Reduce computational time when using Numba - -Improvements -^^^^^^^^^^^^ -* Better documentation on numerical solvers - -Bug fixes -^^^^^^^^^ -* Solve conflict between versions of Numpy and Numba -* Solve incompatibility with Scipy 1.10 - -Tests -^^^^^^^ -* Adopt Pytest as a testing framework - - -v2.0.0 (April 2022) -------------------- - -Breaking changes -^^^^^^^^^^^^^^^^ -* New vegetation growth/expansion capabilities (Bart Van Westen) -* Addition of groundwater module and new moisture routines (Caroline Hallin) -* Incorporation of Okin (2008) vegetation shear coupler (Nick Cohn) -* Addition of Palmsten and Holman (2012) dune erosion module (Nick Cohn) -* Approach to add sand fences into model (Nick Cohn) - -Improvements -^^^^^^^^^^^^ -* Replacement of wave runup driver with Stockdon et al. (2006) (Nick Cohn) -* Non-FFT 1D based topographic shear coupler added for computational speed up (Nick Cohn) - - -v1.2.2 (18 April 2020) ------------------------ - -Breaking changes -^^^^^^^^^^^^^^^^ - -* Removed support for statistical variable names with dot-notation - (e.g. `.avg` and `.sum`) (Bas Hoonhout) - - - -Improvements -^^^^^^^^^^^^ -* Logger shows minute by minute updates (Tom Pak) - -New functions/methods -^^^^^^^^^^^^^^^^^^^^^ - -* Avalanching process included in bed.py (Tom Pak) -* Implementation of non-erodible layers (Tom Pak) - -Bug fixes -^^^^^^^^^ - -* boundary condition definition updated (Tom Pak) -* compatiblity with new NETCDF4 version restored (Sierd de Vries) -* compatiblity with 1D domains (Sierd de Vries) - -Tests -^^^^^ - -None. - -v1.1.5 (unreleased) -------------------- - -Breaking changes -^^^^^^^^^^^^^^^^ - -None. - -Improvements -^^^^^^^^^^^^ - -* Also enable inundation if process_tide is True, but tide_file not - specified. In this case the water level is constant zero. - -* Changed class attributes into instance attributes to support - parallel independent model instances. - -New functions/methods -^^^^^^^^^^^^^^^^^^^^^ - -None. - -Bug fixes -^^^^^^^^^ - -* Fixed double definition of statistics variables in netCDF file in - case both `output_types` is specified and individual statistics - variables are specified in `output_vars`. - -Tests -^^^^^ - -None. - -v1.1.4 (15 February 2018) -------------------------- - -Improvements -^^^^^^^^^^^^ - -* Route all log messages and exceptions through the logging - module. Consequently, all information, warnings, and exceptions, - including tracebacks can be logged to file. - -* Added model version number and Git hash to log files and model - output. - -v1.1.3 (9 February 2018) ------------------------- - -Bug fixes -^^^^^^^^^ - -* Apply precipitation/eaporation only in top bed layer to prevent - mismatching matrix shapes in the multiplication. In the future, - precipitation might be distributed over multiple layers depending on - the porosity. - -v1.1.2 (21 December 2017) -------------------------- - -Breaking changes -^^^^^^^^^^^^^^^^ - -* Changed name of statistics variables that describe the average, - minimum, maximum, cumulative values, or variance of a model state - variable. The variables names that used to end with `.avg`, `.sum`, - etc. now end with `_avg`, `_sum`, etc. The new naming convention was - already adopted in the netCDF output in order to be compatible with - the CF-1.6 convention, but is now also adopted in, for example, the - Basic Model Interface (BMI). Old notation is deprecated but still - supported. - -Improvements -^^^^^^^^^^^^ - -* Prepared for continuous integration through CircleCI. -* Prepared for code coverage checking through codecov. - -Bug fixes -^^^^^^^^^ - -* Use percentages (0-100) rather than fractions (0-1) in the - formulation of Belly and Johnson that describes the effect of soil - moisture on the shear velocity threshold. Thanks to Dano Roelvink - and Susana Costas (b3d992b). - -Tests -^^^^^ - -* Reduced required accuracy for mass conservation tests from - 0.00000000000001% to 1%. - -v1.1.1 (15 November 2017) -------------------------- - -Improvements -^^^^^^^^^^^^ - -* Made code compatible with Python 3.x. -* Prepared and uploaded package to PyPI. -* Switch back to original working directory after finishing - simulation. -* Removed double definition of model state. Now only defined in - `constants.MODEL_STATE`. -* Also write initial model state to output. -* Made netCDF output compatible with CF-1.6 convention. - -New functions/methods -^^^^^^^^^^^^^^^^^^^^^ - -* Added support to run a default model for testing purposes by setting - the configuration file as "DEFAULT". -* Added generic framework for reading and applying spatial - masks. Implemented support for wave, tide and threshold masks - specifically. -* Added option to include a reference date in netCDF output. -* Added experimental option for constant boundary conditions. -* Added support for reading and writing hotstart files to load a - (partial) model state upon initialisation. -* Added preliminary wind shear perturbation module. Untested. -* Added support to switch on or off specific processes. -* Added support for immutable model state variables. This - functionality can be combined with BMI or hotstart files to prevent - external process results to be overwritten by the model. -* Added option to specify wind direction convention (nautical or - cartesian). - -Bug fixes -^^^^^^^^^ - -* Fixed conversion from volume to mass using porosity and density (fe9aa52). -* Update water level with bed updates to prevent loss of water due to - bed level change (fe9aa52). -* Fixed mass bug in base layer that drained sediment from bottom - layers, resulting in empty layers (f612760). -* Made removal of negative concentrations mass conserving by scraping - the concentrations from all other grid cells (03de813). - -Tests -^^^^^ - -* Added tests to check mass conservation in bed mixing routines. -* Added integration tests. - -v1.1.0 (27 July 2016) ---------------------- - -Initial release From e266f4d5133bbe35418ee4e2f8cac8861da22634 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:41:43 +0200 Subject: [PATCH 029/124] Update index.rst --- docs/index.rst | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/index.rst b/docs/index.rst index 343beaa1..94b7e065 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -43,6 +43,7 @@ Contents developer/quickstart developer/testing-introduction developer/unit-testing + developer/whatsnew .. toctree:: :caption: Current Development From 92a22251926027f99e9c2f01bd6988a2bfc260ee Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:42:59 +0200 Subject: [PATCH 030/124] Update index.rst --- docs/index.rst | 3 --- 1 file changed, 3 deletions(-) diff --git a/docs/index.rst b/docs/index.rst index 94b7e065..d5101e1f 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -14,9 +14,6 @@ Welcome to AeoLiS's Documentation ------- -AeoLiS is a process-based model for simulating aeolian sediment transport in situations where supply-limiting factors are important, -like in coastal environments. Supply-limitations currently supported are soil moisture contents, sediment sorting and armouring, bed slope effects, air humidity and roughness elements. - This documentation describes the Python implementation of the AeoLiS model. The source code of the Python implementation can be found in `GitHub `_. From 81ebee6e34add822029b22b4e3b6d82ced040d3c Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:53:14 +0200 Subject: [PATCH 031/124] Update introduction.rst --- docs/user/introduction.rst | 2 ++ 1 file changed, 2 insertions(+) diff --git a/docs/user/introduction.rst b/docs/user/introduction.rst index f7ae24be..bb564d06 100644 --- a/docs/user/introduction.rst +++ b/docs/user/introduction.rst @@ -2,3 +2,5 @@ Introduction ============ +AeoLiS is a process-based model for simulating aeolian sediment transport and morphological evolution in situations where supply-limiting factors are important, +like in coastal environments. Supply-limitations currently supported are soil moisture contents, sediment sorting and armouring, bed slope effects, air humidity and roughness elements. AeoLiS includes a dynamic vegetation module that simulates the interaction between sediment transport and vegetation dynamics. From 6e7a6f40c0f4d85227c165a81a56974ecf7353b3 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:53:58 +0200 Subject: [PATCH 032/124] Update model_description.rst --- docs/user/model_description.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index 3b453e7c..163e453b 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -128,7 +128,7 @@ denote cross-shore and alongshore distances respectively. The formulation is discretized in different ways to allow for different types of simulations balancing accuracy vs. computational resources. The conservative method combined with an euler backward scheme (written by Prof. Rauwoens) is the current default for most simulations. Non-conservative methods end explicit Euler forward schemes are also available. Default scheme -- Conservative Euler Backward Implicit -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The default numerical method assumes the advection scheme in a conservative form in combination with an euler backward scheme. This scheme is prepared to use a TVD method but this is not implemented yet (add footnote{Total Variance Diminishing, this is explained in the lecture notes by Zijlema p94}) From 067b99c8a2d7ea60b6a08ad303c9eb20371a939b Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:58:35 +0200 Subject: [PATCH 033/124] Update model_description.rst --- docs/user/model_description.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index 163e453b..3b453e7c 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -128,7 +128,7 @@ denote cross-shore and alongshore distances respectively. The formulation is discretized in different ways to allow for different types of simulations balancing accuracy vs. computational resources. The conservative method combined with an euler backward scheme (written by Prof. Rauwoens) is the current default for most simulations. Non-conservative methods end explicit Euler forward schemes are also available. Default scheme -- Conservative Euler Backward Implicit -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The default numerical method assumes the advection scheme in a conservative form in combination with an euler backward scheme. This scheme is prepared to use a TVD method but this is not implemented yet (add footnote{Total Variance Diminishing, this is explained in the lecture notes by Zijlema p94}) From ea2130899b51fd34578fbfb2906ef9fe054d725e Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Wed, 24 Jul 2024 23:59:29 +0200 Subject: [PATCH 034/124] Update installation.rst --- docs/user/installation.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user/installation.rst b/docs/user/installation.rst index d209598a..e3eb75b5 100644 --- a/docs/user/installation.rst +++ b/docs/user/installation.rst @@ -13,7 +13,7 @@ Requirements - netCDF4 Dependencies -"""""""""""" +------------ - docopt==0.6.1 - bmi-python From d09d4af8bb52ab31218e82da1824069b155f2bc5 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Thu, 25 Jul 2024 00:11:54 +0200 Subject: [PATCH 035/124] Update index.rst --- docs/index.rst | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/index.rst b/docs/index.rst index d5101e1f..8665848d 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -23,6 +23,7 @@ Contents .. toctree:: :caption: User Documentation :maxdepth: 3 + :hidden: user/introduction user/installation From 3d2a25f8af0f32dbbfbb6de7561ec90f626ef3ed Mon Sep 17 00:00:00 2001 From: bartvanwesten Date: Thu, 25 Jul 2024 00:16:18 +0200 Subject: [PATCH 036/124] Updated the BMI documentation partially --- docs/user/model_interaction.rst | 30 +++++++++++++++++------------- 1 file changed, 17 insertions(+), 13 deletions(-) diff --git a/docs/user/model_interaction.rst b/docs/user/model_interaction.rst index c4d6e3e9..78887b69 100644 --- a/docs/user/model_interaction.rst +++ b/docs/user/model_interaction.rst @@ -6,19 +6,7 @@ ADD INTRODUCTION TO MODEL INTRODUCTION - WHY, HOW Callback function ----------------- - -Hotstart --------- - - -Basic Model Interface (BMI) ---------------------------- - -A Basic Model Interface (BMI, :cite:`Peckham2013`) is implemented -that allows interaction with the model during run time. The model can -be implemented as a library within a larger framework as the interface -exposes the initialization, finalization and time stepping -routines. As a convenience functionality the current implementation +As a convenience functionality the current implementation supports the specification of a callback function. The callback function is called at the start of each time step and can be used to exchange data with the model, e.g. update the topography from @@ -38,3 +26,19 @@ input file or through the model command-line options as val_new[:,:] = np.loadtxt('measured_topography.txt') model.set_var('zb', val_new) + + +Hotstart +-------- + + +Basic Model Interface (BMI) +--------------------------- + +A Basic Model Interface (BMI, :cite:`Peckham2013`) is implemented +that allows interaction with the model during run time. The model can +be implemented as a library within a larger framework as the interface +exposes the initialization, finalization and time stepping +routines. + + From f3fee04ea19bbf6a5017b33b80ad8d1ef53a382b Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Thu, 25 Jul 2024 00:16:41 +0200 Subject: [PATCH 037/124] Update index.rst --- docs/index.rst | 1 - 1 file changed, 1 deletion(-) diff --git a/docs/index.rst b/docs/index.rst index 8665848d..d5101e1f 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -23,7 +23,6 @@ Contents .. toctree:: :caption: User Documentation :maxdepth: 3 - :hidden: user/introduction user/installation From 4615e507563ddccb02074c1db6f2faf7062aba26 Mon Sep 17 00:00:00 2001 From: bartvanwesten Date: Thu, 25 Jul 2024 00:25:26 +0200 Subject: [PATCH 038/124] Update the BMI description --- docs/user/model_interaction.rst | 48 ++++++++++++++++++++++++++++++++- 1 file changed, 47 insertions(+), 1 deletion(-) diff --git a/docs/user/model_interaction.rst b/docs/user/model_interaction.rst index 78887b69..d302a4c3 100644 --- a/docs/user/model_interaction.rst +++ b/docs/user/model_interaction.rst @@ -39,6 +39,52 @@ A Basic Model Interface (BMI, :cite:`Peckham2013`) is implemented that allows interaction with the model during run time. The model can be implemented as a library within a larger framework as the interface exposes the initialization, finalization and time stepping -routines. +routines. Because of that, we can use this set of functions to control +and interact with AeoLiS from a Python environment. + + +.. code:: + + import numpy as np + + # Timing settigns + start_time = 0. + end_time = 157680000. + dt = 3600. # 1 day (output frequency of dfm output) + + # Find file in the same directory as this script that contains aeolis.txt + configfile = 'aeolis.txt' + os.chdir(os.path.dirname(configfile)) + + # Create AeoLiS BMI Wrapper + aeolis_wrapper = AeoLiSRunner(configfile) + + # Initialize the wrapper + aeolis_wrapper.initialize() + + # Loop over all timesteps to run the model + for t in np.arange(start_time, end_time, dt): + + Β  Β  # Update AeoLiS + Β  Β  aeolis_wrapper.update(dt) + Β  Β  aeolis_wrapper.output_write() + Β  Β  + # Make modifications to the variables in the model via data or another model, e.g.: + Β  Β  # x_aeolis = aeolis_wrapper.get_var('x') + Β  Β  # y_aeolis = aeolis_wrapper.get_var('y’) + + Β  Β  # aeolis_wrapper.set_var('zb', zb_aeolis) + + # Finalize the wrapper + aeolis_wrapper.finalize() + + +An overview of recent BMI-AeoLiS applications: +- van Westen, B., Luijendijk, A. P., de Vries, S., Cohn, N., Leijnse, T. W., & de Schipper, M. A. (2024). Predicting marine and aeolian contributions to the Sand Engine’s evolution using coupled modelling. Coastal Engineering, 188, 104444. (https://www.sciencedirect.com/science/article/pii/S0378383923001680) +- van Westen, B., Leijnse, T., de Schipper, M., Cohn, N., & Luijendijk, A. (2023). Integrated modelling of coastal landforms. In Coastal Sediments 2023: The Proceedings of the Coastal Sediments 2023 (pp. 760-771). (https://pure.tudelft.nl/ws/portalfiles/portal/152631531/Integrated_modelling_Bvw_CS23.pdf) + + + + From fdfcf497605bc118706fd57873c0850e0661b118 Mon Sep 17 00:00:00 2001 From: Bart van Westen Date: Thu, 25 Jul 2024 00:27:37 +0200 Subject: [PATCH 039/124] Update model_interaction.rst --- docs/user/model_interaction.rst | 66 ++++++++++++++++----------------- 1 file changed, 33 insertions(+), 33 deletions(-) diff --git a/docs/user/model_interaction.rst b/docs/user/model_interaction.rst index d302a4c3..250354c6 100644 --- a/docs/user/model_interaction.rst +++ b/docs/user/model_interaction.rst @@ -45,39 +45,39 @@ and interact with AeoLiS from a Python environment. .. code:: - import numpy as np - - # Timing settigns - start_time = 0. - end_time = 157680000. - dt = 3600. # 1 day (output frequency of dfm output) - - # Find file in the same directory as this script that contains aeolis.txt - configfile = 'aeolis.txt' - os.chdir(os.path.dirname(configfile)) - - # Create AeoLiS BMI Wrapper - aeolis_wrapper = AeoLiSRunner(configfile) - - # Initialize the wrapper - aeolis_wrapper.initialize() - - # Loop over all timesteps to run the model - for t in np.arange(start_time, end_time, dt): - - Β  Β  # Update AeoLiS - Β  Β  aeolis_wrapper.update(dt) - Β  Β  aeolis_wrapper.output_write() - Β  Β  - # Make modifications to the variables in the model via data or another model, e.g.: - Β  Β  # x_aeolis = aeolis_wrapper.get_var('x') - Β  Β  # y_aeolis = aeolis_wrapper.get_var('y’) - - Β  Β  # aeolis_wrapper.set_var('zb', zb_aeolis) - - # Finalize the wrapper - aeolis_wrapper.finalize() - +import numpy as np + +# Timing settigns +start_time = 0. +end_time = 157680000. +dt = 3600. # 1 day (output frequency of dfm output) + +# Find file in the same directory as this script that contains aeolis.txt +configfile = 'aeolis.txt' +os.chdir(os.path.dirname(configfile)) + +# Create AeoLiS BMI Wrapper +aeolis_wrapper = AeoLiSRunner(configfile) + +# Initialize the wrapper +aeolis_wrapper.initialize() + +# Loop over all timesteps to run the model +for t in np.arange(start_time, end_time, dt): + + # Update AeoLiS + aeolis_wrapper.update(dt) + aeolis_wrapper.output_write() + + # Make modifications to the variables in the model via data or another model, e.g.: + # x_aeolis = aeolis_wrapper.get_var('x') + # y_aeolis = aeolis_wrapper.get_var('y’) + + # aeolis_wrapper.set_var('zb', zb_aeolis) + +# Finalize the wrapper +aeolis_wrapper.finalize() + An overview of recent BMI-AeoLiS applications: - van Westen, B., Luijendijk, A. P., de Vries, S., Cohn, N., Leijnse, T. W., & de Schipper, M. A. (2024). Predicting marine and aeolian contributions to the Sand Engine’s evolution using coupled modelling. Coastal Engineering, 188, 104444. (https://www.sciencedirect.com/science/article/pii/S0378383923001680) From 1103bbc12451a1021a6df0cb3ea447582da9d8dc Mon Sep 17 00:00:00 2001 From: Bart van Westen Date: Thu, 25 Jul 2024 00:27:57 +0200 Subject: [PATCH 040/124] Update model_interaction.rst --- docs/user/model_interaction.rst | 68 ++++++++++++++++----------------- 1 file changed, 34 insertions(+), 34 deletions(-) diff --git a/docs/user/model_interaction.rst b/docs/user/model_interaction.rst index 250354c6..66d6b0ef 100644 --- a/docs/user/model_interaction.rst +++ b/docs/user/model_interaction.rst @@ -45,43 +45,43 @@ and interact with AeoLiS from a Python environment. .. code:: -import numpy as np - -# Timing settigns -start_time = 0. -end_time = 157680000. -dt = 3600. # 1 day (output frequency of dfm output) - -# Find file in the same directory as this script that contains aeolis.txt -configfile = 'aeolis.txt' -os.chdir(os.path.dirname(configfile)) - -# Create AeoLiS BMI Wrapper -aeolis_wrapper = AeoLiSRunner(configfile) - -# Initialize the wrapper -aeolis_wrapper.initialize() - -# Loop over all timesteps to run the model -for t in np.arange(start_time, end_time, dt): - - # Update AeoLiS - aeolis_wrapper.update(dt) - aeolis_wrapper.output_write() - - # Make modifications to the variables in the model via data or another model, e.g.: - # x_aeolis = aeolis_wrapper.get_var('x') - # y_aeolis = aeolis_wrapper.get_var('y’) - - # aeolis_wrapper.set_var('zb', zb_aeolis) - -# Finalize the wrapper -aeolis_wrapper.finalize() + import numpy as np + + # Timing settigns + start_time = 0. + end_time = 157680000. + dt = 3600. # 1 day (output frequency of dfm output) + + # Find file in the same directory as this script that contains aeolis.txt + configfile = 'aeolis.txt' + os.chdir(os.path.dirname(configfile)) + + # Create AeoLiS BMI Wrapper + aeolis_wrapper = AeoLiSRunner(configfile) + + # Initialize the wrapper + aeolis_wrapper.initialize() + + # Loop over all timesteps to run the model + for t in np.arange(start_time, end_time, dt): + + # Update AeoLiS + aeolis_wrapper.update(dt) + aeolis_wrapper.output_write() + + # Make modifications to the variables in the model via data or another model, e.g.: + # x_aeolis = aeolis_wrapper.get_var('x') + # y_aeolis = aeolis_wrapper.get_var('y’) + + # aeolis_wrapper.set_var('zb', zb_aeolis) + + # Finalize the wrapper + aeolis_wrapper.finalize() An overview of recent BMI-AeoLiS applications: -- van Westen, B., Luijendijk, A. P., de Vries, S., Cohn, N., Leijnse, T. W., & de Schipper, M. A. (2024). Predicting marine and aeolian contributions to the Sand Engine’s evolution using coupled modelling. Coastal Engineering, 188, 104444. (https://www.sciencedirect.com/science/article/pii/S0378383923001680) -- van Westen, B., Leijnse, T., de Schipper, M., Cohn, N., & Luijendijk, A. (2023). Integrated modelling of coastal landforms. In Coastal Sediments 2023: The Proceedings of the Coastal Sediments 2023 (pp. 760-771). (https://pure.tudelft.nl/ws/portalfiles/portal/152631531/Integrated_modelling_Bvw_CS23.pdf) + - van Westen, B., Luijendijk, A. P., de Vries, S., Cohn, N., Leijnse, T. W., & de Schipper, M. A. (2024). Predicting marine and aeolian contributions to the Sand Engine’s evolution using coupled modelling. Coastal Engineering, 188, 104444. (https://www.sciencedirect.com/science/article/pii/S0378383923001680) + - van Westen, B., Leijnse, T., de Schipper, M., Cohn, N., & Luijendijk, A. (2023). Integrated modelling of coastal landforms. In Coastal Sediments 2023: The Proceedings of the Coastal Sediments 2023 (pp. 760-771). (https://pure.tudelft.nl/ws/portalfiles/portal/152631531/Integrated_modelling_Bvw_CS23.pdf) From 0f6ac7a4ec5ca53a8c1f70c1ad6c639407447dfd Mon Sep 17 00:00:00 2001 From: Bart van Westen Date: Thu, 25 Jul 2024 00:30:58 +0200 Subject: [PATCH 041/124] Update model_interaction.rst --- docs/user/model_interaction.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user/model_interaction.rst b/docs/user/model_interaction.rst index 66d6b0ef..c4d64022 100644 --- a/docs/user/model_interaction.rst +++ b/docs/user/model_interaction.rst @@ -1,7 +1,7 @@ Model interaction ================= -ADD INTRODUCTION TO MODEL INTRODUCTION - WHY, HOW +AeoLiS includes several features that enable user-model interaction during runtime. These interactions can be used to modify model parameters over time, integrate with other models, or perform model-data assimilation. Callback function ----------------- From 4a418b8da6a7d6c0a458aefccd0247d68f5a1016 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Thu, 25 Jul 2024 00:34:42 +0200 Subject: [PATCH 042/124] Update introduction.rst --- docs/user/introduction.rst | 46 +++++++++++++++++++++++++++++++++++++- 1 file changed, 45 insertions(+), 1 deletion(-) diff --git a/docs/user/introduction.rst b/docs/user/introduction.rst index bb564d06..5f397dd3 100644 --- a/docs/user/introduction.rst +++ b/docs/user/introduction.rst @@ -3,4 +3,48 @@ Introduction ============ AeoLiS is a process-based model for simulating aeolian sediment transport and morphological evolution in situations where supply-limiting factors are important, -like in coastal environments. Supply-limitations currently supported are soil moisture contents, sediment sorting and armouring, bed slope effects, air humidity and roughness elements. AeoLiS includes a dynamic vegetation module that simulates the interaction between sediment transport and vegetation dynamics. +like in coastal environments. Supply-limitations currently supported are soil moisture contents, sediment sorting and armouring, bed slope effects, air humidity and roughness elements. AeoLiS includes a dynamic vegetation module that simulates the interaction between sediment transport and vegetation dynamics that allow for aeolian landform simulations. + +Model overview +-------------- + +Applicability and limitations +----------------------------- + +AeoLiS in publications +---------------------- + +2024 +^^^^ +van Westen, B., Luijendijk, A.P., de Vries, S., Cohn, N., Leijnse, T.W., de Schipper, M.A., 2024. Predicting marine and aeolian contributions to the sand engine’s evolution using coupled modelling. Coast. Eng. 188, 104444. + +2023 +^^^^ +Hallin, C., van IJzendoorn, C., Homberger, J.M., de Vries, S., 2023. Simulating surface soil moisture on sandy beaches. Coast. Eng. 185, 104376. +Hallin, C., van IJzendoorn, C., Skaden, J., de Vries, S., 2023. Evaluation of threshold-based models to account for surface moisture in meso-scale aeolian sediment transport simulations. In: The Proceedings of the Coastal Sediments Conference. pp. 670–683. +van IJzendoorn, C.O., Hallin, C., Reniers, A.J.H.M., de Vries, S., 2023. Modeling multi-fraction coastal aeolian sediment transport with horizontal and vertical grain-size variability. J. Geophys. Res: Earth Surf. 128 (7), e2023JF007155. + +2022 +^^^^ + +2021 +^^^^ + +2020 +^^^^ + +2019 +^^^^ +Hoonhout, B., de Vries, S., 2019. Simulating spatiotemporal aeolian sediment supply at a mega nourishment. Coast. Eng. 145, 21–35. + +2018 +^^^^ +Wittebrood, M., de Vries, S., Goessen, P., Aarninkhof, S., 2018. Aeolian sediment transport at a man-made dune system; building with nature at the hondsbossche dunes. Coast. Eng. Proceedings (36), 83. + +2017 +^^^^ +Hoonhout, B., de Vries, S., 2017. Aeolian sediment supply at a mega nourishment. Coast. Eng. 123, 11–20. + +2016 +^^^^ +Hoonhout, B.M., de Vries, S., 2016. A process-based model for aeolian sediment transport and spatiotemporal varying sediment availability. J. Geophys. Res: Earth Surf. 121 (8), 1555–1575. From c06ed59792b02f93495e57320840d021c6a19926 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Thu, 25 Jul 2024 00:35:11 +0200 Subject: [PATCH 043/124] Update introduction.rst --- docs/user/introduction.rst | 2 ++ 1 file changed, 2 insertions(+) diff --git a/docs/user/introduction.rst b/docs/user/introduction.rst index 5f397dd3..d7a3b416 100644 --- a/docs/user/introduction.rst +++ b/docs/user/introduction.rst @@ -21,7 +21,9 @@ van Westen, B., Luijendijk, A.P., de Vries, S., Cohn, N., Leijnse, T.W., de Schi 2023 ^^^^ Hallin, C., van IJzendoorn, C., Homberger, J.M., de Vries, S., 2023. Simulating surface soil moisture on sandy beaches. Coast. Eng. 185, 104376. + Hallin, C., van IJzendoorn, C., Skaden, J., de Vries, S., 2023. Evaluation of threshold-based models to account for surface moisture in meso-scale aeolian sediment transport simulations. In: The Proceedings of the Coastal Sediments Conference. pp. 670–683. + van IJzendoorn, C.O., Hallin, C., Reniers, A.J.H.M., de Vries, S., 2023. Modeling multi-fraction coastal aeolian sediment transport with horizontal and vertical grain-size variability. J. Geophys. Res: Earth Surf. 128 (7), e2023JF007155. 2022 From e2b783ccd658adba123d3b76298ee480f11d2850 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Thu, 25 Jul 2024 01:47:40 +0200 Subject: [PATCH 044/124] Update introduction.rst --- docs/user/introduction.rst | 30 ++++++++++++++++++++++++------ 1 file changed, 24 insertions(+), 6 deletions(-) diff --git a/docs/user/introduction.rst b/docs/user/introduction.rst index d7a3b416..83195c03 100644 --- a/docs/user/introduction.rst +++ b/docs/user/introduction.rst @@ -16,6 +16,8 @@ AeoLiS in publications 2024 ^^^^ +Heminway, S.S., Cohn, N., Davis, E.H., White, A., Hein, C.J., Zinnert, J.C., 2024. Exploring Ecological, Morphological, and Environmental Controls on Coastal Foredune Evolution at Annual Scales Using a Process-Based Model. Sustainability, 16, 3460. https://doi.org/10.3390/su16083460 + van Westen, B., Luijendijk, A.P., de Vries, S., Cohn, N., Leijnse, T.W., de Schipper, M.A., 2024. Predicting marine and aeolian contributions to the sand engine’s evolution using coupled modelling. Coast. Eng. 188, 104444. 2023 @@ -24,19 +26,20 @@ Hallin, C., van IJzendoorn, C., Homberger, J.M., de Vries, S., 2023. Simulating Hallin, C., van IJzendoorn, C., Skaden, J., de Vries, S., 2023. Evaluation of threshold-based models to account for surface moisture in meso-scale aeolian sediment transport simulations. In: The Proceedings of the Coastal Sediments Conference. pp. 670–683. -van IJzendoorn, C.O., Hallin, C., Reniers, A.J.H.M., de Vries, S., 2023. Modeling multi-fraction coastal aeolian sediment transport with horizontal and vertical grain-size variability. J. Geophys. Res: Earth Surf. 128 (7), e2023JF007155. +Heminway, S.S., Davis, E.H., Cohn, N., Skaden, J., Anderson, D., Hein, C.J., 2023. Modeled Changes in Foredune Morphology Influenced by Variable Storm Intensity and Sea-Level Rise. In Proceedings of the Coastal Sediments 2023; World Scientific: New Orleans, LA, USA, April 2023; pp. 684–697. -2022 -^^^^ +Hovenga, P., Ruggiero, P., Itzkin, M., Jay, K.R., Moore, L., Hacker, H.D., 2023. Quantifying the relative influence of coastal foredune growth factors on the U.S. Mid-Atlantic Coast using field observations and the process-based numerical model Windsurf, Coastal Engineering, Volume 181, 104272, https://doi.org/10.1016/j.coastaleng.2022.104272. -2021 -^^^^ +van IJzendoorn, C.O., Hallin, C., Reniers, A.J.H.M., de Vries, S., 2023. Modeling multi-fraction coastal aeolian sediment transport with horizontal and vertical grain-size variability. J. Geophys. Res: Earth Surf. 128 (7), e2023JF007155. -2020 +2022 ^^^^ +Itzkin, M., Moore, L.J., Ruggiero, P., Hovenga, P.A., Hacker, S.D., 2022. Combining process-based and data-driven approaches to forecast beach and dune change, Environmental Modelling & Software, Volume 153, 105404, ISSN 1364-8152, https://doi.org/10.1016/j.envsoft.2022.105404. 2019 ^^^^ +Cohn, N., Hoonhout, B.M., Goldstein, E.B., De Vries, S., Moore, L.J., DurΓ‘n Vinent, O., Ruggiero, P., 2019 Exploring Marine and Aeolian Controls on Coastal Foredune Growth Using a Coupled Numerical Model. J. Mar. Sci. Eng., 7, 13. https://doi.org/10.3390/jmse7010013 + Hoonhout, B., de Vries, S., 2019. Simulating spatiotemporal aeolian sediment supply at a mega nourishment. Coast. Eng. 145, 21–35. 2018 @@ -50,3 +53,18 @@ Hoonhout, B., de Vries, S., 2017. Aeolian sediment supply at a mega nourishment. 2016 ^^^^ Hoonhout, B.M., de Vries, S., 2016. A process-based model for aeolian sediment transport and spatiotemporal varying sediment availability. J. Geophys. Res: Earth Surf. 121 (8), 1555–1575. + +2014 +^^^^ +de Vries, S., de Vries, J.v.T., Van Rijn, L., Arens, S., 2014. Aeolian sediment transport in supply limited situations. Aeolian Res. 12, 75–85. + + +Student theses +-------------- +Meijer, L.M., 2020. Numerical Modelling of Aeolian Sediment Transport, Vegetation Growth and Blowout Formation in Coastal Dunes. MSc Thesis, Delft University of Technology. + +Pak, T. 2019 Marine and aeolian sediment transport at the Hondsbossche Dunes. MSc Thesis, Delft University of Technology. + +van Manen, M. 2023. Numerical Modeling of Constructed Foredune Blowouts in the Dutch Dunes. MSc Thesis, Delft University of Technology. + +van Westen, B. 2018. Numerical modelling of aeolian coastal landform development. Master’s thesis, Delft University of Technology. From 82208463c17d33d6ae2e4887d50c36de1988a95e Mon Sep 17 00:00:00 2001 From: Christa van IJzendoorn <52737913+christavanijzendoorn@users.noreply.github.com> Date: Wed, 24 Jul 2024 16:56:02 -0700 Subject: [PATCH 045/124] Update constants.py Beach slope now used in vegetation, runup and erosion calculations, not just the erosion module --- aeolis/constants.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/aeolis/constants.py b/aeolis/constants.py index a07fd23a..541b4843 100644 --- a/aeolis/constants.py +++ b/aeolis/constants.py @@ -323,7 +323,7 @@ 'wind_convention' : 'nautical', # Convention used for the wind direction in the input files (cartesian or nautical) 'alfa' : 0, # [deg] Real-world grid cell orientation wrt the North (clockwise) 'dune_toe_elevation' : 3, # Choose dune toe elevation, only used in the PH12 dune erosion solver - 'beach_slope' : 0.1, # Define the beach slope, only used in the PH12 dune erosion solver + 'beach_slope' : 0.1, # Define the beach slope 'veg_min_elevation' : 3, # Choose the minimum elevation where vegetation can grow 'vegshear_type' : 'raupach', # Choose the Raupach grid based solver (1D or 2D) or the Okin approach (1D only) 'okin_c1_veg' : 0.48, #x/h spatial reduction factor in Okin model for use with vegetation From d7595545049d82ad203beacc180cc18eed2f61c7 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Thu, 25 Jul 2024 01:56:15 +0200 Subject: [PATCH 046/124] Update introduction.rst --- docs/user/introduction.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user/introduction.rst b/docs/user/introduction.rst index 83195c03..a840e723 100644 --- a/docs/user/introduction.rst +++ b/docs/user/introduction.rst @@ -11,7 +11,7 @@ Model overview Applicability and limitations ----------------------------- -AeoLiS in publications +AeoLiS publications ---------------------- 2024 From 0b46cc9617560ba567a74791b956210be74d89b6 Mon Sep 17 00:00:00 2001 From: Christa van IJzendoorn <52737913+christavanijzendoorn@users.noreply.github.com> Date: Wed, 24 Jul 2024 17:27:46 -0700 Subject: [PATCH 047/124] Update model_setup.rst Adding explanation of process flags --- docs/user/model_setup.rst | 41 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 41 insertions(+) diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index 8cb286df..ca4fc526 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -241,6 +241,47 @@ configuration is listed below. Activate/deactivate processes ----------------------------- +After creating the input files that are necessary to run an AeoLiS model, the next step is often to decide which processes and methods to use. Several processes are defined in the configuration file that can be turned on and off. Apart from turning processes on and off, there are also several user-defined thresholds and methods that affect the way in which processes are calculated. For example, there are different sediment transport equations available within 'process_transport'. The default is Bagnold, but by defining 'method_transport' in the configuration file a different equation can be used. Here, we provide a description of the processes and methods that are defined in configuration file. More detailed descriptions of the processes and their implementation can be found in :ref:model_description + +An easy way to look up where these process, threshold and method flags are used is by going to the main page of the AeoLiS github and using the search bar at the top. For instance, searching 'process_tide' shows that it is used in :py:mod:`aeolis.threshold.compute`, :py:mod:`aeolis.vegetation.grow`, :py:mod:`aeolis.bed.update`. + +Process_wind +^^^^^^^^^^^^^ +'Process_wind' makes sure the wind file is loaded, and interpolates values of the wind speed and direction to each time step. The model does not work without this flag. Used in :py:mod:`aeolis.wind.interpolate` + +Process_threshold +^^^^^^^^^^^^^^^^^ +'Process_threshold' allows for the alterations of the threshold velocity by processes like grain, moisture and vegetation. This process does not occur if a threshold file is provided as input since this file is used to define the threshold shear velocity. Used in :py:mod:`aeolis.threshold.compute` + +Process_transport +^^^^^^^^^^^^^^^^^^ +'Process_transport' allows the calculation of the equilibrium transport rate based on a user-defined transport method. + +'Method_transport' defines the sediment transport equation used in the calculation of the equilibrium transport rate. Options are: bagnold, bagnold_gs, kawamura, lettau, dk, sauermann, vanrijn_strypsteen. + +'Method_grainspeed' defines at which speed the sediment transport in the air is occurring. Options are: 'duran'/'duran_full', 'windspeed', and 'constant' + +Used in :py:mod:`aeolis.transport.equilibrium` + +Process_bedupdate +^^^^^^^^^^^^^^^^^ +Process_bedupdate allows the bed level to change based on calculated erosion/deposition. Used in :py:mod:`aeolis.bed.update` + +Process_shear +^^^^^^^^^^^^^ +Process_shear calls the shear module in shear.py to calculate the shear stress perturbation caused by topography. Used in :py:mod:`aeolis.wind.initialize` + +Process_tide +^^^^^^^^^^^^ +Process_tide changes the threshold velocity to infinity (no aeolian transport) if the bed level is below the water level. This process is not used if th_moist is used. Used in :py:mod:`aeolis.threshold.compute`, :py:mod:`aeolis.vegetation.grow`, :py:mod:`aeolis.bed.update`. + +Process_wave +^^^^^^^^^^^^ +Process_wave allows calculation of the water depth based on the input tide file and interpolates the input wave data to the timesteps of the model run. If the wave file is not available, the wave height and peak period are set to 0. Turning this process flag on also results in the calculation of Hsmix, which is needed for the calculation of the Depth of Disturbance (process_mixtoplayer). The initialization/calculation is skipped if external variables are imported from another model. + +Process_runup +^^^^^^^^^^^^ +Process_runup allows calculation of the runup extent based on the wave height, peak period and water level. Process_wave and Process_tide need to be on for this to work. The runup is calculated with the Stockdon equation using a user-defined, static beach slope. The initialization/calculation is skipped if external variables are imported from another model. Model state/output From 5674b085bd973901a32ceed28448ae12ce7a15bb Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Thu, 25 Jul 2024 02:29:20 +0200 Subject: [PATCH 048/124] Update introduction.rst --- docs/user/introduction.rst | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) diff --git a/docs/user/introduction.rst b/docs/user/introduction.rst index a840e723..f2e01d3a 100644 --- a/docs/user/introduction.rst +++ b/docs/user/introduction.rst @@ -18,10 +18,16 @@ AeoLiS publications ^^^^ Heminway, S.S., Cohn, N., Davis, E.H., White, A., Hein, C.J., Zinnert, J.C., 2024. Exploring Ecological, Morphological, and Environmental Controls on Coastal Foredune Evolution at Annual Scales Using a Process-Based Model. Sustainability, 16, 3460. https://doi.org/10.3390/su16083460 +Orie, C., Cohn, N., Farthing, M., Dutta, S., Trautz, A., 2024. Examination of Analytical Shear Stress Predictions for Coastal Dune Evolution. EGUsphere, https://doi.org/10.5194/egusphere-2024-855. Preprint under review for ESurf + van Westen, B., Luijendijk, A.P., de Vries, S., Cohn, N., Leijnse, T.W., de Schipper, M.A., 2024. Predicting marine and aeolian contributions to the sand engine’s evolution using coupled modelling. Coast. Eng. 188, 104444. +McFall, B.C., Young, D.L., Whitmeyer, S.J., Buscombe, D., Cohn, N., Stasiewicz, J.B., Skaden, J.E., Walker, B.M., Stever, S.N., 2024. SandSnap: Measuring and mapping beach grain size using crowd-sourced smartphone images, Coastal Engineering, Volume 192, 104554, https://doi.org/10.1016/j.coastaleng.2024.104554. + 2023 ^^^^ +Dickey, J., Wengrove, M., Cohn, N., Ruggiero, P. & Hacker, S.D., 2023. Observations and modeling of shear stress reduction and sediment flux within sparse dune grass canopies on managed coastal dunes. Earth Surface Processes and Landforms, 48(5), 907–922. Available from: https://doi.org/10.1002/esp.5526 + Hallin, C., van IJzendoorn, C., Homberger, J.M., de Vries, S., 2023. Simulating surface soil moisture on sandy beaches. Coast. Eng. 185, 104376. Hallin, C., van IJzendoorn, C., Skaden, J., de Vries, S., 2023. Evaluation of threshold-based models to account for surface moisture in meso-scale aeolian sediment transport simulations. In: The Proceedings of the Coastal Sediments Conference. pp. 670–683. @@ -30,18 +36,28 @@ Heminway, S.S., Davis, E.H., Cohn, N., Skaden, J., Anderson, D., Hein, C.J., 202 Hovenga, P., Ruggiero, P., Itzkin, M., Jay, K.R., Moore, L., Hacker, H.D., 2023. Quantifying the relative influence of coastal foredune growth factors on the U.S. Mid-Atlantic Coast using field observations and the process-based numerical model Windsurf, Coastal Engineering, Volume 181, 104272, https://doi.org/10.1016/j.coastaleng.2022.104272. +Skaden, J., Cohn, N., Goldstein, E., Dickhudt, P., Conery, I., Buscombe, D., 2023. Impact of alongshore and cross-shore variability in surface grain size on sediment supply to dunes. In Coastal Sediments 2023: The Proceedings of the Coastal Sediments 2023 (pp. 720-731). + van IJzendoorn, C.O., Hallin, C., Reniers, A.J.H.M., de Vries, S., 2023. Modeling multi-fraction coastal aeolian sediment transport with horizontal and vertical grain-size variability. J. Geophys. Res: Earth Surf. 128 (7), e2023JF007155. +van Westen, B., Leijnse, T., de Schipper, M., Cohn, N., & Luijendijk, A. (2023). Integrated modelling of coastal landforms. In Coastal Sediments 2023: The Proceedings of the Coastal Sediments 2023 (pp. 760-771). + +Zhu, L., Chen, Q., Cohn, N., Johnson, C., Johnson, B., 2023. Modeling long-term evolution of a beach-dune system: Caminada Headlands, Louisiana. In Coastal Sediments 2023: The Proceedings of the Coastal Sediments 2023 (pp. 782-796). + 2022 ^^^^ Itzkin, M., Moore, L.J., Ruggiero, P., Hovenga, P.A., Hacker, S.D., 2022. Combining process-based and data-driven approaches to forecast beach and dune change, Environmental Modelling & Software, Volume 153, 105404, ISSN 1364-8152, https://doi.org/10.1016/j.envsoft.2022.105404. 2019 ^^^^ +Cohn, N., Brodie, K., Ruggiero, P., van Westen, B, de Vries, S., 2019. Coastal inlet infilling from aeolian sediment transport. In Coastal Sediments 2019: Proceedings of the 9th International Conference, pp. 1212-1225. + Cohn, N., Hoonhout, B.M., Goldstein, E.B., De Vries, S., Moore, L.J., DurΓ‘n Vinent, O., Ruggiero, P., 2019 Exploring Marine and Aeolian Controls on Coastal Foredune Growth Using a Coupled Numerical Model. J. Mar. Sci. Eng., 7, 13. https://doi.org/10.3390/jmse7010013 Hoonhout, B., de Vries, S., 2019. Simulating spatiotemporal aeolian sediment supply at a mega nourishment. Coast. Eng. 145, 21–35. +Ruggiero, P., Cohn, N., Hoonhout, B., Goldstein, E., de Vries, S., Moore, L., Hacker, S. and Vinent, O.D., 2019. Simulating dune evolution on managed coastlines: Exploring management options with the Coastal Recovery from Storms Tool (CReST). Shore & Beach, 87(2), p.36. + 2018 ^^^^ Wittebrood, M., de Vries, S., Goessen, P., Aarninkhof, S., 2018. Aeolian sediment transport at a man-made dune system; building with nature at the hondsbossche dunes. Coast. Eng. Proceedings (36), 83. From e85b07931dfb7e34997d3b000da319bf3d151817 Mon Sep 17 00:00:00 2001 From: Glenn Strypsteen <102021750+GlennStrypsteen@users.noreply.github.com> Date: Wed, 24 Jul 2024 17:30:17 -0700 Subject: [PATCH 049/124] Update model_description.rst Update subchapter vegetation --- docs/user/model_description.rst | 31 ++++++++++++++++++++++++++++++- 1 file changed, 30 insertions(+), 1 deletion(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index 3b453e7c..64111c98 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -910,9 +910,38 @@ grain size dependency is implemented through :math:`u_{\mathrm{th}}`. :math:`u_{\mathrm{th}}` typically varies between 1 and 6 m/s for sand. -Vegetation +Vegetation (from Strypsteen et al., 2024) ------------------------------------- +In AeoLiS, the influence of vegetation on dune evolution is comprehensively +addressed. This includes modelling the intrinsic growth of vegetation, +accounting for factors such as growth and decay due to burial (DurΓ‘n and Moore, 2013), +lateral expansion and establishment (Keijsers et al., 2016), as well as simulating +the destruction of vegetation caused by hydrodynamic processes. In the event of +cell inundation, vegetation density is reduced as a result. Inspired by the +Coastal Dune Model (CDM) proposed by DurΓ‘n and Moore (2013), AeoLiS incorporates +vegetation-wind interaction using the expression established by DurΓ‘n and Herrmann (2006): + +:math:`\frac{u_{\text{veg}}}{u_*} = \frac{1}{\sqrt{1 + \Gamma \rho_{\text{veg}}}}` + +where the ratio of shear velocity in the presence of vegetation (uβˆ—,veg) to the unobstructed +shear velocity (uβˆ—) is determined by a vegetation-related roughness parameter (Ξ“) and the +vegetation density within a unit area of the grid cell (\rho_{\text{veg}}). In the model, Ξ“ = 16 is derived +from plant form drag and geometry values documented for creosote communities (DurΓ‘n and Herrmann, 2006). +This implementation calculates the expression on each model grid cell, with higher vegetation density +(expressed by \rho_{\text{veg}}) leading to a more substantial reduction in shear velocity compared to sparse +vegetation. By integrating these physical and ecological processes, AeoLiS simulates spatial patterns and temporal +variations in sediment transport and morphological changes resulting from aeolian processes in coastal +environments. + +\rho_{\text{veg}} can vary in space and time and is determined by the ratio of the actual vegetation height (hveg) to the +maximum vegetation height (hveg,max), and can vary between 0 and 1 (DurΓ‘n and Herrmann, 2006): + +.. _fig-bed-interaction-parameter: + +.. figure:: /images/bed_interaction_parameter.png + :width: 600px + :align: center Simulation of Sediment Sorting and Beach Armoring ------------------------------------------------- From 4cde585612f8d1808f874de9ec5c930f1fce4f91 Mon Sep 17 00:00:00 2001 From: Glenn Strypsteen <102021750+GlennStrypsteen@users.noreply.github.com> Date: Wed, 24 Jul 2024 17:35:50 -0700 Subject: [PATCH 050/124] Add files via upload Figure vegetation raupach --- docs/images/Veg_growth.png | Bin 0 -> 394550 bytes 1 file changed, 0 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zw{laDImfWMBkaJR{=c3gVrg`(1-3dIbJzK20J40LT>~6q4@&iT#dbXOtFL6t9Z>gd z@gpPO?0PM>7jdYoPCeQ4!yA{W{Cf8xB(uY8x!99a`inzw^BtQsW?$`|_@QEYgsJ|6 z@N{;PyXT_B6?Zdl`aKyC_ObP@<1>}>9Sh2hWhYtwAHPwnGQ{nN3HLhl{gYfWZC4ez zOwK>TnS1Jh2#WofQr*P;5d$$lfw#r*yZF~eS1pz Date: Fri, 26 Jul 2024 09:42:11 -0700 Subject: [PATCH 052/124] Update model_description.rst New update vegetation documentation --- docs/user/model_description.rst | 52 ++++++++++++++++++++++++++++----- 1 file changed, 45 insertions(+), 7 deletions(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index 64111c98..59c2d659 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -910,7 +910,8 @@ grain size dependency is implemented through :math:`u_{\mathrm{th}}`. :math:`u_{\mathrm{th}}` typically varies between 1 and 6 m/s for sand. -Vegetation (from Strypsteen et al., 2024) +Vegetation (from Strypsteen et al., 2024. Vertical Growth Rate of Planted Vegetation Controls Dune Growth on a +Sandy Beach. Coastal Engineering. doi:10.2139/ssrn.4872614) ------------------------------------- In AeoLiS, the influence of vegetation on dune evolution is comprehensively @@ -934,15 +935,52 @@ vegetation. By integrating these physical and ecological processes, AeoLiS simul variations in sediment transport and morphological changes resulting from aeolian processes in coastal environments. -\rho_{\text{veg}} can vary in space and time and is determined by the ratio of the actual vegetation height (hveg) to the -maximum vegetation height (hveg,max), and can vary between 0 and 1 (DurΓ‘n and Herrmann, 2006): - -.. _fig-bed-interaction-parameter: - -.. figure:: /images/bed_interaction_parameter.png +\rho_{\text{veg}} can vary in space and time and is determined by the ratio of the actual vegetation height (hveg) +to the maximum vegetation height (hveg,max), and can vary between 0 and 1 (DurΓ‘n and Herrmann, 2006): + +:math:`\rho_{\text{veg}} = \left( \frac{h_{\text{veg}}}{h_{\text{veg,max}}} \right)^2` + +This assumption is based on the idea that burying vegetation reduces its height, which indicates a decrease in +actual cover. The change in vegetation density per grid cell is directly linked to the alteration in vegetation +height within that specific cell. This height variation is influenced by both the growth rate of the vegetation and +the rate of sediment burial. If the vegetation density remains constant over time, it suggests either no +sedimentation or a growth rate equal to the rate of sediment burial within the cell. Vegetation growth and decay +follow the model proposed by DurΓ‘n and Herrmann (2006), modified to include :math:`\delta z_{\text{b,opt}}` +(m/year), representing sediment burial for optimal growth that shifts the peak of optimal growth: + +:math:`\frac{\delta h_{\text{veg}}}{\delta t} = V_{\text{ver}} \left(1 - \frac{h_{\text{veg}}}{h_{\text{veg,max}}}\right) - \gamma_{\text{veg}} \left| \frac{\delta z_{\text{b,veg}}}{\delta t} - \delta z_{\ + +Here, :math:`\gamma_{\text{veg}}` (default = 1) is a sediment burial factor that accounts for the impact of +sediment burial on vegetation. The height of the vegetation (:math:`h_{\text{veg}}` in m) cannot be less than zero. +Vver represents the maximum vertical growth rate of vegetation given in m/year, while the sediment burial rate +:math:`\delta z_{\text{b,veg}}` [m] is determined as the bed level change per time step. By simply converting this +value to a bed level change per year multiple errors are induced, as the time scale over which the bed level change +actually occurs is much shorter than this one year. To compare the bed level change per time step with the +vegetation growth rate per year, an average bed level change is estimated over a specified time (default is one +day). This average is then extrapolated to an annual rate. This method ensures that sudden changes in the bed level +change over one time step are not used as an estimate of the total bed level change in one year, which would be far +too high. + +The optimal growth rate for certain vegetation species in dune environments is depending upon sediment burial +(Maun, 1998). The optimal burial rate for maximum vegetation growth for marram grass for the neighbouring Dutch +coast is around 0.31 m/year with a burying tolerance of 0.78 to 0.96 m burial/year (Nolet et al., 2018). This +optimal value is used in the model. :math:`V_{\text{ver}}` contains information of meteorological and local +conditions that enhance or inhibit vegetation growth process (Danin, 1991; Hesp, 1991). + +.. _fig-Veg_growth: + +.. figure:: /images/Veg_growth.png :width: 600px :align: center +Vegetation can begin to grow through lateral propagation or random germination. Once established, it can continue +to grow and spread laterally. The uncertainties associated with random germination are handled on a cell-by-cell +basis using a probabilistic approach, similar to the cellular automata method described by Keijsers et al. (2016). +AeoLiS incorporates a germination probability, denoted as ρ_{ger}, for each grid cell. This probability is constant +across the domain, except in eroding grid cells (where bed elevation decreases), where ρ_{ger} is set to 0. Lateral +propagation is determined by identifying the boundaries between vegetated and non-vegetated cells, with the +parameter ρ_{lat} adjusting the likelihood of lateral propagation at these boundaries. + Simulation of Sediment Sorting and Beach Armoring ------------------------------------------------- From 361e4d1cd42da9af8c54f4e64a74a22b58229c48 Mon Sep 17 00:00:00 2001 From: Christa van IJzendoorn <52737913+christavanijzendoorn@users.noreply.github.com> Date: Fri, 26 Jul 2024 09:57:56 -0700 Subject: [PATCH 053/124] Update model_setup.rst Added process flag descriptions --- docs/user/model_setup.rst | 42 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 42 insertions(+) diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index ca4fc526..83f87929 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -283,6 +283,48 @@ Process_runup ^^^^^^^^^^^^ Process_runup allows calculation of the runup extent based on the wave height, peak period and water level. Process_wave and Process_tide need to be on for this to work. The runup is calculated with the Stockdon equation using a user-defined, static beach slope. The initialization/calculation is skipped if external variables are imported from another model. +Process_moist +^^^^^^^^^^^^^ +Process_moist allows calculation of the soil moisture content, based on different methods, infiltration or surface_moist + +method_moist_process + +method_moist_threshold defines the equation used to calculate teh threshold shear veolcity based on the moisture content. Used in :py:mod:`aeolis.threshold.compute_moisture`. + +Process_groundwater, Process_seepage_face and Process_scanning are all related to the calculation of the moisture content. + +Process_mixtoplayer +^^^^^^^^^^^^^^^^^^^ +This process flag allows mixing in the layers that are present down to the depth of disturbance. For the calculation of the DoD the process_wave need to be on. + +Process_wet_bed_reset +^^^^^^^^^^^^^^^^^^^^^ +Resets the bed to the original bathymetry if the bed is under water (zs). Used in :py:mod:`aeolis.bed.wet_bed_reset`. The execution of the wet bed reset is dependent on the TWL calculation, which can be turned on process_runup, process_waves and process_tide. + +Process_meteo +^^^^^^^^^^^^^ +This is a place holder and currently has no functionality + +Process_avalanche +^^^^^^^^^^^^^^^^^^ +Simulates the process of avalanching when slopes of the bed become too steep to be realistic (i.e. > a critical static slope). + +Process_separation +^^^^^^^^^^^^^^^^^^ +This enables the calculation of the separation bubble within the shear perturbation module. Before executing the calculation is checks whether steep slopes are present that might lead to a separation bubble. Process_separation will only be used if process_shear is on. + +Process_vegetation +^^^^^^^^^^^^^^^^^^^ +This process flag allows application of shear stress reduction due to vegetation based on Raupach or Okin. It also allows for germination and lateral growth of vegetation if those values are set to larger than 0. This process is actively being developed. + +Process_fences +^^^^^^^^^^^^^^ +This process enables alteration of the shear velocity if fence characteristics are provided as user input. Calculations happen in 1D or 2D depending on grid size following the Okin model. + +Process_dune_erosion +^^^^^^^^^^^^^^^^^^^^ +This flag turns on dune erosion calculation (:py:mod:`aeolis.erosion`.) based on the Palmsten and Holman (2012) method. After calculating the erosion, the avalanching routine is run in :py:mod:`aeolis.model.update`. This is needed because these modules only get called for aeolian transport in case of winds above threshold. + Model state/output ------------------ From 0e2e57f6af723bdce7aa5de6824141ab513d1d7e Mon Sep 17 00:00:00 2001 From: Christa van IJzendoorn <52737913+christavanijzendoorn@users.noreply.github.com> Date: Fri, 26 Jul 2024 10:11:43 -0700 Subject: [PATCH 054/124] Update model_setup.rst Add threshold flag explanation --- docs/user/model_setup.rst | 43 +++++++++++++++++++++++---------------- 1 file changed, 25 insertions(+), 18 deletions(-) diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index 83f87929..d6c131e3 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -245,15 +245,22 @@ After creating the input files that are necessary to run an AeoLiS model, the ne An easy way to look up where these process, threshold and method flags are used is by going to the main page of the AeoLiS github and using the search bar at the top. For instance, searching 'process_tide' shows that it is used in :py:mod:`aeolis.threshold.compute`, :py:mod:`aeolis.vegetation.grow`, :py:mod:`aeolis.bed.update`. -Process_wind +process_wind ^^^^^^^^^^^^^ 'Process_wind' makes sure the wind file is loaded, and interpolates values of the wind speed and direction to each time step. The model does not work without this flag. Used in :py:mod:`aeolis.wind.interpolate` -Process_threshold +process_threshold ^^^^^^^^^^^^^^^^^ -'Process_threshold' allows for the alterations of the threshold velocity by processes like grain, moisture and vegetation. This process does not occur if a threshold file is provided as input since this file is used to define the threshold shear velocity. Used in :py:mod:`aeolis.threshold.compute` +'Process_threshold' allows for the alterations of the threshold velocity by processes like grain, moisture and vegetation. This process does not occur if a threshold file is provided as input since this file is used to define the threshold shear velocity. Used in :py:mod:`aeolis.threshold.compute`, documentation of threshold alterations can be found in :ref:model_description -Process_transport +th_grainsize: calculates the threshold velocity based on the grain size following Bagnold (:py:mod:`aeolis.threshold.compute_grain_size`) +th_bedslope: currently not implemented, but theoretically would include an alteration of the velocity threshold based on the slope of the bed. (:py:mod:`aeolis.threshold.compute_bedslope`) +th_moisture: alters the threshold velocity based on the moisture content, many different methods are available (:py:mod:`aeolis.threshold.compute_moisture`). Only works if moisture content is defined, which is calculated when process_moisture is on. +th_salt: alters the wind velocity threshold based on salt content following Nickling and Ecclestone (1981) (:py:mod:`aeolis.threshold.compute_salt`) +th_sheltering: modify the wind velocity threshold based on the presence of roughness elements in the grain size fractions following Raupach (1993) (:py:mod:`aeolis.threshold.compute_sheltering`) +th_humidity and th_drylayer: are currently not implemented + +process_transport ^^^^^^^^^^^^^^^^^^ 'Process_transport' allows the calculation of the equilibrium transport rate based on a user-defined transport method. @@ -263,27 +270,27 @@ Process_transport Used in :py:mod:`aeolis.transport.equilibrium` -Process_bedupdate +process_bedupdate ^^^^^^^^^^^^^^^^^ Process_bedupdate allows the bed level to change based on calculated erosion/deposition. Used in :py:mod:`aeolis.bed.update` -Process_shear +process_shear ^^^^^^^^^^^^^ Process_shear calls the shear module in shear.py to calculate the shear stress perturbation caused by topography. Used in :py:mod:`aeolis.wind.initialize` -Process_tide +process_tide ^^^^^^^^^^^^ Process_tide changes the threshold velocity to infinity (no aeolian transport) if the bed level is below the water level. This process is not used if th_moist is used. Used in :py:mod:`aeolis.threshold.compute`, :py:mod:`aeolis.vegetation.grow`, :py:mod:`aeolis.bed.update`. -Process_wave +process_wave ^^^^^^^^^^^^ Process_wave allows calculation of the water depth based on the input tide file and interpolates the input wave data to the timesteps of the model run. If the wave file is not available, the wave height and peak period are set to 0. Turning this process flag on also results in the calculation of Hsmix, which is needed for the calculation of the Depth of Disturbance (process_mixtoplayer). The initialization/calculation is skipped if external variables are imported from another model. -Process_runup +process_runup ^^^^^^^^^^^^ Process_runup allows calculation of the runup extent based on the wave height, peak period and water level. Process_wave and Process_tide need to be on for this to work. The runup is calculated with the Stockdon equation using a user-defined, static beach slope. The initialization/calculation is skipped if external variables are imported from another model. -Process_moist +process_moist ^^^^^^^^^^^^^ Process_moist allows calculation of the soil moisture content, based on different methods, infiltration or surface_moist @@ -293,35 +300,35 @@ method_moist_threshold defines the equation used to calculate teh threshold shea Process_groundwater, Process_seepage_face and Process_scanning are all related to the calculation of the moisture content. -Process_mixtoplayer +process_mixtoplayer ^^^^^^^^^^^^^^^^^^^ This process flag allows mixing in the layers that are present down to the depth of disturbance. For the calculation of the DoD the process_wave need to be on. -Process_wet_bed_reset +process_wet_bed_reset ^^^^^^^^^^^^^^^^^^^^^ Resets the bed to the original bathymetry if the bed is under water (zs). Used in :py:mod:`aeolis.bed.wet_bed_reset`. The execution of the wet bed reset is dependent on the TWL calculation, which can be turned on process_runup, process_waves and process_tide. -Process_meteo +process_meteo ^^^^^^^^^^^^^ This is a place holder and currently has no functionality -Process_avalanche +process_avalanche ^^^^^^^^^^^^^^^^^^ Simulates the process of avalanching when slopes of the bed become too steep to be realistic (i.e. > a critical static slope). -Process_separation +process_separation ^^^^^^^^^^^^^^^^^^ This enables the calculation of the separation bubble within the shear perturbation module. Before executing the calculation is checks whether steep slopes are present that might lead to a separation bubble. Process_separation will only be used if process_shear is on. -Process_vegetation +process_vegetation ^^^^^^^^^^^^^^^^^^^ This process flag allows application of shear stress reduction due to vegetation based on Raupach or Okin. It also allows for germination and lateral growth of vegetation if those values are set to larger than 0. This process is actively being developed. -Process_fences +process_fences ^^^^^^^^^^^^^^ This process enables alteration of the shear velocity if fence characteristics are provided as user input. Calculations happen in 1D or 2D depending on grid size following the Okin model. -Process_dune_erosion +process_dune_erosion ^^^^^^^^^^^^^^^^^^^^ This flag turns on dune erosion calculation (:py:mod:`aeolis.erosion`.) based on the Palmsten and Holman (2012) method. After calculating the erosion, the avalanching routine is run in :py:mod:`aeolis.model.update`. This is needed because these modules only get called for aeolian transport in case of winds above threshold. From a7dfca477ed297f95d852a3e9cd169c8022c9d00 Mon Sep 17 00:00:00 2001 From: Glenn Strypsteen <102021750+GlennStrypsteen@users.noreply.github.com> Date: Fri, 26 Jul 2024 10:13:04 -0700 Subject: [PATCH 055/124] Update aeolis.bib Added references related to the vegetation documentation --- docs/aeolis.bib | 84 +++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 84 insertions(+) diff --git a/docs/aeolis.bib b/docs/aeolis.bib index 1d46d31c..1c31b36c 100644 --- a/docs/aeolis.bib +++ b/docs/aeolis.bib @@ -14,6 +14,90 @@ @MANUAL{Simunek1998 timestamp = {2014.03.07} } +@article{DuranMoore2013, + author = {DurΓ‘n, O. and Moore, L. J.}, + title = {Vegetation controls on the maximum size of coastal dunes}, + journal = {Proceedings of the National Academy of Sciences}, + year = {2013}, + volume = {110}, + number = {43}, + pages = {17217–17222}, + doi = {10.1073/pnas.1307580110}, +} + +@article{Keijsers2016, + author = {Keijsers, J. G. S., de Groot, A. V., and Riksen, M. J. P. M.}, + title = {Modeling the biogeomorphic evolution of coastal dunes in response to climate change}, + journal = {Journal of Geophysical Research: Earth Surface}, + year = {2016}, + volume = {121}, + pages = {1161–1181}, + doi = {10.1002/2015JF003815}, +} + +@article{DuranHerrmann2006b, + author = {DurΓ‘n, O. and Herrmann, H. J.}, + title = {Vegetation against dune mobility}, + journal = {Physical Review Letters}, + year = {2006}, + volume = {97}, + number = {18}, + pages = {1–4}, + doi = {10.1103/PhysRevLett.97.188001}, +} + +@article{Strypsteen2024, + author = {Strypsteen, G. and Bonte, D. and Taelman, C. and Derijckere, J. and Rauwoens, P.}, + title = {Three years of morphological dune development after planting marram grass on a beach}, + journal = {Earth Surface Processes and Landforms}, + year = {2024}, + doi = {10.1002/esp.5870}, +} + +@article{Nolet2018, + author = {Nolet, C. and van Puijenbroek, M. and Suomalainen, J. and Limpens, J. and Riksen, M.}, + title = {UAV-imaging to model growth response of marram grass to sand burial: Implications for coastal dune development}, + journal = {Aeolian Research}, + year = {2018}, + volume = {31}, + pages = {50–61}, + note = {March 2017}, + doi = {10.1016/j.aeolia.2017.08.006}, +} + +@article{Maun1998, + author = {Maun, M. A.}, + title = {Adaptations of plants to burial in coastal sand dunes}, + journal = {Canadian Journal of Botany}, + year = {1998}, + volume = {76}, + number = {5}, + pages = {713–738}, + doi = {10.1139/cjb-76-5-713}, +} + +@article{Danin1991, + author = {Danin, A.}, + title = {Plant adaptations in desert dunes}, + journal = {Journal of Arid Environments}, + year = {1991}, + volume = {21}, + number = {2}, + pages = {193–212}, + doi = {10.1016/s0140-1963(18)30682-7}, +} + +@article{Hesp1991, + author = {Hesp, P. A.}, + title = {Ecological processes and plant adaptations on coastal dunes}, + journal = {Journal of Arid Environments}, + year = {1991}, + volume = {21}, + number = {2}, + pages = {165–191}, + doi = {10.1016/s0140-1963(18)30681-5}, +} + @article{Aagaard2014, author = {Aagaard, T.}, title = {Sediment supply to beaches: Cross-shore sand transport on the lower shoreface}, From b916d361cf3d132b7c3bf3b8651174a703d22b62 Mon Sep 17 00:00:00 2001 From: Christa van IJzendoorn <52737913+christavanijzendoorn@users.noreply.github.com> Date: Fri, 26 Jul 2024 10:16:13 -0700 Subject: [PATCH 056/124] Update model_setup.rst Improved layout of process flags --- docs/user/model_setup.rst | 28 ++++++++++++++-------------- 1 file changed, 14 insertions(+), 14 deletions(-) diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index d6c131e3..21e23101 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -241,32 +241,32 @@ configuration is listed below. Activate/deactivate processes ----------------------------- -After creating the input files that are necessary to run an AeoLiS model, the next step is often to decide which processes and methods to use. Several processes are defined in the configuration file that can be turned on and off. Apart from turning processes on and off, there are also several user-defined thresholds and methods that affect the way in which processes are calculated. For example, there are different sediment transport equations available within 'process_transport'. The default is Bagnold, but by defining 'method_transport' in the configuration file a different equation can be used. Here, we provide a description of the processes and methods that are defined in configuration file. More detailed descriptions of the processes and their implementation can be found in :ref:model_description +After creating the input files that are necessary to run an AeoLiS model, the next step is often to decide which processes and methods to use. Several processes are defined in the configuration file that can be turned on and off. Apart from turning processes on and off, there are also several user-defined thresholds and methods that affect the way in which processes are calculated. For example, there are different sediment transport equations available within *process_transport*. The default is Bagnold, but by defining *method_transport* in the configuration file a different equation can be used. Here, we provide a description of the processes and methods that are defined in configuration file. More detailed descriptions of the processes and their implementation can be found in :ref:model_description -An easy way to look up where these process, threshold and method flags are used is by going to the main page of the AeoLiS github and using the search bar at the top. For instance, searching 'process_tide' shows that it is used in :py:mod:`aeolis.threshold.compute`, :py:mod:`aeolis.vegetation.grow`, :py:mod:`aeolis.bed.update`. +An easy way to look up where these process, threshold and method flags are used is by going to the main page of the AeoLiS github and using the search bar at the top. For instance, searching *process_tide* shows that it is used in :py:mod:`aeolis.threshold.compute`, :py:mod:`aeolis.vegetation.grow`, :py:mod:`aeolis.bed.update`. process_wind ^^^^^^^^^^^^^ -'Process_wind' makes sure the wind file is loaded, and interpolates values of the wind speed and direction to each time step. The model does not work without this flag. Used in :py:mod:`aeolis.wind.interpolate` +*Process_wind* makes sure the wind file is loaded, and interpolates values of the wind speed and direction to each time step. The model does not work without this flag. Used in :py:mod:`aeolis.wind.interpolate` process_threshold ^^^^^^^^^^^^^^^^^ -'Process_threshold' allows for the alterations of the threshold velocity by processes like grain, moisture and vegetation. This process does not occur if a threshold file is provided as input since this file is used to define the threshold shear velocity. Used in :py:mod:`aeolis.threshold.compute`, documentation of threshold alterations can be found in :ref:model_description +*Process_threshold* allows for the alterations of the threshold velocity by processes like grain, moisture and vegetation. This process does not occur if a threshold file is provided as input since this file is used to define the threshold shear velocity. Used in :py:mod:`aeolis.threshold.compute`, documentation of threshold alterations can be found in :ref:model_description -th_grainsize: calculates the threshold velocity based on the grain size following Bagnold (:py:mod:`aeolis.threshold.compute_grain_size`) -th_bedslope: currently not implemented, but theoretically would include an alteration of the velocity threshold based on the slope of the bed. (:py:mod:`aeolis.threshold.compute_bedslope`) -th_moisture: alters the threshold velocity based on the moisture content, many different methods are available (:py:mod:`aeolis.threshold.compute_moisture`). Only works if moisture content is defined, which is calculated when process_moisture is on. -th_salt: alters the wind velocity threshold based on salt content following Nickling and Ecclestone (1981) (:py:mod:`aeolis.threshold.compute_salt`) -th_sheltering: modify the wind velocity threshold based on the presence of roughness elements in the grain size fractions following Raupach (1993) (:py:mod:`aeolis.threshold.compute_sheltering`) -th_humidity and th_drylayer: are currently not implemented +**th_grainsize**: calculates the threshold velocity based on the grain size following Bagnold (:py:mod:`aeolis.threshold.compute_grain_size`) +**th_bedslope**: currently not implemented, but theoretically would include an alteration of the velocity threshold based on the slope of the bed. (:py:mod:`aeolis.threshold.compute_bedslope`) +**th_moisture**: alters the threshold velocity based on the moisture content, many different methods are available (:py:mod:`aeolis.threshold.compute_moisture`). Only works if moisture content is defined, which is calculated when process_moisture is on. +**th_salt**: alters the wind velocity threshold based on salt content following Nickling and Ecclestone (1981) (:py:mod:`aeolis.threshold.compute_salt`) +**th_sheltering**: modify the wind velocity threshold based on the presence of roughness elements in the grain size fractions following Raupach (1993) (:py:mod:`aeolis.threshold.compute_sheltering`) +**th_humidity** and **th_drylayer**: are currently not implemented process_transport ^^^^^^^^^^^^^^^^^^ -'Process_transport' allows the calculation of the equilibrium transport rate based on a user-defined transport method. +*Process_transport* allows the calculation of the equilibrium transport rate based on a user-defined transport method. -'Method_transport' defines the sediment transport equation used in the calculation of the equilibrium transport rate. Options are: bagnold, bagnold_gs, kawamura, lettau, dk, sauermann, vanrijn_strypsteen. +**Method_transport** defines the sediment transport equation used in the calculation of the equilibrium transport rate. Options are: *bagnold, bagnold_gs, kawamura, lettau, dk, sauermann, vanrijn_strypsteen*. -'Method_grainspeed' defines at which speed the sediment transport in the air is occurring. Options are: 'duran'/'duran_full', 'windspeed', and 'constant' +**Method_grainspeed** defines at which speed the sediment transport in the air is occurring. Options are: *duran*/*duran_full*, *windspeed*, and *constant* Used in :py:mod:`aeolis.transport.equilibrium` @@ -284,7 +284,7 @@ Process_tide changes the threshold velocity to infinity (no aeolian transport) i process_wave ^^^^^^^^^^^^ -Process_wave allows calculation of the water depth based on the input tide file and interpolates the input wave data to the timesteps of the model run. If the wave file is not available, the wave height and peak period are set to 0. Turning this process flag on also results in the calculation of Hsmix, which is needed for the calculation of the Depth of Disturbance (process_mixtoplayer). The initialization/calculation is skipped if external variables are imported from another model. +Process_wave allows calculation of the water depth based on the input tide file and interpolates the input wave data to the timesteps of the model run. If the wave file is not available, the wave height and peak period are set to 0. Turning this process flag on also results in the calculation of Hsmix, which is needed for the calculation of the Depth of Disturbance (*process_mixtoplayer*). The initialization/calculation is skipped if external variables are imported from another model. process_runup ^^^^^^^^^^^^ From 8161b65a17c086d2976aeb6b495fb1ef2972b410 Mon Sep 17 00:00:00 2001 From: Christa van IJzendoorn <52737913+christavanijzendoorn@users.noreply.github.com> Date: Fri, 26 Jul 2024 10:17:37 -0700 Subject: [PATCH 057/124] Update model_setup.rst Improved layout --- docs/user/model_setup.rst | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index 21e23101..490d1c37 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -253,12 +253,12 @@ process_threshold ^^^^^^^^^^^^^^^^^ *Process_threshold* allows for the alterations of the threshold velocity by processes like grain, moisture and vegetation. This process does not occur if a threshold file is provided as input since this file is used to define the threshold shear velocity. Used in :py:mod:`aeolis.threshold.compute`, documentation of threshold alterations can be found in :ref:model_description -**th_grainsize**: calculates the threshold velocity based on the grain size following Bagnold (:py:mod:`aeolis.threshold.compute_grain_size`) -**th_bedslope**: currently not implemented, but theoretically would include an alteration of the velocity threshold based on the slope of the bed. (:py:mod:`aeolis.threshold.compute_bedslope`) -**th_moisture**: alters the threshold velocity based on the moisture content, many different methods are available (:py:mod:`aeolis.threshold.compute_moisture`). Only works if moisture content is defined, which is calculated when process_moisture is on. -**th_salt**: alters the wind velocity threshold based on salt content following Nickling and Ecclestone (1981) (:py:mod:`aeolis.threshold.compute_salt`) -**th_sheltering**: modify the wind velocity threshold based on the presence of roughness elements in the grain size fractions following Raupach (1993) (:py:mod:`aeolis.threshold.compute_sheltering`) -**th_humidity** and **th_drylayer**: are currently not implemented +- **th_grainsize**: calculates the threshold velocity based on the grain size following Bagnold (:py:mod:`aeolis.threshold.compute_grain_size`) +- **th_bedslope**: currently not implemented, but theoretically would include an alteration of the velocity threshold based on the slope of the bed. (:py:mod:`aeolis.threshold.compute_bedslope`) +- **th_moisture**: alters the threshold velocity based on the moisture content, many different methods are available (:py:mod:`aeolis.threshold.compute_moisture`). Only works if moisture content is defined, which is calculated when process_moisture is on. +- **th_salt**: alters the wind velocity threshold based on salt content following Nickling and Ecclestone (1981) (:py:mod:`aeolis.threshold.compute_salt`) +- **th_sheltering**: modify the wind velocity threshold based on the presence of roughness elements in the grain size fractions following Raupach (1993) (:py:mod:`aeolis.threshold.compute_sheltering`) +- **th_humidity** and **th_drylayer**: are currently not implemented process_transport ^^^^^^^^^^^^^^^^^^ From 76d19c4a673877649ea3a12150d9edf10ecda91c Mon Sep 17 00:00:00 2001 From: CarolineHalllin Date: Fri, 26 Jul 2024 19:20:50 +0200 Subject: [PATCH 058/124] updates to index and readme file --- README.md | 4 ++-- docs/index.rst | 22 ++++++++++++++++++++++ 2 files changed, 24 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index 8555a64b..5f3786fb 100644 --- a/README.md +++ b/README.md @@ -76,8 +76,8 @@ Read our [Contribution Guidelines](CONTRIBUTING.md) to know how you can help to - [Bart van Westen](mailto:Bart.vanWesten@deltares.nl) at Deltares - [Nick Cohn](mailto:nick.cohn@usace.army.mil) at U.S. Army Engineer Research and Development Center (ERDC) - [Sierd de Vries](mailto:Sierd.deVries@tudelft.nl) (founder) at Delft University of Technology -- [Christa van IJzendoorn](mailto:C.O.vanIJzendoorn@tudelft.nl) at Delft University of Technology -- [Caroline Hallin](mailto:E.C.Hallin@tudelft.nl) at Delft University of Technology +- [Christa van IJzendoorn](mailto:vanijzec@oregonstate.edu) at Oregon State University +- [Caroline Hallin](mailto:caroline.hallin@tvrl.lth.se) at Lund University - [Glenn Strypsteen](mailto:glenn.strypsteen@kuleuven.be) at Katholieke Universiteit Leuven **Previous Members & Contributors:** diff --git a/docs/index.rst b/docs/index.rst index d5101e1f..4c9f9d4a 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -17,6 +17,17 @@ Welcome to AeoLiS's Documentation This documentation describes the Python implementation of the AeoLiS model. The source code of the Python implementation can be found in `GitHub `_. +The code is developed and maintained by a developer group that conist of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the `developer documentation `_. + +.. _fig-developer-group: + +.. figure:: /images/aeolis_developer_group.jpeg + :alt: mass file format 1D + :width: 550px + :align: center + + AeoLiS developer group + Contents -------- @@ -50,6 +61,17 @@ Contents developer/domain-decomposition + +Contact +======= +- [Bart van Westen](mailto:Bart.vanWesten@deltares.nl) at Deltares +- [Nick Cohn](mailto:nick.cohn@usace.army.mil) at U.S. Army Engineer Research and Development Center (ERDC) +- [Sierd de Vries](mailto:Sierd.deVries@tudelft.nl) (founder) at Delft University of Technology +- [Christa van IJzendoorn](mailto:vanijzec@oregonstate.edu) at Oregon State University +- [Caroline Hallin](mailto:caroline.hallin@tvrl.lth.se) at Lund University +- [Glenn Strypsteen](mailto:glenn.strypsteen@kuleuven.be) at Katholieke Universiteit Leuven + + Acknowledgements ================ From 0096f4d96a35351bb5998a9b8203f7b12e91b00c Mon Sep 17 00:00:00 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zH(K&6qZbvOL`|+la5C)?{Ke5APkR65|Lgl?+_3Af-)*S^{2+FMZ)xYu!EM&*v z>_}`E`#^M=LP7K5c@djgK5zs~-f0vs{}Wa;6i9u6>>a%zO_T5uOFZf|gP=R=L$c35 zjln{a<2Tk#Q5Vd}AcENeuK51_j@DA7_ee z$plOe3m?H{Rp3gcro;YgX=o-`EjU39Q>US+ Date: Fri, 26 Jul 2024 10:25:35 -0700 Subject: [PATCH 060/124] Update model_description.rst Updated documentation vegetation and added the references --- docs/user/model_description.rst | 27 +++++++++++++-------------- 1 file changed, 13 insertions(+), 14 deletions(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index 59c2d659..4c20aa86 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -910,25 +910,24 @@ grain size dependency is implemented through :math:`u_{\mathrm{th}}`. :math:`u_{\mathrm{th}}` typically varies between 1 and 6 m/s for sand. -Vegetation (from Strypsteen et al., 2024. Vertical Growth Rate of Planted Vegetation Controls Dune Growth on a -Sandy Beach. Coastal Engineering. doi:10.2139/ssrn.4872614) +Vegetation (from :cite:`Strypsteen2024`) ------------------------------------- In AeoLiS, the influence of vegetation on dune evolution is comprehensively addressed. This includes modelling the intrinsic growth of vegetation, -accounting for factors such as growth and decay due to burial (DurΓ‘n and Moore, 2013), -lateral expansion and establishment (Keijsers et al., 2016), as well as simulating +accounting for factors such as growth and decay due to burial :cite:`DuranMoore2013`, +lateral expansion and establishment :cite:`Keijsers20106`, as well as simulating the destruction of vegetation caused by hydrodynamic processes. In the event of cell inundation, vegetation density is reduced as a result. Inspired by the -Coastal Dune Model (CDM) proposed by DurΓ‘n and Moore (2013), AeoLiS incorporates -vegetation-wind interaction using the expression established by DurΓ‘n and Herrmann (2006): +Coastal Dune Model (CDM) proposed by :cite:`DuranMoore2013`, AeoLiS incorporates +vegetation-wind interaction using the expression established by :cite:`DuranHerrmann2006`: :math:`\frac{u_{\text{veg}}}{u_*} = \frac{1}{\sqrt{1 + \Gamma \rho_{\text{veg}}}}` -where the ratio of shear velocity in the presence of vegetation (uβˆ—,veg) to the unobstructed +where the ratio of shear velocity in the presence of vegetation (:math:`u_{*,\text{veg}}`) to the unobstructed shear velocity (uβˆ—) is determined by a vegetation-related roughness parameter (Ξ“) and the vegetation density within a unit area of the grid cell (\rho_{\text{veg}}). In the model, Ξ“ = 16 is derived -from plant form drag and geometry values documented for creosote communities (DurΓ‘n and Herrmann, 2006). +from plant form drag and geometry values documented for creosote communities :cite:`DuranHerrmann2006`. This implementation calculates the expression on each model grid cell, with higher vegetation density (expressed by \rho_{\text{veg}}) leading to a more substantial reduction in shear velocity compared to sparse vegetation. By integrating these physical and ecological processes, AeoLiS simulates spatial patterns and temporal @@ -936,7 +935,7 @@ variations in sediment transport and morphological changes resulting from aeolia environments. \rho_{\text{veg}} can vary in space and time and is determined by the ratio of the actual vegetation height (hveg) -to the maximum vegetation height (hveg,max), and can vary between 0 and 1 (DurΓ‘n and Herrmann, 2006): +to the maximum vegetation height (hveg,max), and can vary between 0 and 1 (:cite:`DuranHerrmann2006`): :math:`\rho_{\text{veg}} = \left( \frac{h_{\text{veg}}}{h_{\text{veg,max}}} \right)^2` @@ -945,7 +944,7 @@ actual cover. The change in vegetation density per grid cell is directly linked height within that specific cell. This height variation is influenced by both the growth rate of the vegetation and the rate of sediment burial. If the vegetation density remains constant over time, it suggests either no sedimentation or a growth rate equal to the rate of sediment burial within the cell. Vegetation growth and decay -follow the model proposed by DurΓ‘n and Herrmann (2006), modified to include :math:`\delta z_{\text{b,opt}}` +follow the model proposed by :cite:`DuranHerrmann2006`, modified to include :math:`\delta z_{\text{b,opt}}` (m/year), representing sediment burial for optimal growth that shifts the peak of optimal growth: :math:`\frac{\delta h_{\text{veg}}}{\delta t} = V_{\text{ver}} \left(1 - \frac{h_{\text{veg}}}{h_{\text{veg,max}}}\right) - \gamma_{\text{veg}} \left| \frac{\delta z_{\text{b,veg}}}{\delta t} - \delta z_{\ @@ -961,11 +960,11 @@ day). This average is then extrapolated to an annual rate. This method ensures t change over one time step are not used as an estimate of the total bed level change in one year, which would be far too high. -The optimal growth rate for certain vegetation species in dune environments is depending upon sediment burial -(Maun, 1998). The optimal burial rate for maximum vegetation growth for marram grass for the neighbouring Dutch -coast is around 0.31 m/year with a burying tolerance of 0.78 to 0.96 m burial/year (Nolet et al., 2018). This +The optimal growth rate for certain vegetation species in dune environments is depending upon sediment burial :cite:`Maun1998`. +The optimal burial rate for maximum vegetation growth for marram grass for the neighbouring Dutch +coast is around 0.31 m/year with a burying tolerance of 0.78 to 0.96 m burial/year :cite:`Nolet2018`. This optimal value is used in the model. :math:`V_{\text{ver}}` contains information of meteorological and local -conditions that enhance or inhibit vegetation growth process (Danin, 1991; Hesp, 1991). +conditions that enhance or inhibit vegetation growth process :cite:`Danin1991`, :cite:`Hesp1991`. .. _fig-Veg_growth: From 0fea7fbc16d654e2792a9b4dd4871049db4dc2a6 Mon Sep 17 00:00:00 2001 From: Glenn Strypsteen <102021750+GlennStrypsteen@users.noreply.github.com> Date: Fri, 26 Jul 2024 10:26:11 -0700 Subject: [PATCH 061/124] Update aeolis.bib Added some more references related to vegetation documentation --- docs/aeolis.bib | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/docs/aeolis.bib b/docs/aeolis.bib index 1c31b36c..c24a0c28 100644 --- a/docs/aeolis.bib +++ b/docs/aeolis.bib @@ -25,6 +25,14 @@ @article{DuranMoore2013 doi = {10.1073/pnas.1307580110}, } +@article{Strypsteen2024, + author = {Strypsteen, G. and Bonte, D. and Taelman, C. and Derijckere, J. and Rauwoens, P.}, + title = {Vertical Growth Rate of Planted Vegetation Controls Dune Growth on a Sandy Beach}, + journal = {Coastal Engineering}, + year = {2024}, + doi = {10.2139/ssrn.4872614}, +} + @article{Keijsers2016, author = {Keijsers, J. G. S., de Groot, A. V., and Riksen, M. J. P. M.}, title = {Modeling the biogeomorphic evolution of coastal dunes in response to climate change}, From 76c9ef3b6c5719139e3a11ca07156d544a8873da Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 19:26:56 +0200 Subject: [PATCH 062/124] Update aeolis.bib --- docs/aeolis.bib | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/aeolis.bib b/docs/aeolis.bib index c24a0c28..78d83d3a 100644 --- a/docs/aeolis.bib +++ b/docs/aeolis.bib @@ -34,7 +34,7 @@ @article{Strypsteen2024 } @article{Keijsers2016, - author = {Keijsers, J. G. S., de Groot, A. V., and Riksen, M. J. P. M.}, + author = {Keijsers, J. G. S., de Groot, A. V. and Riksen, M. J. P. M.}, title = {Modeling the biogeomorphic evolution of coastal dunes in response to climate change}, journal = {Journal of Geophysical Research: Earth Surface}, year = {2016}, From 4b0b1ae652809e60529a2d1bad07288dce2c2ee8 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 19:32:10 +0200 Subject: [PATCH 063/124] Update index.rst --- docs/index.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/index.rst b/docs/index.rst index 4c9f9d4a..ddd15d57 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -22,7 +22,7 @@ The code is developed and maintained by a developer group that conist of members .. _fig-developer-group: .. figure:: /images/aeolis_developer_group.jpeg - :alt: mass file format 1D + :alt: Aeolis developer group8 :width: 550px :align: center From 8ebeb6cf86884b57e17e3b2f3d97e44d9cdd315e Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 19:36:09 +0200 Subject: [PATCH 064/124] Update aeolis.bib --- docs/aeolis.bib | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/aeolis.bib b/docs/aeolis.bib index 78d83d3a..5f11474a 100644 --- a/docs/aeolis.bib +++ b/docs/aeolis.bib @@ -34,7 +34,7 @@ @article{Strypsteen2024 } @article{Keijsers2016, - author = {Keijsers, J. G. S., de Groot, A. V. and Riksen, M. J. P. M.}, + author = {Keijsers, J. G. S. and de Groot, A. V. and Riksen, M. J. P. M.}, title = {Modeling the biogeomorphic evolution of coastal dunes in response to climate change}, journal = {Journal of Geophysical Research: Earth Surface}, year = {2016}, From 1f55275d0aa18bf1cac087792e2b936e528d97fb Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 19:41:14 +0200 Subject: [PATCH 065/124] Update index.rst --- docs/index.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/index.rst b/docs/index.rst index ddd15d57..eab47e1f 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -21,8 +21,8 @@ The code is developed and maintained by a developer group that conist of members .. _fig-developer-group: -.. figure:: /images/aeolis_developer_group.jpeg - :alt: Aeolis developer group8 +.. figure:: images/aeolis_developer_group.jpeg + :alt: Aeolis developer group :width: 550px :align: center From 6d5529dee37db6940f5c823ab8e69eb9dd03a846 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 19:42:44 +0200 Subject: [PATCH 066/124] Update index.rst --- docs/index.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/index.rst b/docs/index.rst index eab47e1f..eabd510d 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -21,7 +21,7 @@ The code is developed and maintained by a developer group that conist of members .. _fig-developer-group: -.. figure:: images/aeolis_developer_group.jpeg +.. figure:: images/aeolis_developer_group.jpg :alt: Aeolis developer group :width: 550px :align: center From f8e53c815e9a9194bff6924291dedab1f4443974 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 19:45:58 +0200 Subject: [PATCH 067/124] Update index.rst --- docs/index.rst | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/docs/index.rst b/docs/index.rst index eabd510d..c7570e39 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -14,10 +14,9 @@ Welcome to AeoLiS's Documentation ------- -This documentation describes the Python implementation of the AeoLiS -model. The source code of the Python implementation can be found in `GitHub `_. +This documentation describes the Python implementation of the AeoLiS. AeoLiS is an aeolian sediment transport and landform evolution model that is designed to account for sediment-supply-limiting factors in coastal environments. The source code of the Python implementation can be found in `GitHub `_. -The code is developed and maintained by a developer group that conist of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the `developer documentation `_. +The code is developed and maintained by a developer group that conists of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the `developer documentation `_. .. _fig-developer-group: From b566cbb1800acffb0e16e1e9db6620ed659c88c1 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 19:49:43 +0200 Subject: [PATCH 068/124] Update index.rst --- docs/index.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/index.rst b/docs/index.rst index c7570e39..0953c5ca 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -63,7 +63,7 @@ Contents Contact ======= -- [Bart van Westen](mailto:Bart.vanWesten@deltares.nl) at Deltares +- Bart van Westen (Bart.vanWesten@deltares.nl) at Deltares - [Nick Cohn](mailto:nick.cohn@usace.army.mil) at U.S. Army Engineer Research and Development Center (ERDC) - [Sierd de Vries](mailto:Sierd.deVries@tudelft.nl) (founder) at Delft University of Technology - [Christa van IJzendoorn](mailto:vanijzec@oregonstate.edu) at Oregon State University From 68256d2766295f9980fcb2b818c8e8522992ef23 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 19:50:49 +0200 Subject: [PATCH 069/124] Update index.rst --- docs/index.rst | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/docs/index.rst b/docs/index.rst index 0953c5ca..fafef413 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -64,11 +64,11 @@ Contents Contact ======= - Bart van Westen (Bart.vanWesten@deltares.nl) at Deltares -- [Nick Cohn](mailto:nick.cohn@usace.army.mil) at U.S. Army Engineer Research and Development Center (ERDC) -- [Sierd de Vries](mailto:Sierd.deVries@tudelft.nl) (founder) at Delft University of Technology -- [Christa van IJzendoorn](mailto:vanijzec@oregonstate.edu) at Oregon State University -- [Caroline Hallin](mailto:caroline.hallin@tvrl.lth.se) at Lund University -- [Glenn Strypsteen](mailto:glenn.strypsteen@kuleuven.be) at Katholieke Universiteit Leuven +- Nick Cohn (nick.cohn@usace.army.mil) at U.S. Army Engineer Research and Development Center (ERDC) +- Sierd de Vries (Sierd.deVries@tudelft.nl) (founder) at Delft University of Technology +- Christa van IJzendoorn (vanijzec@oregonstate.edu) at Oregon State University +- Caroline Hallin (caroline.hallin@tvrl.lth.se) at Lund University +- Glenn Strypsteen (glenn.strypsteen@kuleuven.be) at Katholieke Universiteit Leuven Acknowledgements @@ -76,7 +76,7 @@ Acknowledgements * AeoLiS was initially developed at Delft University of Technology with support from the ERC-Advanced Grant 291206 Nearshore Monitoring and Modeling (`NEMO `_) and `Deltares `_. * AeoLiS is currently maintained by `Bart van Westen `_ at Deltares, `Nick Cohn `_ at U.S. Army Engineer Research and Development Center (ERDC) and `Sierd de Vries `_ at Delft University of Technology. -* Further developement of AeoLiS is supported by the `Digital Competence Centre `_, Delft University of Technology. +* Further development of AeoLiS is supported by the `Digital Competence Centre `_, Delft University of Technology. Indices and tables From 44c8719c7c1fe6b1b2d99f93ab1bec30c88729d4 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 19:52:11 +0200 Subject: [PATCH 070/124] Update index.rst --- docs/index.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/index.rst b/docs/index.rst index fafef413..297fd3b6 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -16,7 +16,7 @@ Welcome to AeoLiS's Documentation This documentation describes the Python implementation of the AeoLiS. AeoLiS is an aeolian sediment transport and landform evolution model that is designed to account for sediment-supply-limiting factors in coastal environments. The source code of the Python implementation can be found in `GitHub `_. -The code is developed and maintained by a developer group that conists of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the `developer documentation `_. +The code is developed and maintained by a developer group that consists of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the `developer documentation `_. .. _fig-developer-group: From 0fa888c39cd9fbb403b59fd691224f98e887b7b9 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 19:56:40 +0200 Subject: [PATCH 071/124] Update model_description.rst --- docs/user/model_description.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index 4c20aa86..bd2ce5ad 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -1,4 +1,4 @@ -.. _model: +.. _model_description: Model description ================= From 2767cde330b09358464c42ba18ddb82389f9dac6 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 19:57:59 +0200 Subject: [PATCH 072/124] Update quickstart.rst --- docs/developer/quickstart.rst | 2 ++ 1 file changed, 2 insertions(+) diff --git a/docs/developer/quickstart.rst b/docs/developer/quickstart.rst index 5f6da394..71a9bf4c 100644 --- a/docs/developer/quickstart.rst +++ b/docs/developer/quickstart.rst @@ -1,3 +1,5 @@ +.. _quickstart: + Quick start ============= From b2dc815f3770478675795e7ac7d1b20376728fe7 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 19:59:51 +0200 Subject: [PATCH 073/124] Update index.rst --- docs/index.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/index.rst b/docs/index.rst index 297fd3b6..b526eb97 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -16,7 +16,7 @@ Welcome to AeoLiS's Documentation This documentation describes the Python implementation of the AeoLiS. AeoLiS is an aeolian sediment transport and landform evolution model that is designed to account for sediment-supply-limiting factors in coastal environments. The source code of the Python implementation can be found in `GitHub `_. -The code is developed and maintained by a developer group that consists of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the `developer documentation `_. +The code is developed and maintained by a developer group that consists of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the :ref:quickstart . `developer documentation `_. .. _fig-developer-group: From 683ba3a62ed5ee1fb99964f2e8c9e8acf5958e06 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 20:00:47 +0200 Subject: [PATCH 074/124] Update index.rst --- docs/index.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/index.rst b/docs/index.rst index b526eb97..82a807c9 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -16,7 +16,7 @@ Welcome to AeoLiS's Documentation This documentation describes the Python implementation of the AeoLiS. AeoLiS is an aeolian sediment transport and landform evolution model that is designed to account for sediment-supply-limiting factors in coastal environments. The source code of the Python implementation can be found in `GitHub `_. -The code is developed and maintained by a developer group that consists of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the :ref:quickstart . `developer documentation `_. +The code is developed and maintained by a developer group that consists of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the `developer documentation <:ref:quickstart>`_. .. _fig-developer-group: From 38eff708346f741a4ca5604ccc93d6e312a8fe04 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 20:05:07 +0200 Subject: [PATCH 075/124] Update index.rst --- docs/index.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/index.rst b/docs/index.rst index 82a807c9..d30431fe 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -16,7 +16,7 @@ Welcome to AeoLiS's Documentation This documentation describes the Python implementation of the AeoLiS. AeoLiS is an aeolian sediment transport and landform evolution model that is designed to account for sediment-supply-limiting factors in coastal environments. The source code of the Python implementation can be found in `GitHub `_. -The code is developed and maintained by a developer group that consists of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the `developer documentation <:ref:quickstart>`_. +The code is developed and maintained by a developer group that consists of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the `developer documentation `quickstart`_. .. _fig-developer-group: From f263aed4199ec79cdf32dae5bf23a80d638a8fd5 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 20:06:57 +0200 Subject: [PATCH 076/124] Update index.rst --- docs/index.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/index.rst b/docs/index.rst index d30431fe..4e68efc2 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -16,7 +16,7 @@ Welcome to AeoLiS's Documentation This documentation describes the Python implementation of the AeoLiS. AeoLiS is an aeolian sediment transport and landform evolution model that is designed to account for sediment-supply-limiting factors in coastal environments. The source code of the Python implementation can be found in `GitHub `_. -The code is developed and maintained by a developer group that consists of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the `developer documentation `quickstart`_. +The code is developed and maintained by a developer group that consists of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the :ref:`developer documentation `: .. _fig-developer-group: From 4cd3e3da0b60344533fbd30c3ad4e73da1757c00 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 20:10:08 +0200 Subject: [PATCH 077/124] Update index.rst --- docs/index.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/index.rst b/docs/index.rst index 4e68efc2..10ea9b78 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -16,7 +16,7 @@ Welcome to AeoLiS's Documentation This documentation describes the Python implementation of the AeoLiS. AeoLiS is an aeolian sediment transport and landform evolution model that is designed to account for sediment-supply-limiting factors in coastal environments. The source code of the Python implementation can be found in `GitHub `_. -The code is developed and maintained by a developer group that consists of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the :ref:`developer documentation `: +The code is developed and maintained by a developer group that consists of members from Deltares, U.S. Army Engineer Research and Development Center (ERDC), Delft University of Technology, Oregon State University, and Lund University. We encourage contributions from the community. If you are interested in contributing to the code, please read the :ref:`developer documentation `. .. _fig-developer-group: From f0189238f5708669140a9deb2c47ebd595136165 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 20:12:41 +0200 Subject: [PATCH 078/124] Update model_setup.rst --- docs/user/model_setup.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index 490d1c37..71f51e92 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -241,7 +241,7 @@ configuration is listed below. Activate/deactivate processes ----------------------------- -After creating the input files that are necessary to run an AeoLiS model, the next step is often to decide which processes and methods to use. Several processes are defined in the configuration file that can be turned on and off. Apart from turning processes on and off, there are also several user-defined thresholds and methods that affect the way in which processes are calculated. For example, there are different sediment transport equations available within *process_transport*. The default is Bagnold, but by defining *method_transport* in the configuration file a different equation can be used. Here, we provide a description of the processes and methods that are defined in configuration file. More detailed descriptions of the processes and their implementation can be found in :ref:model_description +After creating the input files that are necessary to run an AeoLiS model, the next step is often to decide which processes and methods to use. Several processes are defined in the configuration file that can be turned on and off. Apart from turning processes on and off, there are also several user-defined thresholds and methods that affect the way in which processes are calculated. For example, there are different sediment transport equations available within *process_transport*. The default is Bagnold, but by defining *method_transport* in the configuration file a different equation can be used. Here, we provide a description of the processes and methods that are defined in configuration file. More detailed descriptions of the processes and their implementation can be found in :ref:`the model description `. An easy way to look up where these process, threshold and method flags are used is by going to the main page of the AeoLiS github and using the search bar at the top. For instance, searching *process_tide* shows that it is used in :py:mod:`aeolis.threshold.compute`, :py:mod:`aeolis.vegetation.grow`, :py:mod:`aeolis.bed.update`. 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zOwK>TnS1Jh2#WofQr*P;5d$$lfw#r*yZF~eS1pz Date: Fri, 26 Jul 2024 20:18:43 +0200 Subject: [PATCH 080/124] Update introduction.rst --- docs/user/introduction.rst | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/docs/user/introduction.rst b/docs/user/introduction.rst index f2e01d3a..588f9e20 100644 --- a/docs/user/introduction.rst +++ b/docs/user/introduction.rst @@ -8,6 +8,15 @@ like in coastal environments. Supply-limitations currently supported are soil mo Model overview -------------- +.. _fig-model-overview: + +.. figure:: images/model_overview.png + :alt: Model overview + :width: 550px + :align: center + + Overview of the AeoLiS model - forcing conditions and processes. + Applicability and limitations ----------------------------- From 18b818e95c09614af9d7c82920f2199e11c5a7a4 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 20:20:17 +0200 Subject: [PATCH 081/124] Update introduction.rst --- docs/user/introduction.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user/introduction.rst b/docs/user/introduction.rst index 588f9e20..44aedac6 100644 --- a/docs/user/introduction.rst +++ b/docs/user/introduction.rst @@ -10,7 +10,7 @@ Model overview .. _fig-model-overview: -.. figure:: images/model_overview.png +.. figure:: ../images/model_overview.png :alt: Model overview :width: 550px :align: center From 190483a6665b595d484448338ca490a10a0ea729 Mon Sep 17 00:00:00 2001 From: Glenn Strypsteen <102021750+GlennStrypsteen@users.noreply.github.com> Date: Fri, 26 Jul 2024 12:24:10 -0700 Subject: [PATCH 082/124] Update model_description.rst Update vegetation --- docs/user/model_description.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index bd2ce5ad..41278b46 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -947,7 +947,7 @@ sedimentation or a growth rate equal to the rate of sediment burial within the c follow the model proposed by :cite:`DuranHerrmann2006`, modified to include :math:`\delta z_{\text{b,opt}}` (m/year), representing sediment burial for optimal growth that shifts the peak of optimal growth: -:math:`\frac{\delta h_{\text{veg}}}{\delta t} = V_{\text{ver}} \left(1 - \frac{h_{\text{veg}}}{h_{\text{veg,max}}}\right) - \gamma_{\text{veg}} \left| \frac{\delta z_{\text{b,veg}}}{\delta t} - \delta z_{\ +:math:`\frac{\delta h_{\text{veg}}}{\delta t} = V_{\text{ver}} \left(1 - \frac{h_{\text{veg}}}{h_{\text{veg,max}}}\right) - \gamma_{\text{veg}} \left| \frac{\delta z_{\text{b,veg}}}{\delta t} - \delta z_{\text{b,opt}} \right|` Here, :math:`\gamma_{\text{veg}}` (default = 1) is a sediment burial factor that accounts for the impact of sediment burial on vegetation. The height of the vegetation (:math:`h_{\text{veg}}` in m) cannot be less than zero. From a03766541650f4e64a6af42c186362403d82fdd1 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 23:07:36 +0200 Subject: [PATCH 083/124] Update index.rst --- docs/index.rst | 9 ++++++++- 1 file changed, 8 insertions(+), 1 deletion(-) diff --git a/docs/index.rst b/docs/index.rst index 10ea9b78..a64ea8fd 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -28,7 +28,7 @@ The code is developed and maintained by a developer group that consists of membe AeoLiS developer group Contents --------- +======== .. toctree:: :caption: User Documentation @@ -43,6 +43,13 @@ Contents user/sourcecode user/references +.. toctree:: + :caption: Tutorials and examples + :maxdepth: 3 + + tutorials/shortcourses + tutorials/demonstration_cases + .. toctree:: :caption: Developer Documentation :maxdepth: 3 From dc7624a7d31da0557078adfecd28464c9df7228b Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 23:08:50 +0200 Subject: [PATCH 084/124] Create demonstration_cases --- docs/tutorials/demonstration_cases | 1 + 1 file changed, 1 insertion(+) create mode 100644 docs/tutorials/demonstration_cases diff --git a/docs/tutorials/demonstration_cases b/docs/tutorials/demonstration_cases new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/docs/tutorials/demonstration_cases @@ -0,0 +1 @@ + From ca2ade38a780bb0f482c41d3c12df020e90f81fc Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 23:09:18 +0200 Subject: [PATCH 085/124] Create shortcourses.rst --- docs/tutorials/shortcourses.rst | 1 + 1 file changed, 1 insertion(+) create mode 100644 docs/tutorials/shortcourses.rst diff --git a/docs/tutorials/shortcourses.rst b/docs/tutorials/shortcourses.rst new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/docs/tutorials/shortcourses.rst @@ -0,0 +1 @@ + From 6fdb8bf507065ae66a703a156d5df57f4b34df1e Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 23:09:36 +0200 Subject: [PATCH 086/124] Delete docs/tutorials/demonstration_cases --- docs/tutorials/demonstration_cases | 1 - 1 file changed, 1 deletion(-) delete mode 100644 docs/tutorials/demonstration_cases diff --git a/docs/tutorials/demonstration_cases b/docs/tutorials/demonstration_cases deleted file mode 100644 index 8b137891..00000000 --- a/docs/tutorials/demonstration_cases +++ /dev/null @@ -1 +0,0 @@ - From 0364c89a597b54b1c4765774f8a5eca9ec649fad Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 23:10:30 +0200 Subject: [PATCH 087/124] Create demonstration_cases.rst --- docs/tutorials/demonstration_cases.rst | 1 + 1 file changed, 1 insertion(+) create mode 100644 docs/tutorials/demonstration_cases.rst diff --git a/docs/tutorials/demonstration_cases.rst b/docs/tutorials/demonstration_cases.rst new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/docs/tutorials/demonstration_cases.rst @@ -0,0 +1 @@ + From 6f72de6adb377ad0480eb0f8608890122378fdc9 Mon Sep 17 00:00:00 2001 From: Glenn Strypsteen <102021750+GlennStrypsteen@users.noreply.github.com> Date: Fri, 26 Jul 2024 14:11:10 -0700 Subject: [PATCH 088/124] Update model_description.rst --- docs/user/model_description.rst | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index 41278b46..8bed9536 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -922,7 +922,10 @@ cell inundation, vegetation density is reduced as a result. Inspired by the Coastal Dune Model (CDM) proposed by :cite:`DuranMoore2013`, AeoLiS incorporates vegetation-wind interaction using the expression established by :cite:`DuranHerrmann2006`: -:math:`\frac{u_{\text{veg}}}{u_*} = \frac{1}{\sqrt{1 + \Gamma \rho_{\text{veg}}}}` +.. math:: + :label: shear_reduction_vegetation + + \frac{u_{\text{veg}}}{u_*} = \frac{1}{\sqrt{1 + \Gamma \rho_{\text{veg}}}} where the ratio of shear velocity in the presence of vegetation (:math:`u_{*,\text{veg}}`) to the unobstructed shear velocity (uβˆ—) is determined by a vegetation-related roughness parameter (Ξ“) and the From 8f6a87d04afca750542f978ca3d9e39dac026fe4 Mon Sep 17 00:00:00 2001 From: Glenn Strypsteen <102021750+GlennStrypsteen@users.noreply.github.com> Date: Fri, 26 Jul 2024 14:15:00 -0700 Subject: [PATCH 089/124] Update model_description.rst --- docs/user/model_description.rst | 13 +++++++++++-- 1 file changed, 11 insertions(+), 2 deletions(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index 8bed9536..3750e33c 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -924,6 +924,7 @@ vegetation-wind interaction using the expression established by :cite:`DuranHerr .. math:: :label: shear_reduction_vegetation + :align: center \frac{u_{\text{veg}}}{u_*} = \frac{1}{\sqrt{1 + \Gamma \rho_{\text{veg}}}} @@ -940,7 +941,11 @@ environments. \rho_{\text{veg}} can vary in space and time and is determined by the ratio of the actual vegetation height (hveg) to the maximum vegetation height (hveg,max), and can vary between 0 and 1 (:cite:`DuranHerrmann2006`): -:math:`\rho_{\text{veg}} = \left( \frac{h_{\text{veg}}}{h_{\text{veg,max}}} \right)^2` +.. math:: + :label: changes_vegetation_height + :align: center + + \rho_{\text{veg}} = \left( \frac{h_{\text{veg}}}{h_{\text{veg,max}}} \right)^2 This assumption is based on the idea that burying vegetation reduces its height, which indicates a decrease in actual cover. The change in vegetation density per grid cell is directly linked to the alteration in vegetation @@ -950,7 +955,11 @@ sedimentation or a growth rate equal to the rate of sediment burial within the c follow the model proposed by :cite:`DuranHerrmann2006`, modified to include :math:`\delta z_{\text{b,opt}}` (m/year), representing sediment burial for optimal growth that shifts the peak of optimal growth: -:math:`\frac{\delta h_{\text{veg}}}{\delta t} = V_{\text{ver}} \left(1 - \frac{h_{\text{veg}}}{h_{\text{veg,max}}}\right) - \gamma_{\text{veg}} \left| \frac{\delta z_{\text{b,veg}}}{\delta t} - \delta z_{\text{b,opt}} \right|` +.. math:: + :label: changes_vegetation_height + :align: center + + \frac{\delta h_{\text{veg}}}{\delta t} = V_{\text{ver}} \left(1 - \frac{h_{\text{veg}}}{h_{\text{veg,max}}}\right) - \gamma_{\text{veg}} \left| \frac{\delta z_{\text{b,veg}}}{\delta t} - \delta z_{\text{b,opt}} \right| Here, :math:`\gamma_{\text{veg}}` (default = 1) is a sediment burial factor that accounts for the impact of sediment burial on vegetation. The height of the vegetation (:math:`h_{\text{veg}}` in m) cannot be less than zero. From 43e902c3acacc48f77d95be170fe0c4380736c59 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 23:17:52 +0200 Subject: [PATCH 090/124] Update index.rst --- docs/index.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/index.rst b/docs/index.rst index a64ea8fd..63b92129 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -71,7 +71,7 @@ Contents Contact ======= - Bart van Westen (Bart.vanWesten@deltares.nl) at Deltares -- Nick Cohn (nick.cohn@usace.army.mil) at U.S. Army Engineer Research and Development Center (ERDC) +- Nick Cohn (nicholas.t.cohn@usace.army.mil) at U.S. Army Engineer Research and Development Center (ERDC) - Sierd de Vries (Sierd.deVries@tudelft.nl) (founder) at Delft University of Technology - Christa van IJzendoorn (vanijzec@oregonstate.edu) at Oregon State University - Caroline Hallin (caroline.hallin@tvrl.lth.se) at Lund University @@ -82,7 +82,7 @@ Acknowledgements ================ * AeoLiS was initially developed at Delft University of Technology with support from the ERC-Advanced Grant 291206 Nearshore Monitoring and Modeling (`NEMO `_) and `Deltares `_. -* AeoLiS is currently maintained by `Bart van Westen `_ at Deltares, `Nick Cohn `_ at U.S. Army Engineer Research and Development Center (ERDC) and `Sierd de Vries `_ at Delft University of Technology. +* AeoLiS is currently maintained by `Bart van Westen `_ at Deltares, `Nick Cohn `_ at U.S. Army Engineer Research and Development Center (ERDC) and `Sierd de Vries `_ at Delft University of Technology. * Further development of AeoLiS is supported by the `Digital Competence Centre `_, Delft University of Technology. From e401ec37132ce229f6623a9461a44648bcf1f868 Mon Sep 17 00:00:00 2001 From: Glenn Strypsteen <102021750+GlennStrypsteen@users.noreply.github.com> Date: Fri, 26 Jul 2024 14:19:57 -0700 Subject: [PATCH 091/124] Update model_description.rst --- docs/user/model_description.rst | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index 3750e33c..9b1ef750 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -942,7 +942,7 @@ environments. to the maximum vegetation height (hveg,max), and can vary between 0 and 1 (:cite:`DuranHerrmann2006`): .. math:: - :label: changes_vegetation_height + :label: Vegetation_density :align: center \rho_{\text{veg}} = \left( \frac{h_{\text{veg}}}{h_{\text{veg,max}}} \right)^2 @@ -984,6 +984,8 @@ conditions that enhance or inhibit vegetation growth process :cite:`Danin1991`, :width: 600px :align: center + A) The vegetation growth response varies with different vertical growth rates (example for Vver = 1 and 2 m/year). Optimal vegetation growth is determined by a burial rate of 0.31 m/year, with a maximum vegetation height set at 1 m and a plant height of 0.5 m. Additionally, the growth response for varying burial factors is depicted (Ξ»veg = 1 and 2). B) Shear stress reduction for two different vegetation-related roughness parameters and vegetation densities (Ξ“ = 16 and 32).. + Vegetation can begin to grow through lateral propagation or random germination. Once established, it can continue to grow and spread laterally. The uncertainties associated with random germination are handled on a cell-by-cell basis using a probabilistic approach, similar to the cellular automata method described by Keijsers et al. (2016). From 7c668d02f6954e219cdf6b4989f8cbd4c390e1a5 Mon Sep 17 00:00:00 2001 From: Glenn Strypsteen <102021750+GlennStrypsteen@users.noreply.github.com> Date: Fri, 26 Jul 2024 14:24:37 -0700 Subject: [PATCH 092/124] Update model_description.rst --- docs/user/model_description.rst | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index 9b1ef750..30b648fb 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -929,8 +929,8 @@ vegetation-wind interaction using the expression established by :cite:`DuranHerr \frac{u_{\text{veg}}}{u_*} = \frac{1}{\sqrt{1 + \Gamma \rho_{\text{veg}}}} where the ratio of shear velocity in the presence of vegetation (:math:`u_{*,\text{veg}}`) to the unobstructed -shear velocity (uβˆ—) is determined by a vegetation-related roughness parameter (Ξ“) and the -vegetation density within a unit area of the grid cell (\rho_{\text{veg}}). In the model, Ξ“ = 16 is derived +shear velocity (:math:`u_*`) is determined by a vegetation-related roughness parameter (:math:`\Gamma`) and the +vegetation density within a unit area of the grid cell (\rho_{\text{veg}}). In the model, :math:`\Gamma` = 16 is derived from plant form drag and geometry values documented for creosote communities :cite:`DuranHerrmann2006`. This implementation calculates the expression on each model grid cell, with higher vegetation density (expressed by \rho_{\text{veg}}) leading to a more substantial reduction in shear velocity compared to sparse @@ -984,7 +984,9 @@ conditions that enhance or inhibit vegetation growth process :cite:`Danin1991`, :width: 600px :align: center - A) The vegetation growth response varies with different vertical growth rates (example for Vver = 1 and 2 m/year). Optimal vegetation growth is determined by a burial rate of 0.31 m/year, with a maximum vegetation height set at 1 m and a plant height of 0.5 m. Additionally, the growth response for varying burial factors is depicted (Ξ»veg = 1 and 2). B) Shear stress reduction for two different vegetation-related roughness parameters and vegetation densities (Ξ“ = 16 and 32).. + A) The vegetation growth response varies with different vertical growth rates (example for Vver = 1 and 2 m/year). Optimal vegetation growth is determined by a burial rate of 0.31 + m/year, with a maximum vegetation height set at 1 m and a plant height of 0.5 m. Additionally, the growth response for varying burial factors is depicted (:math:`\lambda_{\text{veg}}` + = 1 and 2). B) Shear stress reduction for two different vegetation-related roughness parameters and vegetation densities (:math:`\Gamma` = 16 and 32). Vegetation can begin to grow through lateral propagation or random germination. Once established, it can continue to grow and spread laterally. The uncertainties associated with random germination are handled on a cell-by-cell From d6f15e3828f03ed0411e0e121a440ab213b04a7e Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 23:42:34 +0200 Subject: [PATCH 093/124] Update index.rst --- docs/index.rst | 2 ++ 1 file changed, 2 insertions(+) diff --git a/docs/index.rst b/docs/index.rst index 63b92129..cddc568e 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -70,6 +70,8 @@ Contents Contact ======= +If you have questions about the model that is of interest for the community, please post your question in the `discussion forum `_. + - Bart van Westen (Bart.vanWesten@deltares.nl) at Deltares - Nick Cohn (nicholas.t.cohn@usace.army.mil) at U.S. Army Engineer Research and Development Center (ERDC) - Sierd de Vries (Sierd.deVries@tudelft.nl) (founder) at Delft University of Technology From 91f07e5e518399130171933b9135bfbabf8c4cf1 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 23:43:45 +0200 Subject: [PATCH 094/124] Update README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 5f3786fb..63620680 100644 --- a/README.md +++ b/README.md @@ -74,7 +74,7 @@ Read our [Contribution Guidelines](CONTRIBUTING.md) to know how you can help to **Current Members:** - [Bart van Westen](mailto:Bart.vanWesten@deltares.nl) at Deltares -- [Nick Cohn](mailto:nick.cohn@usace.army.mil) at U.S. Army Engineer Research and Development Center (ERDC) +- [Nick Cohn](mailto:nicholas.t.cohn@usace.army.mil) at U.S. Army Engineer Research and Development Center (ERDC) - [Sierd de Vries](mailto:Sierd.deVries@tudelft.nl) (founder) at Delft University of Technology - [Christa van IJzendoorn](mailto:vanijzec@oregonstate.edu) at Oregon State University - [Caroline Hallin](mailto:caroline.hallin@tvrl.lth.se) at Lund University From a44227bfe06cb48f32f99acb676e4f44256ba427 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Fri, 26 Jul 2024 23:56:23 +0200 Subject: [PATCH 095/124] Update model_description.rst --- docs/user/model_description.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index 30b648fb..c7c02ab0 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -1266,7 +1266,7 @@ Substitution of :math:`u` (Equation :eq:`gw-discharge`) in the continuity equati \frac{{\partial \eta }}{{\partial t}} = \frac{K}{{{n_e}}}\frac{\partial }{{\partial x}}\left( {(D + \eta )\frac{{\partial \eta }}{{\partial x}}} \right) + \frac{{{U_l}}}{{{n_e}}} Numerical solution of the Boussinesq groundwater equation ---------------------------------------------------------- +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The Boussinesq equation is solved numerically with a central finite difference method in space and a fourth-order Runge-Kutta integration technique in time: From 29479c11acd78e6892d8cb8627b940bcfc4606c2 Mon Sep 17 00:00:00 2001 From: Glenn Strypsteen <102021750+GlennStrypsteen@users.noreply.github.com> Date: Fri, 26 Jul 2024 14:58:26 -0700 Subject: [PATCH 096/124] Update model_description.rst From 3eac3400d9884f1a439926a9c3c0ac78eed935b4 Mon Sep 17 00:00:00 2001 From: Glenn Strypsteen <102021750+GlennStrypsteen@users.noreply.github.com> Date: Fri, 26 Jul 2024 15:02:37 -0700 Subject: [PATCH 097/124] Update model_description.rst --- docs/user/model_description.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index c7c02ab0..c527a9fa 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -939,7 +939,7 @@ variations in sediment transport and morphological changes resulting from aeolia environments. \rho_{\text{veg}} can vary in space and time and is determined by the ratio of the actual vegetation height (hveg) -to the maximum vegetation height (hveg,max), and can vary between 0 and 1 (:cite:`DuranHerrmann2006`): +to the maximum vegetation height (:math:`h_{\text{veg,max}}`), and can vary between 0 and 1 (:cite:`DuranHerrmann2006`): .. math:: :label: Vegetation_density From a2cdc9e63d14705601146f670b79ce13eabb9467 Mon Sep 17 00:00:00 2001 From: Glenn Strypsteen <102021750+GlennStrypsteen@users.noreply.github.com> Date: Fri, 26 Jul 2024 15:14:01 -0700 Subject: [PATCH 098/124] Update introduction.rst --- docs/user/introduction.rst | 2 ++ 1 file changed, 2 insertions(+) diff --git a/docs/user/introduction.rst b/docs/user/introduction.rst index 44aedac6..df616188 100644 --- a/docs/user/introduction.rst +++ b/docs/user/introduction.rst @@ -25,6 +25,8 @@ AeoLiS publications 2024 ^^^^ +Strypsteen, G., de Vries, S., Bonte, D., Homberger, J.M., Hallin, C., Rauwoens, P. (2024). Planted vegetation on a sandy beach regulates maximum size of corresponding dune evolution. Coastal Engineering (preprint under review). Doi: http://dx.doi.org/10.2139/ssrn.4872614 + Heminway, S.S., Cohn, N., Davis, E.H., White, A., Hein, C.J., Zinnert, J.C., 2024. Exploring Ecological, Morphological, and Environmental Controls on Coastal Foredune Evolution at Annual Scales Using a Process-Based Model. Sustainability, 16, 3460. https://doi.org/10.3390/su16083460 Orie, C., Cohn, N., Farthing, M., Dutta, S., Trautz, A., 2024. Examination of Analytical Shear Stress Predictions for Coastal Dune Evolution. EGUsphere, https://doi.org/10.5194/egusphere-2024-855. Preprint under review for ESurf From 2e9705e44cd7d89976fceb1615c55d4a093e6923 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Sat, 27 Jul 2024 01:07:38 +0200 Subject: [PATCH 099/124] Update demonstration_cases.rst --- docs/tutorials/demonstration_cases.rst | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/docs/tutorials/demonstration_cases.rst b/docs/tutorials/demonstration_cases.rst index 8b137891..95021b45 100644 --- a/docs/tutorials/demonstration_cases.rst +++ b/docs/tutorials/demonstration_cases.rst @@ -1 +1,2 @@ - +Demonstration cases +=================== From 317a18ea7d9a300e1254069937bcda77323c20d9 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Sat, 27 Jul 2024 01:07:59 +0200 Subject: [PATCH 100/124] Update shortcourses.rst --- docs/tutorials/shortcourses.rst | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/docs/tutorials/shortcourses.rst b/docs/tutorials/shortcourses.rst index 8b137891..cd4e49bc 100644 --- a/docs/tutorials/shortcourses.rst +++ b/docs/tutorials/shortcourses.rst @@ -1 +1,2 @@ - +Shortcourses +============ From 53a449b7ac855cb68c83b2df9546c41f090658e1 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Sat, 27 Jul 2024 01:31:15 +0200 Subject: [PATCH 101/124] Update demonstration_cases.rst --- docs/tutorials/demonstration_cases.rst | 27 ++++++++++++++++++++++++++ 1 file changed, 27 insertions(+) diff --git a/docs/tutorials/demonstration_cases.rst b/docs/tutorials/demonstration_cases.rst index 95021b45..7d412146 100644 --- a/docs/tutorials/demonstration_cases.rst +++ b/docs/tutorials/demonstration_cases.rst @@ -1,2 +1,29 @@ Demonstration cases =================== +In the `example folder ... you find a collection of input files needed to run example models. + + +1. Install aeolis + +pip install aeolis + +2. Install the examples + +To install the examples do the following: + +.. code-block:: bash + + aeolis examples . + +This will install the examples in the current directory. If you want to install them in a different directory, replace the "." with the path to the directory you want to install the examples in. + +3. Run the simulation + +Run the simulation with: + +.. code-block:: bash + + aeolis run aeolis_examples/parabolic_dune_model/aeolis.txt + + +4. View/plot the results From fff74b3406f2a63efd0a991fe0547aafc8514cc0 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Sat, 27 Jul 2024 01:40:07 +0200 Subject: [PATCH 102/124] Update demonstration_cases.rst --- docs/tutorials/demonstration_cases.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/tutorials/demonstration_cases.rst b/docs/tutorials/demonstration_cases.rst index 7d412146..e9b73d73 100644 --- a/docs/tutorials/demonstration_cases.rst +++ b/docs/tutorials/demonstration_cases.rst @@ -1,6 +1,6 @@ Demonstration cases =================== -In the `example folder ... you find a collection of input files needed to run example models. +In the `example folder .examples.. you find a collection of input files needed to run example models. 1. Install aeolis From a5b4deed493ca2188460b58fb7b87849306a5317 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Sat, 27 Jul 2024 05:40:27 +0200 Subject: [PATCH 103/124] Delete docs/user/tutorials_and_examples.rst --- docs/user/tutorials_and_examples.rst | 1 - 1 file changed, 1 deletion(-) delete mode 100644 docs/user/tutorials_and_examples.rst diff --git a/docs/user/tutorials_and_examples.rst b/docs/user/tutorials_and_examples.rst deleted file mode 100644 index 8b137891..00000000 --- a/docs/user/tutorials_and_examples.rst +++ /dev/null @@ -1 +0,0 @@ - From 1accf00ea7fcd2dfbe35020d71c9ff15a1d96f0b Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Sat, 27 Jul 2024 05:41:57 +0200 Subject: [PATCH 104/124] Update index.rst --- docs/index.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/index.rst b/docs/index.rst index cddc568e..344d814e 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -70,7 +70,7 @@ Contents Contact ======= -If you have questions about the model that is of interest for the community, please post your question in the `discussion forum `_. +If you have questions about the model that is of interest to the community, please post your question in the `discussion forum `_. - Bart van Westen (Bart.vanWesten@deltares.nl) at Deltares - Nick Cohn (nicholas.t.cohn@usace.army.mil) at U.S. Army Engineer Research and Development Center (ERDC) From 52788f1e107bfa900d37b056ed086765a30663f4 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Sat, 27 Jul 2024 05:54:44 +0200 Subject: [PATCH 105/124] Update demonstration_cases.rst --- docs/tutorials/demonstration_cases.rst | 13 ++++++++++--- 1 file changed, 10 insertions(+), 3 deletions(-) diff --git a/docs/tutorials/demonstration_cases.rst b/docs/tutorials/demonstration_cases.rst index e9b73d73..596e1507 100644 --- a/docs/tutorials/demonstration_cases.rst +++ b/docs/tutorials/demonstration_cases.rst @@ -1,10 +1,13 @@ Demonstration cases =================== -In the `example folder .examples.. you find a collection of input files needed to run example models. +The `example folder `_ contains a collection of input files needed to run example models. The different examples are explained in the `readme-file `. They are intended to serve as an example of the model's capabilities and instruction on how to set up and organize models. The model input files can be modified using the pre-processing [ADD LINK] tools, and the model output can be visualized with the post-processing tools [ADD LINK]. +To run the examples: 1. Install aeolis +.. code-block:: bash + pip install aeolis 2. Install the examples @@ -19,11 +22,15 @@ This will install the examples in the current directory. If you want to install 3. Run the simulation -Run the simulation with: +Run the simulation with (example parabolic dune model): .. code-block:: bash aeolis run aeolis_examples/parabolic_dune_model/aeolis.txt -4. View/plot the results +4. View/plot the results (example parabolic dune model): + +.. code-block:: bash + + [ADD DESCRIPTION OF HOW TO PLOT NETCDF] From b5e154942210cfa891095424f643b4c06a036b33 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Sat, 27 Jul 2024 06:06:32 +0200 Subject: [PATCH 106/124] Update shortcourses.rst --- docs/tutorials/shortcourses.rst | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/docs/tutorials/shortcourses.rst b/docs/tutorials/shortcourses.rst index cd4e49bc..055a7e48 100644 --- a/docs/tutorials/shortcourses.rst +++ b/docs/tutorials/shortcourses.rst @@ -1,2 +1,7 @@ -Shortcourses +Short courses ============ +A couple of short courses are available to help new users get acquainted with the model: + +https://github.com/openearth/aeolis-shortcourse + +https://github.com/erdc/aeolis-python/tree/master/tutorial From 25cb6d802e26abdd6002ed14b000625bf797be20 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Sat, 27 Jul 2024 06:08:49 +0200 Subject: [PATCH 107/124] Delete docs/tutorials/2D-parabolic.rst --- docs/tutorials/2D-parabolic.rst | 34 --------------------------------- 1 file changed, 34 deletions(-) delete mode 100644 docs/tutorials/2D-parabolic.rst diff --git a/docs/tutorials/2D-parabolic.rst b/docs/tutorials/2D-parabolic.rst deleted file mode 100644 index 055223de..00000000 --- a/docs/tutorials/2D-parabolic.rst +++ /dev/null @@ -1,34 +0,0 @@ -Parabolic dune model (Tutorial under construction) -=================================================== - - -1. Install aeolis - -pip install aeolis - -2. Install the examples - -To install the examples do the following: - -.. code-block:: bash - - aeolis examples . - -This will install the examples in the current directory. If you want to install them in a different directory, replace the "." with the path to the directory you want to install the examples in. - -3. Run the simulation - -Run the simulation with: - -.. code-block:: bash - - aeolis run aeolis_examples/parabolic_dune_model/aeolis.txt - - -4. View/plot the results - - - - - - From 5adc1cc785a87f40066e84bdf24f0b0a0d92728f Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Sat, 27 Jul 2024 06:09:18 +0200 Subject: [PATCH 108/124] Delete docs/tutorials/sandmotor.rst --- docs/tutorials/sandmotor.rst | 33 --------------------------------- 1 file changed, 33 deletions(-) delete mode 100644 docs/tutorials/sandmotor.rst diff --git a/docs/tutorials/sandmotor.rst b/docs/tutorials/sandmotor.rst deleted file mode 100644 index d66669f0..00000000 --- a/docs/tutorials/sandmotor.rst +++ /dev/null @@ -1,33 +0,0 @@ -SandMotor model (Tutorial under construction) -============================================== - - -1. Install aeolis - -pip install aeolis - -2. Install the sandengine_small_grids example - -To install the example do the following: - -.. code-block:: bash - - aeolis examples . - -This command will create a directory called "aeolis_examples" in the current directory. The model configuration file for the sandengine_small_grids example is placed in the "sandengine_small_grids" subdirectory of "aeolis_examples". - -This will install the examples in the current directory. If you want to install them in a different directory, replace the "." with the path to the directory you want to install the examples in. - -3. Run the simulation - -Run the simulation with: - -.. code-block:: bash - - aeolis run aeolis_examples/sandengine_small_grids/aeolis.txt - - -4. View/plot the results - - - From 7da86e825539eb56c10076a431a99173bb448f3e Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Sat, 27 Jul 2024 06:28:34 +0200 Subject: [PATCH 109/124] Update demonstration_cases.rst --- docs/tutorials/demonstration_cases.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/tutorials/demonstration_cases.rst b/docs/tutorials/demonstration_cases.rst index 596e1507..37ee8ae6 100644 --- a/docs/tutorials/demonstration_cases.rst +++ b/docs/tutorials/demonstration_cases.rst @@ -1,6 +1,6 @@ Demonstration cases =================== -The `example folder `_ contains a collection of input files needed to run example models. The different examples are explained in the `readme-file `. They are intended to serve as an example of the model's capabilities and instruction on how to set up and organize models. The model input files can be modified using the pre-processing [ADD LINK] tools, and the model output can be visualized with the post-processing tools [ADD LINK]. +The `example folder `_ contains a collection of input files needed to run example models. The different examples are explained in the `readme-file `. They are intended to serve as an example of the model's capabilities and instruction on how to set up and organize models. The model input files can be modified using the `pre-processing tools `, and the model output can be visualized with the `post-processing tools https://github.com/openearth/aeolis-python/tree/main/tools/postprocessing>`. To run the examples: From 4bbb509a1c3acddb6916fa091d92e92e38f6aa67 Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Sat, 27 Jul 2024 06:51:16 +0200 Subject: [PATCH 110/124] Update aeolis.bib --- docs/aeolis.bib | 10 ---------- 1 file changed, 10 deletions(-) diff --git a/docs/aeolis.bib b/docs/aeolis.bib index 5f11474a..c25f01a5 100644 --- a/docs/aeolis.bib +++ b/docs/aeolis.bib @@ -33,16 +33,6 @@ @article{Strypsteen2024 doi = {10.2139/ssrn.4872614}, } -@article{Keijsers2016, - author = {Keijsers, J. G. S. and de Groot, A. V. and Riksen, M. J. P. M.}, - title = {Modeling the biogeomorphic evolution of coastal dunes in response to climate change}, - journal = {Journal of Geophysical Research: Earth Surface}, - year = {2016}, - volume = {121}, - pages = {1161–1181}, - doi = {10.1002/2015JF003815}, -} - @article{DuranHerrmann2006b, author = {DurΓ‘n, O. and Herrmann, H. J.}, title = {Vegetation against dune mobility}, From 548103e33e86d55275dbaa2e3607754e0fde0a5e Mon Sep 17 00:00:00 2001 From: CarolineHalllin <64251347+CarolineHalllin@users.noreply.github.com> Date: Sat, 27 Jul 2024 06:54:04 +0200 Subject: [PATCH 111/124] Update aeolis.bib --- docs/aeolis.bib | 10 ++++++++++ 1 file changed, 10 insertions(+) diff --git a/docs/aeolis.bib b/docs/aeolis.bib index c25f01a5..6bd3f58e 100644 --- a/docs/aeolis.bib +++ b/docs/aeolis.bib @@ -14,6 +14,16 @@ @MANUAL{Simunek1998 timestamp = {2014.03.07} } +@article{Keijsers2016, + author = {Keijsers, J. G. S. and de Groot, A. V. and Riksen, M. J. P. M.}, + title = {Modeling the biogeomorphic evolution of coastal dunes in response to climate change}, + journal = {Journal of Geophysical Research: Earth Surface}, + year = {2016}, + volume = {121}, + pages = {1161–1181}, + doi = {10.1002/2015JF003815}, +} + @article{DuranMoore2013, author = {DurΓ‘n, O. and Moore, L. J.}, title = {Vegetation controls on the maximum size of coastal dunes}, From adc638c85360aae7650be8297d05f77f9197c102 Mon Sep 17 00:00:00 2001 From: Sierd Date: Fri, 16 Aug 2024 12:06:36 +0200 Subject: [PATCH 112/124] Update aeolis.bib Strypsteen 2024 was defined twice. This made the references crash. I included an alternative label. The references work again! --- docs/aeolis.bib | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/aeolis.bib b/docs/aeolis.bib index 6bd3f58e..c909b068 100644 --- a/docs/aeolis.bib +++ b/docs/aeolis.bib @@ -54,7 +54,7 @@ @article{DuranHerrmann2006b doi = {10.1103/PhysRevLett.97.188001}, } -@article{Strypsteen2024, +@article{Strypsteen2024b, author = {Strypsteen, G. and Bonte, D. and Taelman, C. and Derijckere, J. and Rauwoens, P.}, title = {Three years of morphological dune development after planting marram grass on a beach}, journal = {Earth Surface Processes and Landforms}, From 096ed2e7d3a0ab6c087035e800437b335174e305 Mon Sep 17 00:00:00 2001 From: Sierd Date: Fri, 16 Aug 2024 12:35:43 +0200 Subject: [PATCH 113/124] dead link removed --- docs/index.rst | 1 - 1 file changed, 1 deletion(-) diff --git a/docs/index.rst b/docs/index.rst index 344d814e..64cf71d6 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -39,7 +39,6 @@ Contents user/model_description user/model_setup user/model_interaction - user/tutorials_and_examples user/sourcecode user/references From e4acc3a67e3beb2982a9ec8343dbb7de5a60356a Mon Sep 17 00:00:00 2001 From: Christa van IJzendoorn <52737913+christavanijzendoorn@users.noreply.github.com> Date: Fri, 16 Aug 2024 11:06:00 -0700 Subject: [PATCH 114/124] Solve minor layout issues --- docs/aeolis.bib | 2 +- docs/developer/modularity.rst | 14 ++++++-------- docs/tutorials/shortcourses.rst | 2 +- docs/user/model_description.rst | 26 ++++++++++++++++++-------- 4 files changed, 26 insertions(+), 18 deletions(-) diff --git a/docs/aeolis.bib b/docs/aeolis.bib index c909b068..db41a642 100644 --- a/docs/aeolis.bib +++ b/docs/aeolis.bib @@ -43,7 +43,7 @@ @article{Strypsteen2024 doi = {10.2139/ssrn.4872614}, } -@article{DuranHerrmann2006b, +@article{DuranHerrmann2006, author = {DurΓ‘n, O. and Herrmann, H. J.}, title = {Vegetation against dune mobility}, journal = {Physical Review Letters}, diff --git a/docs/developer/modularity.rst b/docs/developer/modularity.rst index 564d2444..aa563431 100644 --- a/docs/developer/modularity.rst +++ b/docs/developer/modularity.rst @@ -1,7 +1,7 @@ Modularity ================ -Our ambiton is to make the current version of AeoLiS more modular. Specially, we want the architecture of the software to consist of well defined components (modules) that integrate with each other though well defined interfaces. This will allow us to add new features more easily and to make the software more robust easier to exent. +Our ambition is to make the current version of AeoLiS more modular. Specially, we want the architecture of the software to consist of well-defined components (modules) that integrate with each other through well-defined interfaces. This will allow us to add new features more easily and to make the software more robust and easier to extend. For example, the current version of AeoLiS is organized in a single class, the `AeoLiSRunner`. This class is responsible for the execution of the model. It is also responsible for the reading of the input files, executing the solvers, and writing of the output files. This makes the code difficult to understand, extend and test, see :numref:`fig-uml-model`. @@ -16,15 +16,14 @@ For example, the current version of AeoLiS is organized in a single class, the ` .. _GitHub repository: https://github.com/openearth/aeolis-python/issues -Suggetions for improvement +Suggestions for improvement --------------------------- We have some ideas about how to improve the modularity of the code. However, we are still working on the details of this architecture. If you have any suggestions, please let us know by opening an issue in our `GitHub repository`_ or by proposing improvements to the code via pull requests. -- **Reduce the amount to repeated code by using abstractions.** For example, some of the solvers implement similar alogorithms. We could implement an abstract class that implements the common parts of the algorithms and then extend this class to implement the specific algorithms of each solver. -- **Reduce the number of tasks the `AeoLiSRunner` and AeoLiS classes are responsible for.** This could be achieved by moving some of the code inside those clases to independent fuctions or modules. This will make the code easier to understand and test. -- **Organize code based on componets**.For example, :numref:`fig-step-flowchart` shows a flowchart of a modeling *step* in the AeoLiSRunner. We could use each colored-box in the flowchart to refactor the source code in separated components, each one with a well defined interface that connects to the other components. - +- **Reduce the amount of repeated code by using abstractions.** For example, some of the solvers implement similar algorithms. We could implement an abstract class that implements the common parts of the algorithms and then extend this class to implement the specific algorithms of each solver. +- **Reduce the number of tasks the `AeoLiSRunner` and AeoLiS classes are responsible for.** This could be achieved by moving some of the code inside those classes to independent functions or modules. This will make the code easier to understand and test. +- **Organize code based on components**. For example, :numref:`fig-step-flowchart` shows a flowchart of a modeling *step* in the AeoLiSRunner. We could use each colored-box in the flowchart to refactor the source code into separate components, each one with a well-defined interface that connects to the other components. .. _fig-step-flowchart: @@ -33,8 +32,7 @@ We have some ideas about how to improve the modularity of the code. However, we .. seealso:: - Read about `How to write modular code` for more suggestions on how to make a software more modular. + Read about `How to write modular code` for more suggestions on how to make software more modular. .. _How to write modular code: https://dev.to/prxtikk/how-to-write-clean-and-modular-code-1d87 - diff --git a/docs/tutorials/shortcourses.rst b/docs/tutorials/shortcourses.rst index 055a7e48..ea18905f 100644 --- a/docs/tutorials/shortcourses.rst +++ b/docs/tutorials/shortcourses.rst @@ -1,5 +1,5 @@ Short courses -============ +=============== A couple of short courses are available to help new users get acquainted with the model: https://github.com/openearth/aeolis-shortcourse diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index c527a9fa..d56dd428 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -910,13 +910,15 @@ grain size dependency is implemented through :math:`u_{\mathrm{th}}`. :math:`u_{\mathrm{th}}` typically varies between 1 and 6 m/s for sand. -Vegetation (from :cite:`Strypsteen2024`) -------------------------------------- +Vegetation +------------ + +The text below is based on :cite:`Strypsteen2024` In AeoLiS, the influence of vegetation on dune evolution is comprehensively addressed. This includes modelling the intrinsic growth of vegetation, accounting for factors such as growth and decay due to burial :cite:`DuranMoore2013`, -lateral expansion and establishment :cite:`Keijsers20106`, as well as simulating +lateral expansion and establishment :cite:`Keijsers2016`, as well as simulating the destruction of vegetation caused by hydrodynamic processes. In the event of cell inundation, vegetation density is reduced as a result. Inspired by the Coastal Dune Model (CDM) proposed by :cite:`DuranMoore2013`, AeoLiS incorporates @@ -924,7 +926,11 @@ vegetation-wind interaction using the expression established by :cite:`DuranHerr .. math:: :label: shear_reduction_vegetation - :align: center + :nowrap: + + \begin{center} + \frac{u_{\text{veg}}}{u_*} = \frac{1}{\sqrt{1 + \Gamma \rho_{\text{veg}}}} + \end{center} \frac{u_{\text{veg}}}{u_*} = \frac{1}{\sqrt{1 + \Gamma \rho_{\text{veg}}}} @@ -943,9 +949,11 @@ to the maximum vegetation height (:math:`h_{\text{veg,max}}`), and can vary betw .. math:: :label: Vegetation_density - :align: center + :nowrap: + \begin{center} \rho_{\text{veg}} = \left( \frac{h_{\text{veg}}}{h_{\text{veg,max}}} \right)^2 + \end{center} This assumption is based on the idea that burying vegetation reduces its height, which indicates a decrease in actual cover. The change in vegetation density per grid cell is directly linked to the alteration in vegetation @@ -957,9 +965,11 @@ follow the model proposed by :cite:`DuranHerrmann2006`, modified to include :mat .. math:: :label: changes_vegetation_height - :align: center + :nowrap: + \begin{center} \frac{\delta h_{\text{veg}}}{\delta t} = V_{\text{ver}} \left(1 - \frac{h_{\text{veg}}}{h_{\text{veg,max}}}\right) - \gamma_{\text{veg}} \left| \frac{\delta z_{\text{b,veg}}}{\delta t} - \delta z_{\text{b,opt}} \right| + \end{center} Here, :math:`\gamma_{\text{veg}}` (default = 1) is a sediment burial factor that accounts for the impact of sediment burial on vegetation. The height of the vegetation (:math:`h_{\text{veg}}` in m) cannot be less than zero. @@ -984,9 +994,9 @@ conditions that enhance or inhibit vegetation growth process :cite:`Danin1991`, :width: 600px :align: center - A) The vegetation growth response varies with different vertical growth rates (example for Vver = 1 and 2 m/year). Optimal vegetation growth is determined by a burial rate of 0.31 + A) The vegetation growth response varies with different vertical growth rates (example for Vver = 1 and 2 m/year). Optimal vegetation growth is determined by a burial rate of 0.31 m/year, with a maximum vegetation height set at 1 m and a plant height of 0.5 m. Additionally, the growth response for varying burial factors is depicted (:math:`\lambda_{\text{veg}}` - = 1 and 2). B) Shear stress reduction for two different vegetation-related roughness parameters and vegetation densities (:math:`\Gamma` = 16 and 32). + = 1 and 2). B) Shear stress reduction for two different vegetation-related roughness parameters and vegetation densities (:math:`\Gamma` = 16 and 32). Vegetation can begin to grow through lateral propagation or random germination. Once established, it can continue to grow and spread laterally. The uncertainties associated with random germination are handled on a cell-by-cell From 4691fd3186b0df7d4d8619edb9f990a0a3d78c70 Mon Sep 17 00:00:00 2001 From: Christa van IJzendoorn <52737913+christavanijzendoorn@users.noreply.github.com> Date: Fri, 16 Aug 2024 11:06:23 -0700 Subject: [PATCH 115/124] Add introductory section to Model Setup --- docs/user/model_setup.rst | 62 +++++++++++++++++++++------------------ 1 file changed, 34 insertions(+), 28 deletions(-) diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index 71f51e92..57505edd 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -1,6 +1,12 @@ Model setup ================= -INTRODUCTORY TEXT +Setting up the AeoLiS model involves configuring various parameters and input files to ensure accurate and efficient simulations. In this section, we will cover: + +- **Model Input**: Detailed information on the required input files and their formats. +- **Default settings**: Overview of the various parameters that can be adjusted in the model and their default values. +- **Activate/deactivate processes**: Explanation of different process flags and their effects on the simulation. +- **Model state/output**: Overview of model state variables that can be outputted. +- **Guidance on solver use**: Explanation of the use of different solvers. Model input ----------- @@ -39,7 +45,7 @@ files can be found in the table below. Each file is further defined below. - File containing meteorological time series data aeolis.txt -^^^^^^^^^^ +^^^^^^^^^^^ This is the parameter file for AeoLiS that defines the model processes and boundary conditions. Parameters in the file are specified by various keywords; each keyword has a pre-defined @@ -52,7 +58,7 @@ process keywords in aeolis.txt to T (True) and F (False). Example aeolis.txt pa found in the examples folder on the AeoLiS GitHub. x.grd -^^^^^ +^^^^^^ The x.grd file defines the computational grid in the cross-shore direction defined in meters. In a 1-dimensional (1D) case, the file contains a single column of cross-shore locations @@ -62,7 +68,7 @@ where each value corresponds to a specific location in the 2D grid. The file ca and is referenced from the parameters file with the xgrid_file keyword. y.grd -^^^^^ +^^^^^^ This file defines the computational grid in the alongshore direction. In a 1D case, y.grd will contain a single column of zeros. In a 2D case, similar to the x.grd file, @@ -73,7 +79,7 @@ As with the x.grd file, this file can be renamed and is referenced from the para keyword: ygrid_file. z.grd -^^^^^ +^^^^^^ The z.grd file provides the model with the elevation information for the computational grid defined in x.grd and y.grd. Similar to x.grd and y.grd, when running @@ -84,7 +90,7 @@ positive is up and negative is down. The file can be renamed and is referenced parameters file with the keyword: bed_file. veg.grd -^^^^^^^ +^^^^^^^^ The veg.grd file is an optional grid providing initial vegetation coverage (density) at each position in the model domain defined in x.grd and y.grd. Similar to the grid files, if simulations are in @@ -102,7 +108,7 @@ where each red dots represent vegetation cover at each cross-shore position. File format for a 1D AeoLis vegetation grid. Each red dot is the vegetation density at a specific location in the computational grid. mass.txt -^^^^^^^^ +^^^^^^^^^ The mass.txt file allows users to specify variations in grain size distribution in both horizontal and vertical directions. If the grain size distribution is constant throughout @@ -147,7 +153,7 @@ file for AeoLis can be seen below. at each location in the computational grid (x, y, bed layer). wind.txt -^^^^^^^^ +^^^^^^^^^ The wind.txt file provides the model with wind boundary conditions and is formatted similar to the tide.txt and wave.txt files. The first column is time in seconds from @@ -167,7 +173,7 @@ importance. File format for wind boundary conditions file for AeoLis input. tide.txt -^^^^^^^^ +^^^^^^^^^ The tide.txt file contains the water elevation data for the duration of the simulation. It is formatted such that the first column is time in seconds and @@ -185,7 +191,7 @@ time or water elevation. File format for the water elevation conditions file for AeoLis input. wave.txt -^^^^^^^^ +^^^^^^^^^ The wave.txt file provides the model with wave data used in AeoLiS for runup calculations. The file is formatted similar to tide.txt but has three columns instead of two. @@ -204,7 +210,7 @@ a data value. File format for the wave conditions file for AeoLis input. meteo.txt -^^^^^^^^^ +^^^^^^^^^^ The meteo.txt file contains meteorological data used to simulate surface moisture in the model domain (see Simulation of surface moisture in Model description on for surface moisture implementation in AeoLiS). This file is formatted similar to the other environmental boundary @@ -225,7 +231,7 @@ column is air pressure (kPa). File format for meteorological data used to simulate surface moisture in AeoLiS where each red dot represents a time series value. Default settings ----------------- +----------------- The AeoLiS model can be configured using a model configuration file. For any configuration parameters not defined in the model @@ -240,7 +246,7 @@ configuration is listed below. Activate/deactivate processes ------------------------------ +------------------------------- After creating the input files that are necessary to run an AeoLiS model, the next step is often to decide which processes and methods to use. Several processes are defined in the configuration file that can be turned on and off. Apart from turning processes on and off, there are also several user-defined thresholds and methods that affect the way in which processes are calculated. For example, there are different sediment transport equations available within *process_transport*. The default is Bagnold, but by defining *method_transport* in the configuration file a different equation can be used. Here, we provide a description of the processes and methods that are defined in configuration file. More detailed descriptions of the processes and their implementation can be found in :ref:`the model description `. An easy way to look up where these process, threshold and method flags are used is by going to the main page of the AeoLiS github and using the search bar at the top. For instance, searching *process_tide* shows that it is used in :py:mod:`aeolis.threshold.compute`, :py:mod:`aeolis.vegetation.grow`, :py:mod:`aeolis.bed.update`. @@ -271,27 +277,27 @@ process_transport Used in :py:mod:`aeolis.transport.equilibrium` process_bedupdate -^^^^^^^^^^^^^^^^^ +^^^^^^^^^^^^^^^^^^ Process_bedupdate allows the bed level to change based on calculated erosion/deposition. Used in :py:mod:`aeolis.bed.update` process_shear -^^^^^^^^^^^^^ +^^^^^^^^^^^^^^ Process_shear calls the shear module in shear.py to calculate the shear stress perturbation caused by topography. Used in :py:mod:`aeolis.wind.initialize` process_tide -^^^^^^^^^^^^ +^^^^^^^^^^^^^ Process_tide changes the threshold velocity to infinity (no aeolian transport) if the bed level is below the water level. This process is not used if th_moist is used. Used in :py:mod:`aeolis.threshold.compute`, :py:mod:`aeolis.vegetation.grow`, :py:mod:`aeolis.bed.update`. process_wave -^^^^^^^^^^^^ +^^^^^^^^^^^^^ Process_wave allows calculation of the water depth based on the input tide file and interpolates the input wave data to the timesteps of the model run. If the wave file is not available, the wave height and peak period are set to 0. Turning this process flag on also results in the calculation of Hsmix, which is needed for the calculation of the Depth of Disturbance (*process_mixtoplayer*). The initialization/calculation is skipped if external variables are imported from another model. process_runup -^^^^^^^^^^^^ +^^^^^^^^^^^^^^ Process_runup allows calculation of the runup extent based on the wave height, peak period and water level. Process_wave and Process_tide need to be on for this to work. The runup is calculated with the Stockdon equation using a user-defined, static beach slope. The initialization/calculation is skipped if external variables are imported from another model. process_moist -^^^^^^^^^^^^^ +^^^^^^^^^^^^^^ Process_moist allows calculation of the soil moisture content, based on different methods, infiltration or surface_moist method_moist_process @@ -301,7 +307,7 @@ method_moist_threshold defines the equation used to calculate teh threshold shea Process_groundwater, Process_seepage_face and Process_scanning are all related to the calculation of the moisture content. process_mixtoplayer -^^^^^^^^^^^^^^^^^^^ +^^^^^^^^^^^^^^^^^^^^ This process flag allows mixing in the layers that are present down to the depth of disturbance. For the calculation of the DoD the process_wave need to be on. process_wet_bed_reset @@ -309,7 +315,7 @@ process_wet_bed_reset Resets the bed to the original bathymetry if the bed is under water (zs). Used in :py:mod:`aeolis.bed.wet_bed_reset`. The execution of the wet bed reset is dependent on the TWL calculation, which can be turned on process_runup, process_waves and process_tide. process_meteo -^^^^^^^^^^^^^ +^^^^^^^^^^^^^^ This is a place holder and currently has no functionality process_avalanche @@ -317,24 +323,24 @@ process_avalanche Simulates the process of avalanching when slopes of the bed become too steep to be realistic (i.e. > a critical static slope). process_separation -^^^^^^^^^^^^^^^^^^ +^^^^^^^^^^^^^^^^^^^ This enables the calculation of the separation bubble within the shear perturbation module. Before executing the calculation is checks whether steep slopes are present that might lead to a separation bubble. Process_separation will only be used if process_shear is on. process_vegetation -^^^^^^^^^^^^^^^^^^^ +^^^^^^^^^^^^^^^^^^^^ This process flag allows application of shear stress reduction due to vegetation based on Raupach or Okin. It also allows for germination and lateral growth of vegetation if those values are set to larger than 0. This process is actively being developed. process_fences -^^^^^^^^^^^^^^ +^^^^^^^^^^^^^^^ This process enables alteration of the shear velocity if fence characteristics are provided as user input. Calculations happen in 1D or 2D depending on grid size following the Okin model. process_dune_erosion -^^^^^^^^^^^^^^^^^^^^ +^^^^^^^^^^^^^^^^^^^^^ This flag turns on dune erosion calculation (:py:mod:`aeolis.erosion`.) based on the Palmsten and Holman (2012) method. After calculating the erosion, the avalanching routine is run in :py:mod:`aeolis.model.update`. This is needed because these modules only get called for aeolian transport in case of winds above threshold. Model state/output ------------------- +------------------- The AeoLiS model state is described by a collection of spatial grid variables with at least one value per horizontal grid cell. Specific @@ -349,5 +355,5 @@ are listed below. :end-before: #: AeoLiS model default configuration -Solver selection ----------------- +Guidance on solver use +------------------------ From 380bf622c76538998712fd48064be85fc8e60aa3 Mon Sep 17 00:00:00 2001 From: Christa van IJzendoorn <52737913+christavanijzendoorn@users.noreply.github.com> Date: Fri, 16 Aug 2024 11:13:06 -0700 Subject: [PATCH 116/124] Solve minor layout issues --- docs/user/model_description.rst | 11 +---------- 1 file changed, 1 insertion(+), 10 deletions(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index d56dd428..f0cb212c 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -926,13 +926,9 @@ vegetation-wind interaction using the expression established by :cite:`DuranHerr .. math:: :label: shear_reduction_vegetation - :nowrap: - \begin{center} \frac{u_{\text{veg}}}{u_*} = \frac{1}{\sqrt{1 + \Gamma \rho_{\text{veg}}}} - \end{center} - \frac{u_{\text{veg}}}{u_*} = \frac{1}{\sqrt{1 + \Gamma \rho_{\text{veg}}}} where the ratio of shear velocity in the presence of vegetation (:math:`u_{*,\text{veg}}`) to the unobstructed shear velocity (:math:`u_*`) is determined by a vegetation-related roughness parameter (:math:`\Gamma`) and the @@ -949,11 +945,9 @@ to the maximum vegetation height (:math:`h_{\text{veg,max}}`), and can vary betw .. math:: :label: Vegetation_density - :nowrap: - \begin{center} \rho_{\text{veg}} = \left( \frac{h_{\text{veg}}}{h_{\text{veg,max}}} \right)^2 - \end{center} + This assumption is based on the idea that burying vegetation reduces its height, which indicates a decrease in actual cover. The change in vegetation density per grid cell is directly linked to the alteration in vegetation @@ -965,11 +959,8 @@ follow the model proposed by :cite:`DuranHerrmann2006`, modified to include :mat .. math:: :label: changes_vegetation_height - :nowrap: - \begin{center} \frac{\delta h_{\text{veg}}}{\delta t} = V_{\text{ver}} \left(1 - \frac{h_{\text{veg}}}{h_{\text{veg,max}}}\right) - \gamma_{\text{veg}} \left| \frac{\delta z_{\text{b,veg}}}{\delta t} - \delta z_{\text{b,opt}} \right| - \end{center} Here, :math:`\gamma_{\text{veg}}` (default = 1) is a sediment burial factor that accounts for the impact of sediment burial on vegetation. The height of the vegetation (:math:`h_{\text{veg}}` in m) cannot be less than zero. From 88a6ed70859d16f1ea69e68616b8dc8e24a089b8 Mon Sep 17 00:00:00 2001 From: Christa van IJzendoorn <52737913+christavanijzendoorn@users.noreply.github.com> Date: Fri, 16 Aug 2024 11:53:25 -0700 Subject: [PATCH 117/124] Improve demonstration cases page --- README.md | 6 ++++++ docs/tutorials/demonstration_cases.rst | 6 ++---- 2 files changed, 8 insertions(+), 4 deletions(-) diff --git a/README.md b/README.md index 63620680..f26d3c8e 100644 --- a/README.md +++ b/README.md @@ -64,6 +64,12 @@ aeolis wind --mean=6 --duration=3600 ## Documentation Detailed documentation can be found at [AeoLiS ReadTheDocs](http://aeolis.readthedocs.io/) +A couple of short courses are available to help new users get acquainted with the model: +- [AeoLiS short course](https://github.com/openearth/aeolis-shortcourse) +- [AeoLiS case study documentation by ERDC](https://github.com/erdc/aeolis-python/tree/master/tutorial) + +Example case studies can also be found in the [examples folder](https://github.com/openearth/aeolis-python/tree/main/aeolis/examples) that is part of the AeoLiS installation. + ## AeoLiS Developer Team The maintenance and development is done by a group of very enthusiastic people. diff --git a/docs/tutorials/demonstration_cases.rst b/docs/tutorials/demonstration_cases.rst index 37ee8ae6..658f17e1 100644 --- a/docs/tutorials/demonstration_cases.rst +++ b/docs/tutorials/demonstration_cases.rst @@ -8,7 +8,7 @@ To run the examples: .. code-block:: bash -pip install aeolis + pip install aeolis 2. Install the examples @@ -31,6 +31,4 @@ Run the simulation with (example parabolic dune model): 4. View/plot the results (example parabolic dune model): -.. code-block:: bash - - [ADD DESCRIPTION OF HOW TO PLOT NETCDF] +Run the plotting_run.py file to visualize the example. Make sure the in the code that the correct nc file from the correct directory is being read. From 4f465456eb5cacf08d704eb577955c49380f73c7 Mon Sep 17 00:00:00 2001 From: Christa van IJzendoorn <52737913+christavanijzendoorn@users.noreply.github.com> Date: Fri, 16 Aug 2024 15:13:41 -0700 Subject: [PATCH 118/124] Restructure model description section --- docs/user/model_description.rst | 2259 ++++++++++++++++--------------- 1 file changed, 1147 insertions(+), 1112 deletions(-) diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index f0cb212c..6e353999 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -3,7 +3,11 @@ Model description ================= -The model approach of :cite:`deVries2014a` is extended to compute the +Sediment Transport +------------------- + +Calculating aeolian sediment transport is the core of the AeoLiS model. +The model is based on the approach of :cite:`deVries2014a` which is extended to compute the spatiotemporal varying sediment availability through simulation of the process of beach armoring. For this purpose the bed is discretized in horizontal grid cells and in vertical bed layers (2DV). Moreover, the @@ -13,10 +17,7 @@ bed composition module is used to compute the sediment availability for each sediment fraction individually. This model approach is a generalization of existing model concepts, like the shear velocity threshold and critical fetch, and therefore compatible with these -existing concepts.. - -Advection Scheme ----------------- +existing concepts. A 1D advection scheme is adopted in correspondence with :cite:`deVries2014a` in which :math:`c` [:math:`\mathrm{kg/m^2}`] is @@ -103,1430 +104,1464 @@ simulation. The model is initially intended to provide accurate sediment fluxes from the beach to the dunes rather than to simulate subsequent dune formation. -Numerical implementation of the advection equation --------------------------------------------------- +Multi-fraction sediment transport +------------------------------------- -The advection equation is implemented in two-dimensional form -following: +The formulation for the equilibrium or saturated sediment +concentration :math:`c_{\mathrm{sat}}` (Equation +:eq:`equilibrium-conc`) is capable of dealing with variations in +grain size through the variables :math:`u_{\mathrm{th}}`, +:math:`d_{\mathrm{n}}` and :math:`C` :cite:`Bagnold1937a`. However, +the transport formulation only describes the saturated sediment +concentration assuming a fixed grain size distribution, but does not +define how multiple fractions coexist in transport. If the saturated +sediment concentration formulation would be applied to each fraction +separately and summed up to a total transport, the total sediment +transport would increase with the number of sediment fractions. Since +this is unrealistic behavior the saturated sediment concentration +:math:`c_{\mathrm{sat}}` for the different fractions should be +weighted in order to obtain a realistic total sediment +transport. Equation :eq:`erodep` therefore is modified to include a +weighting factor :math:`\hat{w}_k` in which :math:`k` represents the +sediment fraction index: .. math:: - :label: apx-advection - - \frac{\partial c}{\partial t} + - u_{z,\mathrm{x}} \frac{\partial c}{\partial x} + - u_{z,\mathrm{y}} \frac{\partial c}{\partial y} = - \frac{c_{\mathrm{sat}} - c}{T} - -in which :math:`c` [:math:`\mathrm{kg/m^2}`] is the sediment mass per -unit area in the air, :math:`c_{\mathrm{sat}}` [:math:`\mathrm{kg/m^2}`] is the -maximum sediment mass in the air that is reached in case of -saturation, :math:`u_{z,\mathrm{x}}` and :math:`u_{z,\mathrm{y}}` are the x- and -y-component of the wind velocity at height :math:`z` [m], :math:`T` [s] is an -adaptation time scale, :math:`t` [s] denotes time and :math:`x` [m] and :math:`y` [m] -denote cross-shore and alongshore distances respectively. - -The formulation is discretized in different ways to allow for different types of simulations balancing accuracy vs. computational resources. The conservative method combined with an euler backward scheme (written by Prof. Rauwoens) is the current default for most simulations. Non-conservative methods end explicit Euler forward schemes are also available. - -Default scheme -- Conservative Euler Backward Implicit -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -The default numerical method assumes the advection scheme in a conservative form in combination with an euler backward scheme. This scheme is prepared to use a TVD method but this is not implemented yet (add footnote{Total Variance Diminishing, this is explained in the lecture notes by Zijlema p94}) + :label: erodep_multi + + E_k - D_k = \min \left ( \frac{\partial m_{\mathrm{a},k}}{\partial t} \quad ; \quad \frac{\hat{w}_k \cdot c_{\mathrm{sat},k} - c_k}{T} \right ) -The fluxes at the interface of the cells are defined used in the advection terms: +It is common to use the grain size distribution in the bed as +weighting factor for the saturated sediment concentration +(e.g. :cite:`Delft3DManual`, section 11.6.4). Using the grain size +distribution at the bed surface as a weighting factor assumes, in case +of erosion, that all sediment at the bed surface is equally exposed to +the wind. -.. math:: - :label: conservative1 - - \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t} + \\ - \frac{u_{\text{x},i+1/2,j} \cdot c^{n+1}_{i+1/2,j,k} - u_{\text{x},i-1/2,j} \cdot c^{n+1}_{i-1/2,j,k}}{\Delta x} + \\ - \frac{u_{\text{y},i,j+1/2} \cdot c^{n+1}_{i,j+1/2,k} - u_{\text{y},i,j-1/2} \cdot c^{n+1}_{i,j-1/2,k}}{\Delta y} + - \\ = \\ - \frac{\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i.j.k} + c^{n+1}_{i,j,k} ) - c^{n+1}_{i,j,k}}{T} - -In which :math:`n` is the time step index, :math:`i` and :math:`j` are the cross-shore and alongshore spatial grid cell indices and :math:`k` is the grain size fraction index. :math:`w` [-] is the weighting factor used for the weighted addition of the saturated sediment concentrations over all grain size fractions. Note that u is spatially varying but has no temporal index. This is because u is a result of a separate wind solver and considered temporally invariant in the advection solver. +Using the grain size distribution at the bed surface as weighting +factor in case of deposition would lead to the behavior where +deposition becomes dependent on the bed composition. Alternatively, in +case of deposition, the saturated sediment concentration can be +weighted based on the grain size distribution in the air. Due to the +nature of saltation, in which continuous interaction with the bed +forms the saltation cascade, both the grain size distribution in the +bed and in the air are likely to contribute to the interaction between +sediment fractions. The ratio between both contributions in the model +is determined by a bed interaction parameter :math:`\zeta`. -Now we use a correction algorithm where: +The weighting of erosion and deposition of individual fractions is +computed according to: .. math:: - :label: conservative2 - - c^{n+1}_{i,j,k} = c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} + :label: weigh -where :math:`\delta c_{i,j,k}` is solved for and :math:`*` denotes the previous iteration. - -When now assuming an upwind scheme in space, we can derive 4 concentrations at the cell faces which are dependent on the velocity at the cell faces. + \begin{align} + \hat{w}_k &= \frac{w_k}{ \sum_{k=1}^{n_{\mathrm{k}}}{w_k} } \\ + \mathrm{where} \quad w_k &= (1 - \zeta) \cdot w^{\mathrm{air}}_k + (1 - \hat{S}_k) \cdot w^{\mathrm{bed}}_k + \end{align} -We assume in x direction: +in which :math:`k` represents the sediment fraction index, +:math:`n_{\mathrm{k}}` the total number of sediment fractions, :math:`w_k` is the +unnormalized weighting factor for fraction :math:`k`, :math:`\hat{w}_k` is its +normalized counterpart, :math:`w^{\mathrm{air}}_k` and :math:`w^{\mathrm{bed}}_k` +are the weighting factors based on the grain size distribution in the +air and bed respectively and :math:`\hat{S}_k` is the effective sediment +saturation of the air. The weighting factors based on the grain size +distribution in the air and the bed are computed using mass ratios: .. math:: + :label: weights + + w^{\mathrm{air}}_k = \frac{c_k}{c_{\mathrm{sat},k}} \quad ; \quad + w^{\mathrm{bed}}_k = \frac{m_{\mathrm{a},k}}{\sum_{k=1}^{n_{\mathrm{k}}}{m_{\mathrm{a},k}}} - c^{n+1}_{i+1/2,j,k} = - \begin{cases} - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{x},i+1/2,j} > 0$,}\\ - c^{n+1 *}_{i+1,j,k} + \delta c_{i+1,j,k} & \text{if $u_{\text{x},i+1/2,j} < 0$.} - \end{cases} +The sum of the ratio :math:`w^{\mathrm{air}}_k` over the fractions +denotes the degree of saturation of the air column for fraction +:math:`k`. The degree of saturation determines if erosion of a fraction may +occur. Also in saturated situations erosion of a sediment fraction can +occur due to an exchange of momentum between sediment fractions, which +is represented by the bed interaction parameter :math:`\zeta`. The effective +degree of saturation is therefore also influenced by the bed +interaction parameter and defined as: .. math:: + :label: saturation + + \hat{S}_k = \min \left ( 1 \quad ; \quad (1 - \zeta) \cdot \sum_{k=1}^{n_{\mathrm{k}}} w_k^{\mathrm{air}} \right ) - c^{n+1}_{i-1/2,j,k} = - \begin{cases} - c^{n+1 *}_{i-1,j,k} + \delta c_{i-1,j,k} & \text{if $u_{\text{x},i-1/2,j} > 0$,}\\ - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{x},i-1/2,j} < 0$.} - \end{cases} +When the effective saturation is greater than or equal to unity the +air is (over)saturated and no erosion will occur. The grain size +distribution in the bed is consequently less relevant and the second +term in Equation :eq:`weights` is thus minimized and zero in case +:math:`\zeta = 0`. In case the effective saturation is less than unity erosion +may occur and the grain size distribution of the bed also contributes +to the weighting over the sediment fractions. The weighting factors +for erosion are then composed from both the grain size distribution in +the air and the grain size distribution at the bed surface. Finally, +the resulting weighting factors are normalized to sum to unity over +all fractions (:math:`\hat{w}_k`). -and in y-direction: +The composition of weighting factors for erosion is based on the +saturation of the air column. The non-saturated fraction determines +the potential erosion of the bed. Therefore the non-saturated fraction +can be used to scale the grain size distribution in the bed in order +to combine it with the grain size distribution in the air according to +Equation :eq:`weights`. The non-saturated fraction of the air column +that can be used for scaling is therefore :math:`1 - \hat{S}_k`. -.. math:: +For example, if bed interaction is disabled (:math:`\zeta = 0`) and +the air is 70\% saturated, then the grain size distribution in the air +contributes 70\% to the weighting factors for erosion, while the grain +size distribution in the bed contributes the other 30\% (Figure +:numref:`fig-bed-interaction-parameter`, upper left panel). In case of +(over)saturation the grain size distribution in transport contributes +100\% to the weighting factors and the grain size distribution in the +bed is of no influence. Transport progresses in downwind direction +without interaction with the bed. - c^{n+1}_{i,j+1/2,k} = - \begin{cases} - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{y},i,j+1/2} > 0$,}\\ - c^{n+1 *}_{i,j+1,k} + \delta c_{i,j+1,k} & \text{if $u_{\text{y},i,j+1/2} < 0$.} - \end{cases} +.. _fig-bed-interaction-parameter: -.. math:: +.. figure:: /images/bed_interaction_parameter.png + :width: 600px + :align: center - c^{n+1}_{i,j-1/2,k} = - \begin{cases} - c^{n+1 *}_{i,j-1,k} + \delta c_{i,j-1,k} & \text{if $u_{\text{y},i,j-1/2} > 0$,}\\ - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{y},i,j-1/2} < 0$.} - \end{cases} + Contributions of the grain size distribution in the bed and in the + air to the weighting factors :math:`\hat{w}_k` for the equilibrium + sediment concentration in Equation :eq:`erodep_multi` for different + values of the bed interaction parameter. -Now we assume: +To allow for bed interaction in saturated situations in which no net +erosion can occur, the bed interaction parameter :math:`\zeta` is used (Figure +:numref:`fig-bed-interaction-parameter`). The bed interaction parameter +can take values between 0.0 and 1.0 in which the weighting factors for +the equilibrium or saturated sediment concentration in an +(over)saturated situation are fully determined by the grain size +distribution in the bed or in the air respectively. A bed interaction +value of 0.2 represents the situation in which the grain size +distribution at the bed surface contributes 20\% to the weighting of +the saturated sediment concentration over the fractions. In the +example situation where the air is 70\% saturated such value for the +bed interaction parameter would lead to weighting factors that are +constituted for :math:`70\% \cdot (100\% - 20\%) = 56\%` based on the grain +size distribution in the air and for the other 44\% based on the grain +size distribution at the bed surface (Figure +:numref:`fig-bed-interaction-parameter`, upper right panel). -- :math:`\Gamma_x = 1` if :math:`u_{\text{x},i+1/2,j,k} > 0` and :math:`\Gamma_x = 0` if :math:`u_{\text{x},i+1/2,j,k} \leq 0` -- :math:`\Gamma_y = 1` if :math:`u_{\text{y},i,j+1/2,k} > 0` and :math:`\Gamma_x = 0` if :math:`u_{\text{y},i,j+1/2,k} \leq 0` - -(We did not test if this works well with diverging and converging flows. We may need another term that describes the conditions at the negative cell faces if they are of opposite direction than the positive cell faces and vice versa) +The parameterization of the exchange of momentum between sediment +fractions is an aspect of saltation that is still poorly +understood. Therefore calibration of the bed interaction parameter +:math:`\zeta` is necessary. The model parameters in Equation +:eq:`equilibrium-conc` can be chosen in accordance with the +assumptions underlying multi-fraction sediment transport. :math:`C` should +be set to 1.5 as each individual sediment fraction is well-sorted, +:math:`d_{\mathrm{n}}` should be chosen equal to :math:`D_{\mathrm{n}}` as the +grain size dependency is implemented through +:math:`u_{\mathrm{th}}`. :math:`u_{\mathrm{th}}` typically varies between 1 and 6 +m/s for sand. -Let's continue for the moment so that +Sediment Sorting and Beach Armoring +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -.. math:: +Since the equilibrium or saturated sediment concentration +:math:`c_{\mathrm{sat},k}` is weighted over multiple sediment fractions in +the extended advection model, also the instantaneous sediment +concentration :math:`c_k` is computed for each sediment fraction +individually. Consequently, grain size distributions may vary over the +model domain and in time. These variations are thereby not limited to +the horizontal, but may also vary over the vertical since fine +sediment may be deposited on top of coarse sediment or, reversely, +fines may be eroded from the bed surface leaving coarse sediment to +reside on top of the original mixed sediment. In order to allow the +model to simulate the processes of sediment sorting and beach armoring +the bed is discretized in horizontal grid cells and vertical bed +layers (2DV; Figure :numref:`fig-bedcomposition`). - \begin{gathered} - \frac{c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} - c^n_{i,j,k}}{\Delta t} + \\ - \Gamma_x \cdot \frac{u_{\text{x},i+1/2,j} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}) - u_{\text{x},i-1/2,j} \cdot (c^{n+1 *}_{i-1,j,k} + \delta c_{i-1,j,k})}{\Delta x} + \\ - (1-\Gamma_x) \cdot \frac{u_{\text{x},i+1/2,j} \cdot (c^{n+1 *}_{i+1,j,k} + \delta c_{i+1,j,k}) - u_{\text{x},i-1/2,j} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k})}{\Delta x} + \\ - \Gamma_y \cdot \frac{u_{\text{y},i,j+1/2} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}) - u_{\text{y},i,j-1/2} \cdot (c^{n+1 *}_{i,j-1,k} + \delta c_{i,j-1,k})}{\Delta y} + \\ - (1-\Gamma_y) \cdot \frac{u_{\text{y},i,j+1/2} \cdot (c^{n+1 *}_{i,j+1,k} + \delta c_{i,j+1,k}) - u_{\text{y},i,j-1/2} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k})}{\Delta y} + - \\ = \\ - \frac{\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i,j,k}+c^{n+1 *}_{i,j,k} + \xcancel{\delta c_{i,j,k}}) - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}}{T} - \end{gathered} +The discretization of the bed consists of a minimum of three vertical +bed layers with a constant thickness and an unlimited number of +horizontal grid cells. The top layer is the *bed surface layer* and is +the only layer that interacts with the wind and hence determines the +spatiotemporal varying sediment availability and the contribution of +the grain size distribution in the bed to the weighting of the +saturated sediment concentration. One or more *bed composition layers* +are located underneath the bed surface layer and form the upper part +of the erodible bed. The bottom layer is the *base layer* and contains +an infinite amount of erodible sediment according to the initial grain +size distribution. The base layer cannot be eroded, but can supply +sediment to the other layers. -(note that the above does not take converging and diverging flows into account, also :math:`\delta c_{i,j,k}` at the right hand side in the "min" brackets is difficult to solve for. In the code, this term is neglected which may cause some inaccuracy when calculating pickup. Although mass continuity is corrected for in the implicit scheme when calculating pickup using equation ???) +.. _fig-bedcomposition: -Now we simplify: +.. figure:: /images/bed_composition.png + :align: center -.. math:: + Schematic of bed composition discretisation and advection + scheme. Horizontal exchange of sediment may occur solely through + the air that interacts with the *bed surface layer*. The detail + presents the simulation of sorting and beach armoring where the bed + surface layer in the upwind grid cell becomes coarser due to + non-uniform erosion over the sediment fractions, while the bed + surface layer in the downwind grid cell becomes finer due to + non-uniform deposition over the sediment fractions. Symbols refer + to Equations :eq:`advection` and :eq:`erodep`. - \begin{gathered} - (\frac{\Delta x \Delta y}{\Delta t} + \Gamma_x\Delta y \cdot u_{\text{x},i+1/2,j} - (1-\Gamma_x)\Delta y \cdot u_{\text{x},i-1/2,j} + \Gamma_y\Delta x \cdot u_{\text{y},i,j+1/2}\\ - (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j-1/2}+\frac{\Delta x \Delta y}{T_s})\cdot \delta c_{i,j,k}\\ - -(\Gamma_x\Delta y \cdot u_{\text{x},i-1/2,j})\cdot \delta c_{i-1,j,k}\\ - +((1-\Gamma_x)\Delta y \cdot u_{\text{x},i+1/2,j})\cdot \delta c_{i+1,j,k}\\ - -(\Gamma_y\Delta x \cdot u_{\text{y},i,j-1/2})\cdot \delta c_{i,j-1,k}\\ - + ((1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j+1/2})\cdot \delta c_{i,j+1,k}\\ - \end{gathered} +Each layer in each grid cell describes a grain size distribution over +a predefined number of sediment fractions (Figure +:numref:`fig-bedcomposition`, detail). Sediment may enter or leave a +grid cell only through the bed surface layer. Since the velocity +threshold depends among others on the grain size, erosion from the bed +surface layer will not be uniform over all sediment fractions, but +will tend to erode fines more easily than coarse sediment (Figure +:numref:`fig-bedcomposition`, detail, upper left panel). If sediment +is eroded from the bed surface layer, the layer is repleted by +sediment from the lower bed composition layers. The repleted sediment +has a different grain size distribution than the sediment eroded from +the bed surface layer. If more fines are removed from the bed surface +layer in a grid cell than repleted, the median grain size +increases. If erosion of fines continues the bed surface layer becomes +increasingly coarse. Deposition of fines or erosion of coarse material +may resume the erosion of fines from the bed. -or +In case of deposition the process is similar. Sediment is deposited in +the bed surface layer that then passes its excess sediment to the +lower bed layers (Figure :numref:`fig-bedcomposition`, detail, upper +right panel). If more fines are deposited than passed to the lower bed +layers the bed surface layer becomes increasingly fine. -.. math:: +.. _roughness-elements: - \begin{gathered} - A0 \cdot \delta c_{i,j,k} - + A\text{m1} \cdot \delta c_{i-1,j,k} - + A\text{p1} \cdot \delta c_{i+1,j,k}\\ - + A\text{mx} \cdot \delta c_{i,j-1,k} - + A\text{px} \cdot \delta c_{i,j+1,k} = y_{i,j,k} - \label{eq:lin} - \end{gathered} +Non-erodible Roughness Elements +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -or the linear system of equations in general form: +Sediment sorting may lead to the emergence of non-erodible elements +from the bed. Non-erodible roughness elements may shelter the erodible +bed from wind erosion due to shear partitioning, resulting in a +reduced sediment availability :cite:`Raupach1993`. Therefore the +equation of :cite:`Raupach1993` is implemented according to: .. math:: - :label: conservative_general + :label: raupach + + u_{\mathrm{* th, R}} = u_{\mathrm{* th}} \cdot \sqrt{ \left( 1 - m \cdot \sum_{k=k_0}^{n_{\mathrm{k}}}{w_k^{\mathrm{bed}}} \right) \left( 1 + \frac{m \beta}{\sigma} \cdot \sum_{k=k_0}^{n_{\mathrm{k}}}{w_k^{\mathrm{bed}}} \right) } - A \cdot \delta c_{i,j,k} = y_{i,j,k} +in which :math:`\sigma` is the ratio between the frontal area and the +basal area of the roughness elements and :math:`\beta` is the ratio +between the drag coefficients of the roughness elements and the bed +without roughness elements. :math:`m` is a factor to account for the +difference between the mean and maximum shear stress and is usually +chosen 1.0 in wind tunnel experiments and may be lowered to 0.5 for +field applications. The roughness density :math:`\lambda` in the +original equation of :cite:`Raupach1993` is obtained from the mass +fraction in the bed surface layer :math:`w_k^{\mathrm{bed}}` according +to: -Where :math:`A` is a 3-dimensional sparse matrix that is compiled using the matrix diagonals (:math:`A0, Am1, Ap1, Amx, Apx`) which are defined as: +.. math:: + :label: rough + + \lambda = \frac{\sum_{k=k_0}^{n_{\mathrm{k}}}{w_k^{\mathrm{bed}}}}{\sigma} -.. math:: +in which :math:`k_0` is the index of the smallest non-erodible +sediment fraction in current conditions and :math:`n_{\mathrm{k}}` is the +total number of sediment fractions. It is assumed that the sediment +fractions are ordered by increasing size. Whether a fraction is +erodible depends on the sediment transport capacity. - \begin{aligned} - A0 = & +\frac{\Delta x \Delta y}{\Delta t} \\ - & +\frac{\Delta x \Delta y}{T_s} \\ - & - (1-\Gamma_x)\Delta y \cdot u_{\text{x},i-1/2,j} \\ - & + \Gamma_x\Delta y \cdot u_{\text{x},i+1/2,j} \\ - & - (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j-1/2} \\ - & + \Gamma_y\Delta x \cdot u_{\text{y},i,j+1/2} \\ - \end{aligned} +Hydraulic Mixing +^^^^^^^^^^^^^^^^^^^^^ -and +As sediment sorting due to aeolian processes can lead to armoring of a +beach surface, mixing of the beach surface or erosion of course +material may undo the effects of armoring. To ensure a proper balance +between processes that limit and enhance sediment availability in the +model both types of processes need to be sufficiently represented when +simulating spatiotemporal varying bed surface properties and sediment +availability. + +A typical upwind boundary in coastal environments during onshore winds +is the water line. For aeolian sediment transport the water line is a +zero-transport boundary. In the presence of tides, the intertidal +beach is flooded periodically. Hydraulic processes like wave breaking +mix the bed surface layer of the intertidal beach, break the beach +armoring and thereby influence the availability of sediment. + +In the model the mixing of sediment is simulated by averaging the +sediment distribution over the depth of disturbance +(:math:`\Delta z_{\mathrm{d}}`). The depth of disturbance is linearly +related to the breaker height (e.g. :cite:`King1951`, :cite:`Williams1971`, :cite:`Masselink2007`). :cite:`Masselink2007` proposes an empirical factor +:math:`f_{\Delta z_{\mathrm{d}}}` [-] that relates the depth of disturbance +directly to the local breaker height according to: .. math:: + :label: disturbance_depth + + \Delta z_{\mathrm{d}} = f_{\Delta z_{\mathrm{d}}} \cdot \min \left ( H \quad ; \quad \gamma \cdot d \right ) - A\text{m}1 = -\Gamma_x\Delta y \cdot u_{\text{x},i-1/2,j} +in which the offshore wave height :math:`H` [m] is taken as the +local wave height maximized by a maximum wave height over depth ratio +:math:`\gamma` [-]. :math:`d` [m] is the water depth that is provided to the model +through an input time series of water levels. Typical values for +:math:`f_{\Delta z_{\mathrm{d}}}` are 0.05 to 0.4 and 0.5 for :math:`\gamma`. -and +Shear velocity threshold +------------------------ + +The shear velocity threshold represents the influence of bed surface +properties in the saturated sediment transport equation. The shear +velocity threshold is computed for each grid cell and sediment +fraction separately based on local bed surface properties, like +moisture, roughness elements and salt content. For each bed surface +property supported by the model a factor is computed to increase the +initial shear velocity threshold: .. math:: + :label: apx-shearvelocity + + u_{\mathrm{* th}} = + f_{u_{\mathrm{* th}}, \mathrm{M}} \cdot + f_{u_{\mathrm{* th}}, \mathrm{R}} \cdot + f_{u_{\mathrm{* th}}, \mathrm{S}} \cdot + u_{\mathrm{* th, 0}} - A\text{p}1 = (1-\Gamma_x)\Delta y \cdot u_{\text{x},i+1/2,j} +The initial shear velocity threshold :math:`u_{\mathrm{* th, 0}}` [m/s] is +computed based on the grain size following :cite:`Bagnold1937b`: -and +.. math:: + :label: shear + + u_{\mathrm{* th, 0}} = A \sqrt{ \frac{\rho_{\mathrm{p}} - \rho_{\mathrm{a}}}{\rho_{\mathrm{a}}} \cdot g \cdot d_{\mathrm{n}}} + +where :math:`A` [-] is an empirical constant, :math:`\rho_{\mathrm{p}}` +[:math:`\mathrm{kg/m^3}`] is the grain density, :math:`\rho_{\mathrm{a}}` +[:math:`\mathrm{kg/m^3}`] is the air density, :math:`g` [:math:`\mathrm{m/s^2}`] is the +gravitational constant and :math:`d_{\mathrm{n}}` [m] is the nominal grain +size of the sediment fraction. + +Moisture content +^^^^^^^^^^^^^^^^^ + +The shear velocity threshold is updated based on moisture content +following :cite:`Belly1964`: .. math:: - A\text{mx} = -\Gamma_y\Delta x \cdot u_{\text{y},i,j-1/2} + :label: apx-moist + + f_{u_{\mathrm{* th}}, \mathrm{M}} = \max(1 \quad ; \quad 1.8 + 0.6 \cdot \log(p_{\mathrm{g}})) -and +where :math:`f_{u_{\mathrm{* th},M}}` [-] is a factor in Equation :eq:`apx-shearvelocity`, :math:`p_{\mathrm{g}}` [-] is the geotechnical +mass content of water, which is the percentage of water compared to +the dry mass. The geotechnical mass content relates to the volumetric +water content :math:`p_{\mathrm{V}}` [-] according to: .. math:: + :label: vol-water - A\text{px} = (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j+1/2} + p_{\mathrm{g}} = \frac{p_{\mathrm{V}} \cdot \rho_{\mathrm{w}}}{\rho_{\mathrm{p}} \cdot (1 - p)} -Let's go towards the RHS +where :math:`\rho_{\mathrm{w}}` [:math:`\mathrm{kg/m^3}`] and +:math:`\rho_{\mathrm{p}}` [:math:`\mathrm{kg/m^3}`] are the water and particle +density respectively and :math:`p` [-] is the porosity. Values for +:math:`p_{\mathrm{g}}` smaller than 0.005 do not affect the shear velocity +threshold :cite:`Pye1990`. Values larger than 0.064 (or 10\% +volumetric content) cease transport :cite:`DelgadoFernandez2010`, +which is implemented as an infinite shear velocity threshold. -.. math:: - \begin{aligned} - y_{i,j,k} = & - \frac{\Delta x \Delta y}{\Delta t}(c^{n+1 *}_{i,j,k}-c^{n}_{i,j,k}) \\ - & + \frac{\Delta x \Delta y}{T_s}(\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i,j,k} + c^{n+1 *}_{i,j,k}) - c^{n+1 *}_{i,j,k}) \\ - & + \Delta y \cdot u_{\text{x},i-1/2,j} \cdot - (\Gamma_x \cdot c^{n+1 *}_{i-1,j,k} + (1-\Gamma_x) c^{n+1 *}_{i,j,k})\\ - & - \Delta y \cdot u_{\text{x},i+1/2,j} \cdot (\Gamma_x \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_x) c^{n+1 *}_{i+1,j,k})\\ - & + \Delta x \cdot u_{\text{y},i,j-1/2} \cdot (\Gamma_y \cdot c^{n+1 *}_{i,j-1,k} + (1-\Gamma_y) c^{n+1 *}_{i,j,k})\\ - & - \Delta x \cdot u_{\text{y},i,j+1/2} \cdot (\Gamma_y \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_y) c^{n+1 *}_{i,j+1,k})\\ - \end{aligned} +Roughness elements +^^^^^^^^^^^^^^^^^^^ -in the python code some intermediate variable is defined to make it easier to shift indexes +The shear velocity threshold is updated based on the presence of +roughness elements following :cite:`Raupach1993`: .. math:: + :label: shear-rough - \text{Ctxfs} =(\Gamma_x \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_x) c^{n+1 *}_{i+1,j,k}) + f_{u_{\mathrm{* th},R}} = \sqrt{(1 - m \cdot \sum_{k=k_0}^{n_k}{\hat{w}_k^{\mathrm{bed}}}) + (1 + \frac{m \beta}{\sigma} \cdot \sum_{k=k_0}^{n_k}{\hat{w}_k^{\mathrm{bed}}})} -and +by assuming: .. math:: + :label: lambda-rough + + \lambda = \frac{\sum_{k=k_0}^{n_k}{\hat{w}_k^{\mathrm{bed}}}}{\sigma} - \text{Ctxfn} =(\Gamma_y \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_y) c^{n+1 *}_{i,j+1,k}) +where :math:`f_{u_{\mathrm{* th},R}}` [-] is a factor in Equation +:eq:`apx-shearvelocity`, :math:`k_0` is the sediment fraction index of +the smallest non-erodible fraction in current conditions and :math:`n_k` is +the number of sediment fractions defined. The implementation is +discussed in detail in section \ref{sec:roughness}. -also Erosion and deposition are defined using seperate variables. +Salt content +^^^^^^^^^^^^ + +The shear velocity threshold is updated based on salt content +following :cite:`Nickling1981`: .. math:: - D_{i,j,k}= \frac{\Delta x \Delta y}{T_s}c^{n+1 *}_{i,j,k} + :label: salt-rough + + f_{u_{\mathrm{* th}},S} = 1.03 \cdot \exp(0.1027 \cdot p_{\mathrm{s}}) -and +where :math:`f_{u_{\mathrm{* th},S}}` [-] is a factor in Equation +:eq:`apx-shearvelocity` and :math:`p_{\mathrm{s}}` [-] is the salt +content [mg/g]. Currently, no model is implemented that predicts the +instantaneous salt content. The spatial varying salt content needs to +be specified by the user, for example through the BMI interface. -.. math:: - A_{i,j,k}= \frac{\Delta x \Delta y}{T_s}m_{i,j,k} + D_{i,j,k} +Wind shear and topographic steering +--------------------------------------------------------------- -and +The shear stress perturbation π›Ώπœ is estimated following the analytical description of the influence of alow and smooth hill in the wind profile by Weng et al. (1991). The perturbation is given by the Fourier transformed components of the shear stress perturbation in the unperturbed wind direction which are the functions π›Ώπœπ‘₯(π‘˜) and π›Ώπœπ‘¦(π‘˜). The x-direction is defined by the direction of the wind velocity :math:`v_{0}` on a flat bed, while the y direction is then the transverse. -.. math:: - U_{i,j,k}= \frac{\Delta x \Delta y}{T_s}\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} +As a result, the perturbation theory can only estimate the shear stress induced by the morphology-wind interaction in parallel direction of wind. Therefore, model simulations were, up to now, limited to input wind directions parallel to the crossΒ­shore axis of the grid. -and +To overcome this limitation and to allow for modelling directional winds, an overlaying computational grid is introduced in AeoLiS, which rotates with the changing wind direction per time step. By doing this, the shear stresses are always estimated in the positive x-direction of the computational grid. The following steps are executed for each time step: -.. math:: - E_{i,j,k} = \min(U_{i,j,k},A_{i,j,k}) +1. Create a computational grid alligned with the wind direction (set_computational_grid) +2. Add and fill buffer around the original grid +3. Populate computation grid by rotating it to the current wind direction and interpolate the original topography on it. Additionally, edges around +4. Compute the morphology-wind induced shear stress by using the perturbation theory +5. Add the only wind induced wind shear stresses to the computational grid +6. Rotate both the grids and the total shear stress results in opposite direction +7. Interpolate the total shear stress results from the computational grid to the original grid +8. Rotate the wind shear stress results and the original grid back to the original orientation -After solving equation :math:`\delta c_{i,j,k}` using :eq:`conservative_general`, :math:`c^{n+1}_{i,j,k}` can be calculated using equation :eq:`conservative2`. +.. note:: + The extra rotations in the last two steps are necessary as a simplified, but faster in terms of computational time, interpolation method is used. -Also, the pickup per grid cell can be calculated using: + +Vegetation +------------ + +The description of the implementation of vegetation dynamics in AeoLiS is based on :cite:`Strypsteen2024`. + +In AeoLiS, the influence of vegetation on dune evolution is comprehensively +addressed. This includes modelling the intrinsic growth of vegetation, +accounting for factors such as growth and decay due to burial :cite:`DuranMoore2013`, +lateral expansion and establishment :cite:`Keijsers2016`, as well as simulating +the destruction of vegetation caused by hydrodynamic processes.In the event of +cell inundation, vegetation density is reduced as a result. + +Shear stress reduction +^^^^^^^^^^^^^^^^^^^^^^^^ +Inspired by the Coastal Dune Model (CDM) proposed by :cite:`DuranMoore2013`, AeoLiS +incorporates vegetation-wind interaction using the expression established by :cite:`DuranHerrmann2006`: .. math:: + :label: shear_reduction_vegetation - \text{pickup} = \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k}- c^{n+1}_{i,j,k}}{T_s}\Delta t - \label{eq:pickup} + \frac{u_{\text{veg}}}{u_*} = \frac{1}{\sqrt{1 + \Gamma \rho_{\text{veg}}}} -note that this is only valid when using an Euler backward scheme. -Solving the Linear System of Equations -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +where the ratio of shear velocity in the presence of vegetation (:math:`u_{*,\text{veg}}`) to the unobstructed +shear velocity (:math:`u_*`) is determined by a vegetation-related roughness parameter (:math:`\Gamma`) and the +vegetation density within a unit area of the grid cell (:math:`\rho_{\text{veg}}`). In the model, :math:`\Gamma` = 16 is derived +from plant form drag and geometry values documented for creosote communities :cite:`DuranHerrmann2006`. +This implementation calculates the expression on each model grid cell, with higher vegetation density +(expressed by :math:`\rho_{\text{veg}}`) leading to a more substantial reduction in shear velocity compared to sparse +vegetation. By integrating these physical and ecological processes, AeoLiS simulates spatial patterns and temporal +variations in sediment transport and morphological changes resulting from aeolian processes in coastal +environments. -The linear system of equations can be elaborated : +Vegetation density +^^^^^^^^^^^^^^^^^^^ -.. math:: - :label: apx-system - - \left[ - \begin{array}{cccccc} - A^0_1 & A^{1}_1 & \textbf{0} & \cdots & \textbf{0} & A^{n_{\mathrm{y}}+1}_1 \\ - A^{-1}_2 & A^0_2 & \ddots & \ddots & & \textbf{0} \\ - \textbf{0} & \ddots & \ddots & \ddots & \ddots & \vdots \\ - \vdots & \ddots & \ddots & \ddots & \ddots & \textbf{0} \\ - \textbf{0} & & \ddots & \ddots & A^0_{n_{\mathrm{y}}} & A^1_{n_{\mathrm{y}}} \\ - A^{-n_{\mathrm{y}}-1}_{n_{\mathrm{y}}+1} & \textbf{0} & \cdots & \textbf{0} & A^{-1}_{n_{\mathrm{y}}+1} & A^0_{n_{\mathrm{y}}+1} \\ - \end{array} - \right] \left[ - \begin{array}{c} - \vec{\delta c}_1 \\ \vec{\delta c}_2 \\ \vdots \\ \vdots \\ \vec{\delta c}_{n_{\mathrm{y}}} \\ \vec{\delta c}_{n_{\mathrm{y}}+1} \\ - \end{array} - \right] = \left[ - \begin{array}{c} - \vec{y}_1 \\ \vec{y}_2 \\ \vdots \\ \vdots \\ \vec{y}_{n_{\mathrm{y}}} \\ \vec{y}_{n_{\mathrm{y}}+1} \\ - \end{array} - \right] - -where each item in the matrix is again a matrix :math:`A^l_j` and -each item in the vectors is again a vector :math:`\vec{\delta c}_j` and -:math:`\vec{y}_j` respectively. The form of the matrix :math:`A^l_j` depends on -the diagonal index :math:`l` and reads: - -.. math:: - :label: apx-diagonal - - A^0_j = - \left[ - \begin{array}{ccccccc} - 0 & 0 & 0 & 0 - & \cdots & \cdots & 0 \\ - a^{0,-1}_{2,j} & a^{0,0}_{2,j} & a^{0,1}_{2,j} & \ddots - & & & \vdots \\ - 0 & a^{0,-1}_{3,j} & a^{0,0}_{3,j} & a^{0,1}_{3,j} - & \ddots & & \vdots \\ - \vdots & \ddots & \ddots & \ddots - & \ddots & \ddots & \vdots \\ - \vdots & & \ddots & a^{0,-1}_{n_{\mathrm{x}}-1,j} - & a^{0,0}_{n_{\mathrm{x}}-1,j} & a^{0,1}_{n_{\mathrm{x}}-1,j} & 0 \\ - \vdots & & & 0 - & a^{0,-1}_{n_{\mathrm{x}},j} & a^{0,0}_{n_{\mathrm{x}},j} & a^{0,1}_{n_{\mathrm{x}},j} \\ - 0 & \cdots & \cdots & 0 - & 1 & -2 & 1 \\ - \end{array} - \right] - -for :math:`l = 0` and - -.. math:: - :label: apx-offdiagonal - - A^l_j = - \left[ - \begin{array}{ccccccc} - 1 & 0 & \cdots & \cdots - & \cdots & \cdots & 0 \\ - 0 & a^{l,0}_{2,j} & \ddots & - & & & \vdots \\ - \vdots & \ddots & a^{l,0}_{3,j} & \ddots - & & & \vdots \\ - \vdots & & \ddots & \ddots - & \ddots & & \vdots \\ - \vdots & & & \ddots - & a^{l,0}_{n_{\mathrm{x}}-1,j} & \ddots & \vdots \\ - \vdots & & & - & \ddots & a^{l,0}_{n_{\mathrm{x}},j} & 0 \\ - 0 & \cdots & \cdots & \cdots - & \cdots & 0 & 1 \\ - \end{array} - \right] - -for :math:`l \neq 0`. The vectors :math:`\vec{\delta c}_{j,k}` and :math:`\vec{y}_{j,k}` -read: - -.. math:: - :label: c-array - - \begin{array}{rclrcl} - \vec{\delta c}_{j,k} &=& \left[ - \begin{array}{c} - \delta c^{n+1}_{1,j,k} \\ - \delta c^{n+1}_{2,j,k} \\ - \delta c^{n+1}_{3,j,k} \\ - \vdots \\ - \delta c^{n+1}_{n_{\mathrm{x}}-1,j,k} \\ - \delta c^{n+1}_{n_{\mathrm{x}},j,k} \\ - \delta c^{n+1}_{n_{\mathrm{x}}+1,j,k} \\ - \end{array} - \right] & ~ \mathrm{and} ~ - \vec{y}_{j,k} &=& \left[ - \begin{array}{c} - 0 \\ - y^n_{2,j,k} \\ - y^n_{3,j,k} \\ - \vdots \\ - y^n_{n_{\mathrm{x}}-1,j,k} \\ - y^n_{n_{\mathrm{x}},j,k} \\ - 0 \\ - \end{array} - \right] \\ - \end{array} - -:math:`n_{\mathrm{x}}` and :math:`n_{\mathrm{y}}` denote the number of -spatial grid cells in x- and y-direction. - -Iterations to solve for multiple fractions -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -The linear system defined in Equation :eq:`apx-system` is solved by a -sparse matrix solver for each sediment fraction separately in -ascending order of grain size. Initially, the weights -:math:`\hat{w}^{n+1}_{i,j,k}` are chosen according to the grain size -distribution in the bed and the air. The sediment availability -constraint is checked after each solve: - -.. math:: - :label: solve - - m_{\mathrm{a}} \geq \frac{\hat{w}^{n+1}_{i,j,k} c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \Delta t^n - -If the constraint if violated, a new estimate for the weights -is back-calculated following: - -.. math:: - :label: solve-weights - - \hat{w}^{n+1}_{i,j,k} = \frac{ c^{n+1}_{i,j,k} + m_{\mathrm{a}} \frac{T}{\Delta t^n} }{c^{n+1}_{\mathrm{sat},i,j,k}} - -The system is solved again using the new weights. This -procedure is repeated until a weight is found that does not violate -the sediment availability constraint. If the time step is not too -large, the procedure typically converges in only a few -iterations. Finally, the weights of the larger grains are increased -proportionally as to ensure that the sum of all weights remains -unity. If no larger grains are defined, not enough sediment is -available for transport and the grid cell is truly -availability-limited. This situation should only occur occasionally as -the weights in the next time step are computed based on the new bed -composition and thus will be skewed towards the large fractions. If -the situation occurs regularly, the time step is chosen too large -compared to the rate of armoring. - -Euler Schemes in non-conservative form -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -Early model results relied on Euler schemes in a non conservative form. This allowed for a relatively easy implementation but did not guarantee mass conservation. In version 2 of AEOLIS the conservative form became the default. However, some users still use the older scheme. - -The formulation is discretized following a first order upwind scheme -assuming that the wind velocity :math:`u_z` is positive in both -x-direction and y-direction: - -.. math:: - :label: apx-explicit - - \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + - u^n_{z,\mathrm{x}} \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x_{i,j}} + - u^n_{z,\mathrm{y}} \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y_{i,j}} \\ = - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} - -in which :math:`n` is the time step index, :math:`i` and :math:`j` are -the cross-shore and alongshore spatial grid cell indices and :math:`k` -is the grain size fraction index. :math:`w` [-] is the weighting -factor used for the weighted addition of the saturated sediment -concentrations over all grain size fractions. - -The discretization can be generalized for any wind direction as: - -.. math:: - :label: apx-explicit-generalized - - \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + - u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + - u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \\ + - u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + - u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} = - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} - -in which: - -.. math:: - :label: apx-upwind1 - - \begin{array}{rclcrcl} - u^n_{z,\mathrm{x+}} &=& \max( 0, u^n_{z,\mathrm{x}} ) &;& u^n_{z,\mathrm{y+}} &=& \max( 0, u^n_{z,\mathrm{y}} ) \\ - u^n_{z,\mathrm{x-}} &=& \min( 0, u^n_{z,\mathrm{x}} ) &;& u^n_{z,\mathrm{y-}} &=& \min( 0, u^n_{z,\mathrm{y}} ) \\ - \end{array} - -and - -.. math:: - :label: apx-upwind2 - - \begin{array}{rclcrcl} - c^n_{i,j,k,\mathrm{x+}} &=& \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x} &;& - c^n_{i,j,k,\mathrm{y+}} &=& \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y} \\ - c^n_{i,j,k,\mathrm{x-}} &=& \frac{c^n_{i,j,k} - c^n_{i-1,j,k}}{\Delta x} &;& - c^n_{i,j,k,\mathrm{y-}} &=& \frac{c^n_{i,j,k} - c^n_{i,j-1,k}}{\Delta y} \\ - \end{array} - -Equation :eq:`apx-explicit-generalized` is explicit in -time and adheres to the Courant-Friedrich-Lewis (CFL) condition for -numerical stability. Alternatively, the advection equation can be -discretized implicitly in time for unconditional stability: - -.. math:: - :label: apx-implicit-generalized - - \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + - u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + - u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \\ + - u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + - u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} = - \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} - -Equation :eq:`apx-explicit-generalized` and -:eq:apx-implicit-generalized` can be rewritten as: +The vegetation density :math:`\rho_{\text{veg}}` can vary in space and time and is determined by the ratio of the actual vegetation height (hveg) +to the maximum vegetation height (:math:`h_{\text{veg,max}}`), and can vary between 0 and 1 (:cite:`DuranHerrmann2006`): .. math:: - :label: apx-explicit-rewritten - - c^{n+1}_{i,j,k} = c^n_{i,j,k} - \Delta t^n \left[ - u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + - u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \phantom{\frac{c^n_{i,j,k}}{T}} \right. \\ + \left. - u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + - u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} + - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] - -and + :label: Vegetation_density -.. math:: - :label: apx-implicit-rewritten - - c^{n+1}_{i,j,k} + \Delta t^n \left[ - u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + - u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \phantom{\frac{c^{n+1}_{i,j,k}}{T}} \right. \\ + \left. - u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + - u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} + - \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] = c^n_{i,j,k} + \rho_{\text{veg}} = \left( \frac{h_{\text{veg}}}{h_{\text{veg,max}}} \right)^2 -and combined using a weighted average: -.. math:: - :label: apx-combined - - c^{n+1}_{i,j,k} + \Gamma \Delta t^n \left[ - u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + - u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \phantom{\frac{c^{n+1}_{i,j,k}}{T}} \right. \\ + \left. - u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + - u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} + - \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] \\ = - c^n_{i,j,k} - (1 - \Gamma) \Delta t^n \left[ - u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + - u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \phantom{\frac{c^n_{i,j,k}}{T}} \right. \\ + \left. - u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + - u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} + - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] +This assumption is based on the idea that burying vegetation reduces its height, which indicates a decrease in +actual cover. The change in vegetation density per grid cell is directly linked to the alteration in vegetation +height within that specific cell. This height variation is influenced by both the growth rate of the vegetation and +the rate of sediment burial. If the vegetation density remains constant over time, it suggests either no +sedimentation or a growth rate equal to the rate of sediment burial within the cell. -in which :math:`\Gamma` is a weight that ranges from 0 -- 1 and -determines the implicitness of the scheme. The scheme is implicit with -:math:`\Gamma = 0`, explicit with :math:`\Gamma = 1` and semi-implicit -otherwise. :math:`\Gamma = 0.5` results in the semi-implicit Crank-Nicolson -scheme. +Growth and decay +^^^^^^^^^^^^^^^^^ -Equation :eq:`apx-upwind2` is back-substituted in Equation -:eq:`apx-combined`: +Vegetation growth and decay follow the model proposed by :cite:`DuranHerrmann2006`, modified to include :math:`\delta z_{\text{b,opt}}` +(m/year), representing sediment burial for optimal growth that shifts the peak of optimal growth: .. math:: - :label: apx-combined-substituted - - c^{n+1}_{i,j,k} + \Gamma \Delta t^n \left[ - u^{n+1}_{z,\mathrm{x+}} \frac{c^{n+1}_{i+1,j,k} - c^{n+1}_{i,j,k}}{\Delta x} + - u^{n+1}_{z,\mathrm{y+}} \frac{c^{n+1}_{i,j+1,k} - c^{n+1}_{i,j,k}}{\Delta y} \right. \\ + \left. - u^{n+1}_{z,\mathrm{x-}} \frac{c^{n+1}_{i,j,k} - c^{n+1}_{i-1,j,k}}{\Delta x} + - u^{n+1}_{z,\mathrm{y-}} \frac{c^{n+1}_{i,j,k} - c^{n+1}_{i,j-1,k}}{\Delta y} + - \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] \\ = - c^n_{i,j,k} - (1 - \Gamma) \Delta t^n \left[ - u^n_{z,\mathrm{x+}} \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x} + - u^n_{z,\mathrm{y+}} \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y} \right. \\ + \left. - u^n_{z,\mathrm{x-}} \frac{c^n_{i,j,k} - c^n_{i-1,j,k}}{\Delta x} + - u^n_{z,\mathrm{y-}} \frac{c^n_{i,j,k} - c^n_{i,j-1,k}}{\Delta y} + - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] + :label: changes_vegetation_height -and rewritten: + \frac{\delta h_{\text{veg}}}{\delta t} = V_{\text{ver}} \left(1 - \frac{h_{\text{veg}}}{h_{\text{veg,max}}}\right) - \gamma_{\text{veg}} \left| \frac{\delta z_{\text{b,veg}}}{\delta t} - \delta z_{\text{b,opt}} \right| -.. math:: - :label: apx-combined-rewritten - - \left[ 1 - \Gamma \left( - u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + - u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - - u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - - u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + - \frac{\Delta t^n}{T} - \right) - \right] c^{n+1}_{i,j,k} \\ + - \Gamma \left( - u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^{n+1}_{i+1,j,k} + - u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^{n+1}_{i,j+1,k} - %\right. \\ - \left. - u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^{n+1}_{i-1,j,k} - - u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^{n+1}_{i,j-1,k} - \right) \\ = - \left[ 1 + (1 - \Gamma) \left( - u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + - u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - - u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - - u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + - \frac{\Delta t^n}{T} - \right) - \right] c^n_{i,j,k} \\ + - (1 - \Gamma) \left( - u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^n_{i+1,j,k} + - u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^n_{i,j+1,k} - %\right. \\ - \left. - u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^n_{i-1,j,k} - - u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^n_{i,j-1,k} - \right) \\ - - \Gamma \hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - - (1 - \Gamma) \hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} +Here, :math:`\gamma_{\text{veg}}` (default = 1) is a sediment burial factor that accounts for the impact of +sediment burial on vegetation. The height of the vegetation (:math:`h_{\text{veg}}` in m) cannot be less than zero. +Vver represents the maximum vertical growth rate of vegetation given in m/year, while the sediment burial rate +:math:`\delta z_{\text{b,veg}}` [m] is determined as the bed level change per time step. By simply converting this +value to a bed level change per year multiple errors are induced, as the time scale over which the bed level change +actually occurs is much shorter than this one year. To compare the bed level change per time step with the +vegetation growth rate per year, an average bed level change is estimated over a specified time (default is one +day). This average is then extrapolated to an annual rate. This method ensures that sudden changes in the bed level +change over one time step are not used as an estimate of the total bed level change in one year, which would be far +too high. -and simplified: +The optimal growth rate for certain vegetation species in dune environments is depending upon sediment burial :cite:`Maun1998`. +The optimal burial rate for maximum vegetation growth for marram grass for the neighbouring Dutch +coast is around 0.31 m/year with a burying tolerance of 0.78 to 0.96 m burial/year :cite:`Nolet2018`. This +optimal value is used in the model. :math:`V_{\text{ver}}` contains information of meteorological and local +conditions that enhance or inhibit vegetation growth process :cite:`Danin1991`, :cite:`Hesp1991`. -.. math:: - :label: apx-combined-simplified - - a^{0,0}_{i,j} c^{n+1}_{i,j,k} + - a^{1,0}_{i,j} c^{n+1}_{i+1,j,k} + - a^{0,1}_{i,j} c^{n+1}_{i,j+1,k} - - a^{-1,0}_{i,j} c^{n+1}_{i-1,j,k} - - a^{0,-1}_{i,j} c^{n+1}_{i,j-1,k} = y_{i,j,k} +.. _fig-Veg_growth: -where the implicit coefficients are defined as: +.. figure:: /images/Veg_growth.png + :width: 600px + :align: center -.. math:: - :label: apx-implicitcoef - - \begin{array}{rclcrcl} - a^{0,0}_{i,j} &=& \left[1 - \Gamma \left( - u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + - u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - - u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - - u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + - \frac{\Delta t^n}{T} - \right) \right] \\ - a^{1,0}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} \\ - a^{0,1}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} \\ - a^{-1,0}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} \\ - a^{0,-1}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} \\ - \end{array} + A) The vegetation growth response varies with different vertical growth rates (example for Vver = 1 and 2 m/year). Optimal vegetation growth is determined by a burial rate of 0.31 + m/year, with a maximum vegetation height set at 1 m and a plant height of 0.5 m. Additionally, the growth response for varying burial factors is depicted (:math:`\lambda_{\text{veg}}` + = 1 and 2). B) Shear stress reduction for two different vegetation-related roughness parameters and vegetation densities (:math:`\Gamma` = 16 and 32). -and the explicit right-hand side as: +Vegetation can begin to grow through lateral propagation or random germination. Once established, it can continue +to grow and spread laterally. The uncertainties associated with random germination are handled on a cell-by-cell +basis using a probabilistic approach, similar to the cellular automata method described by Keijsers et al. (2016). +AeoLiS incorporates a germination probability, denoted as ρ_{ger}, for each grid cell. This probability is constant +across the domain, except in eroding grid cells (where bed elevation decreases), where ρ_{ger} is set to 0. Lateral +propagation is determined by identifying the boundaries between vegetated and non-vegetated cells, with the +parameter ρ_{lat} adjusting the likelihood of lateral propagation at these boundaries. -.. math:: - :label: apx-explicitrhs - - y^n_{i,j,k} = \left[ 1 + (1 - \Gamma) \left( - u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + - u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - - u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - - u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + - \frac{\Delta t^n}{T} - \right) - \right] c^n_{i,j,k} \\ + - (1 - \Gamma) \left( - u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^n_{i+1,j,k} + - u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^n_{i,j+1,k} - - u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^n_{i-1,j,k} - - u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^n_{i,j-1,k} - \right) \\ - - \Gamma \hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - - (1 - \Gamma) \hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} +Inundation +^^^^^^^^^^^^ -The offshore boundary is defined to be zero-flux, the -onshore boundary has a constant transport gradient and the lateral -boundaries are circular: -.. math:: - :label: apx-boundaryconditions - - \begin{array}{rclcrcl} - c^{n+1}_{1,j,k} &=& 0 \\ - c^{n+1}_{n_{\mathrm{x}}+1,j,k} &=& 2 c^{n+1}_{n_{\mathrm{x}},j,k} - c^{n+1}_{n_{\mathrm{x}}-1,j,k} \\ - c^{n+1}_{i,1,k} &=& c^{n+1}_{i,n_{\mathrm{y}}+1,k} \\ - c^{n+1}_{i,n_{\mathrm{y}}+1,k} &=& c^{n+1}_{i,1,k} \\ - \end{array} +Surface moisture +----------------- -Shear stress perturbation for non-perpendicular wind directions ---------------------------------------------------------------- +Wave runup, capillary rise from the beach groundwater, and precipitation periodically wet the intertidal beach +temporally increasing the shear velocity threshold ( +:numref:`fig-moisture-processes`). Infiltration and +evaporation subsequently dry the beach. -The shear stress perturbation π›Ώπœ is estimated following the analytical description of the influence of alow and smooth hill in the wind profile by Weng et al. (1991). The perturbation is given by the Fouriertransformed components of the shear stress perturbation in the unperturbed wind direction which are the functions π›Ώπœπ‘₯(π‘˜) and π›Ώπœπ‘¦(π‘˜). The x-direction is defined by the direction of the wind velocity 𝑣0 on a flat bed, while the y direction is then the transverse. +.. _fig-moisture-processes: -As a result, the perturbation theory can only estimate the shear stress induced by the morphology-wind interaction in parallel direction of wind. Therefore, model simulations were, up to now, limited to input wind directions parallel to the crossΒ­shore axis of the grid. +.. figure:: /images/moisture_processes.jpg + :align: center -To overcome this limitation and to allow for modelling directional winds, an overlaying computational grid is introduced in AeoLiS, which rotates with the changing wind direction per time step. By doing this, the shear stresses are always estimated in the positive x-direction of the computational grid. The following steps are executed for each time step: + Illustration of processes influencing the volumetric moisture content :math:`\theta` at the beach surface. -1. Create a computational grid alligned with the wind direction (set_computational_grid) -2. Add and fill buffer around the original grid -3. Populate computation grid by rotating it to the current wind direction and interpolate the original topography on it. Additionally, edges around -4. Compute the morphology-wind induced shear stress by using the perturbation theory -5. Add the only wind induced wind shear stresses to the computational grid -6. Rotate both the grids and the total shear stress results in opposite direction -7. Interpolate the total shear stress results from the computational grid to the original grid -8. Rotate the wind shear stress results and the original grid back to the original orientation +The structure of the surface moisture module and included processes are schematized in :numref:`fig-moisture-scheme`. +The resulting surface moisture is obtained by selecting the largest of the moisture contents computed +with the water balance approach (right column) and due to capillary rise from the groundwater table (left column). +The method is based on the assumption that the flow of soil water is small compared to the flow of groundwater +and that the beach groundwater dynamics primarily is controlled by the water level and wave action at +the seaward boundary :cite:`Raubenheimer1999`, :cite:`Schmutz2014`. Thus, there is no feedback between the processes +in the right column of :numref:`fig-moisture-scheme` and the groundwater dynamics described in the left column. -.. note:: - The extra rotations in the last two steps are necessary as a simplified, but faster in terms of computational time, interpolation method is used. +.. _fig-moisture-scheme: +.. figure:: /images/moisture_scheme.jpg + :width: 600px + :align: center -Multi-fraction Erosion and Deposition -------------------------------------- + Implementation of surface moisture processes in the AeoLiS. -The formulation for the equilibrium or saturated sediment -concentration :math:`c_{\mathrm{sat}}` (Equation -:eq:`equilibrium-conc`) is capable of dealing with variations in -grain size through the variables :math:`u_{\mathrm{th}}`, -:math:`d_{\mathrm{n}}` and :math:`C` :cite:`Bagnold1937a`. However, -the transport formulation only describes the saturated sediment -concentration assuming a fixed grain size distribution, but does not -define how multiple fractions coexist in transport. If the saturated -sediment concentration formulation would be applied to each fraction -separately and summed up to a total transport, the total sediment -transport would increase with the number of sediment fractions. Since -this is unrealistic behavior the saturated sediment concentration -:math:`c_{\mathrm{sat}}` for the different fractions should be -weighted in order to obtain a realistic total sediment -transport. Equation :eq:`erodep` therefore is modified to include a -weighting factor :math:`\hat{w}_k` in which :math:`k` represents the -sediment fraction index: + +Runup and wave setup +^^^^^^^^^^^^^^^^^^^^ +The runup height and wave setup are computed using the Stockdon formulas :cite:`Stockdon2006`. +Their parameterization differs depending on the dynamic beach steepness expressed through the Irribaren number: .. math:: - :label: erodep_multi - - E_k - D_k = \min \left ( \frac{\partial m_{\mathrm{a},k}}{\partial t} \quad ; \quad \frac{\hat{w}_k \cdot c_{\mathrm{sat},k} - c_k}{T} \right ) + :label: irribaren + + \xi = \tan \beta /\sqrt {{H_0}/{L_0}} -It is common to use the grain size distribution in the bed as -weighting factor for the saturated sediment concentration -(e.g. :cite:`Delft3DManual`, section 11.6.4). Using the grain size -distribution at the bed surface as a weighting factor assumes, in case -of erosion, that all sediment at the bed surface is equally exposed to -the wind. +where :math:`{H_0}` is the significant offshore wave height, :math:`{L_0}` is the deepwater wavelength, and :math:`{\tan \beta}` is the foreshore slope. -Using the grain size distribution at the bed surface as weighting -factor in case of deposition would lead to the behavior where -deposition becomes dependent on the bed composition. Alternatively, in -case of deposition, the saturated sediment concentration can be -weighted based on the grain size distribution in the air. Due to the -nature of saltation, in which continuous interaction with the bed -forms the saltation cascade, both the grain size distribution in the -bed and in the air are likely to contribute to the interaction between -sediment fractions. The ratio between both contributions in the model -is determined by a bed interaction parameter :math:`\zeta`. +For dissipative conditions, :math:`{\xi}` < 0.3, the runup, :math:`{R_2}`, is parameterized as, -The weighting of erosion and deposition of individual fractions is -computed according to: +.. math:: + :label: runup_dissipative + + {R_2} = 0.043\sqrt {{H_0}{L_0}} + +and wave setup: .. math:: - :label: weigh + :label: setup_dissipative - \begin{align} - \hat{w}_k &= \frac{w_k}{ \sum_{k=1}^{n_{\mathrm{k}}}{w_k} } \\ - \mathrm{where} \quad w_k &= (1 - \zeta) \cdot w^{\mathrm{air}}_k + (1 - \hat{S}_k) \cdot w^{\mathrm{bed}}_k - \end{align} + < \eta > = 0.02\sqrt {{H_0}{L_0}} -in which :math:`k` represents the sediment fraction index, -:math:`n_{\mathrm{k}}` the total number of sediment fractions, :math:`w_k` is the -unnormalized weighting factor for fraction :math:`k`, :math:`\hat{w}_k` is its -normalized counterpart, :math:`w^{\mathrm{air}}_k` and :math:`w^{\mathrm{bed}}_k` -are the weighting factors based on the grain size distribution in the -air and bed respectively and :math:`\hat{S}_k` is the effective sediment -saturation of the air. The weighting factors based on the grain size -distribution in the air and the bed are computed using mass ratios: +For :math:`{\xi}` > 0.3, runup is paramterized as, .. math:: - :label: weights - - w^{\mathrm{air}}_k = \frac{c_k}{c_{\mathrm{sat},k}} \quad ; \quad - w^{\mathrm{bed}}_k = \frac{m_{\mathrm{a},k}}{\sum_{k=1}^{n_{\mathrm{k}}}{m_{\mathrm{a},k}}} + :label: runup + + {R_2} = 1.1\left( {0.35\beta \sqrt {{H_0}{L_0}} + \frac{{\sqrt {{H_0}{L_0}\left( {0.563{\beta ^2} + 0.004} \right)} }}{2}} \right) -The sum of the ratio :math:`w^{\mathrm{air}}_k` over the fractions -denotes the degree of saturation of the air column for fraction -:math:`k`. The degree of saturation determines if erosion of a fraction may -occur. Also in saturated situations erosion of a sediment fraction can -occur due to an exchange of momentum between sediment fractions, which -is represented by the bed interaction parameter :math:`\zeta`. The effective -degree of saturation is therefore also influenced by the bed -interaction parameter and defined as: +and wave setup: .. math:: - :label: saturation + :label: setup - \hat{S}_k = \min \left ( 1 \quad ; \quad (1 - \zeta) \cdot \sum_{k=1}^{n_{\mathrm{k}}} w_k^{\mathrm{air}} \right ) + < \eta > = 0.35\xi -When the effective saturation is greater than or equal to unity the -air is (over)saturated and no erosion will occur. The grain size -distribution in the bed is consequently less relevant and the second -term in Equation :eq:`weights` is thus minimized and zero in case -:math:`\zeta = 0`. In case the effective saturation is less than unity erosion -may occur and the grain size distribution of the bed also contributes -to the weighting over the sediment fractions. The weighting factors -for erosion are then composed from both the grain size distribution in -the air and the grain size distribution at the bed surface. Finally, -the resulting weighting factors are normalized to sum to unity over -all fractions (:math:`\hat{w}_k`). -The composition of weighting factors for erosion is based on the -saturation of the air column. The non-saturated fraction determines -the potential erosion of the bed. Therefore the non-saturated fraction -can be used to scale the grain size distribution in the bed in order -to combine it with the grain size distribution in the air according to -Equation :eq:`weights`. The non-saturated fraction of the air column -that can be used for scaling is therefore :math:`1 - \hat{S}_k`. +Tide- and wave-induced groundwater variations +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -For example, if bed interaction is disabled (:math:`\zeta = 0`) and -the air is 70\% saturated, then the grain size distribution in the air -contributes 70\% to the weighting factors for erosion, while the grain -size distribution in the bed contributes the other 30\% (Figure -:numref:`fig-bed-interaction-parameter`, upper left panel). In case of -(over)saturation the grain size distribution in transport contributes -100\% to the weighting factors and the grain size distribution in the -bed is of no influence. Transport progresses in downwind direction -without interaction with the bed. +Groundwater under sandy beaches can be considered as shallow aquifers, with only horizontal groundwater +flow so that the pressure distribution is hydrostatic :cite:`Baird1998,Brakenhoff2019,Nielsen1990,Raubenheimer1999`. +The cross-shore flow dominates temporal variations of groundwater levels. Alongshore, groundwater table variations are typically small :cite:`Schmutz2014`. +Although the surface moisture model can be extended over a two-dimensional grid, the groundwater simulations are performed for 1D transects cross-shore +to avoid numerical instabilities at the seaward boundary and reduce computational time. -.. _fig-bed-interaction-parameter: +The beach aquifers is schematised as a sandy body, with saturated hydraulic conductivity, :math:`K`, and effective porosity, :math:`{n_e}`. +The aquifer is assumed to rest on an impermeable surface, where :math:`D` is the aquifer depth. +The groundwater elevation relative to the mean sea level (MSL) is denoted :math:`\eta`, and the shore-perpendicular x-axis is positive landwards, +with an arbitrary starting point. The sand is assumed to be homogenous and isotropic. In this context, isotropy implies that hydraulic conductivity +is independent of flow direction. -.. figure:: /images/bed_interaction_parameter.png - :width: 600px - :align: center +The horizontal groundwater discharge per unit area, :math:`u`, is then governed by Darcy’s law, - Contributions of the grain size distribution in the bed and in the - air to the weighting factors :math:`\hat{w}_k` for the equilibrium - sediment concentration in Equation :eq:`erodep_multi` for different - values of the bed interaction parameter. +.. math:: + :label: gw-discharge + + u = - K\frac{{\partial \eta }}{{\partial x}} -To allow for bed interaction in saturated situations in which no net -erosion can occur, the bed interaction parameter :math:`\zeta` is used (Figure -:numref:`fig-bed-interaction-parameter`). The bed interaction parameter -can take values between 0.0 and 1.0 in which the weighting factors for -the equilibrium or saturated sediment concentration in an -(over)saturated situation are fully determined by the grain size -distribution in the bed or in the air respectively. A bed interaction -value of 0.2 represents the situation in which the grain size -distribution at the bed surface contributes 20\% to the weighting of -the saturated sediment concentration over the fractions. In the -example situation where the air is 70\% saturated such value for the -bed interaction parameter would lead to weighting factors that are -constituted for :math:`70\% \cdot (100\% - 20\%) = 56\%` based on the grain -size distribution in the air and for the other 44\% based on the grain -size distribution at the bed surface (Figure -:numref:`fig-bed-interaction-parameter`, upper right panel). +and the continuity equation (see e.g., :cite:`Nielsen2009`), -The parameterization of the exchange of momentum between sediment -fractions is an aspect of saltation that is still poorly -understood. Therefore calibration of the bed interaction parameter -:math:`\zeta` is necessary. The model parameters in Equation -:eq:`equilibrium-conc` can be chosen in accordance with the -assumptions underlying multi-fraction sediment transport. :math:`C` should -be set to 1.5 as each individual sediment fraction is well-sorted, -:math:`d_{\mathrm{n}}` should be chosen equal to :math:`D_{\mathrm{n}}` as the -grain size dependency is implemented through -:math:`u_{\mathrm{th}}`. :math:`u_{\mathrm{th}}` typically varies between 1 and 6 -m/s for sand. +.. math:: + :label: gw-continuity -Vegetation ------------- + \frac{{\partial \eta }}{{\partial t}} = - \frac{1}{{{n_e}}}\frac{\partial }{{\partial x}}((D + \eta )u) -The text below is based on :cite:`Strypsteen2024` +where :math:`t` is time. -In AeoLiS, the influence of vegetation on dune evolution is comprehensively -addressed. This includes modelling the intrinsic growth of vegetation, -accounting for factors such as growth and decay due to burial :cite:`DuranMoore2013`, -lateral expansion and establishment :cite:`Keijsers2016`, as well as simulating -the destruction of vegetation caused by hydrodynamic processes. In the event of -cell inundation, vegetation density is reduced as a result. Inspired by the -Coastal Dune Model (CDM) proposed by :cite:`DuranMoore2013`, AeoLiS incorporates -vegetation-wind interaction using the expression established by :cite:`DuranHerrmann2006`: +The groundwater overheight due to runup, :math:`{U_l}`, is computed by :cite:`Kang1994,Nielsen1988`, + +.. math:: + :label: gw-runup + + {U_l} = \left\{ \begin{gathered}{C_l}Kf(x)\,\,\,\,{\text{if }}{x_S} \leqslant x \leqslant {x_R} \hfill \\0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{if }}x > {x_R} \hfill \\\end{gathered} \right. + +where :math:`{C_l}` is an infiltration coefficient (-), and :math:`f(x)` is a function of :math:`x` ranging from 0 to 1. :math:`{x_S}` is +the horizontal location of the sum of the still water level and wave setup, and :math:`{x_R}` is the horizontal location of the runup limit: + +.. math:: + :label: gw-runup-distribution + + f(x) = \left\{ \begin{gathered} + \frac{{x - {x_s}}}{{\frac{2}{3}\left( {{x_{ru}} - {x_s}} \right)}}\,\,\,\,\,\,\,\,\,\,\,\,\,if\,{x_s} < x \leqslant {x_s} + \frac{2}{3}\left( {{x_{ru}} - {x_s}} \right)\, \hfill \\ + 3 - \frac{{x - {x_s}}}{{\frac{1}{3}\left( {{x_{ru}} - {x_s}} \right)}}\,\,\,\,\,if\,{x_s} + \frac{2}{3}\left( {{x_{ru}} - {x_s}} \right)\, < x < {x_{ru}} \hfill \\ + \end{gathered} \right. + +Substitution of :math:`u` (Equation :eq:`gw-discharge`) in the continuity equation (Equation :eq:`gw-continuity`) with the addition of :math:`{U_l}/{n_e}` gives the nonlinear Boussinesq equation: + +.. math:: + :label: boussinesq + + \frac{{\partial \eta }}{{\partial t}} = \frac{K}{{{n_e}}}\frac{\partial }{{\partial x}}\left( {(D + \eta )\frac{{\partial \eta }}{{\partial x}}} \right) + \frac{{{U_l}}}{{{n_e}}} + +Numerical solution of the Boussinesq groundwater equation +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +The Boussinesq equation is solved numerically with a central finite difference +method in space and a fourth-order Runge-Kutta integration technique in time: .. math:: - :label: shear_reduction_vegetation - - \frac{u_{\text{veg}}}{u_*} = \frac{1}{\sqrt{1 + \Gamma \rho_{\text{veg}}}} - + :label: solve-boussinesq -where the ratio of shear velocity in the presence of vegetation (:math:`u_{*,\text{veg}}`) to the unobstructed -shear velocity (:math:`u_*`) is determined by a vegetation-related roughness parameter (:math:`\Gamma`) and the -vegetation density within a unit area of the grid cell (\rho_{\text{veg}}). In the model, :math:`\Gamma` = 16 is derived -from plant form drag and geometry values documented for creosote communities :cite:`DuranHerrmann2006`. -This implementation calculates the expression on each model grid cell, with higher vegetation density -(expressed by \rho_{\text{veg}}) leading to a more substantial reduction in shear velocity compared to sparse -vegetation. By integrating these physical and ecological processes, AeoLiS simulates spatial patterns and temporal -variations in sediment transport and morphological changes resulting from aeolian processes in coastal -environments. + f(\eta ) = \frac{K}{{{n_e}}}\left[ {D\underbrace {\frac{{{\partial ^2}\eta }}{{\partial {x^2}}}}_a + \underbrace {\frac{\partial }{{\partial x}}\underbrace {\left\{ {\eta \frac{{\partial \eta }}{{\partial x}}} \right\}}_b}_c} \right] -\rho_{\text{veg}} can vary in space and time and is determined by the ratio of the actual vegetation height (hveg) -to the maximum vegetation height (:math:`h_{\text{veg,max}}`), and can vary between 0 and 1 (:cite:`DuranHerrmann2006`): +The Runge-Kutta time-stepping, where :math:`\Delta t` is the length of the timestep, is defined as, .. math:: - :label: Vegetation_density - - \rho_{\text{veg}} = \left( \frac{h_{\text{veg}}}{h_{\text{veg,max}}} \right)^2 - + :label: runge-kutta + + \begin{gathered} + \eta _i^{t + 1} = \eta _i^t + \frac{{\Delta t}}{6}\left( {{f_1} + 2{f_2} + 2{f_3} + {f_4}} \right) \hfill \\ + {f_1} = f(\eta _i^t) \hfill \\ + {f_2} = f\left( {\eta _i^t + \frac{{\Delta t}}{2}{f_1}} \right) \hfill \\ + {f_3} = f\left( {\eta _i^t + \frac{{\Delta t}}{2}{f_2}} \right) \hfill \\ + {f_4} = f\left( {\eta _i^t + \Delta t{f_3}} \right) \hfill \\ + \end{gathered} -This assumption is based on the idea that burying vegetation reduces its height, which indicates a decrease in -actual cover. The change in vegetation density per grid cell is directly linked to the alteration in vegetation -height within that specific cell. This height variation is influenced by both the growth rate of the vegetation and -the rate of sediment burial. If the vegetation density remains constant over time, it suggests either no -sedimentation or a growth rate equal to the rate of sediment burial within the cell. Vegetation growth and decay -follow the model proposed by :cite:`DuranHerrmann2006`, modified to include :math:`\delta z_{\text{b,opt}}` -(m/year), representing sediment burial for optimal growth that shifts the peak of optimal growth: +where, :math:`i` is the grid cell in x-direction and :math:`t` is the timestep. The central difference solution to :math:`f(\eta)` is obtained through discretisation of the Boussinesq equation, .. math:: - :label: changes_vegetation_height + :label: a-solve + + {a_i} = \frac{{\eta _{i + 1}^{} - 2\eta _i^{} + \eta _{i - 1}^{}}}{{{{(\Delta x)}^2}}} - \frac{\delta h_{\text{veg}}}{\delta t} = V_{\text{ver}} \left(1 - \frac{h_{\text{veg}}}{h_{\text{veg,max}}}\right) - \gamma_{\text{veg}} \left| \frac{\delta z_{\text{b,veg}}}{\delta t} - \delta z_{\text{b,opt}} \right| +.. math:: + {b_i} = \frac{{\eta _i^{}\left( {\eta _{i + 1}^{} - \eta _{i - 1}^{}} \right)}}{{\Delta x}} -Here, :math:`\gamma_{\text{veg}}` (default = 1) is a sediment burial factor that accounts for the impact of -sediment burial on vegetation. The height of the vegetation (:math:`h_{\text{veg}}` in m) cannot be less than zero. -Vver represents the maximum vertical growth rate of vegetation given in m/year, while the sediment burial rate -:math:`\delta z_{\text{b,veg}}` [m] is determined as the bed level change per time step. By simply converting this -value to a bed level change per year multiple errors are induced, as the time scale over which the bed level change -actually occurs is much shorter than this one year. To compare the bed level change per time step with the -vegetation growth rate per year, an average bed level change is estimated over a specified time (default is one -day). This average is then extrapolated to an annual rate. This method ensures that sudden changes in the bed level -change over one time step are not used as an estimate of the total bed level change in one year, which would be far -too high. +.. math:: + {c_i} = \frac{{\left( {b_{i + 1}^{} - b_{i - 1}^{}} \right)}}{{\Delta x}} -The optimal growth rate for certain vegetation species in dune environments is depending upon sediment burial :cite:`Maun1998`. -The optimal burial rate for maximum vegetation growth for marram grass for the neighbouring Dutch -coast is around 0.31 m/year with a burying tolerance of 0.78 to 0.96 m burial/year :cite:`Nolet2018`. This -optimal value is used in the model. :math:`V_{\text{ver}}` contains information of meteorological and local -conditions that enhance or inhibit vegetation growth process :cite:`Danin1991`, :cite:`Hesp1991`. +The seaward boundary condition is defined as the still water level plus the wave setup . +If the groundwater elevation is larger than the bed elevation, there is a seepage face, +and the groundwater elevation is set equal to the bed elevation. On the landward boundary, +a no-flow condition, :math:`\frac{{\partial \eta }}{{\partial t}} = 0` (Neumann condition), or constant head, :math:`\eta = constant` (Dirichlet condition), is prescribed. -.. _fig-Veg_growth: +Capillary rise +^^^^^^^^^^^^^^ +Soil water retention (SWR) functions describe the surface moisture due to capillary transport +of water from the groundwater table :cite:`VanGenuchten1980`: -.. figure:: /images/Veg_growth.png - :width: 600px - :align: center +.. math:: + :label: vangenuchten - A) The vegetation growth response varies with different vertical growth rates (example for Vver = 1 and 2 m/year). Optimal vegetation growth is determined by a burial rate of 0.31 - m/year, with a maximum vegetation height set at 1 m and a plant height of 0.5 m. Additionally, the growth response for varying burial factors is depicted (:math:`\lambda_{\text{veg}}` - = 1 and 2). B) Shear stress reduction for two different vegetation-related roughness parameters and vegetation densities (:math:`\Gamma` = 16 and 32). + \theta (h) = {\theta _r} + \frac{{{\theta _s} - {\theta _r}}}{{{{\left[ {1 + {{\left| {\alpha h} \right|}^n}} \right]}^m}}} -Vegetation can begin to grow through lateral propagation or random germination. Once established, it can continue -to grow and spread laterally. The uncertainties associated with random germination are handled on a cell-by-cell -basis using a probabilistic approach, similar to the cellular automata method described by Keijsers et al. (2016). -AeoLiS incorporates a germination probability, denoted as ρ_{ger}, for each grid cell. This probability is constant -across the domain, except in eroding grid cells (where bed elevation decreases), where ρ_{ger} is set to 0. Lateral -propagation is determined by identifying the boundaries between vegetated and non-vegetated cells, with the -parameter ρ_{lat} adjusting the likelihood of lateral propagation at these boundaries. -Simulation of Sediment Sorting and Beach Armoring -------------------------------------------------- +where :math:`h` is the groundwater table depth, :math:`\alpha` and :math:`n` are fitting parameters +related to the air entry suction and the pore size distribution. The parameter :math:`m` is commonly +parameterised as :math:`m = 1 - 1/n`. -Since the equilibrium or saturated sediment concentration -:math:`c_{\mathrm{sat},k}` is weighted over multiple sediment fractions in -the extended advection model, also the instantaneous sediment -concentration :math:`c_k` is computed for each sediment fraction -individually. Consequently, grain size distributions may vary over the -model domain and in time. These variations are thereby not limited to -the horizontal, but may also vary over the vertical since fine -sediment may be deposited on top of coarse sediment or, reversely, -fines may be eroded from the bed surface leaving coarse sediment to -reside on top of the original mixed sediment. In order to allow the -model to simulate the processes of sediment sorting and beach armoring -the bed is discretized in horizontal grid cells and vertical bed -layers (2DV; Figure :numref:`fig-bedcomposition`). +The resulting surface moisture is computed for both drying and +wetting conditions, i.e., including the +effect of hysteresis. The moisture contents computed with drying and wetting SWR functions are denoted :math:`{\theta ^d}(h)` and :math:`{\theta ^w}(h)`, respectively. +When moving between wetting and drying conditions, the soil moisture content follows an intermediate +retention curve called a scanning curve. The drying scanning curves are scaled from the main +drying curve and wetting scanning curves from the main wetting curve. The drying scanning curve is then obtained from :cite:`Mualem1974`: -The discretization of the bed consists of a minimum of three vertical -bed layers with a constant thickness and an unlimited number of -horizontal grid cells. The top layer is the *bed surface layer* and is -the only layer that interacts with the wind and hence determines the -spatiotemporal varying sediment availability and the contribution of -the grain size distribution in the bed to the weighting of the -saturated sediment concentration. One or more *bed composition layers* -are located underneath the bed surface layer and form the upper part -of the erodible bed. The bottom layer is the *base layer* and contains -an infinite amount of erodible sediment according to the initial grain -size distribution. The base layer cannot be eroded, but can supply -sediment to the other layers. +.. math:: + :label: mualem-drying -.. _fig-bedcomposition: + {\theta ^d}({h_\Delta },h) = {\theta ^w}(h) + \frac{{\left[ {{\theta ^w}({h_\Delta }) - {\theta ^w}(h)} \right]}}{{\left[ {{\theta _s} - {\theta ^w}(h)} \right]}}\left[ {{\theta ^d}(h) - {\theta ^w}(h)} \right] -.. figure:: /images/bed_composition.png - :align: center +where :math:`{h_\Delta}` is the groundwater table depth at the reversal on the wetting curve. - Schematic of bed composition discretisation and advection - scheme. Horizontal exchange of sediment may occur solely through - the air that interacts with the *bed surface layer*. The detail - presents the simulation of sorting and beach armoring where the bed - surface layer in the upwind grid cell becomes coarser due to - non-uniform erosion over the sediment fractions, while the bed - surface layer in the downwind grid cell becomes finer due to - non-uniform deposition over the sediment fractions. Symbols refer - to Equations :eq:`advection` and :eq:`erodep`. +The wetting scanning curve is obtained from :cite:`Mualem1974`: -Each layer in each grid cell describes a grain size distribution over -a predefined number of sediment fractions (Figure -:numref:`fig-bedcomposition`, detail). Sediment may enter or leave a -grid cell only through the bed surface layer. Since the velocity -threshold depends among others on the grain size, erosion from the bed -surface layer will not be uniform over all sediment fractions, but -will tend to erode fines more easily than coarse sediment (Figure -:numref:`fig-bedcomposition`, detail, upper left panel). If sediment -is eroded from the bed surface layer, the layer is repleted by -sediment from the lower bed composition layers. The repleted sediment -has a different grain size distribution than the sediment eroded from -the bed surface layer. If more fines are removed from the bed surface -layer in a grid cell than repleted, the median grain size -increases. If erosion of fines continues the bed surface layer becomes -increasingly coarse. Deposition of fines or erosion of coarse material -may resume the erosion of fines from the bed. +.. math:: + :label: mualem-wetting + + {\theta ^w}({h_\Delta },h) = {\theta ^w}(h) + \frac{{\left[ {{\theta _s} - {\theta ^w}(h)} \right]}}{{\left[ {{\theta _s} - {\theta ^w}({h_\Delta })} \right]}}\left[ {{\theta ^d}({h_\Delta }) - {\theta ^w}({h_\Delta })} \right] -In case of deposition the process is similar. Sediment is deposited in -the bed surface layer that then passes its excess sediment to the -lower bed layers (Figure :numref:`fig-bedcomposition`, detail, upper -right panel). If more fines are deposited than passed to the lower bed -layers the bed surface layer becomes increasingly fine. +where :math:`{h_\Delta}` is the groundwater table depth at the reversal on the drying curve. -Simulation of the Emergence of Non-erodible Roughness Elements --------------------------------------------------------------- +Infiltration +^^^^^^^^^^^^ +Infiltration is accounted for by assuming that excess water infiltrates until the moisture content reaches +field capacity, :math:`{\theta_fc}`. The moisture content at field capacity is the maximum amount of water +that the unsaturated zone of soil can hold against the pull of gravity. For sandy soils, +the matric potential at this soil moisture condition is around - 1/10 bar. In equilibrium, +this potential would be exerted on the soil capillaries at the soil surface when the water +table is about 100 cm below the soil surface, :math:`{\theta _{fc}} = {\theta ^d}(100)`. -Sediment sorting may lead to the emergence of non-erodible elements -from the bed. Non-erodible roughness elements may shelter the erodible -bed from wind erosion due to shear partitioning, resulting in a -reduced sediment availability :cite:`Raupach1993`. Therefore the -equation of :cite:`Raupach1993` is implemented according to: +Infiltration is represented by an +exponential decay function that is governed by a drying time scale +:math:`T_{\mathrm{dry}}`. Exploratory model runs of the unsaturated soil with the HYDRUS1D +:cite:`Simunek1998` hydrology model show that the increase of the +volumetric water content to saturation is almost instantaneous with +rising tide. The drying of the beach surface through infiltration +shows an exponential decay. In order to capture this behavior the +volumetric water content is implemented according to: .. math:: - :label: raupach - - u_{\mathrm{* th, R}} = u_{\mathrm{* th}} \cdot \sqrt{ \left( 1 - m \cdot \sum_{k=k_0}^{n_{\mathrm{k}}}{w_k^{\mathrm{bed}}} \right) \left( 1 + \frac{m \beta}{\sigma} \cdot \sum_{k=k_0}^{n_{\mathrm{k}}}{w_k^{\mathrm{bed}}} \right) } + :label: infiltration -in which :math:`\sigma` is the ratio between the frontal area and the -basal area of the roughness elements and :math:`\beta` is the ratio -between the drag coefficients of the roughness elements and the bed -without roughness elements. :math:`m` is a factor to account for the -difference between the mean and maximum shear stress and is usually -chosen 1.0 in wind tunnel experiments and may be lowered to 0.5 for -field applications. The roughness density :math:`\lambda` in the -original equation of :cite:`Raupach1993` is obtained from the mass -fraction in the bed surface layer :math:`w_k^{\mathrm{bed}}` according -to: + \frac{{d\theta }}{{dt}} = \left( {\theta - {\theta _{fc}}} \right)\left( {{e^{ - \ln (2)\frac{{dt}}{{{T_{dry}}}}}}} \right) + +An alternative formulation is used for simulations that does not account for ground water and SWR processes, .. math:: - :label: rough + :label: apx-drying - \lambda = \frac{\sum_{k=k_0}^{n_{\mathrm{k}}}{w_k^{\mathrm{bed}}}}{\sigma} + p_{\mathrm{V}}^{n+1} = \left\{ + \begin{array}{ll} + p & \mathrm{if} ~ \eta > z_{\mathrm{b}} \\ + p_{\mathrm{V}}^n \cdot e^{\frac{\log \left( 0.5 \right)}{T_{\mathrm{dry}}} \cdot \Delta t^n} - E_{\mathrm{v}} \cdot \frac{\Delta t^n}{\Delta z} & \mathrm{if} ~ \eta \leq z_{\mathrm{b}} \\ + \end{array} + \right. -in which :math:`k_0` is the index of the smallest non-erodible -sediment fraction in current conditions and :math:`n_{\mathrm{k}}` is the -total number of sediment fractions. It is assumed that the sediment -fractions are ordered by increasing size. Whether a fraction is -erodible depends on the sediment transport capacity. +where :math:`\eta` [m+MSL] is the instantaneous water level, +:math:`z_{\mathrm{b}}` [m+MSL] is the local bed elevation, +:math:`p_{\mathrm{V}}^n` [-] is the volumetric water content in time step +:math:`n`, :math:`\Delta t^n` [s] is the model time step and :math:`\Delta z` is the bed +composition layer thickness. :math:`T_{\mathrm{dry}}` [s] is the beach +drying time scale, defined as the time in which the beach moisture +content halves. -Simulation of the Hydraulic Mixing ----------------------------------- +Precipitation and evaporation +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +A water balance approach accounts for the effect of precipitation and evaporation, -As sediment sorting due to aeolian processes can lead to armoring of a -beach surface, mixing of the beach surface or erosion of course -material may undo the effects of armoring. To ensure a proper balance -between processes that limit and enhance sediment availability in the -model both types of processes need to be sufficiently represented when -simulating spatiotemporal varying bed surface properties and sediment -availability. +.. math:: + :label: precipitation -A typical upwind boundary in coastal environments during onshore winds -is the water line. For aeolian sediment transport the water line is a -zero-transport boundary. In the presence of tides, the intertidal -beach is flooded periodically. Hydraulic processes like wave breaking -mix the bed surface layer of the intertidal beach, break the beach -armoring and thereby influence the availability of sediment. + \frac{{d\theta }}{{dt}} = \frac{{\left( {P - E} \right)\,}}{{\Delta z}}\, -In the model the mixing of sediment is simulated by averaging the -sediment distribution over the depth of disturbance -(:math:`\Delta z_{\mathrm{d}}`). The depth of disturbance is linearly -related to the breaker height (e.g. :cite:`King1951`, :cite:`Williams1971`, :cite:`Masselink2007`). :cite:`Masselink2007` proposes an empirical factor -:math:`f_{\Delta z_{\mathrm{d}}}` [-] that relates the depth of disturbance -directly to the local breaker height according to: +where :math:`P` is the precipitation, :math:`E` is the evaporation, and :math:`\Delta z` is the thickness of the surface layer. + +Evaporation is simulated using an adapted version +of the Penman-Monteith equation :cite:`Shuttleworth1993` that is +governed by meteorological time series of solar radiation, temperature +and humidity. + +:math:`E_{\mathrm{v}}` [m/s] is the evaporation rate that is +implemented through an adapted version of the Penman equation +:cite:`Shuttleworth1993`: .. math:: - :label: disturbance_depth + :label: apx-penman - \Delta z_{\mathrm{d}} = f_{\Delta z_{\mathrm{d}}} \cdot \min \left ( H \quad ; \quad \gamma \cdot d \right ) + E_{\mathrm{v}} = \frac{m_{\mathrm{v}} \cdot R_{\mathrm{n}} + 6.43 \cdot \gamma_{\mathrm{v}} \cdot (1 + 0.536 \cdot u_2) \cdot \delta e} + {\lambda_{\mathrm{v}} \cdot (m_{\mathrm{v}} + \gamma_{\mathrm{v}})} \cdot 9 \cdot 10^7 -in which the offshore wave height :math:`H` [m] is taken as the -local wave height maximized by a maximum wave height over depth ratio -:math:`\gamma` [-]. :math:`d` [m] is the water depth that is provided to the model -through an input time series of water levels. Typical values for -:math:`f_{\Delta z_{\mathrm{d}}}` are 0.05 to 0.4 and 0.5 for :math:`\gamma`. +where :math:`m_{\mathrm{v}}` [kPa/K] is the slope of the +saturation vapor pressure curve, :math:`R_{\mathrm{n}}` +[:math:`\mathrm{MJ/m^2/day}`] is the net radiance, :math:`\gamma_{\mathrm{v}}` +[kPa/K] is the psychrometric constant, :math:`u_2` [m/s] is the wind speed +at 2 m above the bed, :math:`\delta e` [kPa] is the vapor pressure deficit +(related to the relative humidity) and :math:`\lambda_{\mathrm{v}}` [MJ/kg] +is the latent heat vaporization. To obtain an evaporation rate in +[m/s], the original formulation is multiplied by :math:`9 \cdot 10^7`. -Simulation of surface moisture ------------------------------- -Wave runup, capillary rise from the beach groundwater, and precipitation periodically wet the intertidal beach -temporally increasing the shear velocity threshold ( -:numref:`fig-moisture-processes`). Infiltration and -evaporation subsequently dry the beach. +Sand fences +------------ -.. _fig-moisture-processes: +Marine erosion +--------------- -.. figure:: /images/moisture_processes.jpg - :align: center - Illustration of processes influencing the volumetric moisture content :math:`\theta` at the beach surface. +Morphological change +--------------------- -The structure of the surface moisture module and included processes are schematized in :numref:`fig-moisture-scheme`. -The resulting surface moisture is obtained by selecting the largest of the moisture contents computed -with the water balance approach (right column) and due to capillary rise from the groundwater table (left column). -The method is based on the assumption that the flow of soil water is small compared to the flow of groundwater -and that the beach groundwater dynamics primarily is controlled by the water level and wave action at -the seaward boundary :cite:`Raubenheimer1999`, :cite:`Schmutz2014`. Thus, there is no feedback between the processes -in the right column of :numref:`fig-moisture-scheme` and the groundwater dynamics described in the left column. +Avalanching +^^^^^^^^^^^^ -.. _fig-moisture-scheme: +Wet bed reset +^^^^^^^^^^^^^^^^ -.. figure:: /images/moisture_scheme.jpg - :width: 600px - :align: center - Implementation of surface moisture processes in the AeoLiS. +Numerical implementation of the advection equation +-------------------------------------------------- -Runup and wave setup -^^^^^^^^^^^^^^^^^^^^ -The runup height and wave setup are computed using the Stockdon formulas :cite:`Stockdon2006`. -Their parameterization differs depending on the dynamic beach steepness expressed through the Irribaren number: +The advection equation is implemented in two-dimensional form +following: .. math:: - :label: irribaren + :label: apx-advection - \xi = \tan \beta /\sqrt {{H_0}/{L_0}} + \frac{\partial c}{\partial t} + + u_{z,\mathrm{x}} \frac{\partial c}{\partial x} + + u_{z,\mathrm{y}} \frac{\partial c}{\partial y} = + \frac{c_{\mathrm{sat}} - c}{T} -where :math:`{H_0}` is the significant offshore wave height, :math:`{L_0}` is the deepwater wavelength, and :math:`{\tan \beta}` is the foreshore slope. +in which :math:`c` [:math:`\mathrm{kg/m^2}`] is the sediment mass per +unit area in the air, :math:`c_{\mathrm{sat}}` [:math:`\mathrm{kg/m^2}`] is the +maximum sediment mass in the air that is reached in case of +saturation, :math:`u_{z,\mathrm{x}}` and :math:`u_{z,\mathrm{y}}` are the x- and +y-component of the wind velocity at height :math:`z` [m], :math:`T` [s] is an +adaptation time scale, :math:`t` [s] denotes time and :math:`x` [m] and :math:`y` [m] +denote cross-shore and alongshore distances respectively. -For dissipative conditions, :math:`{\xi}` < 0.3, the runup, :math:`{R_2}`, is parameterized as, +The formulation is discretized in different ways to allow for different types of simulations balancing accuracy vs. computational resources. The conservative method combined with an euler backward scheme (written by Prof. Rauwoens) is the current default for most simulations. Non-conservative methods end explicit Euler forward schemes are also available. + +Default scheme -- Conservative Euler Backward Implicit +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The default numerical method assumes the advection scheme in a conservative form in combination with an euler backward scheme. This scheme is prepared to use a TVD method but this is not implemented yet (add footnote{Total Variance Diminishing, this is explained in the lecture notes by Zijlema p94}) + +The fluxes at the interface of the cells are defined used in the advection terms: .. math:: - :label: runup_dissipative + :label: conservative1 - {R_2} = 0.043\sqrt {{H_0}{L_0}} + \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t} + \\ + \frac{u_{\text{x},i+1/2,j} \cdot c^{n+1}_{i+1/2,j,k} - u_{\text{x},i-1/2,j} \cdot c^{n+1}_{i-1/2,j,k}}{\Delta x} + \\ + \frac{u_{\text{y},i,j+1/2} \cdot c^{n+1}_{i,j+1/2,k} - u_{\text{y},i,j-1/2} \cdot c^{n+1}_{i,j-1/2,k}}{\Delta y} + + \\ = \\ + \frac{\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i.j.k} + c^{n+1}_{i,j,k} ) - c^{n+1}_{i,j,k}}{T} -and wave setup: +In which :math:`n` is the time step index, :math:`i` and :math:`j` are the cross-shore and alongshore spatial grid cell indices and :math:`k` is the grain size fraction index. :math:`w` [-] is the weighting factor used for the weighted addition of the saturated sediment concentrations over all grain size fractions. Note that u is spatially varying but has no temporal index. This is because u is a result of a separate wind solver and considered temporally invariant in the advection solver. + +Now we use a correction algorithm where: .. math:: - :label: setup_dissipative + :label: conservative2 - < \eta > = 0.02\sqrt {{H_0}{L_0}} + c^{n+1}_{i,j,k} = c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} + +where :math:`\delta c_{i,j,k}` is solved for and :math:`*` denotes the previous iteration. -For :math:`{\xi}` > 0.3, runup is paramterized as, +When now assuming an upwind scheme in space, we can derive 4 concentrations at the cell faces which are dependent on the velocity at the cell faces. + +We assume in x direction: .. math:: - :label: runup - - {R_2} = 1.1\left( {0.35\beta \sqrt {{H_0}{L_0}} + \frac{{\sqrt {{H_0}{L_0}\left( {0.563{\beta ^2} + 0.004} \right)} }}{2}} \right) -and wave setup: + c^{n+1}_{i+1/2,j,k} = + \begin{cases} + c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{x},i+1/2,j} > 0$,}\\ + c^{n+1 *}_{i+1,j,k} + \delta c_{i+1,j,k} & \text{if $u_{\text{x},i+1/2,j} < 0$.} + \end{cases} .. math:: - :label: setup + + c^{n+1}_{i-1/2,j,k} = + \begin{cases} + c^{n+1 *}_{i-1,j,k} + \delta c_{i-1,j,k} & \text{if $u_{\text{x},i-1/2,j} > 0$,}\\ + c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{x},i-1/2,j} < 0$.} + \end{cases} + +and in y-direction: + +.. math:: + + c^{n+1}_{i,j+1/2,k} = + \begin{cases} + c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{y},i,j+1/2} > 0$,}\\ + c^{n+1 *}_{i,j+1,k} + \delta c_{i,j+1,k} & \text{if $u_{\text{y},i,j+1/2} < 0$.} + \end{cases} + +.. math:: + + c^{n+1}_{i,j-1/2,k} = + \begin{cases} + c^{n+1 *}_{i,j-1,k} + \delta c_{i,j-1,k} & \text{if $u_{\text{y},i,j-1/2} > 0$,}\\ + c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{y},i,j-1/2} < 0$.} + \end{cases} + +Now we assume: + +- :math:`\Gamma_x = 1` if :math:`u_{\text{x},i+1/2,j,k} > 0` and :math:`\Gamma_x = 0` if :math:`u_{\text{x},i+1/2,j,k} \leq 0` +- :math:`\Gamma_y = 1` if :math:`u_{\text{y},i,j+1/2,k} > 0` and :math:`\Gamma_x = 0` if :math:`u_{\text{y},i,j+1/2,k} \leq 0` - < \eta > = 0.35\xi +(We did not test if this works well with diverging and converging flows. We may need another term that describes the conditions at the negative cell faces if they are of opposite direction than the positive cell faces and vice versa) +Let's continue for the moment so that -Tide- and wave-induced groundwater variations -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +.. math:: -Groundwater under sandy beaches can be considered as shallow aquifers, with only horizontal groundwater -flow so that the pressure distribution is hydrostatic :cite:`Baird1998,Brakenhoff2019,Nielsen1990,Raubenheimer1999`. -The cross-shore flow dominates temporal variations of groundwater levels. Alongshore, groundwater table variations are typically small :cite:`Schmutz2014`. -Although the surface moisture model can be extended over a two-dimensional grid, the groundwater simulations are performed for 1D transects cross-shore -to avoid numerical instabilities at the seaward boundary and reduce computational time. + \begin{gathered} + \frac{c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} - c^n_{i,j,k}}{\Delta t} + \\ + \Gamma_x \cdot \frac{u_{\text{x},i+1/2,j} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}) - u_{\text{x},i-1/2,j} \cdot (c^{n+1 *}_{i-1,j,k} + \delta c_{i-1,j,k})}{\Delta x} + \\ + (1-\Gamma_x) \cdot \frac{u_{\text{x},i+1/2,j} \cdot (c^{n+1 *}_{i+1,j,k} + \delta c_{i+1,j,k}) - u_{\text{x},i-1/2,j} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k})}{\Delta x} + \\ + \Gamma_y \cdot \frac{u_{\text{y},i,j+1/2} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}) - u_{\text{y},i,j-1/2} \cdot (c^{n+1 *}_{i,j-1,k} + \delta c_{i,j-1,k})}{\Delta y} + \\ + (1-\Gamma_y) \cdot \frac{u_{\text{y},i,j+1/2} \cdot (c^{n+1 *}_{i,j+1,k} + \delta c_{i,j+1,k}) - u_{\text{y},i,j-1/2} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k})}{\Delta y} + + \\ = \\ + \frac{\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i,j,k}+c^{n+1 *}_{i,j,k} + \xcancel{\delta c_{i,j,k}}) - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}}{T} + \end{gathered} -The beach aquifers is schematised as a sandy body, with saturated hydraulic conductivity, :math:`K`, and effective porosity, :math:`{n_e}`. -The aquifer is assumed to rest on an impermeable surface, where :math:`D` is the aquifer depth. -The groundwater elevation relative to the mean sea level (MSL) is denoted :math:`\eta`, and the shore-perpendicular x-axis is positive landwards, -with an arbitrary starting point. The sand is assumed to be homogenous and isotropic. In this context, isotropy implies that hydraulic conductivity -is independent of flow direction. +(note that the above does not take converging and diverging flows into account, also :math:`\delta c_{i,j,k}` at the right hand side in the "min" brackets is difficult to solve for. In the code, this term is neglected which may cause some inaccuracy when calculating pickup. Although mass continuity is corrected for in the implicit scheme when calculating pickup using equation ???) -The horizontal groundwater discharge per unit area, :math:`u`, is then governed by Darcy’s law, +Now we simplify: .. math:: - :label: gw-discharge - - u = - K\frac{{\partial \eta }}{{\partial x}} -and the continuity equation (see e.g., :cite:`Nielsen2009`), + \begin{gathered} + (\frac{\Delta x \Delta y}{\Delta t} + \Gamma_x\Delta y \cdot u_{\text{x},i+1/2,j} - (1-\Gamma_x)\Delta y \cdot u_{\text{x},i-1/2,j} + \Gamma_y\Delta x \cdot u_{\text{y},i,j+1/2}\\ - (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j-1/2}+\frac{\Delta x \Delta y}{T_s})\cdot \delta c_{i,j,k}\\ + -(\Gamma_x\Delta y \cdot u_{\text{x},i-1/2,j})\cdot \delta c_{i-1,j,k}\\ + +((1-\Gamma_x)\Delta y \cdot u_{\text{x},i+1/2,j})\cdot \delta c_{i+1,j,k}\\ + -(\Gamma_y\Delta x \cdot u_{\text{y},i,j-1/2})\cdot \delta c_{i,j-1,k}\\ + + ((1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j+1/2})\cdot \delta c_{i,j+1,k}\\ + \end{gathered} + +or .. math:: - :label: gw-continuity - \frac{{\partial \eta }}{{\partial t}} = - \frac{1}{{{n_e}}}\frac{\partial }{{\partial x}}((D + \eta )u) + \begin{gathered} + A0 \cdot \delta c_{i,j,k} + + A\text{m1} \cdot \delta c_{i-1,j,k} + + A\text{p1} \cdot \delta c_{i+1,j,k}\\ + + A\text{mx} \cdot \delta c_{i,j-1,k} + + A\text{px} \cdot \delta c_{i,j+1,k} = y_{i,j,k} + \label{eq:lin} + \end{gathered} -where :math:`t` is time. +or the linear system of equations in general form: -The groundwater overheight due to runup, :math:`{U_l}`, is computed by :cite:`Kang1994,Nielsen1988`, +.. math:: + :label: conservative_general + + A \cdot \delta c_{i,j,k} = y_{i,j,k} + +Where :math:`A` is a 3-dimensional sparse matrix that is compiled using the matrix diagonals (:math:`A0, Am1, Ap1, Amx, Apx`) which are defined as: + +.. math:: + + \begin{aligned} + A0 = & +\frac{\Delta x \Delta y}{\Delta t} \\ + & +\frac{\Delta x \Delta y}{T_s} \\ + & - (1-\Gamma_x)\Delta y \cdot u_{\text{x},i-1/2,j} \\ + & + \Gamma_x\Delta y \cdot u_{\text{x},i+1/2,j} \\ + & - (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j-1/2} \\ + & + \Gamma_y\Delta x \cdot u_{\text{y},i,j+1/2} \\ + \end{aligned} + +and .. math:: - :label: gw-runup - {U_l} = \left\{ \begin{gathered}{C_l}Kf(x)\,\,\,\,{\text{if }}{x_S} \leqslant x \leqslant {x_R} \hfill \\0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{if }}x > {x_R} \hfill \\\end{gathered} \right. + A\text{m}1 = -\Gamma_x\Delta y \cdot u_{\text{x},i-1/2,j} -where :math:`{C_l}` is an infiltration coefficient (-), and :math:`f(x)` is a function of :math:`x` ranging from 0 to 1. :math:`{x_S}` is -the horizontal location of the sum of the still water level and wave setup, and :math:`{x_R}` is the horizontal location of the runup limit: +and .. math:: - :label: gw-runup-distribution - f(x) = \left\{ \begin{gathered} - \frac{{x - {x_s}}}{{\frac{2}{3}\left( {{x_{ru}} - {x_s}} \right)}}\,\,\,\,\,\,\,\,\,\,\,\,\,if\,{x_s} < x \leqslant {x_s} + \frac{2}{3}\left( {{x_{ru}} - {x_s}} \right)\, \hfill \\ - 3 - \frac{{x - {x_s}}}{{\frac{1}{3}\left( {{x_{ru}} - {x_s}} \right)}}\,\,\,\,\,if\,{x_s} + \frac{2}{3}\left( {{x_{ru}} - {x_s}} \right)\, < x < {x_{ru}} \hfill \\ - \end{gathered} \right. + A\text{p}1 = (1-\Gamma_x)\Delta y \cdot u_{\text{x},i+1/2,j} -Substitution of :math:`u` (Equation :eq:`gw-discharge`) in the continuity equation (Equation :eq:`gw-continuity`) with the addition of :math:`{U_l}/{n_e}` gives the nonlinear Boussinesq equation: +and .. math:: - :label: boussinesq + A\text{mx} = -\Gamma_y\Delta x \cdot u_{\text{y},i,j-1/2} - \frac{{\partial \eta }}{{\partial t}} = \frac{K}{{{n_e}}}\frac{\partial }{{\partial x}}\left( {(D + \eta )\frac{{\partial \eta }}{{\partial x}}} \right) + \frac{{{U_l}}}{{{n_e}}} +and -Numerical solution of the Boussinesq groundwater equation -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -The Boussinesq equation is solved numerically with a central finite difference -method in space and a fourth-order Runge-Kutta integration technique in time: +.. math:: + + A\text{px} = (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j+1/2} + +Let's go towards the RHS .. math:: - :label: solve-boussinesq - f(\eta ) = \frac{K}{{{n_e}}}\left[ {D\underbrace {\frac{{{\partial ^2}\eta }}{{\partial {x^2}}}}_a + \underbrace {\frac{\partial }{{\partial x}}\underbrace {\left\{ {\eta \frac{{\partial \eta }}{{\partial x}}} \right\}}_b}_c} \right] + \begin{aligned} + y_{i,j,k} = & - \frac{\Delta x \Delta y}{\Delta t}(c^{n+1 *}_{i,j,k}-c^{n}_{i,j,k}) \\ + & + \frac{\Delta x \Delta y}{T_s}(\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i,j,k} + c^{n+1 *}_{i,j,k}) - c^{n+1 *}_{i,j,k}) \\ + & + \Delta y \cdot u_{\text{x},i-1/2,j} \cdot + (\Gamma_x \cdot c^{n+1 *}_{i-1,j,k} + (1-\Gamma_x) c^{n+1 *}_{i,j,k})\\ + & - \Delta y \cdot u_{\text{x},i+1/2,j} \cdot (\Gamma_x \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_x) c^{n+1 *}_{i+1,j,k})\\ + & + \Delta x \cdot u_{\text{y},i,j-1/2} \cdot (\Gamma_y \cdot c^{n+1 *}_{i,j-1,k} + (1-\Gamma_y) c^{n+1 *}_{i,j,k})\\ + & - \Delta x \cdot u_{\text{y},i,j+1/2} \cdot (\Gamma_y \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_y) c^{n+1 *}_{i,j+1,k})\\ + \end{aligned} -The Runge-Kutta time-stepping, where :math:`\Delta t` is the length of the timestep, is defined as, +in the python code some intermediate variable is defined to make it easier to shift indexes .. math:: - :label: runge-kutta - - \begin{gathered} - \eta _i^{t + 1} = \eta _i^t + \frac{{\Delta t}}{6}\left( {{f_1} + 2{f_2} + 2{f_3} + {f_4}} \right) \hfill \\ - {f_1} = f(\eta _i^t) \hfill \\ - {f_2} = f\left( {\eta _i^t + \frac{{\Delta t}}{2}{f_1}} \right) \hfill \\ - {f_3} = f\left( {\eta _i^t + \frac{{\Delta t}}{2}{f_2}} \right) \hfill \\ - {f_4} = f\left( {\eta _i^t + \Delta t{f_3}} \right) \hfill \\ - \end{gathered} -where, :math:`i` is the grid cell in x-direction and :math:`t` is the timestep. The central difference solution to :math:`f(\eta)` is obtained through discretisation of the Boussinesq equation, + \text{Ctxfs} =(\Gamma_x \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_x) c^{n+1 *}_{i+1,j,k}) + +and .. math:: - :label: a-solve - - {a_i} = \frac{{\eta _{i + 1}^{} - 2\eta _i^{} + \eta _{i - 1}^{}}}{{{{(\Delta x)}^2}}} + + \text{Ctxfn} =(\Gamma_y \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_y) c^{n+1 *}_{i,j+1,k}) + +also Erosion and deposition are defined using seperate variables. .. math:: - {b_i} = \frac{{\eta _i^{}\left( {\eta _{i + 1}^{} - \eta _{i - 1}^{}} \right)}}{{\Delta x}} + D_{i,j,k}= \frac{\Delta x \Delta y}{T_s}c^{n+1 *}_{i,j,k} + +and .. math:: - {c_i} = \frac{{\left( {b_{i + 1}^{} - b_{i - 1}^{}} \right)}}{{\Delta x}} -The seaward boundary condition is defined as the still water level plus the wave setup . -If the groundwater elevation is larger than the bed elevation, there is a seepage face, -and the groundwater elevation is set equal to the bed elevation. On the landward boundary, -a no-flow condition, :math:`\frac{{\partial \eta }}{{\partial t}} = 0` (Neumann condition), or constant head, :math:`\eta = constant` (Dirichlet condition), is prescribed. + A_{i,j,k}= \frac{\Delta x \Delta y}{T_s}m_{i,j,k} + D_{i,j,k} -Capillary rise -^^^^^^^^^^^^^^ -Soil water retention (SWR) functions describe the surface moisture due to capillary transport -of water from the groundwater table :cite:`VanGenuchten1980`: +and .. math:: - :label: vangenuchten + U_{i,j,k}= \frac{\Delta x \Delta y}{T_s}\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - \theta (h) = {\theta _r} + \frac{{{\theta _s} - {\theta _r}}}{{{{\left[ {1 + {{\left| {\alpha h} \right|}^n}} \right]}^m}}} +and +.. math:: + E_{i,j,k} = \min(U_{i,j,k},A_{i,j,k}) -where :math:`h` is the groundwater table depth, :math:`\alpha` and :math:`n` are fitting parameters -related to the air entry suction and the pore size distribution. The parameter :math:`m` is commonly -parameterised as :math:`m = 1 - 1/n`. +After solving equation :math:`\delta c_{i,j,k}` using :eq:`conservative_general`, :math:`c^{n+1}_{i,j,k}` can be calculated using equation :eq:`conservative2`. -The resulting surface moisture is computed for both drying and -wetting conditions, i.e., including the -effect of hysteresis. The moisture contents computed with drying and wetting SWR functions are denoted :math:`{\theta ^d}(h)` and :math:`{\theta ^w}(h)`, respectively. -When moving between wetting and drying conditions, the soil moisture content follows an intermediate -retention curve called a scanning curve. The drying scanning curves are scaled from the main -drying curve and wetting scanning curves from the main wetting curve. The drying scanning curve is then obtained from :cite:`Mualem1974`: +Also, the pickup per grid cell can be calculated using: .. math:: - :label: mualem-drying - {\theta ^d}({h_\Delta },h) = {\theta ^w}(h) + \frac{{\left[ {{\theta ^w}({h_\Delta }) - {\theta ^w}(h)} \right]}}{{\left[ {{\theta _s} - {\theta ^w}(h)} \right]}}\left[ {{\theta ^d}(h) - {\theta ^w}(h)} \right] + \text{pickup} = \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k}- c^{n+1}_{i,j,k}}{T_s}\Delta t + \label{eq:pickup} -where :math:`{h_\Delta}` is the groundwater table depth at the reversal on the wetting curve. +note that this is only valid when using an Euler backward scheme. -The wetting scanning curve is obtained from :cite:`Mualem1974`: +Solving the Linear System of Equations +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The linear system of equations can be elaborated : .. math:: - :label: mualem-wetting + :label: apx-system + + \left[ + \begin{array}{cccccc} + A^0_1 & A^{1}_1 & \textbf{0} & \cdots & \textbf{0} & A^{n_{\mathrm{y}}+1}_1 \\ + A^{-1}_2 & A^0_2 & \ddots & \ddots & & \textbf{0} \\ + \textbf{0} & \ddots & \ddots & \ddots & \ddots & \vdots \\ + \vdots & \ddots & \ddots & \ddots & \ddots & \textbf{0} \\ + \textbf{0} & & \ddots & \ddots & A^0_{n_{\mathrm{y}}} & A^1_{n_{\mathrm{y}}} \\ + A^{-n_{\mathrm{y}}-1}_{n_{\mathrm{y}}+1} & \textbf{0} & \cdots & \textbf{0} & A^{-1}_{n_{\mathrm{y}}+1} & A^0_{n_{\mathrm{y}}+1} \\ + \end{array} + \right] \left[ + \begin{array}{c} + \vec{\delta c}_1 \\ \vec{\delta c}_2 \\ \vdots \\ \vdots \\ \vec{\delta c}_{n_{\mathrm{y}}} \\ \vec{\delta c}_{n_{\mathrm{y}}+1} \\ + \end{array} + \right] = \left[ + \begin{array}{c} + \vec{y}_1 \\ \vec{y}_2 \\ \vdots \\ \vdots \\ \vec{y}_{n_{\mathrm{y}}} \\ \vec{y}_{n_{\mathrm{y}}+1} \\ + \end{array} + \right] + +where each item in the matrix is again a matrix :math:`A^l_j` and +each item in the vectors is again a vector :math:`\vec{\delta c}_j` and +:math:`\vec{y}_j` respectively. The form of the matrix :math:`A^l_j` depends on +the diagonal index :math:`l` and reads: + +.. math:: + :label: apx-diagonal - {\theta ^w}({h_\Delta },h) = {\theta ^w}(h) + \frac{{\left[ {{\theta _s} - {\theta ^w}(h)} \right]}}{{\left[ {{\theta _s} - {\theta ^w}({h_\Delta })} \right]}}\left[ {{\theta ^d}({h_\Delta }) - {\theta ^w}({h_\Delta })} \right] + A^0_j = + \left[ + \begin{array}{ccccccc} + 0 & 0 & 0 & 0 + & \cdots & \cdots & 0 \\ + a^{0,-1}_{2,j} & a^{0,0}_{2,j} & a^{0,1}_{2,j} & \ddots + & & & \vdots \\ + 0 & a^{0,-1}_{3,j} & a^{0,0}_{3,j} & a^{0,1}_{3,j} + & \ddots & & \vdots \\ + \vdots & \ddots & \ddots & \ddots + & \ddots & \ddots & \vdots \\ + \vdots & & \ddots & a^{0,-1}_{n_{\mathrm{x}}-1,j} + & a^{0,0}_{n_{\mathrm{x}}-1,j} & a^{0,1}_{n_{\mathrm{x}}-1,j} & 0 \\ + \vdots & & & 0 + & a^{0,-1}_{n_{\mathrm{x}},j} & a^{0,0}_{n_{\mathrm{x}},j} & a^{0,1}_{n_{\mathrm{x}},j} \\ + 0 & \cdots & \cdots & 0 + & 1 & -2 & 1 \\ + \end{array} + \right] -where :math:`{h_\Delta}` is the groundwater table depth at the reversal on the drying curve. +for :math:`l = 0` and -Infiltration -^^^^^^^^^^^^ -Infiltration is accounted for by assuming that excess water infiltrates until the moisture content reaches -field capacity, :math:`{\theta_fc}`. The moisture content at field capacity is the maximum amount of water -that the unsaturated zone of soil can hold against the pull of gravity. For sandy soils, -the matric potential at this soil moisture condition is around - 1/10 bar. In equilibrium, -this potential would be exerted on the soil capillaries at the soil surface when the water -table is about 100 cm below the soil surface, :math:`{\theta _{fc}} = {\theta ^d}(100)`. +.. math:: + :label: apx-offdiagonal + + A^l_j = + \left[ + \begin{array}{ccccccc} + 1 & 0 & \cdots & \cdots + & \cdots & \cdots & 0 \\ + 0 & a^{l,0}_{2,j} & \ddots & + & & & \vdots \\ + \vdots & \ddots & a^{l,0}_{3,j} & \ddots + & & & \vdots \\ + \vdots & & \ddots & \ddots + & \ddots & & \vdots \\ + \vdots & & & \ddots + & a^{l,0}_{n_{\mathrm{x}}-1,j} & \ddots & \vdots \\ + \vdots & & & + & \ddots & a^{l,0}_{n_{\mathrm{x}},j} & 0 \\ + 0 & \cdots & \cdots & \cdots + & \cdots & 0 & 1 \\ + \end{array} + \right] -Infiltration is represented by an -exponential decay function that is governed by a drying time scale -:math:`T_{\mathrm{dry}}`. Exploratory model runs of the unsaturated soil with the HYDRUS1D -:cite:`Simunek1998` hydrology model show that the increase of the -volumetric water content to saturation is almost instantaneous with -rising tide. The drying of the beach surface through infiltration -shows an exponential decay. In order to capture this behavior the -volumetric water content is implemented according to: +for :math:`l \neq 0`. The vectors :math:`\vec{\delta c}_{j,k}` and :math:`\vec{y}_{j,k}` +read: .. math:: - :label: infiltration + :label: c-array - \frac{{d\theta }}{{dt}} = \left( {\theta - {\theta _{fc}}} \right)\left( {{e^{ - \ln (2)\frac{{dt}}{{{T_{dry}}}}}}} \right) + \begin{array}{rclrcl} + \vec{\delta c}_{j,k} &=& \left[ + \begin{array}{c} + \delta c^{n+1}_{1,j,k} \\ + \delta c^{n+1}_{2,j,k} \\ + \delta c^{n+1}_{3,j,k} \\ + \vdots \\ + \delta c^{n+1}_{n_{\mathrm{x}}-1,j,k} \\ + \delta c^{n+1}_{n_{\mathrm{x}},j,k} \\ + \delta c^{n+1}_{n_{\mathrm{x}}+1,j,k} \\ + \end{array} + \right] & ~ \mathrm{and} ~ + \vec{y}_{j,k} &=& \left[ + \begin{array}{c} + 0 \\ + y^n_{2,j,k} \\ + y^n_{3,j,k} \\ + \vdots \\ + y^n_{n_{\mathrm{x}}-1,j,k} \\ + y^n_{n_{\mathrm{x}},j,k} \\ + 0 \\ + \end{array} + \right] \\ + \end{array} -An alternative formulation is used for simulations that does not account for ground water and SWR processes, +:math:`n_{\mathrm{x}}` and :math:`n_{\mathrm{y}}` denote the number of +spatial grid cells in x- and y-direction. + +Iterations to solve for multiple fractions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The linear system defined in Equation :eq:`apx-system` is solved by a +sparse matrix solver for each sediment fraction separately in +ascending order of grain size. Initially, the weights +:math:`\hat{w}^{n+1}_{i,j,k}` are chosen according to the grain size +distribution in the bed and the air. The sediment availability +constraint is checked after each solve: .. math:: - :label: apx-drying - - p_{\mathrm{V}}^{n+1} = \left\{ - \begin{array}{ll} - p & \mathrm{if} ~ \eta > z_{\mathrm{b}} \\ - p_{\mathrm{V}}^n \cdot e^{\frac{\log \left( 0.5 \right)}{T_{\mathrm{dry}}} \cdot \Delta t^n} - E_{\mathrm{v}} \cdot \frac{\Delta t^n}{\Delta z} & \mathrm{if} ~ \eta \leq z_{\mathrm{b}} \\ - \end{array} - \right. + :label: solve -where :math:`\eta` [m+MSL] is the instantaneous water level, -:math:`z_{\mathrm{b}}` [m+MSL] is the local bed elevation, -:math:`p_{\mathrm{V}}^n` [-] is the volumetric water content in time step -:math:`n`, :math:`\Delta t^n` [s] is the model time step and :math:`\Delta z` is the bed -composition layer thickness. :math:`T_{\mathrm{dry}}` [s] is the beach -drying time scale, defined as the time in which the beach moisture -content halves. + m_{\mathrm{a}} \geq \frac{\hat{w}^{n+1}_{i,j,k} c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \Delta t^n -Precipitation and evaporation -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -A water balance approach accounts for the effect of precipitation and evaporation, +If the constraint if violated, a new estimate for the weights +is back-calculated following: .. math:: - :label: precipitation + :label: solve-weights - \frac{{d\theta }}{{dt}} = \frac{{\left( {P - E} \right)\,}}{{\Delta z}}\, + \hat{w}^{n+1}_{i,j,k} = \frac{ c^{n+1}_{i,j,k} + m_{\mathrm{a}} \frac{T}{\Delta t^n} }{c^{n+1}_{\mathrm{sat},i,j,k}} -where :math:`P` is the precipitation, :math:`E` is the evaporation, and :math:`\Delta z` is the thickness of the surface layer. +The system is solved again using the new weights. This +procedure is repeated until a weight is found that does not violate +the sediment availability constraint. If the time step is not too +large, the procedure typically converges in only a few +iterations. Finally, the weights of the larger grains are increased +proportionally as to ensure that the sum of all weights remains +unity. If no larger grains are defined, not enough sediment is +available for transport and the grid cell is truly +availability-limited. This situation should only occur occasionally as +the weights in the next time step are computed based on the new bed +composition and thus will be skewed towards the large fractions. If +the situation occurs regularly, the time step is chosen too large +compared to the rate of armoring. -Evaporation is simulated using an adapted version -of the Penman-Monteith equation :cite:`Shuttleworth1993` that is -governed by meteorological time series of solar radiation, temperature -and humidity. +Euler Schemes in non-conservative form +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -:math:`E_{\mathrm{v}}` [m/s] is the evaporation rate that is -implemented through an adapted version of the Penman equation -:cite:`Shuttleworth1993`: +Early model results relied on Euler schemes in a non conservative form. This allowed for a relatively easy implementation but did not guarantee mass conservation. In version 2 of AEOLIS the conservative form became the default. However, some users still use the older scheme. -.. math:: - :label: apx-penman - - E_{\mathrm{v}} = \frac{m_{\mathrm{v}} \cdot R_{\mathrm{n}} + 6.43 \cdot \gamma_{\mathrm{v}} \cdot (1 + 0.536 \cdot u_2) \cdot \delta e} - {\lambda_{\mathrm{v}} \cdot (m_{\mathrm{v}} + \gamma_{\mathrm{v}})} \cdot 9 \cdot 10^7 +The formulation is discretized following a first order upwind scheme +assuming that the wind velocity :math:`u_z` is positive in both +x-direction and y-direction: -where :math:`m_{\mathrm{v}}` [kPa/K] is the slope of the -saturation vapor pressure curve, :math:`R_{\mathrm{n}}` -[:math:`\mathrm{MJ/m^2/day}`] is the net radiance, :math:`\gamma_{\mathrm{v}}` -[kPa/K] is the psychrometric constant, :math:`u_2` [m/s] is the wind speed -at 2 m above the bed, :math:`\delta e` [kPa] is the vapor pressure deficit -(related to the relative humidity) and :math:`\lambda_{\mathrm{v}}` [MJ/kg] -is the latent heat vaporization. To obtain an evaporation rate in -[m/s], the original formulation is multiplied by :math:`9 \cdot 10^7`. +.. math:: + :label: apx-explicit + + \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + + u^n_{z,\mathrm{x}} \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x_{i,j}} + + u^n_{z,\mathrm{y}} \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y_{i,j}} \\ = + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} +in which :math:`n` is the time step index, :math:`i` and :math:`j` are +the cross-shore and alongshore spatial grid cell indices and :math:`k` +is the grain size fraction index. :math:`w` [-] is the weighting +factor used for the weighted addition of the saturated sediment +concentrations over all grain size fractions. -Shear velocity threshold ------------------------- +The discretization can be generalized for any wind direction as: -The shear velocity threshold represents the influence of bed surface -properties in the saturated sediment transport equation. The shear -velocity threshold is computed for each grid cell and sediment -fraction separately based on local bed surface properties, like -moisture, roughness elements and salt content. For each bed surface -property supported by the model a factor is computed to increase the -initial shear velocity threshold: +.. math:: + :label: apx-explicit-generalized + + \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + + u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + + u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \\ + + u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + + u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} = + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} + +in which: .. math:: - :label: apx-shearvelocity + :label: apx-upwind1 - u_{\mathrm{* th}} = - f_{u_{\mathrm{* th}}, \mathrm{M}} \cdot - f_{u_{\mathrm{* th}}, \mathrm{R}} \cdot - f_{u_{\mathrm{* th}}, \mathrm{S}} \cdot - u_{\mathrm{* th, 0}} + \begin{array}{rclcrcl} + u^n_{z,\mathrm{x+}} &=& \max( 0, u^n_{z,\mathrm{x}} ) &;& u^n_{z,\mathrm{y+}} &=& \max( 0, u^n_{z,\mathrm{y}} ) \\ + u^n_{z,\mathrm{x-}} &=& \min( 0, u^n_{z,\mathrm{x}} ) &;& u^n_{z,\mathrm{y-}} &=& \min( 0, u^n_{z,\mathrm{y}} ) \\ + \end{array} -The initial shear velocity threshold :math:`u_{\mathrm{* th, 0}}` [m/s] is -computed based on the grain size following :cite:`Bagnold1937b`: +and .. math:: - :label: shear - - u_{\mathrm{* th, 0}} = A \sqrt{ \frac{\rho_{\mathrm{p}} - \rho_{\mathrm{a}}}{\rho_{\mathrm{a}}} \cdot g \cdot d_{\mathrm{n}}} + :label: apx-upwind2 + + \begin{array}{rclcrcl} + c^n_{i,j,k,\mathrm{x+}} &=& \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x} &;& + c^n_{i,j,k,\mathrm{y+}} &=& \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y} \\ + c^n_{i,j,k,\mathrm{x-}} &=& \frac{c^n_{i,j,k} - c^n_{i-1,j,k}}{\Delta x} &;& + c^n_{i,j,k,\mathrm{y-}} &=& \frac{c^n_{i,j,k} - c^n_{i,j-1,k}}{\Delta y} \\ + \end{array} -where :math:`A` [-] is an empirical constant, :math:`\rho_{\mathrm{p}}` -[:math:`\mathrm{kg/m^3}`] is the grain density, :math:`\rho_{\mathrm{a}}` -[:math:`\mathrm{kg/m^3}`] is the air density, :math:`g` [:math:`\mathrm{m/s^2}`] is the -gravitational constant and :math:`d_{\mathrm{n}}` [m] is the nominal grain -size of the sediment fraction. +Equation :eq:`apx-explicit-generalized` is explicit in +time and adheres to the Courant-Friedrich-Lewis (CFL) condition for +numerical stability. Alternatively, the advection equation can be +discretized implicitly in time for unconditional stability: -Moisture content -^^^^^^^^^^^^^^^^ +.. math:: + :label: apx-implicit-generalized + + \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + + u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + + u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \\ + + u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + + u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} = + \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} -The shear velocity threshold is updated based on moisture content -following :cite:`Belly1964`: +Equation :eq:`apx-explicit-generalized` and +:eq:apx-implicit-generalized` can be rewritten as: .. math:: - :label: apx-moist + :label: apx-explicit-rewritten - f_{u_{\mathrm{* th}}, \mathrm{M}} = \max(1 \quad ; \quad 1.8 + 0.6 \cdot \log(p_{\mathrm{g}})) + c^{n+1}_{i,j,k} = c^n_{i,j,k} - \Delta t^n \left[ + u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + + u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \phantom{\frac{c^n_{i,j,k}}{T}} \right. \\ + \left. + u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + + u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} + + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] -where :math:`f_{u_{\mathrm{* th},M}}` [-] is a factor in Equation :eq:`apx-shearvelocity`, :math:`p_{\mathrm{g}}` [-] is the geotechnical -mass content of water, which is the percentage of water compared to -the dry mass. The geotechnical mass content relates to the volumetric -water content :math:`p_{\mathrm{V}}` [-] according to: +and .. math:: - :label: vol-water - - p_{\mathrm{g}} = \frac{p_{\mathrm{V}} \cdot \rho_{\mathrm{w}}}{\rho_{\mathrm{p}} \cdot (1 - p)} + :label: apx-implicit-rewritten + + c^{n+1}_{i,j,k} + \Delta t^n \left[ + u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + + u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \phantom{\frac{c^{n+1}_{i,j,k}}{T}} \right. \\ + \left. + u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + + u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} + + \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] = c^n_{i,j,k} -where :math:`\rho_{\mathrm{w}}` [:math:`\mathrm{kg/m^3}`] and -:math:`\rho_{\mathrm{p}}` [:math:`\mathrm{kg/m^3}`] are the water and particle -density respectively and :math:`p` [-] is the porosity. Values for -:math:`p_{\mathrm{g}}` smaller than 0.005 do not affect the shear velocity -threshold :cite:`Pye1990`. Values larger than 0.064 (or 10\% -volumetric content) cease transport :cite:`DelgadoFernandez2010`, -which is implemented as an infinite shear velocity threshold. +and combined using a weighted average: +.. math:: + :label: apx-combined + + c^{n+1}_{i,j,k} + \Gamma \Delta t^n \left[ + u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + + u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \phantom{\frac{c^{n+1}_{i,j,k}}{T}} \right. \\ + \left. + u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + + u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} + + \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] \\ = + c^n_{i,j,k} - (1 - \Gamma) \Delta t^n \left[ + u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + + u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \phantom{\frac{c^n_{i,j,k}}{T}} \right. \\ + \left. + u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + + u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} + + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] -Roughness elements -^^^^^^^^^^^^^^^^^^ +in which :math:`\Gamma` is a weight that ranges from 0 -- 1 and +determines the implicitness of the scheme. The scheme is implicit with +:math:`\Gamma = 0`, explicit with :math:`\Gamma = 1` and semi-implicit +otherwise. :math:`\Gamma = 0.5` results in the semi-implicit Crank-Nicolson +scheme. -The shear velocity threshold is updated based on the presence of -roughness elements following :cite:`Raupach1993`: +Equation :eq:`apx-upwind2` is back-substituted in Equation +:eq:`apx-combined`: .. math:: - :label: shear-rough + :label: apx-combined-substituted + + c^{n+1}_{i,j,k} + \Gamma \Delta t^n \left[ + u^{n+1}_{z,\mathrm{x+}} \frac{c^{n+1}_{i+1,j,k} - c^{n+1}_{i,j,k}}{\Delta x} + + u^{n+1}_{z,\mathrm{y+}} \frac{c^{n+1}_{i,j+1,k} - c^{n+1}_{i,j,k}}{\Delta y} \right. \\ + \left. + u^{n+1}_{z,\mathrm{x-}} \frac{c^{n+1}_{i,j,k} - c^{n+1}_{i-1,j,k}}{\Delta x} + + u^{n+1}_{z,\mathrm{y-}} \frac{c^{n+1}_{i,j,k} - c^{n+1}_{i,j-1,k}}{\Delta y} + + \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] \\ = + c^n_{i,j,k} - (1 - \Gamma) \Delta t^n \left[ + u^n_{z,\mathrm{x+}} \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x} + + u^n_{z,\mathrm{y+}} \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y} \right. \\ + \left. + u^n_{z,\mathrm{x-}} \frac{c^n_{i,j,k} - c^n_{i-1,j,k}}{\Delta x} + + u^n_{z,\mathrm{y-}} \frac{c^n_{i,j,k} - c^n_{i,j-1,k}}{\Delta y} + + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] - f_{u_{\mathrm{* th},R}} = \sqrt{(1 - m \cdot \sum_{k=k_0}^{n_k}{\hat{w}_k^{\mathrm{bed}}}) - (1 + \frac{m \beta}{\sigma} \cdot \sum_{k=k_0}^{n_k}{\hat{w}_k^{\mathrm{bed}}})} +and rewritten: -by assuming: +.. math:: + :label: apx-combined-rewritten + + \left[ 1 - \Gamma \left( + u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + + u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - + u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - + u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + + \frac{\Delta t^n}{T} + \right) + \right] c^{n+1}_{i,j,k} \\ + + \Gamma \left( + u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^{n+1}_{i+1,j,k} + + u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^{n+1}_{i,j+1,k} - %\right. \\ - \left. + u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^{n+1}_{i-1,j,k} - + u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^{n+1}_{i,j-1,k} + \right) \\ = + \left[ 1 + (1 - \Gamma) \left( + u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + + u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - + u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - + u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + + \frac{\Delta t^n}{T} + \right) + \right] c^n_{i,j,k} \\ + + (1 - \Gamma) \left( + u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^n_{i+1,j,k} + + u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^n_{i,j+1,k} - %\right. \\ - \left. + u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^n_{i-1,j,k} - + u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^n_{i,j-1,k} + \right) \\ - + \Gamma \hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - + (1 - \Gamma) \hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} + +and simplified: .. math:: - :label: lambda-rough + :label: apx-combined-simplified - \lambda = \frac{\sum_{k=k_0}^{n_k}{\hat{w}_k^{\mathrm{bed}}}}{\sigma} + a^{0,0}_{i,j} c^{n+1}_{i,j,k} + + a^{1,0}_{i,j} c^{n+1}_{i+1,j,k} + + a^{0,1}_{i,j} c^{n+1}_{i,j+1,k} - + a^{-1,0}_{i,j} c^{n+1}_{i-1,j,k} - + a^{0,-1}_{i,j} c^{n+1}_{i,j-1,k} = y_{i,j,k} -where :math:`f_{u_{\mathrm{* th},R}}` [-] is a factor in Equation -:eq:`apx-shearvelocity`, :math:`k_0` is the sediment fraction index of -the smallest non-erodible fraction in current conditions and :math:`n_k` is -the number of sediment fractions defined. The implementation is -discussed in detail in section \ref{sec:roughness}. +where the implicit coefficients are defined as: -Salt content -^^^^^^^^^^^^ +.. math:: + :label: apx-implicitcoef + + \begin{array}{rclcrcl} + a^{0,0}_{i,j} &=& \left[1 - \Gamma \left( + u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + + u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - + u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - + u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + + \frac{\Delta t^n}{T} + \right) \right] \\ + a^{1,0}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} \\ + a^{0,1}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} \\ + a^{-1,0}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} \\ + a^{0,-1}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} \\ + \end{array} -The shear velocity threshold is updated based on salt content -following :cite:`Nickling1981`: +and the explicit right-hand side as: .. math:: - :label: salt-rough + :label: apx-explicitrhs - f_{u_{\mathrm{* th}},S} = 1.03 \cdot \exp(0.1027 \cdot p_{\mathrm{s}}) + y^n_{i,j,k} = \left[ 1 + (1 - \Gamma) \left( + u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + + u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - + u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - + u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + + \frac{\Delta t^n}{T} + \right) + \right] c^n_{i,j,k} \\ + + (1 - \Gamma) \left( + u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^n_{i+1,j,k} + + u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^n_{i,j+1,k} - + u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^n_{i-1,j,k} - + u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^n_{i,j-1,k} + \right) \\ - + \Gamma \hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - + (1 - \Gamma) \hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} -where :math:`f_{u_{\mathrm{* th},S}}` [-] is a factor in Equation -:eq:`apx-shearvelocity` and :math:`p_{\mathrm{s}}` [-] is the salt -content [mg/g]. Currently, no model is implemented that predicts the -instantaneous salt content. The spatial varying salt content needs to -be specified by the user, for example through the BMI interface. +The offshore boundary is defined to be zero-flux, the +onshore boundary has a constant transport gradient and the lateral +boundaries are circular: +.. math:: + :label: apx-boundaryconditions + + \begin{array}{rclcrcl} + c^{n+1}_{1,j,k} &=& 0 \\ + c^{n+1}_{n_{\mathrm{x}}+1,j,k} &=& 2 c^{n+1}_{n_{\mathrm{x}},j,k} - c^{n+1}_{n_{\mathrm{x}}-1,j,k} \\ + c^{n+1}_{i,1,k} &=& c^{n+1}_{i,n_{\mathrm{y}}+1,k} \\ + c^{n+1}_{i,n_{\mathrm{y}}+1,k} &=& c^{n+1}_{i,1,k} \\ + \end{array} \ No newline at end of file From 58d7dd958269d2cff8de3340d6963b22f37de68d Mon Sep 17 00:00:00 2001 From: Christa van IJzendoorn <52737913+christavanijzendoorn@users.noreply.github.com> Date: Fri, 16 Aug 2024 15:14:04 -0700 Subject: [PATCH 119/124] correct small mistake in text model setup --- docs/user/model_setup.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index 57505edd..40c60933 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -257,7 +257,7 @@ process_wind process_threshold ^^^^^^^^^^^^^^^^^ -*Process_threshold* allows for the alterations of the threshold velocity by processes like grain, moisture and vegetation. This process does not occur if a threshold file is provided as input since this file is used to define the threshold shear velocity. Used in :py:mod:`aeolis.threshold.compute`, documentation of threshold alterations can be found in :ref:model_description +*Process_threshold* allows for the alterations of the threshold velocity by processes like grain and moisture. This process does not occur if a threshold file is provided as input since this file is used to define the threshold shear velocity. Used in :py:mod:`aeolis.threshold.compute`, documentation of threshold alterations can be found in :ref:model_description - **th_grainsize**: calculates the threshold velocity based on the grain size following Bagnold (:py:mod:`aeolis.threshold.compute_grain_size`) - **th_bedslope**: currently not implemented, but theoretically would include an alteration of the velocity threshold based on the slope of the bed. (:py:mod:`aeolis.threshold.compute_bedslope`) From 7c53b7ea4ce67721abe4bc3ed7b9186888eb071b Mon Sep 17 00:00:00 2001 From: Christa van IJzendoorn <52737913+christavanijzendoorn@users.noreply.github.com> Date: Fri, 16 Aug 2024 15:46:57 -0700 Subject: [PATCH 120/124] General tips and getting help --- README.md | 3 ++- docs/user/model_setup.rst | 2 ++ 2 files changed, 4 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index f26d3c8e..4f09fff8 100644 --- a/README.md +++ b/README.md @@ -61,7 +61,7 @@ aeolis run aeolis wind --mean=6 --duration=3600 ``` -## Documentation +## Documentation and help Detailed documentation can be found at [AeoLiS ReadTheDocs](http://aeolis.readthedocs.io/) A couple of short courses are available to help new users get acquainted with the model: @@ -70,6 +70,7 @@ A couple of short courses are available to help new users get acquainted with th Example case studies can also be found in the [examples folder](https://github.com/openearth/aeolis-python/tree/main/aeolis/examples) that is part of the AeoLiS installation. +We encourage (new) users to post questions and case studies on the [AeoLiS Discussion Board](https://github.com/openearth/aeolis-python/discussions). We use this public forum so our help and advice is available to everyone. ## AeoLiS Developer Team The maintenance and development is done by a group of very enthusiastic people. diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index 40c60933..7d1e9cc1 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -8,6 +8,8 @@ Setting up the AeoLiS model involves configuring various parameters and input fi - **Model state/output**: Overview of model state variables that can be outputted. - **Guidance on solver use**: Explanation of the use of different solvers. +A general tip for setting up a model like AeoLiS is to start simple and build up the complexity. As a starting point, you can use the default values and then slowly deviate from those and turn on processes. In case you run into issues, we encourage (new) users to post questions and case studies on the [AeoLiS Discussion Board](https://github.com/openearth/aeolis-python/discussions). We use this public forum so our help and advice is available to everyone. + Model input ----------- From 62b10374b71e9466f0fb74bf595e87d9b0e5b01a Mon Sep 17 00:00:00 2001 From: Christa van IJzendoorn <52737913+christavanijzendoorn@users.noreply.github.com> Date: Fri, 16 Aug 2024 15:54:52 -0700 Subject: [PATCH 121/124] Update model_setup.rst fix url --- docs/user/model_setup.rst | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index 7d1e9cc1..81b6543a 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -8,7 +8,9 @@ Setting up the AeoLiS model involves configuring various parameters and input fi - **Model state/output**: Overview of model state variables that can be outputted. - **Guidance on solver use**: Explanation of the use of different solvers. -A general tip for setting up a model like AeoLiS is to start simple and build up the complexity. As a starting point, you can use the default values and then slowly deviate from those and turn on processes. In case you run into issues, we encourage (new) users to post questions and case studies on the [AeoLiS Discussion Board](https://github.com/openearth/aeolis-python/discussions). We use this public forum so our help and advice is available to everyone. +A general tip for setting up a model like AeoLiS is to start simple and build up the complexity. As a starting point, you can use the default values and then slowly deviate from those and turn on processes. In case you run into issues, we encourage (new) users to post questions and case studies on the `AeoLiS Discussion Board`_. We use this public forum so our help and advice is available to everyone. + +.. _AeoLiS Discussion Board: https://github.com/openearth/aeolis-python/discussions Model input ----------- From 1e475884c5e0bd4d9b5368969e45617520fdd6b0 Mon Sep 17 00:00:00 2001 From: Sierd Date: Sat, 17 Aug 2024 09:54:20 +0200 Subject: [PATCH 122/124] Dropdown menu added Added the dropdown menu Fixed some bugs --- aeolis/console.py | 2 ++ docs/aeolis.bib | 13 +++++++++++++ docs/conf.py | 6 ++++++ docs/developer/modularity.rst | 4 +++- docs/user/installation.rst | 2 +- docs/user/introduction.rst | 2 ++ docs/user/model_setup.rst | 2 ++ 7 files changed, 29 insertions(+), 2 deletions(-) diff --git a/aeolis/console.py b/aeolis/console.py index 70281e8c..676538b7 100644 --- a/aeolis/console.py +++ b/aeolis/console.py @@ -70,6 +70,7 @@ @aeolis_app.command(name="mycommand", help="My command help") def mycommand(): + You can then run the command from the command line as follows: @@ -79,6 +80,7 @@ def mycommand(): *************************************************************************** + """ diff --git a/docs/aeolis.bib b/docs/aeolis.bib index db41a642..d823d595 100644 --- a/docs/aeolis.bib +++ b/docs/aeolis.bib @@ -73,6 +73,19 @@ @article{Nolet2018 doi = {10.1016/j.aeolia.2017.08.006}, } +@article{VANWESTEN2024106093, +title = {AeoLiS: Numerical modelling of coastal dunes and aeolian landform development for real-world applications}, +journal = {Environmental Modelling & Software}, +volume = {179}, +pages = {106093}, +year = {2024}, +issn = {1364-8152}, +doi = {https://doi.org/10.1016/j.envsoft.2024.106093}, +url = {https://www.sciencedirect.com/science/article/pii/S1364815224001543}, +author = {Bart {van Westen} and Sierd {de Vries} and Nicholas Cohn and Christa {van IJzendoorn} and Glenn Strypsteen and Caroline Hallin}, +keywords = {Aeolian sediment transport, Dune vegetation, Dune geomorphology, Blowout, Embryo dune, Parabolic dune}, +} + @article{Maun1998, author = {Maun, M. A.}, title = {Adaptations of plants to burial in coastal sand dunes}, diff --git a/docs/conf.py b/docs/conf.py index a11e1d75..fda47403 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -44,6 +44,7 @@ def setup(app): 'sphinx.ext.viewcode', 'sphinx_copybutton', 'sphinxcontrib.bibtex', + 'sphinx_rtd_theme', # 'nbsphinx', ] @@ -134,6 +135,11 @@ def setup(app): # further. For a list of options available for each theme, see the # documentation. #html_theme_options = {} +html_theme_options = { + 'collapse_navigation': True, # Enable collapsing titles in the sidebar + 'navigation_depth': 3, # Adjust the depth of the navigation tree + 'titles_only': False, # Show only titles in the sidebar +} # Add any paths that contain custom themes here, relative to this directory. html_theme_path = [sphinx_rtd_theme.get_html_theme_path()] diff --git a/docs/developer/modularity.rst b/docs/developer/modularity.rst index aa563431..15668833 100644 --- a/docs/developer/modularity.rst +++ b/docs/developer/modularity.rst @@ -28,7 +28,9 @@ We have some ideas about how to improve the modularity of the code. However, we .. _fig-step-flowchart: .. figure:: /images/model-step-flowchart.PNG - :alt: AeoLiS architecture + :alt: Step Flowchart + + Flowchart of a modeling step in the AeoLiSRunner. .. seealso:: diff --git a/docs/user/installation.rst b/docs/user/installation.rst index e3eb75b5..7bd099cb 100644 --- a/docs/user/installation.rst +++ b/docs/user/installation.rst @@ -63,4 +63,4 @@ Example from command line: .. note:: - Model parameters and other configuration is passed in a `params.txt`. See the :ref:`default settings` for more details. + Model parameters and other configuration is passed in a `params.txt`. See the :ref:`default-settings` for more details. diff --git a/docs/user/introduction.rst b/docs/user/introduction.rst index df616188..2a07ec4c 100644 --- a/docs/user/introduction.rst +++ b/docs/user/introduction.rst @@ -25,6 +25,8 @@ AeoLiS publications 2024 ^^^^ +Van Westen, B., De Vries, S., Cohn, N., Van IJzendoorn, C., Strypsteen, G., Hallin, C. (2024). AeoLiS: Numerical modelling of coastal dunes and aeolian landform development for real-world applications, Environmental Modelling & Software, 179, 106093, Doi: https://doi.org/10.1016/j.envsoft.2024.106093. + Strypsteen, G., de Vries, S., Bonte, D., Homberger, J.M., Hallin, C., Rauwoens, P. (2024). Planted vegetation on a sandy beach regulates maximum size of corresponding dune evolution. Coastal Engineering (preprint under review). Doi: http://dx.doi.org/10.2139/ssrn.4872614 Heminway, S.S., Cohn, N., Davis, E.H., White, A., Hein, C.J., Zinnert, J.C., 2024. Exploring Ecological, Morphological, and Environmental Controls on Coastal Foredune Evolution at Annual Scales Using a Process-Based Model. Sustainability, 16, 3460. https://doi.org/10.3390/su16083460 diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index 81b6543a..cc994b06 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -234,6 +234,8 @@ column is air pressure (kPa). File format for meteorological data used to simulate surface moisture in AeoLiS where each red dot represents a time series value. +.. _default-settings: + Default settings ----------------- From b5a5343743f44c6eecc187a7b3429ff7618e8049 Mon Sep 17 00:00:00 2001 From: Sierd Date: Sat, 17 Aug 2024 17:46:16 +0200 Subject: [PATCH 123/124] cleaned up bib-file, added appendix, explained solvers --- docs/aeolis.bib | 1835 +------------------------------ docs/index.rst | 1 + docs/user/appendix.rst | 620 +++++++++++ docs/user/model_description.rst | 632 ----------- docs/user/model_setup.rst | 70 ++ 5 files changed, 740 insertions(+), 2418 deletions(-) create mode 100644 docs/user/appendix.rst diff --git a/docs/aeolis.bib b/docs/aeolis.bib index d823d595..8835a096 100644 --- a/docs/aeolis.bib +++ b/docs/aeolis.bib @@ -1,5 +1,3 @@ -% This file was created with JabRef 2.9.2. -% Encoding: UTF-8 @MANUAL{Simunek1998, title = {The HYDRUS-1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably- saturated @@ -81,7 +79,6 @@ @article{VANWESTEN2024106093 year = {2024}, issn = {1364-8152}, doi = {https://doi.org/10.1016/j.envsoft.2024.106093}, -url = {https://www.sciencedirect.com/science/article/pii/S1364815224001543}, author = {Bart {van Westen} and Sierd {de Vries} and Nicholas Cohn and Christa {van IJzendoorn} and Glenn Strypsteen and Caroline Hallin}, keywords = {Aeolian sediment transport, Dune vegetation, Dune geomorphology, Blowout, Embryo dune, Parabolic dune}, } @@ -119,78 +116,6 @@ @article{Hesp1991 doi = {10.1016/s0140-1963(18)30681-5}, } -@article{Aagaard2014, - author = {Aagaard, T.}, - title = {Sediment supply to beaches: Cross-shore sand transport on the lower shoreface}, - journal = {Journal of Geophysical Research}, - year = {2014}, - volume = {119}, - pages = {913--926}, - number = {4}, - note = {2013JF003041}, - doi = {10.1002/2013JF003041}, - issn = {2169-9011}, - keywords = {Marine sediments: processes and transport, Littoral processes, Nearshore - processes, sediment transport, sediment budgets, shoreline change, - equilibrium profile}, - owner = {hoonhout}, - timestamp = {2015.06.15} -} - -@article{Arens2002, - author = {Arens, SM and Van Boxel, JH and Abuodha, JOZ}, - title = {Changes in grain size of sand in transport over a foredune}, - journal = {Earth Surface Processes and Landforms}, - year = {2002}, - volume = {27}, - pages = {1163--1175}, - number = {11}, - owner = {hoonhout}, - publisher = {Wiley Online Library}, - timestamp = {2016.04.29} -} - -@article{Arens1996, - author = {Arens, S. M.}, - title = {Patterns of sand transport on vegetated foredunes}, - journal = {Geomorphology}, - year = {1996}, - volume = {17}, - pages = {339--350}, - file = {Arens1996.pdf:Arens1996.pdf:PDF}, - owner = {hoonhout}, - timestamp = {2015.05.26} -} - -@techreport{Arens2010, - author = {Arens, S M and Puijvelde, S P and Bri\`{e}re, C}, - title = {Effecten van suppleties op duinontwikkeling}, - institution = {Arens Bureau voor Strand- en Duinonderzoek}, - year = {2010}, - number = {2010.03}, - note = {for LNV Directie Kennis (OBN) en Rijkswaterstaat Waterdienst}, - owner = {hoonhout}, - timestamp = {2015.05.26}, - url = {http://dt.natuurkennis.nl/uploads/OBN142_DK_Effecten_van_suppleties_op_duinontwikkeling.zip} -} - -@article{Baas2005, - author = {Baas, A. C. W. and Sherman, D. J.}, - title = {Formation and behavior of aeolian streamers}, - journal = {Journal of Geophysical Research}, - year = {2005}, - volume = {110}, - number = {F3}, - note = {F03011}, - doi = {10.1029/2004JF000270}, - issn = {2156-2202}, - keywords = {Atmospheric Processes: Boundary layer processes, Atmospheric Processes: - Turbulence, Nonlinear Geophysics: Complex systems, aeolian, sediment - transport, streamers}, - owner = {hoonhout}, - timestamp = {2015.06.15} -} - @article{Bagnold1937a, author = {Bagnold, RA}, title = {The transport of sand by wind}, @@ -214,40 +139,6 @@ @article{Bagnold1937b timestamp = {2015.10.01} } -@article{Bagnold1936, - author = {Bagnold, RA}, - title = {The movement of desert sand}, - journal = {Proceedings of the Royal Society of London. Series A, Mathematical - and Physical Sciences}, - year = {1936}, - pages = {594--620}, - owner = {hoonhout}, - publisher = {JSTOR}, - timestamp = {2015.10.01} -} - -@article{Bagnold1935, - author = {Bagnold, RA}, - title = {The movement of desert sand}, - journal = {Geographical Journal}, - year = {1935}, - pages = {342--365}, - owner = {hoonhout}, - publisher = {JSTOR}, - timestamp = {2015.10.01} -} - -@book{Bagnold1941, - title = {The Physics of Blown Sand and Desert Dunes}, - publisher = {Methuen}, - year = {1941}, - author = {Bagnold, R A}, - pages = {265 pp.}, - address = {London}, - owner = {hoonhout}, - timestamp = {2015.05.26} -} - @article{Baird1998, abstract = {A numerical solution to the 1-D Boussinesq ground water equation is used to predict water table response to tidal and wave forcing. We argue that the solution presented here offers considerable advantages over other solutions to the 1-D Boussinesq ground water equation and is simpler to apply than 2-D ground water models. The main assumption in using the Boussinesq equation is that ground water flow in a shallow aquifer can be described using the Dupuit-Forchheimer approximation, in which it is assumed that changes in hydraulic head with depth below the water table are negligible. The predictive ability of the solution was tested against field data from ten wells and ten piezometers on a microtidal sandy beach. Two model runs were carried out: in the first the effect of tides only was considered; in the second setup due to waves was also considered. The arithmetic mean of independently measured values of hydraulic conductivity was used to describe sediment characteristics. The piezometer data show that changes in hydraulic head with depth are negligible for much of the beach, suggesting that the use of the Boussinesq equation is appropriate. The correspondence between model predictions of water table elevations and field observations is good for both the tide-only and the tide plus setup model runs, with the latter giving the better predictions.}, author = {Baird, Andrew J. and Mason, Travis and Horn, Diane P.}, @@ -262,93 +153,6 @@ @article{Baird1998 year = {1998} } -@article{Barchyn2015, - author = {Barchyn, T. E. and Hugenholtz, C. H.}, - title = {Predictability of dune activity in real dune fields under unidirectional - wind regimes}, - journal = {Journal of Geophysical Research}, - year = {2015}, - volume = {120}, - pages = {159--182}, - number = {2}, - note = {2014JF003248}, - doi = {10.1002/2014JF003248}, - issn = {2169-9011}, - keywords = {Modeling, Land cover change, Earth system modeling, aeolian, stabilization, - reactivation, vegetation cover}, - owner = {hoonhout}, - timestamp = {2015.06.15} -} - -@article{Barchyn2014, - author = {Barchyn, T. E. and Hugenholtz, C. H. and Li, B. and McKenna Neuman, - C. and Sanderson, S.}, - title = {From particle counts to flux: Wind tunnel testing and calibration of the "Wenglor" aeolian sediment transport sensor}, - journal = {Aeolian Research}, - year = {2014}, - volume = {15}, - pages = {311--318}, - doi = {10.1016/j.aeolia.2014.06.009}, - owner = {hoonhout}, - timestamp = {2016.06.09} -} - -@PHDTHESIS{Battjes1974, - author = {Battjes, Jurjen Anno}, - title = {Computation of set-up, longshore currents, run-up and overtopping due to wind-generated waves}, - school = {TU Delft, Delft University of Technology}, - year = {1974}, - owner = {hoonhout}, - timestamp = {2016.07.08}, - url = {http://repository.tudelft.nl/assets/uuid:e126e043-a858-4e58-b4c7-8a7bc5be1a44/Battjes.pdf} -} - -@article{Bauer2014, - author = {Bauer, B. O. and Davidson-Arnott, R. G. D.}, - title = {Aeolian particle flux profiles and transport unsteadiness}, - journal = {Journal of Geophysical Research}, - year = {2014}, - volume = {119}, - pages = {1542--1563}, - number = {7}, - note = {2014JF003128}, - doi = {10.1002/2014JF003128}, - issn = {2169-9011}, - keywords = {Geomorphology and weathering, Land/atmosphere interactions, Geomorphology: - general, Sediment transport, Surface materials and properties, sediment - flux profiles, exponential decay, vegetated coastal foredune, wind - gusts, transport intermittency, sediment flurries}, - owner = {hoonhout}, - timestamp = {2015.06.15}, - url = {http://dx.doi.org/10.1002/2014JF003128} -} - -@article{Bauer2002, - author = {Bauer, B O and Davidson-Arnott, R G D}, - title = {A general framework for modeling sediment supply to coastal dunes - including wind angle, beach geometry, and fetch effects}, - journal = {Geomorphology}, - year = {2002}, - volume = {49}, - pages = {89--108}, - doi = {10.1016/S0169-555X(02)00165-4}, - owner = {hoonhout}, - timestamp = {2015.05.24} -} - -@article{Bauer2009, - author = {Bauer, B O and Davidson-Arnott, R G D and Hesp, P A and Namikas, - S L and Ollerhead, J and Walker, I J}, - title = {Aeolian sediment transport on a beach: Surface moisture, wind fetch, and mean transport}, - journal = {Geomorphology}, - year = {2009}, - volume = {105}, - pages = {106--116}, - doi = {10.1016/j.geomorph.2008.02.016}, - owner = {hoonhout}, - timestamp = {2015.05.24} -} - @techreport{Belly1964, author = {Belly, P Y}, title = {Sand movement by wind}, @@ -373,998 +177,64 @@ @article{Brakenhoff2019 year = {2019} } -@article{Buscombe2010, - author = {Buscombe, D and Rubin, D M and Warrick, J A}, - title = {A universal approximation of grain size from images of noncohesive sediment}, - journal = {Journal of Geophysical Research}, - year = {2010}, - volume = {115}, - number = {F2}, - note = {F02015}, - doi = {10.1029/2009JF001477}, - owner = {hoonhout}, - timestamp = {2015.05.26} -} - -@article{Cheng2015, - author = {Cheng, Hong and Liu, Chenchen and Zou, Xueyong and Li, Jifeng and - He, Jiajia and Liu, Bo and Wu, Yongqiu and Kang, Liqiang and Fang, - Yi}, - title = {Aeolian creeping mass of different grain sizes over sand beds of varying length}, - journal = {Journal of Geophysical Research}, - year = {2015}, - note = {2014JF003367}, - doi = {10.1002/2014JF003367}, - issn = {2169-9011}, - keywords = {Aerosols and particles, Erosion and weathering, creeping sand grains, - transport mass, length of sand bed, grain size, wind tunnel}, - owner = {hoonhout}, - timestamp = {2015.07.07}, - url = {http://dx.doi.org/10.1002/2014JF003367} -} - -@inproceedings{Cohn2015, - author = {Cohn, N and Anderson, D and Ruggiero, P}, - title = {Observations of intertidal bar welding along a high energy, dissipative coastline}, - booktitle = {Proceedings Coastal Sediments}, - year = {2015}, - owner = {hoonhout}, - timestamp = {2015.05.26} -} - -@article{Courant1967, - author = {Courant, Richard and Friedrichs, Kurt and Lewy, Hans}, - title = {On the partial difference equations of mathematical physics}, - journal = {IBM journal of Research and Development}, - year = {1967}, - volume = {11}, - pages = {215--234}, - number = {2}, - owner = {hoonhout}, - publisher = {IBM}, - timestamp = {2015.10.06}, - url = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5391985} -} - -@techreport{Curto2013, - author = {Curto, V}, - title = {Field measurements of grain size distributions - {K}ijkduin and {S}and {M}otor}, - institution = {Delft University of Technology / Deltares}, - year = {2013}, - number = {4257162}, - note = {Traineeship Report}, - owner = {hoonhout}, - timestamp = {2015.05.26} -} - -@article{Darke2008, - author = {Darke, I and McKenna Neuman, C}, - title = {Field study of beach water content as a guide to wind erosion potential}, - journal = {Journal of Coastal Research}, - year = {2008}, - volume = {24}, - pages = {1200--1208}, - number = {5}, - doi = {10.2112/00-000.1}, - owner = {hoonhout}, - timestamp = {2015.05.26} -} - -@article{DavidsonArnott1997, - author = {Davidson-Arnott, Robin GD and White, Davina C and Ollerhead, Jeff}, - title = {The effects of artificial pebble concentrations on eolion sand transport on a beach}, - journal = {Canadian Journal of Earth Sciences}, - year = {1997}, - volume = {34}, - pages = {1499--1508}, - number = {11}, - owner = {hoonhout}, - publisher = {NRC Research Press}, - timestamp = {2015.10.01}, - url = {http://www.nrcresearchpress.com/doi/pdf/10.1139/e17-122} -} - -@article{DavidsonArnott2009, - author = {Davidson-Arnott, R G D and Bauer, B O}, - title = {Aeolian sediment transport on a beach: Thresholds, intermittency, and high frequency variability}, - journal = {Geomorphology}, - year = {2009}, - volume = {105}, - pages = {117--126}, - doi = {10.1016/j.geomorph.2008.02.018}, - owner = {hoonhout}, - timestamp = {2015.05.24} -} - -@article{DavidsonArnott2005, - author = {Davidson-Arnott, R G D and MacQuarrie, K and Aagaard, T}, - title = {The effect of wind gusts, moisture content and fetch length on sand transport on a beach}, - journal = {Geomorphology}, - year = {2005}, - volume = {68}, - pages = {115--129}, - doi = {10.1016/j.geomorph.2004.04.008}, - owner = {hoonhout}, - timestamp = {2015.05.24} -} - -@article{DavidsonArnott2008, - author = {Davidson-Arnott, R G D and Yang, Y and Ollerhead, J and Hesp, P A - and Walker, I J}, - title = {The effects of surface moisture on aeolian sediment transport threshold and mass flux on a beach}, - journal = {Earth Surface Processes and Landforms}, - year = {2008}, - volume = {33}, - pages = {55--74}, - number = {1}, - doi = {10.1002/esp.1527}, - owner = {hoonhout}, - timestamp = {2015.05.24} -} - -@manual{Delft3DManual, - title = {Delft3D - 3D/2D modelling suite for integral water solutions - Hydro-Morphodynamics}, - author = {{Delft3D-FLOW Manual}}, - organization = {Deltares}, - address = {Delft}, - month = {May}, - year = {2014}, - note = {Version 3.15.34158}, - owner = {hoonhout}, - timestamp = {2015.05.26} -} - @article{DelgadoFernandez2010, author = {Delgado-Fernandez, I}, title = {A review of the application of the fetch effect to modelling sand supply to coastal foredunes}, journal = {Aeolian Research}, year = {2010}, volume = {2}, - pages = {61--70}, - doi = {10.1016/j.aeolia.2010.04.001}, - owner = {hoonhout}, - timestamp = {2015.05.24} -} - -@article{DelgadoFernandez2011, - author = {Delgado-Fernandez, Irene and Davidson-Arnott, Robin A}, - title = {Meso-scale aeolian sediment input to coastal dunes: The nature of aeolian transport events}, - journal = {Geomorphology}, - year = {2011}, - volume = {126}, - pages = {217--232}, - number = {1}, - doi = {10.1016/j.geomorph.2010.11.005}, - owner = {hoonhout}, - publisher = {Elsevier}, - timestamp = {2015.10.02} -} - -@article{DelgadoFernandez2012, - author = {Delgado-Fernandez, Irene and Davidson-Arnott, Robin and Bauer, Bernard - O and Walker, Ian J and Ollerhead, Jeff and Rhew, Hosahng}, - title = {Assessing aeolian beach-surface dynamics using a remote sensing approach}, - journal = {Earth Surface Processes and Landforms}, - year = {2012}, - volume = {37}, - pages = {1651--1660}, - number = {15}, - doi = {10.1002/esp.3301}, - owner = {hoonhout}, - publisher = {Wiley Online Library}, - timestamp = {2015.10.07} -} - -@article{Dong2004a, - author = {Dong, Zhibao and Wang, Hongtao and Liu, Xiaoping and Wang, Xunming}, - title = {The blown sand flux over a sandy surface: a wind tunnel investigation on the fetch effect}, - journal = {Geomorphology}, - year = {2004}, - volume = {57}, - pages = {117--127}, - doi = {10.1016/S0169-555X(03)00087-4}, - owner = {hoonhout}, - timestamp = {2015.05.26} -} - -@article{Dong2004b, - author = {Dong, Zhibao and Wang, Hongtao and Liu, Xiaoping and Wang, Xunming}, - title = {A wind tunnel investigation of the influences of fetch length on the flux profile of a sand cloud blowing over a gravel surface}, - journal = {Earth Surface Processes and Landforms}, - year = {2004}, - volume = {29}, - pages = {1613--1626}, - number = {13}, - doi = {10.1002/esp.1116}, - owner = {hoonhout}, - publisher = {Wiley Online Library}, - timestamp = {2015.10.01} -} - -@article{Dupont2014, - author = {Dupont, S. and Bergametti, G. and Simo\"{e}ns, S.}, - title = {Modeling aeolian erosion in presence of vegetation}, - 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J.}, - title = {Vegetation controls on the maximum size of coastal dunes}, - journal = {Proceedings of the National Academy of Sciences of the United States of America}, - year = {2013}, - volume = {110}, - pages = {17217--17222}, - doi = {10.1073/pnas.1307580110}, - owner = {hoonhout}, - timestamp = {2015.05.27} -} - -@book{Dyer1986, - title = {Coastal and estuarine sediment dynamics}, - publisher = {Wiley}, - year = {1986}, - author = {Dyer, K R}, - pages = {342 pp}, - address = {Chichester}, - owner = {hoonhout}, - timestamp = {2014.06.11} -} - -@article{Dymin1954, - author = {Dymin}, - title = {}, - year = {1954}, - note = {quoted by Greeley and Iverson (1985)}, - owner = {hoonhout}, - journal = {}, - timestamp = {2015.10.01} -} - -@article{Edwards2009, - author = {Edwards, B L and Namikas, S L}, - title = {Small-scale variability in surface moisture on a fine-grained beach: implications for modeling aeolian transport}, - journal = {Earth Surface Processes and Landforms}, - year = {2009}, - volume = {34}, - pages = {1333--1338}, - doi = {10.1002/esp.1817}, - owner = {hoonhout}, - timestamp = {2015.05.26} -} - -@article{Edwards2013, - author = {Edwards, Brandon L and Namikas, Steven L and D'Sa, Eurico J}, - title = {Simple infrared techniques for measuring beach surface moisture}, - journal = {Earth Surface Processes and Landforms}, - year = {2013}, - volume = {38}, - pages = {192--197}, - number = {2}, - doi = {10.1002/esp.3319}, - owner = {hoonhout}, - publisher = {Wiley Online Library}, - timestamp = {2015.10.07} -} - -@article{Furieri2013, - author = {Furieri, B and Russeil, S and Santos, JM and Harion, JL}, - title = {Effects of non-erodible particles on aeolian erosion: Wind-tunnel simulations of a sand oblong storage pile}, - journal = {Atmospheric Environment}, - year = {2013}, - volume = {79}, - pages = {672--680}, - doi = {10.1016/j.atmosenv.2013.07.026}, - owner = {hoonhout}, - publisher = {Elsevier}, - timestamp = {2015.10.01} -} - -@article{Gallagher2011, - author = {Gallagher, Edith L and MacMahan, Jamie and Reniers, AJHM and Brown, - Jenna and Thornton, Edward B}, - title = {Grain size variability on a rip-channeled beach}, - journal = {Marine Geology}, - year = {2011}, - volume = {287}, - pages = {43--53}, - number = {1}, - doi = {10.1016/j.margeo.2011.06.010}, - owner = {hoonhout}, - publisher = {Elsevier}, - timestamp = {2015.10.06} -} - -@techreport{Genuchten1978, - author = {van Genuchten, M. 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M.}, + title = {Depth of disturbance of sand on sea beaches by waves}, + journal = {Journal of Sedimentary Petrology}, + year = {1951}, + volume = {21}, + pages = {131--140}, + number = {3}, owner = {hoonhout}, - timestamp = {2015.05.26} + timestamp = {2015.08.06}, + url = {http://archives.datapages.com/data/sepm/journals/v01-32/data/021/021003/pdfs/0131.pdf} } @article{Masselink2007, @@ -1381,79 +251,6 @@ @article{Masselink2007 timestamp = {2015.05.26} } -@inproceedings{McCall2011, - author = {McCall, R T and van Geer, P F C and Hoonhout, B M}, - title = {Physical modeling of storm-induced erosion and overwash}, - booktitle = {Proceedings 7th Coastal Sediments Conference}, - year = {2011}, - address = {Miami, Florida, USA}, - owner = {hoonhout}, - timestamp = {2015.05.22} -} - -@article{McKennaNeuman2012, - author = {McKenna Neuman, C. and Li, B. and Nash, D.}, - title = {Micro-topographic analysis of shell pavements formed by aeolian transport - in a wind tunnel simulation}, - journal = {Journal of Geophysical Research}, - year = {2012}, - volume = {117}, - number = {F4}, - note = {F04003}, - doi = {10.1029/2012JF002381}, - issn = {2156-2202}, - keywords = {Erosion, Hydrology: Geographic Information Systems (GIS), Geomechanics, - Geomorphology: general, armoring, beach, shear stress, shells, wind - erosion, wind tunnel}, - owner = {hoonhout}, - timestamp = {2015.06.15} -} - -@article{McKennaNeuman1995, - author = {McKenna Neuman, Cheryl and Nickling, WG}, - title = {Aeolian sediment flux decay: Non-linear behaviour on developing deflation - lag surfaces}, - journal = {Earth Surface Processes and Landforms}, - year = {1995}, - volume = {20}, - pages = {423--435}, - number = {5}, - owner = {hoonhout}, - publisher = {Wiley Online Library}, - timestamp = {2015.10.01}, - url = {http://onlinelibrary.wiley.com/doi/10.1002/esp.3290200504/abstract} -} - -@article{McKennaNeuman1989, - author = {McKenna Neuman, C. and Nickling, W. G.}, - title = {A theoretical and wind tunnel investigation of the effect of capillary - water on the entrainment of sediment by wind}, - journal = {Canadian Journal of Soil Science}, - year = {1989}, - volume = {69}, - pages = {79--96}, - owner = {hoonhout}, - timestamp = {2015.05.26} -} - -@article{McKennaNeuman2008, - author = {McKenna Neuman, C. and Sanderson, S.}, - title = {Humidity control of particle emissions in aeolian systems}, - journal = {Journal of Geophysical Research}, - year = {2008}, - volume = {113}, - number = {F2}, - note = {F02S14}, - doi = {10.1029/2007JF000780}, - issn = {2156-2202}, - keywords = {Global Change: Land/atmosphere interactions, Global Change: Earth - system modeling, Global Change: Instruments and techniques, Global - Change: Atmosphere, humidity, adhesion, wind erosion, transport threshold, - wind tunnel}, - owner = {hoonhout}, - timestamp = {2015.06.15} -} - @article{Mualem1974, author = {Mualem, Y}, journal = {Water Resources Research}, @@ -1464,34 +261,6 @@ @article{Mualem1974 year = {1974} } -@article{Namikas2010, - author = {Namikas, S L and Edwards, B L and Bitton, M C A and Booth, J L and - Zhu, Y}, - title = {Temporal and spatial variabilities in the surface moisture content - of a fine-grained beach}, - journal = {Geomorphology}, - year = {2010}, - volume = {114}, - pages = {303--310}, - doi = {10.1016/j.geomorph.2009.07.011}, - owner = {hoonhout}, - timestamp = {2015.05.26} -} - -@article{Nickling1995, - author = {Nickling, WG and McKenna Neuman, C.}, - title = {Development of deflation lag surfaces}, - journal = {Sedimentology}, - year = {1995}, - volume = {42}, - pages = {403--414}, - number = {3}, - owner = {hoonhout}, - publisher = {Wiley Online Library}, - timestamp = {2015.10.01}, - url = {http://onlinelibrary.wiley.com/store/10.1111/j.1365-3091.1995.tb00381.x/asset/j.1365-3091.1995.tb00381.x.pdf?v=1&t=if84x8ic&s=48d0b8adf74d856b7d050fc83e67448c24808e05} -} - @article{Nickling1981, author = {Nickling, W G and Ecclestone, M}, title = {The effects of soluble salts on the threshold shear velocity of fine @@ -1533,47 +302,6 @@ @book{Nielsen2009 year = {2009} } -@article{Okin2008, - author = {Okin, G S}, - title = {A new model of wind erosion in the presence of vegetation}, - journal = {Journal of Geophysical Research}, - year = {2008}, - volume = {113}, - number = {F2}, - note = {F02S10}, - doi = {10.1029/2007JF000758}, - owner = {hoonhout}, - timestamp = {2015.05.26} -} - -@article{Owen1964, - author = {Owen, P R}, - title = {Saltation of uniform grains in air}, - journal = {J. Fluid Mech}, - year = {1964}, - volume = {20}, - pages = {225--242}, - number = {2}, - owner = {hoonhout}, - publisher = {Cambridge Univ Press}, - timestamp = {2015.10.01} -} - -@article{Parteli2009, - author = {Parteli, E. J. R. and Dur\'{a}n, O. and Tsoar, H. and Schw\"{a}mmle, - V. and Hermann, H. J.}, - title = {Dune formation under bimodal winds}, - journal = {Proceedings of the National Academy of Sciences of the United States - of America}, - year = {2009}, - volume = {106}, - pages = {22085--22089}, - number = {52}, - doi = {10.1073/pnas.0808646106}, - owner = {hoonhout}, - timestamp = {2015.05.27} -} - @article{Peckham2013, author = {Peckham, S. D. and Hutton, E. W. H. and Norris, B.}, title = {A component-based approach to integrated modeling in the geosciences: @@ -1587,16 +315,6 @@ @article{Peckham2013 timestamp = {2015.05.26} } -@techreport{dePree2009, - author = {de Pree, E}, - title = {Field measurements of grain size distributions - {V}lugtenburg}, - institution = {Delft University of Technology}, - year = {2009}, - file = {:Verslag_21novemberdeel2.docx:Word 2007+;:Verslag_21novemberdeel1.docx:Word 2007+}, - owner = {hoonhout}, - timestamp = {2015.05.26} -} - @book{Pye1990, title = {Aeolian Sand and Sand Dunes}, publisher = {Unwin Hyman}, @@ -1635,157 +353,6 @@ @article{Raupach1993 timestamp = {2015.10.01} } -@article{Raupach1992, - author = {Raupach, M R}, - title = {Drag and drag partition on rough surfaces}, - journal = {Boundary-Layer Meteorology}, - year = {1992}, - volume = {60}, - pages = {375--395}, - number = {4}, - owner = {hoonhout}, - publisher = {Springer}, - timestamp = {2015.10.01}, - url = {http://link.springer.com/article/10.1007/BF00155203} -} - -@article{Reniers2013, - author = {Reniers, AJHM and Gallagher, EL and MacMahan, JH and Brown, JA and - Rooijen, AA and Thiel de Vries, JSM and Prooijen, BC}, - title = {Observations and modeling of steep-beach grain-size variability}, - journal = {Journal of Geophysical Research: Oceans}, - year = {2013}, - volume = {118}, - pages = {577--591}, - number = {2}, - owner = {hoonhout}, - publisher = {Wiley Online Library}, - timestamp = {2016.04.29} -} - -@misc{Waterbase2013, - author = {Rijkswaterstaat}, - year = {2013}, - title = {http://live.waterbase.nl}, - howpublished = {website}, - organization = {Directorate-General for Public Works and Water Management}, - url = {http://live.waterbase.nl}, - owner = {hoonhout}, - timestamp = {2015.07.06} -} - -@article{Roelvink2009, - author = {Roelvink, J. A. and Reniers, A. and van Dongeren, A. P. and van Thiel - de Vries, J. S. M. and McCall, R. T. and Lescinski, J.}, - title = {Modelling storm impacts on beaches, dunes and barrier islands}, - journal = {Coastal Engineering}, - year = {2009}, - volume = {56}, - pages = {1133--1152}, - number = {11}, - doi = {10.1016/j.coastaleng.2009.08.006}, - owner = {hoonhout}, - timestamp = {2015.05.26} -} - -@inproceedings{Roelvink2012, - author = {Roelvink, J A and Stelling, G and Hoonhout, B M and Risandi, J and - Jacobs, W and Merli, D}, - title = {Development and field validation of a 2DH curvilinear storm impact - model}, - booktitle = {Proceedings of 33nd International Conference on Coastal Engineering}, - year = {2012}, - address = {Santander, Spain}, - owner = {hoonhout}, - timestamp = {2015.05.22} -} - -@article{Sorensen2004, - author = {S{\o}rensen, Michael}, - title = {On the rate of aeolian sand transport}, - journal = {Geomorphology}, - year = {2004}, - volume = {59}, - pages = {53--62}, - number = {1}, - owner = {hoonhout}, - publisher = {Elsevier}, - timestamp = {2015.10.01} -} - -@article{Scheidt2010, - author = {Scheidt, S. and Ramsey, M. and Lancaster, N.}, - title = {Determining soil moisture and sediment availability at White Sands - Dune Field, New Mexico, from apparent thermal inertia data}, - journal = {Journal of Geophysical Research}, - year = {2010}, - volume = {115}, - number = {F2}, - note = {F02019}, - doi = {10.1029/2009JF001378}, - issn = {2156-2202}, - keywords = {Geomorphology and weathering, Remote sensing, Sediment transport, - Soil moisture, Erosion and weathering, apparent thermal inertia, - soil moisture, sediment availability}, - owner = {hoonhout}, - timestamp = {2015.06.15} -} - -@article{deSchipper2016, - author = {de Schipper, Matthieu A and de Vries, Sierd and Ruessink, Gerben - and de Zeeuw, Roeland C and Rutten, Jantien and van Gelder-Maas, - Carola and Stive, Marcel JF}, - title = {Initial spreading of a mega feeder nourishment: Observations of the - Sand Engine pilot project}, - journal = {Coastal Engineering}, - year = {2016}, - volume = {111}, - pages = {23--38}, - doi = {10.1016/j.coastaleng.2015.10.011}, - owner = {hoonhout}, - publisher = {Elsevier}, - timestamp = {2016.02.24} -} - -@inproceedings{deSchipper2012, - author = {M.A. de {Schipper} and S. de {Vries} and R. {Ranasinghe} and A.J.H.M. - {Reniers} and M.J.F. {Stive}}, - title = {Morphological developments after a beach and shoreface nourishment - at Vlugtenburg beach}, - booktitle = {NCK-days 2012 : Crossing borders in coastal research}, - year = {2012}, - pages = {115--118}, - abstract = {Typically a beach is out of equilibrium after a nourishment is installed. - To observe how a nourished beach behaves on the timescale of storms - a monitoring campaign was set up at Vlugtenburg beach after a nourishment - in the spring of 2009. Here we show a sediment budget analysis of - the first 2.5 years for a coastal domain spanning 1750 m alongshore - from -9 to +5 m NAP. To investigate the redistribution of nourished - sand different sections of the profile are examined. Observations - show that the initial response (first 6 to 12 months after construction) - is large where the sediment eroded from the beach is transported - offshore to form a subtidal bar. In the following period (until present) - the losses in the domain are on the order of 40 m3 per m alongshore - per year. These losses are concentrated in the profile around the - waterline.}, - doi = {10.3990/2.180}, - owner = {hoonhout}, - timestamp = {2015.08.05} -} - -@article{Schlichting1936, - author = {Schlichting, Hermann}, - title = {Experimentelle untersuchungen zum rauhigkeitsproblem}, - journal = {Archive of Applied Mechanics}, - year = {1936}, - volume = {7}, - pages = {1--34}, - number = {1}, - owner = {hoonhout}, - publisher = {Springer}, - timestamp = {2015.10.01}, -} - @PHDTHESIS{Schmutz2014, author = {Schmutz, Phillip P}, title = {Investigation of Factors Controlling the Dynamics of Beach Surface Moisture}, @@ -1793,51 +360,6 @@ @PHDTHESIS{Schmutz2014 year = {2014} } - -@article{Sherman1998, - author = {Sherman, Douglas J and Jackson, Derek WT and Namikas, Steven L and - Wang, Jinkang}, - title = {Wind-blown sand on beaches: an evaluation of models}, - journal = {Geomorphology}, - year = {1998}, - volume = {22}, - pages = {113--133}, - number = {2}, - doi = {10.1016/S0169-555X(97)00062-7}, - owner = {hoonhout}, - publisher = {Elsevier}, - timestamp = {2015.10.01} -} - -@article{Sherman2012, - author = {Sherman, Douglas J and Li, Bailiang}, - title = {Predicting aeolian sand transport rates: a reevaluation of models}, - journal = {Aeolian Research}, - year = {2012}, - volume = {3}, - pages = {371--378}, - number = {4}, - doi = {10.1016/j.aeolia.2011.06.002}, - owner = {hoonhout}, - publisher = {Elsevier}, - timestamp = {2015.10.01} -} - -@article{Sherman2013, - author = {Sherman, Douglas J and Li, Bailiang and Ellis, Jean T and Farrell, - Eugene J and Maia, Luis Parente and Granja, Helena}, - title = {Recalibrating aeolian sand transport models}, - journal = {Earth Surface Processes and Landforms}, - year = {2013}, - volume = {38}, - pages = {169--178}, - number = {2}, - doi = {10.1002/esp.3310}, - owner = {hoonhout}, - publisher = {Wiley Online Library}, - timestamp = {2015.10.01} -} - @INCOLLECTION{Shuttleworth1993, author = {Shuttleworth, W J}, title = {Evaporation}, @@ -1851,48 +373,6 @@ @INCOLLECTION{Shuttleworth1993 timestamp = {2015.10.07} } -@article{Spearman1904, - author = {Spearman, C}, - title = {The proof and measurement of association between two things}, - journal = {American Journal of Psychology}, - year = {1904}, - volume = {15}, - pages = {72--101}, - doi = {10.2307/1412159}, - owner = {hoonhout}, - timestamp = {2016.06.21} -} - -@article{Stive2013, - author = {Stive, M J F and de Schipper, M A and Luijendijk, A P and Aarninkhof, - S G J and van Gelder-Maas, C and van Thiel de Vries, J S M and de - Vries, S and Henriquez, M and Marx, S and Ranasinghe, R}, - title = {A new alternative to saving our beaches from sea-level rise: the - {S}and {E}ngine}, - journal = {Journal of Coastal Research}, - year = {2013}, - volume = {29}, - pages = {1001--1008}, - number = {5}, - doi = {10.2112/JCOASTRES-D-13-00070.1}, - owner = {hoonhout}, - timestamp = {2015.05.22} -} - -@article{Stout2004, - author = {Stout, John E}, - title = {A method for establishing the critical threshold for aeolian transport - in the field}, - journal = {Earth Surface Processes and Landforms}, - year = {2004}, - volume = {29}, - pages = {1195--1207}, - number = {10}, - owner = {hoonhout}, - publisher = {Wiley Online Library}, - timestamp = {2016.04.29} -} - @article{Stockdon2006, author = {Hilary F. Stockdon and Rob A. Holman and Peter A. Howd and Asbury H. Sallenger}, title = {Empirical parameterization of setup, swash, and runup}, @@ -1906,134 +386,6 @@ @article{Stockdon2006 url = {https://www.sciencedirect.com/science/article/pii/S0378383906000044}, } -@article{Tan2013, - author = {Tan, Lihai and Zhang, Weimin and Qu, Jianjun and Zhang, Kecun and - An, Zhishan and Wang, Xiao}, - title = {Aeolian sand transport over gobi with different gravel coverages - under limited sand supply: a mobile wind tunnel investigation}, - journal = {Aeolian Research}, - year = {2013}, - volume = {11}, - pages = {67--74}, - doi = {10.1016/j.aeolia.2013.10.003}, - owner = {hoonhout}, - publisher = {Elsevier}, - timestamp = {2015.10.01} -} - -@article{Turpin2010, - author = {Turpin, C and Badr, T and Harion, J L}, - title = {Numerical modelling of aeolian erosion over rough surfaces}, - journal = {Earth Surface Processes and Landforms}, - year = {2010}, - volume = {35}, - pages = {1418--1429}, - number = {12}, - doi = {10.1002/esp.1980}, - owner = {hoonhout}, - publisher = {Wiley Online Library}, - timestamp = {2015.10.01} -} - -@article{Udo2008, - author = {Udo, K. and Kuriyama, Y. and Jackson, D. W. T.}, - title = {Observations of wind-blown sand under various meteorological conditions - at a beach}, - journal = {Journal of Geophysical Research}, - year = {2008}, - volume = {113}, - number = {F4}, - note = {F04008}, - doi = {10.1029/2007JF000936}, - owner = {hoonhout}, - timestamp = {2015.06.15} -} - -@PHDTHESIS{deVries2012, - author = {de Vries, S}, - title = {Physics of Blown Sand and Coastal Dunes}, - school = {Delft University of Technology}, - year = {2012}, - doi = {10.4233/uuid:9a701423-8559-4a44-be5d-370d292b0df3}, - owner = {hoonhout}, - timestamp = {2015.05.24} -} - -@article{deVries2014b, - author = {de Vries, S and Arens, S M and de Schipper, M A and Ranasinghe, R}, - title = {Aeolian sediment transport on a beach with a varying sediment supply}, - journal = {Aeolian Research}, - year = {2014}, - volume = {15}, - pages = {235--244}, - doi = {10.1016/j.aeolia.2014.08.001}, - owner = {hoonhout}, - timestamp = {2015.05.24} -} - -@inproceedings{deVries2011, - author = {de Vries, S and Arens, S M and Stive, M J F and Ranasinghe, R}, - title = {Dune growth trends and the effect of beach width on annual timescales}, - booktitle = {Proceedings 7th Coastal Sediments Conference}, - year = {2011}, - address = {Miami, Florida, USA}, - owner = {hoonhout}, - timestamp = {2015.05.24} -} - -@inproceedings{deVries2015, - author = {de Vries, S. and Radermacher, M. and de Schipper, M.A. and Stive, - M.J.F.}, - title = {Tidal Dynamics in the Sand Motor Lagoon}, - booktitle = {E-proceedings of the 36th IAHR World Congress}, - year = {2015}, - owner = {hoonhout}, - timestamp = {2016.05.26}, - url = {http://repository.tudelft.nl/islandora/object/uuid:e49d8911-72c2-4f6c-a8b4-7009954134c0/?collection=research} -} - -@inproceedings{deVries2010, - author = {de Vries, S and de Schipper, M A and Stive, M J F and Ranasinghe, - R}, - title = {Sediment exchange between the sub-aqueous and sub-aerial coastal - zones}, - booktitle = {Proceedings of 32nd International Conference on Coastal Engineering}, - year = {2010}, - owner = {hoonhout}, - timestamp = {2015.05.22} -} - -@article{deVries2012a, - author = {de Vries, S and Southgate, H N and Kanning, W and Ranasinghe, R}, - title = {Dune behavior and aeolian transport on decadal timescales}, - journal = {Coastal Engineering}, - year = {2012}, - volume = {67}, - pages = {41--53}, - doi = {10.1016/j.coastaleng.2012.04.002}, - owner = {hoonhout}, - timestamp = {2015.05.22} -} - -@inproceedings{deVries2012b, - author = {de Vries, S and Southgate, H N and Kanning, W and Ranasinghe, R}, - title = {Dune development and aeolian transport along the Holland coast}, - booktitle = {Jubilee Conference Proceedings, NCK-Days 2012}, - year = {2012}, - owner = {hoonhout}, - timestamp = {2015.05.22} -} - -@inproceedings{deVries2012c, - author = {de Vries, S and Stive, M J F and van Rijn, L C and Ranasinghe, R}, - title = {A new conceptual model for aeolian transport rates on beaches}, - booktitle = {Proceedings of 33nd International Conference on Coastal Engineering}, - year = {2012}, - address = {Santander, Spain}, - owner = {hoonhout}, - timestamp = {2015.05.22} -} - @article{deVries2014a, author = {de Vries, S and van Thiel de Vries, J S M and van Rijn, L C and Arens, S M and Ranasinghe, R}, @@ -2047,85 +399,14 @@ @article{deVries2014a timestamp = {2015.05.22} } -@article{VanDerWal2000, - author = {van der Wal, Daphne}, - title = {Grain-size-selective aeolian sand transport on a nourished beach}, - journal = {Journal of Coastal Research}, - year = {2000}, - pages = {896--908}, - owner = {hoonhout}, - publisher = {JSTOR}, - timestamp = {2016.04.29} -} - -@article{VanDerWal1998, - author = {van der Wal, Daphne}, - title = {The impact of the grain-size distribution of nourishment sand on - aeolian sand transport}, - journal = {Journal of Coastal Research}, - year = {1998}, - pages = {620--631}, - owner = {hoonhout}, - publisher = {JSTOR}, - timestamp = {2016.04.29} -} - -@inproceedings{Walstra2012, - author = {Walstra, D J R and de Vroeg, J and van Thiel de Vries, J S M and - Swinkels, C and Luijendijk, A P and de Boer, W and Hoekstra, R and - Hoonhout, B M and Henrotte, J and Smolders, T and Dekker, F and Godsey, - E}, - title = {A comprehensive sediment budget for the mississippi barrier islands}, - booktitle = {Proceedings of 33nd International Conference on Coastal Engineering}, - year = {2012}, - address = {Santander, Spain}, - owner = {hoonhout}, - timestamp = {2015.05.22} -} - -@article{Walters2014, - author = {Walters, D. and Moore, L. J. and Dur\'{a}n, O. and Fagherazzi, S. - and Mariotti, G.}, - title = {Interactions between barrier islands and backbarrier marshes affect - island system response to sea level rise: Insights from a coupled - model}, - journal = {Journal of Geophysical Research}, +@manual{Delft3DManual, + title = {Delft3D - 3D/2D modelling suite for integral water solutions - Hydro-Morphodynamics}, + author = {{Delft3D-FLOW Manual}}, + organization = {Deltares}, + address = {Delft}, + month = {May}, year = {2014}, - volume = {119}, - pages = {2013--2031}, - number = {9}, - note = {2014JF003091}, - doi = {10.1002/2014JF003091}, - issn = {2169-9011}, - keywords = {Wetlands, Geomorphology: general, Littoral processes, Coastal processes, - Continental shelf and slope processes, backbarrier marsh, barrier - island, overwash, sea level rise, coastal erosion}, - owner = {hoonhout}, - timestamp = {2015.06.15} -} - -@article{Weng1991, - author = {Weng, W. S. and Hunt, J. C. R. and Carruthers, D. J. and Warren, - A. and Wiggs, G. F. S.}, - title = {Air flow and sand transport over sand-dunes}, - journal = {Acta Mechanica}, - year = {1991}, - volume = {2}, - pages = {1--22}, - file = {Weng1991.pdf:Weng1991.pdf:PDF}, - owner = {hoonhout}, - timestamp = {2015.05.27} -} - -@article{Wiggs2004, - author = {Wiggs, G F S and Baird, A J and Atherton, R J}, - title = {The dynamic effects of moisture on the entrainment and transport - of sand by wind}, - journal = {Geomorphology}, - year = {2004}, - volume = {59}, - pages = {13--30}, - doi = {10.1016/j.geomorph.2003.09.002}, + note = {Version 3.15.34158}, owner = {hoonhout}, timestamp = {2015.05.26} } @@ -2143,21 +424,3 @@ @article{Williams1971 owner = {hoonhout}, timestamp = {2015.08.06} } - -@article{Zhang2010, - author = {Zhang, D. and Narteau, C. and Rozier, O.}, - title = {Morphodynamics of barchan and transverse dunes using a cellular automaton - model}, - journal = {Journal of Geophysical Research}, - year = {2010}, - volume = {115}, - number = {F3}, - note = {F03041}, - doi = {10.1029/2009JF001620}, - issn = {2156-2202}, - keywords = {Cellular automata, Sediment transport, Geomorphology: general, Geomorphology: - fluvial, dunes, bed shear stress, cellular automaton}, - owner = {hoonhout}, - timestamp = {2015.06.15} -} - diff --git a/docs/index.rst b/docs/index.rst index 64cf71d6..06dc381c 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -41,6 +41,7 @@ Contents user/model_interaction user/sourcecode user/references + user/appendix .. toctree:: :caption: Tutorials and examples diff --git a/docs/user/appendix.rst b/docs/user/appendix.rst new file mode 100644 index 00000000..64fdd18e --- /dev/null +++ b/docs/user/appendix.rst @@ -0,0 +1,620 @@ +Appendix +========= + +Numerical details of solving the advection equation +----------------------------------------------------- + + +.. _pieter_num: + +Conservative Euler Backward Implicit (pieter solver) +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The default numerical method assumes the advection scheme in a conservative form in combination with an euler backward scheme. This scheme is prepared to use a TVD method but this is not implemented yet (add footnote{Total Variance Diminishing, this is explained in the lecture notes by Zijlema p94}) + +The fluxes at the interface of the cells are defined used in the advection terms: + +.. math:: + :label: conservative1 + + \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t} + \\ + \frac{u_{\text{x},i+1/2,j} \cdot c^{n+1}_{i+1/2,j,k} - u_{\text{x},i-1/2,j} \cdot c^{n+1}_{i-1/2,j,k}}{\Delta x} + \\ + \frac{u_{\text{y},i,j+1/2} \cdot c^{n+1}_{i,j+1/2,k} - u_{\text{y},i,j-1/2} \cdot c^{n+1}_{i,j-1/2,k}}{\Delta y} + + \\ = \\ + \frac{\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i.j.k} + c^{n+1}_{i,j,k} ) - c^{n+1}_{i,j,k}}{T} + +In which :math:`n` is the time step index, :math:`i` and :math:`j` are the cross-shore and alongshore spatial grid cell indices and :math:`k` is the grain size fraction index. :math:`w` [-] is the weighting factor used for the weighted addition of the saturated sediment concentrations over all grain size fractions. Note that u is spatially varying but has no temporal index. This is because u is a result of a separate wind solver and considered temporally invariant in the advection solver. + +Now we use a correction algorithm where: + +.. math:: + :label: conservative2 + + c^{n+1}_{i,j,k} = c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} + +where :math:`\delta c_{i,j,k}` is solved for and :math:`*` denotes the previous iteration. + +When now assuming an upwind scheme in space, we can derive 4 concentrations at the cell faces which are dependent on the velocity at the cell faces. + +We assume in x direction: + +.. math:: + + c^{n+1}_{i+1/2,j,k} = + \begin{cases} + c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{x},i+1/2,j} > 0$,}\\ + c^{n+1 *}_{i+1,j,k} + \delta c_{i+1,j,k} & \text{if $u_{\text{x},i+1/2,j} < 0$.} + \end{cases} + +.. math:: + + c^{n+1}_{i-1/2,j,k} = + \begin{cases} + c^{n+1 *}_{i-1,j,k} + \delta c_{i-1,j,k} & \text{if $u_{\text{x},i-1/2,j} > 0$,}\\ + c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{x},i-1/2,j} < 0$.} + \end{cases} + +and in y-direction: + +.. math:: + + c^{n+1}_{i,j+1/2,k} = + \begin{cases} + c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{y},i,j+1/2} > 0$,}\\ + c^{n+1 *}_{i,j+1,k} + \delta c_{i,j+1,k} & \text{if $u_{\text{y},i,j+1/2} < 0$.} + \end{cases} + +.. math:: + + c^{n+1}_{i,j-1/2,k} = + \begin{cases} + c^{n+1 *}_{i,j-1,k} + \delta c_{i,j-1,k} & \text{if $u_{\text{y},i,j-1/2} > 0$,}\\ + c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{y},i,j-1/2} < 0$.} + \end{cases} + +Now we assume: + +- :math:`\Gamma_x = 1` if :math:`u_{\text{x},i+1/2,j,k} > 0` and :math:`\Gamma_x = 0` if :math:`u_{\text{x},i+1/2,j,k} \leq 0` +- :math:`\Gamma_y = 1` if :math:`u_{\text{y},i,j+1/2,k} > 0` and :math:`\Gamma_x = 0` if :math:`u_{\text{y},i,j+1/2,k} \leq 0` + +(We did not test if this works well with diverging and converging flows. We may need another term that describes the conditions at the negative cell faces if they are of opposite direction than the positive cell faces and vice versa) + +Let's continue for the moment so that + +.. math:: + + \begin{gathered} + \frac{c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} - c^n_{i,j,k}}{\Delta t} + \\ + \Gamma_x \cdot \frac{u_{\text{x},i+1/2,j} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}) - u_{\text{x},i-1/2,j} \cdot (c^{n+1 *}_{i-1,j,k} + \delta c_{i-1,j,k})}{\Delta x} + \\ + (1-\Gamma_x) \cdot \frac{u_{\text{x},i+1/2,j} \cdot (c^{n+1 *}_{i+1,j,k} + \delta c_{i+1,j,k}) - u_{\text{x},i-1/2,j} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k})}{\Delta x} + \\ + \Gamma_y \cdot \frac{u_{\text{y},i,j+1/2} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}) - u_{\text{y},i,j-1/2} \cdot (c^{n+1 *}_{i,j-1,k} + \delta c_{i,j-1,k})}{\Delta y} + \\ + (1-\Gamma_y) \cdot \frac{u_{\text{y},i,j+1/2} \cdot (c^{n+1 *}_{i,j+1,k} + \delta c_{i,j+1,k}) - u_{\text{y},i,j-1/2} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k})}{\Delta y} + + \\ = \\ + \frac{\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i,j,k}+c^{n+1 *}_{i,j,k} + \xcancel{\delta c_{i,j,k}}) - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}}{T} + \end{gathered} + +(note that the above does not take converging and diverging flows into account, also :math:`\delta c_{i,j,k}` at the right hand side in the "min" brackets is difficult to solve for. In the code, this term is neglected which may cause some inaccuracy when calculating pickup. Although mass continuity is corrected for in the implicit scheme when calculating pickup using equation ???) + +Now we simplify: + +.. math:: + + \begin{gathered} + (\frac{\Delta x \Delta y}{\Delta t} + \Gamma_x\Delta y \cdot u_{\text{x},i+1/2,j} - (1-\Gamma_x)\Delta y \cdot u_{\text{x},i-1/2,j} + \Gamma_y\Delta x \cdot u_{\text{y},i,j+1/2}\\ - (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j-1/2}+\frac{\Delta x \Delta y}{T_s})\cdot \delta c_{i,j,k}\\ + -(\Gamma_x\Delta y \cdot u_{\text{x},i-1/2,j})\cdot \delta c_{i-1,j,k}\\ + +((1-\Gamma_x)\Delta y \cdot u_{\text{x},i+1/2,j})\cdot \delta c_{i+1,j,k}\\ + -(\Gamma_y\Delta x \cdot u_{\text{y},i,j-1/2})\cdot \delta c_{i,j-1,k}\\ + + ((1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j+1/2})\cdot \delta c_{i,j+1,k}\\ + \end{gathered} + +or + +.. math:: + + \begin{gathered} + A0 \cdot \delta c_{i,j,k} + + A\text{m1} \cdot \delta c_{i-1,j,k} + + A\text{p1} \cdot \delta c_{i+1,j,k}\\ + + A\text{mx} \cdot \delta c_{i,j-1,k} + + A\text{px} \cdot \delta c_{i,j+1,k} = y_{i,j,k} + \label{eq:lin} + \end{gathered} + +or the linear system of equations in general form: + +.. math:: + :label: conservative_general + + A \cdot \delta c_{i,j,k} = y_{i,j,k} + +Where :math:`A` is a 3-dimensional sparse matrix that is compiled using the matrix diagonals (:math:`A0, Am1, Ap1, Amx, Apx`) which are defined as: + +.. math:: + + \begin{aligned} + A0 = & +\frac{\Delta x \Delta y}{\Delta t} \\ + & +\frac{\Delta x \Delta y}{T_s} \\ + & - (1-\Gamma_x)\Delta y \cdot u_{\text{x},i-1/2,j} \\ + & + \Gamma_x\Delta y \cdot u_{\text{x},i+1/2,j} \\ + & - (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j-1/2} \\ + & + \Gamma_y\Delta x \cdot u_{\text{y},i,j+1/2} \\ + \end{aligned} + +and + +.. math:: + + A\text{m}1 = -\Gamma_x\Delta y \cdot u_{\text{x},i-1/2,j} + +and + +.. math:: + + A\text{p}1 = (1-\Gamma_x)\Delta y \cdot u_{\text{x},i+1/2,j} + +and + +.. math:: + A\text{mx} = -\Gamma_y\Delta x \cdot u_{\text{y},i,j-1/2} + +and + +.. math:: + + A\text{px} = (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j+1/2} + +Let's go towards the RHS + +.. math:: + + \begin{aligned} + y_{i,j,k} = & - \frac{\Delta x \Delta y}{\Delta t}(c^{n+1 *}_{i,j,k}-c^{n}_{i,j,k}) \\ + & + \frac{\Delta x \Delta y}{T_s}(\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i,j,k} + c^{n+1 *}_{i,j,k}) - c^{n+1 *}_{i,j,k}) \\ + & + \Delta y \cdot u_{\text{x},i-1/2,j} \cdot + (\Gamma_x \cdot c^{n+1 *}_{i-1,j,k} + (1-\Gamma_x) c^{n+1 *}_{i,j,k})\\ + & - \Delta y \cdot u_{\text{x},i+1/2,j} \cdot (\Gamma_x \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_x) c^{n+1 *}_{i+1,j,k})\\ + & + \Delta x \cdot u_{\text{y},i,j-1/2} \cdot (\Gamma_y \cdot c^{n+1 *}_{i,j-1,k} + (1-\Gamma_y) c^{n+1 *}_{i,j,k})\\ + & - \Delta x \cdot u_{\text{y},i,j+1/2} \cdot (\Gamma_y \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_y) c^{n+1 *}_{i,j+1,k})\\ + \end{aligned} + +in the python code some intermediate variable is defined to make it easier to shift indexes + +.. math:: + + \text{Ctxfs} =(\Gamma_x \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_x) c^{n+1 *}_{i+1,j,k}) + +and + +.. math:: + + \text{Ctxfn} =(\Gamma_y \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_y) c^{n+1 *}_{i,j+1,k}) + +also Erosion and deposition are defined using seperate variables. + +.. math:: + D_{i,j,k}= \frac{\Delta x \Delta y}{T_s}c^{n+1 *}_{i,j,k} + +and + +.. math:: + + A_{i,j,k}= \frac{\Delta x \Delta y}{T_s}m_{i,j,k} + D_{i,j,k} + +and + +.. math:: + U_{i,j,k}= \frac{\Delta x \Delta y}{T_s}\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} + +and + +.. math:: + E_{i,j,k} = \min(U_{i,j,k},A_{i,j,k}) + +After solving equation :math:`\delta c_{i,j,k}` using :eq:`conservative_general`, :math:`c^{n+1}_{i,j,k}` can be calculated using equation :eq:`conservative2`. + +Also, the pickup per grid cell can be calculated using: + +.. math:: + + \text{pickup} = \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k}- c^{n+1}_{i,j,k}}{T_s}\Delta t + \label{eq:pickup} + +note that this is only valid when using an Euler backward scheme. + + +.. _trunk_num: + +Euler Schemes in non-conservative form (trunk solver) +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Early model results relied on Euler schemes in a non conservative form. This allowed for a relatively easy implementation but did not guarantee mass conservation. In version 2 of AEOLIS the conservative form became the default. However, some users still use the older scheme. + +The formulation is discretized following a first order upwind scheme +assuming that the wind velocity :math:`u_z` is positive in both +x-direction and y-direction: + +.. math:: + :label: apx-explicit + + \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + + u^n_{z,\mathrm{x}} \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x_{i,j}} + + u^n_{z,\mathrm{y}} \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y_{i,j}} \\ = + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} + +in which :math:`n` is the time step index, :math:`i` and :math:`j` are +the cross-shore and alongshore spatial grid cell indices and :math:`k` +is the grain size fraction index. :math:`w` [-] is the weighting +factor used for the weighted addition of the saturated sediment +concentrations over all grain size fractions. + +The discretization can be generalized for any wind direction as: + +.. math:: + :label: apx-explicit-generalized + + \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + + u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + + u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \\ + + u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + + u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} = + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} + +in which: + +.. math:: + :label: apx-upwind1 + + \begin{array}{rclcrcl} + u^n_{z,\mathrm{x+}} &=& \max( 0, u^n_{z,\mathrm{x}} ) &;& u^n_{z,\mathrm{y+}} &=& \max( 0, u^n_{z,\mathrm{y}} ) \\ + u^n_{z,\mathrm{x-}} &=& \min( 0, u^n_{z,\mathrm{x}} ) &;& u^n_{z,\mathrm{y-}} &=& \min( 0, u^n_{z,\mathrm{y}} ) \\ + \end{array} + +and + +.. math:: + :label: apx-upwind2 + + \begin{array}{rclcrcl} + c^n_{i,j,k,\mathrm{x+}} &=& \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x} &;& + c^n_{i,j,k,\mathrm{y+}} &=& \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y} \\ + c^n_{i,j,k,\mathrm{x-}} &=& \frac{c^n_{i,j,k} - c^n_{i-1,j,k}}{\Delta x} &;& + c^n_{i,j,k,\mathrm{y-}} &=& \frac{c^n_{i,j,k} - c^n_{i,j-1,k}}{\Delta y} \\ + \end{array} + +Equation :eq:`apx-explicit-generalized` is explicit in +time and adheres to the Courant-Friedrich-Lewis (CFL) condition for +numerical stability. Alternatively, the advection equation can be +discretized implicitly in time for unconditional stability: + +.. math:: + :label: apx-implicit-generalized + + \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + + u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + + u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \\ + + u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + + u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} = + \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} + +Equation :eq:`apx-explicit-generalized` and +:eq:apx-implicit-generalized` can be rewritten as: + +.. math:: + :label: apx-explicit-rewritten + + c^{n+1}_{i,j,k} = c^n_{i,j,k} - \Delta t^n \left[ + u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + + u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \phantom{\frac{c^n_{i,j,k}}{T}} \right. \\ + \left. + u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + + u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} + + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] + +and + +.. math:: + :label: apx-implicit-rewritten + + c^{n+1}_{i,j,k} + \Delta t^n \left[ + u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + + u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \phantom{\frac{c^{n+1}_{i,j,k}}{T}} \right. \\ + \left. + u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + + u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} + + \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] = c^n_{i,j,k} + +and combined using a weighted average: + +.. math:: + :label: apx-combined + + c^{n+1}_{i,j,k} + \Gamma \Delta t^n \left[ + u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + + u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \phantom{\frac{c^{n+1}_{i,j,k}}{T}} \right. \\ + \left. + u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + + u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} + + \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] \\ = + c^n_{i,j,k} - (1 - \Gamma) \Delta t^n \left[ + u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + + u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \phantom{\frac{c^n_{i,j,k}}{T}} \right. \\ + \left. + u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + + u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} + + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] + +in which :math:`\Gamma` is a weight that ranges from 0 -- 1 and +determines the implicitness of the scheme. The scheme is implicit with +:math:`\Gamma = 0`, explicit with :math:`\Gamma = 1` and semi-implicit +otherwise. :math:`\Gamma = 0.5` results in the semi-implicit Crank-Nicolson +scheme. + +Equation :eq:`apx-upwind2` is back-substituted in Equation +:eq:`apx-combined`: + +.. math:: + :label: apx-combined-substituted + + c^{n+1}_{i,j,k} + \Gamma \Delta t^n \left[ + u^{n+1}_{z,\mathrm{x+}} \frac{c^{n+1}_{i+1,j,k} - c^{n+1}_{i,j,k}}{\Delta x} + + u^{n+1}_{z,\mathrm{y+}} \frac{c^{n+1}_{i,j+1,k} - c^{n+1}_{i,j,k}}{\Delta y} \right. \\ + \left. + u^{n+1}_{z,\mathrm{x-}} \frac{c^{n+1}_{i,j,k} - c^{n+1}_{i-1,j,k}}{\Delta x} + + u^{n+1}_{z,\mathrm{y-}} \frac{c^{n+1}_{i,j,k} - c^{n+1}_{i,j-1,k}}{\Delta y} + + \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] \\ = + c^n_{i,j,k} - (1 - \Gamma) \Delta t^n \left[ + u^n_{z,\mathrm{x+}} \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x} + + u^n_{z,\mathrm{y+}} \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y} \right. \\ + \left. + u^n_{z,\mathrm{x-}} \frac{c^n_{i,j,k} - c^n_{i-1,j,k}}{\Delta x} + + u^n_{z,\mathrm{y-}} \frac{c^n_{i,j,k} - c^n_{i,j-1,k}}{\Delta y} + + \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] + +and rewritten: + +.. math:: + :label: apx-combined-rewritten + + \left[ 1 - \Gamma \left( + u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + + u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - + u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - + u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + + \frac{\Delta t^n}{T} + \right) + \right] c^{n+1}_{i,j,k} \\ + + \Gamma \left( + u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^{n+1}_{i+1,j,k} + + u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^{n+1}_{i,j+1,k} - %\right. \\ - \left. + u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^{n+1}_{i-1,j,k} - + u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^{n+1}_{i,j-1,k} + \right) \\ = + \left[ 1 + (1 - \Gamma) \left( + u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + + u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - + u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - + u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + + \frac{\Delta t^n}{T} + \right) + \right] c^n_{i,j,k} \\ + + (1 - \Gamma) \left( + u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^n_{i+1,j,k} + + u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^n_{i,j+1,k} - %\right. \\ - \left. + u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^n_{i-1,j,k} - + u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^n_{i,j-1,k} + \right) \\ - + \Gamma \hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - + (1 - \Gamma) \hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} + +and simplified: + +.. math:: + :label: apx-combined-simplified + + a^{0,0}_{i,j} c^{n+1}_{i,j,k} + + a^{1,0}_{i,j} c^{n+1}_{i+1,j,k} + + a^{0,1}_{i,j} c^{n+1}_{i,j+1,k} - + a^{-1,0}_{i,j} c^{n+1}_{i-1,j,k} - + a^{0,-1}_{i,j} c^{n+1}_{i,j-1,k} = y_{i,j,k} + +where the implicit coefficients are defined as: + +.. math:: + :label: apx-implicitcoef + + \begin{array}{rclcrcl} + a^{0,0}_{i,j} &=& \left[1 - \Gamma \left( + u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + + u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - + u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - + u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + + \frac{\Delta t^n}{T} + \right) \right] \\ + a^{1,0}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} \\ + a^{0,1}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} \\ + a^{-1,0}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} \\ + a^{0,-1}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} \\ + \end{array} + +and the explicit right-hand side as: + +.. math:: + :label: apx-explicitrhs + + y^n_{i,j,k} = \left[ 1 + (1 - \Gamma) \left( + u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + + u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - + u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - + u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + + \frac{\Delta t^n}{T} + \right) + \right] c^n_{i,j,k} \\ + + (1 - \Gamma) \left( + u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^n_{i+1,j,k} + + u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^n_{i,j+1,k} - + u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^n_{i-1,j,k} - + u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^n_{i,j-1,k} + \right) \\ - + \Gamma \hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - + (1 - \Gamma) \hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} + +The offshore boundary is defined to be zero-flux, the +onshore boundary has a constant transport gradient and the lateral +boundaries are circular: + +.. math:: + :label: apx-boundaryconditions + + \begin{array}{rclcrcl} + c^{n+1}_{1,j,k} &=& 0 \\ + c^{n+1}_{n_{\mathrm{x}}+1,j,k} &=& 2 c^{n+1}_{n_{\mathrm{x}},j,k} - c^{n+1}_{n_{\mathrm{x}}-1,j,k} \\ + c^{n+1}_{i,1,k} &=& c^{n+1}_{i,n_{\mathrm{y}}+1,k} \\ + c^{n+1}_{i,n_{\mathrm{y}}+1,k} &=& c^{n+1}_{i,1,k} \\ + \end{array} + + +Solving the Linear System of Equations +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The linear system of equations can be elaborated : + +.. math:: + :label: apx-system + + \left[ + \begin{array}{cccccc} + A^0_1 & A^{1}_1 & \textbf{0} & \cdots & \textbf{0} & A^{n_{\mathrm{y}}+1}_1 \\ + A^{-1}_2 & A^0_2 & \ddots & \ddots & & \textbf{0} \\ + \textbf{0} & \ddots & \ddots & \ddots & \ddots & \vdots \\ + \vdots & \ddots & \ddots & \ddots & \ddots & \textbf{0} \\ + \textbf{0} & & \ddots & \ddots & A^0_{n_{\mathrm{y}}} & A^1_{n_{\mathrm{y}}} \\ + A^{-n_{\mathrm{y}}-1}_{n_{\mathrm{y}}+1} & \textbf{0} & \cdots & \textbf{0} & A^{-1}_{n_{\mathrm{y}}+1} & A^0_{n_{\mathrm{y}}+1} \\ + \end{array} + \right] \left[ + \begin{array}{c} + \vec{\delta c}_1 \\ \vec{\delta c}_2 \\ \vdots \\ \vdots \\ \vec{\delta c}_{n_{\mathrm{y}}} \\ \vec{\delta c}_{n_{\mathrm{y}}+1} \\ + \end{array} + \right] = \left[ + \begin{array}{c} + \vec{y}_1 \\ \vec{y}_2 \\ \vdots \\ \vdots \\ \vec{y}_{n_{\mathrm{y}}} \\ \vec{y}_{n_{\mathrm{y}}+1} \\ + \end{array} + \right] + +where each item in the matrix is again a matrix :math:`A^l_j` and +each item in the vectors is again a vector :math:`\vec{\delta c}_j` and +:math:`\vec{y}_j` respectively. The form of the matrix :math:`A^l_j` depends on +the diagonal index :math:`l` and reads: + +.. math:: + :label: apx-diagonal + + A^0_j = + \left[ + \begin{array}{ccccccc} + 0 & 0 & 0 & 0 + & \cdots & \cdots & 0 \\ + a^{0,-1}_{2,j} & a^{0,0}_{2,j} & a^{0,1}_{2,j} & \ddots + & & & \vdots \\ + 0 & a^{0,-1}_{3,j} & a^{0,0}_{3,j} & a^{0,1}_{3,j} + & \ddots & & \vdots \\ + \vdots & \ddots & \ddots & \ddots + & \ddots & \ddots & \vdots \\ + \vdots & & \ddots & a^{0,-1}_{n_{\mathrm{x}}-1,j} + & a^{0,0}_{n_{\mathrm{x}}-1,j} & a^{0,1}_{n_{\mathrm{x}}-1,j} & 0 \\ + \vdots & & & 0 + & a^{0,-1}_{n_{\mathrm{x}},j} & a^{0,0}_{n_{\mathrm{x}},j} & a^{0,1}_{n_{\mathrm{x}},j} \\ + 0 & \cdots & \cdots & 0 + & 1 & -2 & 1 \\ + \end{array} + \right] + +for :math:`l = 0` and + +.. math:: + :label: apx-offdiagonal + + A^l_j = + \left[ + \begin{array}{ccccccc} + 1 & 0 & \cdots & \cdots + & \cdots & \cdots & 0 \\ + 0 & a^{l,0}_{2,j} & \ddots & + & & & \vdots \\ + \vdots & \ddots & a^{l,0}_{3,j} & \ddots + & & & \vdots \\ + \vdots & & \ddots & \ddots + & \ddots & & \vdots \\ + \vdots & & & \ddots + & a^{l,0}_{n_{\mathrm{x}}-1,j} & \ddots & \vdots \\ + \vdots & & & + & \ddots & a^{l,0}_{n_{\mathrm{x}},j} & 0 \\ + 0 & \cdots & \cdots & \cdots + & \cdots & 0 & 1 \\ + \end{array} + \right] + +for :math:`l \neq 0`. The vectors :math:`\vec{\delta c}_{j,k}` and :math:`\vec{y}_{j,k}` +read: + +.. math:: + :label: c-array + + \begin{array}{rclrcl} + \vec{\delta c}_{j,k} &=& \left[ + \begin{array}{c} + \delta c^{n+1}_{1,j,k} \\ + \delta c^{n+1}_{2,j,k} \\ + \delta c^{n+1}_{3,j,k} \\ + \vdots \\ + \delta c^{n+1}_{n_{\mathrm{x}}-1,j,k} \\ + \delta c^{n+1}_{n_{\mathrm{x}},j,k} \\ + \delta c^{n+1}_{n_{\mathrm{x}}+1,j,k} \\ + \end{array} + \right] & ~ \mathrm{and} ~ + \vec{y}_{j,k} &=& \left[ + \begin{array}{c} + 0 \\ + y^n_{2,j,k} \\ + y^n_{3,j,k} \\ + \vdots \\ + y^n_{n_{\mathrm{x}}-1,j,k} \\ + y^n_{n_{\mathrm{x}},j,k} \\ + 0 \\ + \end{array} + \right] \\ + \end{array} + +:math:`n_{\mathrm{x}}` and :math:`n_{\mathrm{y}}` denote the number of +spatial grid cells in x- and y-direction. + +Iterations to solve for multiple fractions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The linear system defined in Equation :eq:`apx-system` is solved by a +sparse matrix solver for each sediment fraction separately in +ascending order of grain size. Initially, the weights +:math:`\hat{w}^{n+1}_{i,j,k}` are chosen according to the grain size +distribution in the bed and the air. The sediment availability +constraint is checked after each solve: + +.. math:: + :label: solve + + m_{\mathrm{a}} \geq \frac{\hat{w}^{n+1}_{i,j,k} c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \Delta t^n + +If the constraint if violated, a new estimate for the weights +is back-calculated following: + +.. math:: + :label: solve-weights + + \hat{w}^{n+1}_{i,j,k} = \frac{ c^{n+1}_{i,j,k} + m_{\mathrm{a}} \frac{T}{\Delta t^n} }{c^{n+1}_{\mathrm{sat},i,j,k}} + +The system is solved again using the new weights. This +procedure is repeated until a weight is found that does not violate +the sediment availability constraint. If the time step is not too +large, the procedure typically converges in only a few +iterations. Finally, the weights of the larger grains are increased +proportionally as to ensure that the sum of all weights remains +unity. If no larger grains are defined, not enough sediment is +available for transport and the grid cell is truly +availability-limited. This situation should only occur occasionally as +the weights in the next time step are computed based on the new bed +composition and thus will be skewed towards the large fractions. If +the situation occurs regularly, the time step is chosen too large +compared to the rate of armoring. + diff --git a/docs/user/model_description.rst b/docs/user/model_description.rst index 6e353999..f093d387 100644 --- a/docs/user/model_description.rst +++ b/docs/user/model_description.rst @@ -933,635 +933,3 @@ Avalanching Wet bed reset ^^^^^^^^^^^^^^^^ - - -Numerical implementation of the advection equation --------------------------------------------------- - -The advection equation is implemented in two-dimensional form -following: - -.. math:: - :label: apx-advection - - \frac{\partial c}{\partial t} + - u_{z,\mathrm{x}} \frac{\partial c}{\partial x} + - u_{z,\mathrm{y}} \frac{\partial c}{\partial y} = - \frac{c_{\mathrm{sat}} - c}{T} - -in which :math:`c` [:math:`\mathrm{kg/m^2}`] is the sediment mass per -unit area in the air, :math:`c_{\mathrm{sat}}` [:math:`\mathrm{kg/m^2}`] is the -maximum sediment mass in the air that is reached in case of -saturation, :math:`u_{z,\mathrm{x}}` and :math:`u_{z,\mathrm{y}}` are the x- and -y-component of the wind velocity at height :math:`z` [m], :math:`T` [s] is an -adaptation time scale, :math:`t` [s] denotes time and :math:`x` [m] and :math:`y` [m] -denote cross-shore and alongshore distances respectively. - -The formulation is discretized in different ways to allow for different types of simulations balancing accuracy vs. computational resources. The conservative method combined with an euler backward scheme (written by Prof. Rauwoens) is the current default for most simulations. Non-conservative methods end explicit Euler forward schemes are also available. - -Default scheme -- Conservative Euler Backward Implicit -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -The default numerical method assumes the advection scheme in a conservative form in combination with an euler backward scheme. This scheme is prepared to use a TVD method but this is not implemented yet (add footnote{Total Variance Diminishing, this is explained in the lecture notes by Zijlema p94}) - -The fluxes at the interface of the cells are defined used in the advection terms: - -.. math:: - :label: conservative1 - - \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t} + \\ - \frac{u_{\text{x},i+1/2,j} \cdot c^{n+1}_{i+1/2,j,k} - u_{\text{x},i-1/2,j} \cdot c^{n+1}_{i-1/2,j,k}}{\Delta x} + \\ - \frac{u_{\text{y},i,j+1/2} \cdot c^{n+1}_{i,j+1/2,k} - u_{\text{y},i,j-1/2} \cdot c^{n+1}_{i,j-1/2,k}}{\Delta y} + - \\ = \\ - \frac{\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i.j.k} + c^{n+1}_{i,j,k} ) - c^{n+1}_{i,j,k}}{T} - -In which :math:`n` is the time step index, :math:`i` and :math:`j` are the cross-shore and alongshore spatial grid cell indices and :math:`k` is the grain size fraction index. :math:`w` [-] is the weighting factor used for the weighted addition of the saturated sediment concentrations over all grain size fractions. Note that u is spatially varying but has no temporal index. This is because u is a result of a separate wind solver and considered temporally invariant in the advection solver. - -Now we use a correction algorithm where: - -.. math:: - :label: conservative2 - - c^{n+1}_{i,j,k} = c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} - -where :math:`\delta c_{i,j,k}` is solved for and :math:`*` denotes the previous iteration. - -When now assuming an upwind scheme in space, we can derive 4 concentrations at the cell faces which are dependent on the velocity at the cell faces. - -We assume in x direction: - -.. math:: - - c^{n+1}_{i+1/2,j,k} = - \begin{cases} - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{x},i+1/2,j} > 0$,}\\ - c^{n+1 *}_{i+1,j,k} + \delta c_{i+1,j,k} & \text{if $u_{\text{x},i+1/2,j} < 0$.} - \end{cases} - -.. math:: - - c^{n+1}_{i-1/2,j,k} = - \begin{cases} - c^{n+1 *}_{i-1,j,k} + \delta c_{i-1,j,k} & \text{if $u_{\text{x},i-1/2,j} > 0$,}\\ - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{x},i-1/2,j} < 0$.} - \end{cases} - -and in y-direction: - -.. math:: - - c^{n+1}_{i,j+1/2,k} = - \begin{cases} - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{y},i,j+1/2} > 0$,}\\ - c^{n+1 *}_{i,j+1,k} + \delta c_{i,j+1,k} & \text{if $u_{\text{y},i,j+1/2} < 0$.} - \end{cases} - -.. math:: - - c^{n+1}_{i,j-1/2,k} = - \begin{cases} - c^{n+1 *}_{i,j-1,k} + \delta c_{i,j-1,k} & \text{if $u_{\text{y},i,j-1/2} > 0$,}\\ - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} & \text{if $u_{\text{y},i,j-1/2} < 0$.} - \end{cases} - -Now we assume: - -- :math:`\Gamma_x = 1` if :math:`u_{\text{x},i+1/2,j,k} > 0` and :math:`\Gamma_x = 0` if :math:`u_{\text{x},i+1/2,j,k} \leq 0` -- :math:`\Gamma_y = 1` if :math:`u_{\text{y},i,j+1/2,k} > 0` and :math:`\Gamma_x = 0` if :math:`u_{\text{y},i,j+1/2,k} \leq 0` - -(We did not test if this works well with diverging and converging flows. We may need another term that describes the conditions at the negative cell faces if they are of opposite direction than the positive cell faces and vice versa) - -Let's continue for the moment so that - -.. math:: - - \begin{gathered} - \frac{c^{n+1 *}_{i,j,k} + \delta c_{i,j,k} - c^n_{i,j,k}}{\Delta t} + \\ - \Gamma_x \cdot \frac{u_{\text{x},i+1/2,j} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}) - u_{\text{x},i-1/2,j} \cdot (c^{n+1 *}_{i-1,j,k} + \delta c_{i-1,j,k})}{\Delta x} + \\ - (1-\Gamma_x) \cdot \frac{u_{\text{x},i+1/2,j} \cdot (c^{n+1 *}_{i+1,j,k} + \delta c_{i+1,j,k}) - u_{\text{x},i-1/2,j} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k})}{\Delta x} + \\ - \Gamma_y \cdot \frac{u_{\text{y},i,j+1/2} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}) - u_{\text{y},i,j-1/2} \cdot (c^{n+1 *}_{i,j-1,k} + \delta c_{i,j-1,k})}{\Delta y} + \\ - (1-\Gamma_y) \cdot \frac{u_{\text{y},i,j+1/2} \cdot (c^{n+1 *}_{i,j+1,k} + \delta c_{i,j+1,k}) - u_{\text{y},i,j-1/2} \cdot (c^{n+1 *}_{i,j,k} + \delta c_{i,j,k})}{\Delta y} + - \\ = \\ - \frac{\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i,j,k}+c^{n+1 *}_{i,j,k} + \xcancel{\delta c_{i,j,k}}) - c^{n+1 *}_{i,j,k} + \delta c_{i,j,k}}{T} - \end{gathered} - -(note that the above does not take converging and diverging flows into account, also :math:`\delta c_{i,j,k}` at the right hand side in the "min" brackets is difficult to solve for. In the code, this term is neglected which may cause some inaccuracy when calculating pickup. Although mass continuity is corrected for in the implicit scheme when calculating pickup using equation ???) - -Now we simplify: - -.. math:: - - \begin{gathered} - (\frac{\Delta x \Delta y}{\Delta t} + \Gamma_x\Delta y \cdot u_{\text{x},i+1/2,j} - (1-\Gamma_x)\Delta y \cdot u_{\text{x},i-1/2,j} + \Gamma_y\Delta x \cdot u_{\text{y},i,j+1/2}\\ - (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j-1/2}+\frac{\Delta x \Delta y}{T_s})\cdot \delta c_{i,j,k}\\ - -(\Gamma_x\Delta y \cdot u_{\text{x},i-1/2,j})\cdot \delta c_{i-1,j,k}\\ - +((1-\Gamma_x)\Delta y \cdot u_{\text{x},i+1/2,j})\cdot \delta c_{i+1,j,k}\\ - -(\Gamma_y\Delta x \cdot u_{\text{y},i,j-1/2})\cdot \delta c_{i,j-1,k}\\ - + ((1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j+1/2})\cdot \delta c_{i,j+1,k}\\ - \end{gathered} - -or - -.. math:: - - \begin{gathered} - A0 \cdot \delta c_{i,j,k} - + A\text{m1} \cdot \delta c_{i-1,j,k} - + A\text{p1} \cdot \delta c_{i+1,j,k}\\ - + A\text{mx} \cdot \delta c_{i,j-1,k} - + A\text{px} \cdot \delta c_{i,j+1,k} = y_{i,j,k} - \label{eq:lin} - \end{gathered} - -or the linear system of equations in general form: - -.. math:: - :label: conservative_general - - A \cdot \delta c_{i,j,k} = y_{i,j,k} - -Where :math:`A` is a 3-dimensional sparse matrix that is compiled using the matrix diagonals (:math:`A0, Am1, Ap1, Amx, Apx`) which are defined as: - -.. math:: - - \begin{aligned} - A0 = & +\frac{\Delta x \Delta y}{\Delta t} \\ - & +\frac{\Delta x \Delta y}{T_s} \\ - & - (1-\Gamma_x)\Delta y \cdot u_{\text{x},i-1/2,j} \\ - & + \Gamma_x\Delta y \cdot u_{\text{x},i+1/2,j} \\ - & - (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j-1/2} \\ - & + \Gamma_y\Delta x \cdot u_{\text{y},i,j+1/2} \\ - \end{aligned} - -and - -.. math:: - - A\text{m}1 = -\Gamma_x\Delta y \cdot u_{\text{x},i-1/2,j} - -and - -.. math:: - - A\text{p}1 = (1-\Gamma_x)\Delta y \cdot u_{\text{x},i+1/2,j} - -and - -.. math:: - A\text{mx} = -\Gamma_y\Delta x \cdot u_{\text{y},i,j-1/2} - -and - -.. math:: - - A\text{px} = (1-\Gamma_y)\Delta x \cdot u_{\text{y},i,j+1/2} - -Let's go towards the RHS - -.. math:: - - \begin{aligned} - y_{i,j,k} = & - \frac{\Delta x \Delta y}{\Delta t}(c^{n+1 *}_{i,j,k}-c^{n}_{i,j,k}) \\ - & + \frac{\Delta x \Delta y}{T_s}(\min(\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k},m_{i,j,k} + c^{n+1 *}_{i,j,k}) - c^{n+1 *}_{i,j,k}) \\ - & + \Delta y \cdot u_{\text{x},i-1/2,j} \cdot - (\Gamma_x \cdot c^{n+1 *}_{i-1,j,k} + (1-\Gamma_x) c^{n+1 *}_{i,j,k})\\ - & - \Delta y \cdot u_{\text{x},i+1/2,j} \cdot (\Gamma_x \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_x) c^{n+1 *}_{i+1,j,k})\\ - & + \Delta x \cdot u_{\text{y},i,j-1/2} \cdot (\Gamma_y \cdot c^{n+1 *}_{i,j-1,k} + (1-\Gamma_y) c^{n+1 *}_{i,j,k})\\ - & - \Delta x \cdot u_{\text{y},i,j+1/2} \cdot (\Gamma_y \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_y) c^{n+1 *}_{i,j+1,k})\\ - \end{aligned} - -in the python code some intermediate variable is defined to make it easier to shift indexes - -.. math:: - - \text{Ctxfs} =(\Gamma_x \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_x) c^{n+1 *}_{i+1,j,k}) - -and - -.. math:: - - \text{Ctxfn} =(\Gamma_y \cdot c^{n+1 *}_{i,j,k} + (1-\Gamma_y) c^{n+1 *}_{i,j+1,k}) - -also Erosion and deposition are defined using seperate variables. - -.. math:: - D_{i,j,k}= \frac{\Delta x \Delta y}{T_s}c^{n+1 *}_{i,j,k} - -and - -.. math:: - - A_{i,j,k}= \frac{\Delta x \Delta y}{T_s}m_{i,j,k} + D_{i,j,k} - -and - -.. math:: - U_{i,j,k}= \frac{\Delta x \Delta y}{T_s}\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - -and - -.. math:: - E_{i,j,k} = \min(U_{i,j,k},A_{i,j,k}) - -After solving equation :math:`\delta c_{i,j,k}` using :eq:`conservative_general`, :math:`c^{n+1}_{i,j,k}` can be calculated using equation :eq:`conservative2`. - -Also, the pickup per grid cell can be calculated using: - -.. math:: - - \text{pickup} = \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k}- c^{n+1}_{i,j,k}}{T_s}\Delta t - \label{eq:pickup} - -note that this is only valid when using an Euler backward scheme. - -Solving the Linear System of Equations -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -The linear system of equations can be elaborated : - -.. math:: - :label: apx-system - - \left[ - \begin{array}{cccccc} - A^0_1 & A^{1}_1 & \textbf{0} & \cdots & \textbf{0} & A^{n_{\mathrm{y}}+1}_1 \\ - A^{-1}_2 & A^0_2 & \ddots & \ddots & & \textbf{0} \\ - \textbf{0} & \ddots & \ddots & \ddots & \ddots & \vdots \\ - \vdots & \ddots & \ddots & \ddots & \ddots & \textbf{0} \\ - \textbf{0} & & \ddots & \ddots & A^0_{n_{\mathrm{y}}} & A^1_{n_{\mathrm{y}}} \\ - A^{-n_{\mathrm{y}}-1}_{n_{\mathrm{y}}+1} & \textbf{0} & \cdots & \textbf{0} & A^{-1}_{n_{\mathrm{y}}+1} & A^0_{n_{\mathrm{y}}+1} \\ - \end{array} - \right] \left[ - \begin{array}{c} - \vec{\delta c}_1 \\ \vec{\delta c}_2 \\ \vdots \\ \vdots \\ \vec{\delta c}_{n_{\mathrm{y}}} \\ \vec{\delta c}_{n_{\mathrm{y}}+1} \\ - \end{array} - \right] = \left[ - \begin{array}{c} - \vec{y}_1 \\ \vec{y}_2 \\ \vdots \\ \vdots \\ \vec{y}_{n_{\mathrm{y}}} \\ \vec{y}_{n_{\mathrm{y}}+1} \\ - \end{array} - \right] - -where each item in the matrix is again a matrix :math:`A^l_j` and -each item in the vectors is again a vector :math:`\vec{\delta c}_j` and -:math:`\vec{y}_j` respectively. The form of the matrix :math:`A^l_j` depends on -the diagonal index :math:`l` and reads: - -.. math:: - :label: apx-diagonal - - A^0_j = - \left[ - \begin{array}{ccccccc} - 0 & 0 & 0 & 0 - & \cdots & \cdots & 0 \\ - a^{0,-1}_{2,j} & a^{0,0}_{2,j} & a^{0,1}_{2,j} & \ddots - & & & \vdots \\ - 0 & a^{0,-1}_{3,j} & a^{0,0}_{3,j} & a^{0,1}_{3,j} - & \ddots & & \vdots \\ - \vdots & \ddots & \ddots & \ddots - & \ddots & \ddots & \vdots \\ - \vdots & & \ddots & a^{0,-1}_{n_{\mathrm{x}}-1,j} - & a^{0,0}_{n_{\mathrm{x}}-1,j} & a^{0,1}_{n_{\mathrm{x}}-1,j} & 0 \\ - \vdots & & & 0 - & a^{0,-1}_{n_{\mathrm{x}},j} & a^{0,0}_{n_{\mathrm{x}},j} & a^{0,1}_{n_{\mathrm{x}},j} \\ - 0 & \cdots & \cdots & 0 - & 1 & -2 & 1 \\ - \end{array} - \right] - -for :math:`l = 0` and - -.. math:: - :label: apx-offdiagonal - - A^l_j = - \left[ - \begin{array}{ccccccc} - 1 & 0 & \cdots & \cdots - & \cdots & \cdots & 0 \\ - 0 & a^{l,0}_{2,j} & \ddots & - & & & \vdots \\ - \vdots & \ddots & a^{l,0}_{3,j} & \ddots - & & & \vdots \\ - \vdots & & \ddots & \ddots - & \ddots & & \vdots \\ - \vdots & & & \ddots - & a^{l,0}_{n_{\mathrm{x}}-1,j} & \ddots & \vdots \\ - \vdots & & & - & \ddots & a^{l,0}_{n_{\mathrm{x}},j} & 0 \\ - 0 & \cdots & \cdots & \cdots - & \cdots & 0 & 1 \\ - \end{array} - \right] - -for :math:`l \neq 0`. The vectors :math:`\vec{\delta c}_{j,k}` and :math:`\vec{y}_{j,k}` -read: - -.. math:: - :label: c-array - - \begin{array}{rclrcl} - \vec{\delta c}_{j,k} &=& \left[ - \begin{array}{c} - \delta c^{n+1}_{1,j,k} \\ - \delta c^{n+1}_{2,j,k} \\ - \delta c^{n+1}_{3,j,k} \\ - \vdots \\ - \delta c^{n+1}_{n_{\mathrm{x}}-1,j,k} \\ - \delta c^{n+1}_{n_{\mathrm{x}},j,k} \\ - \delta c^{n+1}_{n_{\mathrm{x}}+1,j,k} \\ - \end{array} - \right] & ~ \mathrm{and} ~ - \vec{y}_{j,k} &=& \left[ - \begin{array}{c} - 0 \\ - y^n_{2,j,k} \\ - y^n_{3,j,k} \\ - \vdots \\ - y^n_{n_{\mathrm{x}}-1,j,k} \\ - y^n_{n_{\mathrm{x}},j,k} \\ - 0 \\ - \end{array} - \right] \\ - \end{array} - -:math:`n_{\mathrm{x}}` and :math:`n_{\mathrm{y}}` denote the number of -spatial grid cells in x- and y-direction. - -Iterations to solve for multiple fractions -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -The linear system defined in Equation :eq:`apx-system` is solved by a -sparse matrix solver for each sediment fraction separately in -ascending order of grain size. Initially, the weights -:math:`\hat{w}^{n+1}_{i,j,k}` are chosen according to the grain size -distribution in the bed and the air. The sediment availability -constraint is checked after each solve: - -.. math:: - :label: solve - - m_{\mathrm{a}} \geq \frac{\hat{w}^{n+1}_{i,j,k} c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \Delta t^n - -If the constraint if violated, a new estimate for the weights -is back-calculated following: - -.. math:: - :label: solve-weights - - \hat{w}^{n+1}_{i,j,k} = \frac{ c^{n+1}_{i,j,k} + m_{\mathrm{a}} \frac{T}{\Delta t^n} }{c^{n+1}_{\mathrm{sat},i,j,k}} - -The system is solved again using the new weights. This -procedure is repeated until a weight is found that does not violate -the sediment availability constraint. If the time step is not too -large, the procedure typically converges in only a few -iterations. Finally, the weights of the larger grains are increased -proportionally as to ensure that the sum of all weights remains -unity. If no larger grains are defined, not enough sediment is -available for transport and the grid cell is truly -availability-limited. This situation should only occur occasionally as -the weights in the next time step are computed based on the new bed -composition and thus will be skewed towards the large fractions. If -the situation occurs regularly, the time step is chosen too large -compared to the rate of armoring. - -Euler Schemes in non-conservative form -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -Early model results relied on Euler schemes in a non conservative form. This allowed for a relatively easy implementation but did not guarantee mass conservation. In version 2 of AEOLIS the conservative form became the default. However, some users still use the older scheme. - -The formulation is discretized following a first order upwind scheme -assuming that the wind velocity :math:`u_z` is positive in both -x-direction and y-direction: - -.. math:: - :label: apx-explicit - - \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + - u^n_{z,\mathrm{x}} \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x_{i,j}} + - u^n_{z,\mathrm{y}} \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y_{i,j}} \\ = - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} - -in which :math:`n` is the time step index, :math:`i` and :math:`j` are -the cross-shore and alongshore spatial grid cell indices and :math:`k` -is the grain size fraction index. :math:`w` [-] is the weighting -factor used for the weighted addition of the saturated sediment -concentrations over all grain size fractions. - -The discretization can be generalized for any wind direction as: - -.. math:: - :label: apx-explicit-generalized - - \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + - u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + - u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \\ + - u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + - u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} = - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} - -in which: - -.. math:: - :label: apx-upwind1 - - \begin{array}{rclcrcl} - u^n_{z,\mathrm{x+}} &=& \max( 0, u^n_{z,\mathrm{x}} ) &;& u^n_{z,\mathrm{y+}} &=& \max( 0, u^n_{z,\mathrm{y}} ) \\ - u^n_{z,\mathrm{x-}} &=& \min( 0, u^n_{z,\mathrm{x}} ) &;& u^n_{z,\mathrm{y-}} &=& \min( 0, u^n_{z,\mathrm{y}} ) \\ - \end{array} - -and - -.. math:: - :label: apx-upwind2 - - \begin{array}{rclcrcl} - c^n_{i,j,k,\mathrm{x+}} &=& \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x} &;& - c^n_{i,j,k,\mathrm{y+}} &=& \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y} \\ - c^n_{i,j,k,\mathrm{x-}} &=& \frac{c^n_{i,j,k} - c^n_{i-1,j,k}}{\Delta x} &;& - c^n_{i,j,k,\mathrm{y-}} &=& \frac{c^n_{i,j,k} - c^n_{i,j-1,k}}{\Delta y} \\ - \end{array} - -Equation :eq:`apx-explicit-generalized` is explicit in -time and adheres to the Courant-Friedrich-Lewis (CFL) condition for -numerical stability. Alternatively, the advection equation can be -discretized implicitly in time for unconditional stability: - -.. math:: - :label: apx-implicit-generalized - - \frac{c^{n+1}_{i,j,k} - c^n_{i,j,k}}{\Delta t^n} + - u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + - u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \\ + - u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + - u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} = - \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} - -Equation :eq:`apx-explicit-generalized` and -:eq:apx-implicit-generalized` can be rewritten as: - -.. math:: - :label: apx-explicit-rewritten - - c^{n+1}_{i,j,k} = c^n_{i,j,k} - \Delta t^n \left[ - u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + - u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \phantom{\frac{c^n_{i,j,k}}{T}} \right. \\ + \left. - u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + - u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} + - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] - -and - -.. math:: - :label: apx-implicit-rewritten - - c^{n+1}_{i,j,k} + \Delta t^n \left[ - u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + - u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \phantom{\frac{c^{n+1}_{i,j,k}}{T}} \right. \\ + \left. - u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + - u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} + - \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] = c^n_{i,j,k} - -and combined using a weighted average: - -.. math:: - :label: apx-combined - - c^{n+1}_{i,j,k} + \Gamma \Delta t^n \left[ - u^{n+1}_{z,\mathrm{x+}} c^{n+1}_{i,j,k,\mathrm{x+}} + - u^{n+1}_{z,\mathrm{y+}} c^{n+1}_{i,j,k,\mathrm{y+}} \phantom{\frac{c^{n+1}_{i,j,k}}{T}} \right. \\ + \left. - u^{n+1}_{z,\mathrm{x-}} c^{n+1}_{i,j,k,\mathrm{x-}} + - u^{n+1}_{z,\mathrm{y-}} c^{n+1}_{i,j,k,\mathrm{y-}} + - \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] \\ = - c^n_{i,j,k} - (1 - \Gamma) \Delta t^n \left[ - u^n_{z,\mathrm{x+}} c^n_{i,j,k,\mathrm{x+}} + - u^n_{z,\mathrm{y+}} c^n_{i,j,k,\mathrm{y+}} \phantom{\frac{c^n_{i,j,k}}{T}} \right. \\ + \left. - u^n_{z,\mathrm{x-}} c^n_{i,j,k,\mathrm{x-}} + - u^n_{z,\mathrm{y-}} c^n_{i,j,k,\mathrm{y-}} + - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] - -in which :math:`\Gamma` is a weight that ranges from 0 -- 1 and -determines the implicitness of the scheme. The scheme is implicit with -:math:`\Gamma = 0`, explicit with :math:`\Gamma = 1` and semi-implicit -otherwise. :math:`\Gamma = 0.5` results in the semi-implicit Crank-Nicolson -scheme. - -Equation :eq:`apx-upwind2` is back-substituted in Equation -:eq:`apx-combined`: - -.. math:: - :label: apx-combined-substituted - - c^{n+1}_{i,j,k} + \Gamma \Delta t^n \left[ - u^{n+1}_{z,\mathrm{x+}} \frac{c^{n+1}_{i+1,j,k} - c^{n+1}_{i,j,k}}{\Delta x} + - u^{n+1}_{z,\mathrm{y+}} \frac{c^{n+1}_{i,j+1,k} - c^{n+1}_{i,j,k}}{\Delta y} \right. \\ + \left. - u^{n+1}_{z,\mathrm{x-}} \frac{c^{n+1}_{i,j,k} - c^{n+1}_{i-1,j,k}}{\Delta x} + - u^{n+1}_{z,\mathrm{y-}} \frac{c^{n+1}_{i,j,k} - c^{n+1}_{i,j-1,k}}{\Delta y} + - \frac{\hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} - c^{n+1}_{i,j,k}}{T} \right] \\ = - c^n_{i,j,k} - (1 - \Gamma) \Delta t^n \left[ - u^n_{z,\mathrm{x+}} \frac{c^n_{i+1,j,k} - c^n_{i,j,k}}{\Delta x} + - u^n_{z,\mathrm{y+}} \frac{c^n_{i,j+1,k} - c^n_{i,j,k}}{\Delta y} \right. \\ + \left. - u^n_{z,\mathrm{x-}} \frac{c^n_{i,j,k} - c^n_{i-1,j,k}}{\Delta x} + - u^n_{z,\mathrm{y-}} \frac{c^n_{i,j,k} - c^n_{i,j-1,k}}{\Delta y} + - \frac{\hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} - c^n_{i,j,k}}{T} \right] - -and rewritten: - -.. math:: - :label: apx-combined-rewritten - - \left[ 1 - \Gamma \left( - u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + - u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - - u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - - u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + - \frac{\Delta t^n}{T} - \right) - \right] c^{n+1}_{i,j,k} \\ + - \Gamma \left( - u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^{n+1}_{i+1,j,k} + - u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^{n+1}_{i,j+1,k} - %\right. \\ - \left. - u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^{n+1}_{i-1,j,k} - - u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^{n+1}_{i,j-1,k} - \right) \\ = - \left[ 1 + (1 - \Gamma) \left( - u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + - u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - - u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - - u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + - \frac{\Delta t^n}{T} - \right) - \right] c^n_{i,j,k} \\ + - (1 - \Gamma) \left( - u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^n_{i+1,j,k} + - u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^n_{i,j+1,k} - %\right. \\ - \left. - u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^n_{i-1,j,k} - - u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^n_{i,j-1,k} - \right) \\ - - \Gamma \hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - - (1 - \Gamma) \hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - -and simplified: - -.. math:: - :label: apx-combined-simplified - - a^{0,0}_{i,j} c^{n+1}_{i,j,k} + - a^{1,0}_{i,j} c^{n+1}_{i+1,j,k} + - a^{0,1}_{i,j} c^{n+1}_{i,j+1,k} - - a^{-1,0}_{i,j} c^{n+1}_{i-1,j,k} - - a^{0,-1}_{i,j} c^{n+1}_{i,j-1,k} = y_{i,j,k} - -where the implicit coefficients are defined as: - -.. math:: - :label: apx-implicitcoef - - \begin{array}{rclcrcl} - a^{0,0}_{i,j} &=& \left[1 - \Gamma \left( - u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + - u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - - u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - - u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + - \frac{\Delta t^n}{T} - \right) \right] \\ - a^{1,0}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} \\ - a^{0,1}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} \\ - a^{-1,0}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} \\ - a^{0,-1}_{i,j} &=& \Gamma u^{n+1}_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} \\ - \end{array} - -and the explicit right-hand side as: - -.. math:: - :label: apx-explicitrhs - - y^n_{i,j,k} = \left[ 1 + (1 - \Gamma) \left( - u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} + - u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} - - u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} - - u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} + - \frac{\Delta t^n}{T} - \right) - \right] c^n_{i,j,k} \\ + - (1 - \Gamma) \left( - u^n_{z,\mathrm{x+}} \frac{\Delta t^n}{\Delta x} c^n_{i+1,j,k} + - u^n_{z,\mathrm{y+}} \frac{\Delta t^n}{\Delta y} c^n_{i,j+1,k} - - u^n_{z,\mathrm{x-}} \frac{\Delta t^n}{\Delta x} c^n_{i-1,j,k} - - u^n_{z,\mathrm{y-}} \frac{\Delta t^n}{\Delta y} c^n_{i,j-1,k} - \right) \\ - - \Gamma \hat{w}^{n+1}_{i,j,k} \cdot c^{n+1}_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - - (1 - \Gamma) \hat{w}^n_{i,j,k} \cdot c^n_{\mathrm{sat},i,j,k} \frac{\Delta t^n}{T} - -The offshore boundary is defined to be zero-flux, the -onshore boundary has a constant transport gradient and the lateral -boundaries are circular: - -.. math:: - :label: apx-boundaryconditions - - \begin{array}{rclcrcl} - c^{n+1}_{1,j,k} &=& 0 \\ - c^{n+1}_{n_{\mathrm{x}}+1,j,k} &=& 2 c^{n+1}_{n_{\mathrm{x}},j,k} - c^{n+1}_{n_{\mathrm{x}}-1,j,k} \\ - c^{n+1}_{i,1,k} &=& c^{n+1}_{i,n_{\mathrm{y}}+1,k} \\ - c^{n+1}_{i,n_{\mathrm{y}}+1,k} &=& c^{n+1}_{i,1,k} \\ - \end{array} \ No newline at end of file diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index cc994b06..a6260a91 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -363,3 +363,73 @@ are listed below. Guidance on solver use ------------------------ + +Different numerical solvers are available in the latest AeoLiS version. +The numerical solvers are used to solve the transport equation numerically. +Other modules such as the shear module, vegetation module, and the moisture module +use other equations and numerical implementations that currently do not have +different options for numerical solvers. + +The advection equation is implemented in two-dimensional form +following: + +.. math:: + :label: apx-advection + + \frac{\partial c}{\partial t} + + u_{z,\mathrm{x}} \frac{\partial c}{\partial x} + + u_{z,\mathrm{y}} \frac{\partial c}{\partial y} = + \frac{c_{\mathrm{sat}} - c}{T} + +in which :math:`c` [:math:`\mathrm{kg/m^2}`] is the sediment mass per +unit area in the air, :math:`c_{\mathrm{sat}}` [:math:`\mathrm{kg/m^2}`] is the +maximum sediment mass in the air that is reached in case of +saturation, :math:`u_{z,\mathrm{x}}` and :math:`u_{z,\mathrm{y}}` are the x- and +y-component of the wind velocity at height :math:`z` [m], :math:`T` [s] is an +adaptation time scale, :math:`t` [s] denotes time and :math:`x` [m] and :math:`y` [m] +denote cross-shore and alongshore distances respectively. + +The formulation is discretized in different ways to allow for different types of simulations balancing accuracy vs. computational resources. +The conservative method combined with a steady state solution is the current default for most simulations. +Non-conservative methods and explicit/implicit Euler forward/backward schemes are also available. + +The available solvers are *steadystate*, *trunk*, and *pieter*. Some details are given below. As of version 3 of the AeoLiS +model, the steadystate solver is the default solver. The steadystate solver is most suitable for practical cases. +The other solvers are still available for specific applications. + +steadystate (default since v3) +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +The *steadystate* solver is based on the assumption that dc/dt = 0 and uses a finite difference scheme to solve the transport equation. + +.. math:: + :label: ss-advection + + u_{z,\mathrm{x}} \frac{\partial c}{\partial x} + + u_{z,\mathrm{y}} \frac{\partial c}{\partial y} = + \frac{c_{\mathrm{sat}} - c}{T} + +When solving for equation :eq:`ss-advection` a sweeping algorithm is used that propagates the boundary conditions through the +4 possible quadrants of the computational grid. The 4 quadrants depend on the signs of the sediment velocities and the +remaining grid cells that are not part of a quadrant (because winds diverge or converge in that cell) are solved as well. + +The steadystate solver is most suitable for case study simulations with larger timeframes and timesteps. All landform +simulations in the :cite:t:`VANWESTEN2024106093` publication were done with the steadystate solver. + +trunk +^^^^^ +The *trunk* solver was the first solver that was implemented in AeoLiS. The trunk solver allows a time-varying solution for +sediment concentration with options for explicit and implicit Euler forward/backward schemes. The 1D simulations by :cite:t:`deVries2014a` +were done with the trunk solver in explicit mode. However, the explicit mode is not recommended for most simulations as +very strict requirements for stability are needed which results in large calculation times. The implicit mode is more stable +and allows for larger timesteps. However, the implicit numerical scheme lacks accuracy when larger timesteps are used. The +2D simulations by :cite:t:`Hoonhout2016` were done with the trunk solver in implicit mode. + +See :ref:`trunk_num` for details on the numerical implementation of the trunk solver. + +Pieter +^^^^^^ +The *pieter* solver was built on the basis of using a conservative numerical scheme. This conservative scheme allowed for a better +implementation of spatially varying wind(/sediment) velocities. In simple cases (spatially non-varying winds) the solver is +identical to the trunk solver. The solver was built by Professor Pieter Rauwoens, hence the name. + +See :ref:`pieter_num` for details on the numerical implementation of the Pieter solver. \ No newline at end of file From 916a8636659ab3696fee224712db5930f593a623 Mon Sep 17 00:00:00 2001 From: Sierd Date: Sun, 18 Aug 2024 16:29:30 +0200 Subject: [PATCH 124/124] 1D/2D documentation added --- docs/aeolis.bib | 1 - docs/user/model_setup.rst | 12 ++++++++++++ 2 files changed, 12 insertions(+), 1 deletion(-) diff --git a/docs/aeolis.bib b/docs/aeolis.bib index 8835a096..13c72037 100644 --- a/docs/aeolis.bib +++ b/docs/aeolis.bib @@ -246,7 +246,6 @@ @article{Masselink2007 volume = {54}, pages = {39--53}, doi = {10.1111/j.1365-3091.2006.00825.x}, - dor = {10.1111/j.1365-3091.2006.00825.x}, owner = {hoonhout}, timestamp = {2015.05.26} } diff --git a/docs/user/model_setup.rst b/docs/user/model_setup.rst index a6260a91..406316cd 100644 --- a/docs/user/model_setup.rst +++ b/docs/user/model_setup.rst @@ -234,6 +234,18 @@ column is air pressure (kPa). File format for meteorological data used to simulate surface moisture in AeoLiS where each red dot represents a time series value. + + +1D and 2D models +----------------- + +The model can be run in 1D and 2D mode depending on the definition of the input. Most processes are implemented in 2D mode. To run the model in 2D mode all grid files should contain 2D matrices of the same size. + +To run the model in 1D mode, all grid files should contain vectors. In 1D mode, the ygrd_file typically contains vector with constant values (ones or zeros). +Because some processes are easier to solve in 2D, the 1D model is converted to a 2D model by repeating the vectors 3 times assuming the same resolution +spacing as in the xgrid direction. The model will run in a quasi 2D mode. Results are then converted to 1D again by taking the middle of the 3 vectors. + + .. _default-settings: Default settings

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