From ced3044d60cda2d7040190ec45fe1b0e6ede4b93 Mon Sep 17 00:00:00 2001
From: William Jones <william.jones@physics.ox.ac.uk>
Date: Fri, 28 Jul 2023 21:39:15 +0100
Subject: [PATCH 1/7] Fix to strict_thresholding that now works for both minima
 and maxima, and provides the same results as strict_thresholding=False if
 n_min_threshold is a fixed value

---
 tobac/feature_detection.py | 150 +++++++++++++++++++++++++++----------
 1 file changed, 111 insertions(+), 39 deletions(-)

diff --git a/tobac/feature_detection.py b/tobac/feature_detection.py
index 108069ae..0a4d7c63 100644
--- a/tobac/feature_detection.py
+++ b/tobac/feature_detection.py
@@ -258,7 +258,9 @@ def test_overlap(region_inner, region_outer):
     return not overlap
 
 
-def remove_parents(features_thresholds, regions_i, regions_old):
+def remove_parents(
+    features_thresholds, regions_i, regions_old, strict_thresholding=False
+):
     """Remove parents of newly detected feature regions.
 
     Remove features where its regions surround newly
@@ -279,6 +281,9 @@ def remove_parents(features_thresholds, regions_i, regions_old):
         threshold from previous threshold
         (feature ids as keys).
 
+    strict_thresholding: Bool, optional
+        If True, a feature can only be detected if all previous thresholds have been met.
+        Default is False.
     Returns
     -------
     features_thresholds : pandas.DataFrame
@@ -288,26 +293,73 @@ def remove_parents(features_thresholds, regions_i, regions_old):
 
     try:
         all_curr_pts = np.concatenate([vals for idx, vals in regions_i.items()])
+    except ValueError:
+        # the case where there are no new regions
+        if strict_thresholding:
+            return features_thresholds, {}
+        else:
+            return features_thresholds, regions_old
+    try:
         all_old_pts = np.concatenate([vals for idx, vals in regions_old.items()])
     except ValueError:
-        # the case where there are no regions
-        return features_thresholds
+        # the case where there are no old regions
+        if strict_thresholding:
+            return (
+                features_thresholds[
+                    ~features_thresholds["idx"].isin(list(regions_i.keys()))
+                ],
+                {},
+            )
+        else:
+            return features_thresholds, regions_i
+
     old_feat_arr = np.empty((len(all_old_pts)))
     curr_loc = 0
     for idx_old in regions_old:
         old_feat_arr[curr_loc : curr_loc + len(regions_old[idx_old])] = idx_old
         curr_loc += len(regions_old[idx_old])
 
-    _, _, common_ix_old = np.intersect1d(all_curr_pts, all_old_pts, return_indices=True)
+    _, common_ix_new, common_ix_old = np.intersect1d(
+        all_curr_pts, all_old_pts, return_indices=True
+    )
     list_remove = np.unique(old_feat_arr[common_ix_old])
 
+    if strict_thresholding:
+        new_feat_arr = np.empty((len(all_curr_pts)))
+        curr_loc = 0
+        for idx_new in regions_i:
+            new_feat_arr[curr_loc : curr_loc + len(regions_i[idx_new])] = idx_new
+            curr_loc += len(regions_i[idx_new])
+        # _, _, common_ix_new = np.intersect1d(all_old_pts, all_curr_pts, return_indices=True)
+        regions_i_overlap = np.unique(new_feat_arr[common_ix_new])
+        no_prev_feature = np.array(list(regions_i.keys()))[
+            np.logical_not(np.isin(list(regions_i.keys()), regions_i_overlap))
+        ]
+        list_remove = np.concatenate([list_remove, no_prev_feature])
+
     # remove parent regions:
     if features_thresholds is not None:
         features_thresholds = features_thresholds[
             ~features_thresholds["idx"].isin(list_remove)
         ]
 
-    return features_thresholds
+        if strict_thresholding:
+            keep_new_keys = np.isin(list(regions_i.keys()), features_thresholds["idx"])
+            regions_old = {
+                k: v for i, (k, v) in enumerate(regions_i.items()) if keep_new_keys[i]
+            }
+        else:
+            keep_old_keys = np.isin(
+                list(regions_old.keys()), features_thresholds["idx"]
+            )
+            regions_old = {
+                k: v for i, (k, v) in enumerate(regions_old.items()) if keep_old_keys[i]
+            }
+            regions_old.update(regions_i)
+    else:
+        regions_old = regions_i
+
+    return features_thresholds, regions_old
 
 
 def feature_detection_threshold(
@@ -994,45 +1046,65 @@ def feature_detection_multithreshold_timestep(
                 [features_thresholds, features_threshold_i], ignore_index=True
             )
 
+        # if i_threshold>0:
+        #     print(regions_old.keys())
+
         # For multiple threshold, and features found both in the current and previous step, remove "parent" features from Dataframe
-        if i_threshold > 0 and not features_thresholds.empty and regions_old:
+        if i_threshold > 0 and not features_thresholds.empty:
             # for each threshold value: check if newly found features are surrounded by feature based on less restrictive threshold
-            features_thresholds = remove_parents(
-                features_thresholds, regions_i, regions_old
-            )
-
-        if strict_thresholding:
-            if regions_i:
-                # remove data in regions where no features were detected
-                valid_regions: np.ndarray = np.zeros_like(track_data)
-                region_indices: list[int] = list(regions_i.values())[
-                    0
-                ]  # linear indices
-                valid_regions.ravel()[region_indices] = 1
-                track_data: np.ndarray = np.multiply(valid_regions, track_data)
-            else:
-                # since regions_i is empty no further features can be detected
-                logging.debug(
-                    "Finished feature detection for threshold "
-                    + str(i_threshold)
-                    + " : "
-                    + str(threshold_i)
-                )
-                return features_thresholds
-
-        if i_threshold > 0 and not features_thresholds.empty and regions_old:
-            # Work out which regions are still in feature_thresholds to keep
-            # This is faster than calling "in" for every idx
-            keep_old_keys = np.isin(
-                list(regions_old.keys()), features_thresholds["idx"]
+            features_thresholds, regions_old = remove_parents(
+                features_thresholds,
+                regions_i,
+                regions_old,
+                strict_thresholding=strict_thresholding,
             )
-            regions_old = {
-                k: v for i, (k, v) in enumerate(regions_old.items()) if keep_old_keys[i]
-            }
-            regions_old.update(regions_i)
-        else:
+        elif i_threshold == 0:
             regions_old = regions_i
 
+        # print(regions_i.keys())
+        # if i_threshold>0:
+        #     print(regions_old.keys())
+
+        # if strict_thresholding:
+        #     if regions_i:
+        #         # remove data in regions where no features were detected
+        #         valid_regions: np.ndarray = np.zeros_like(track_data, dtype=bool)
+        #         region_indices: list[int] = list(regions_i.values())[
+        #             0
+        #         ]  # linear indices
+        #         valid_regions.ravel()[region_indices] = 1
+        #         if i_threshold > 2:
+        #             raise RuntimeError
+        #         # track_data[np.logical_not(valid_regions)] = threshold_i
+        #         if target=="maximum":
+        #             track_data[np.logical_not(valid_regions)] = np.minimum(track_data[np.logical_not(valid_regions)], threshold_i)
+        #         #     track_data[np.logical_not(valid_regions)] = -np.inf
+        #         elif target=="minimum":
+        #             track_data[np.logical_not(valid_regions)] = np.maximum(track_data[np.logical_not(valid_regions)], threshold_i)
+        #         #     track_data[np.logical_not(valid_regions)] = np.inf
+        #     else:
+        #         # since regions_i is empty no further features can be detected
+        #         logging.debug(
+        #             "Finished feature detection for threshold "
+        #             + str(i_threshold)
+        #             + " : "
+        #             + str(threshold_i)
+        #         )
+        #         return features_thresholds
+
+        # if i_threshold > 0 and not features_thresholds.empty and regions_old:
+        #     # Work out which regions are still in feature_thresholds to keep
+        #     # This is faster than calling "in" for every idx
+        #     keep_old_keys = np.isin(
+        #         list(regions_old.keys()), features_thresholds["idx"]
+        #     )
+        #     regions_old = {
+        #         k: v for i, (k, v) in enumerate(regions_old.items()) if keep_old_keys[i]
+        #     }
+        #     regions_old.update(regions_i)
+        # else:
+        #     regions_old = regions_i
+
         logging.debug(
             "Finished feature detection for threshold "
             + str(i_threshold)

From b762ee540f61acd34f6925c822ccb40f1da05d5b Mon Sep 17 00:00:00 2001
From: William Jones <william.jones@physics.ox.ac.uk>
Date: Fri, 28 Jul 2023 21:53:43 +0100
Subject: [PATCH 2/7] Remove commented out code

---
 tobac/feature_detection.py | 48 --------------------------------------
 1 file changed, 48 deletions(-)

diff --git a/tobac/feature_detection.py b/tobac/feature_detection.py
index 0a4d7c63..25f9faa0 100644
--- a/tobac/feature_detection.py
+++ b/tobac/feature_detection.py
@@ -330,7 +330,6 @@ def remove_parents(
         for idx_new in regions_i:
             new_feat_arr[curr_loc : curr_loc + len(regions_i[idx_new])] = idx_new
             curr_loc += len(regions_i[idx_new])
-        # _, _, common_ix_new = np.intersect1d(all_old_pts, all_curr_pts, return_indices=True)
         regions_i_overlap = np.unique(new_feat_arr[common_ix_new])
         no_prev_feature = np.array(list(regions_i.keys()))[
             np.logical_not(np.isin(list(regions_i.keys()), regions_i_overlap))
@@ -1046,9 +1045,6 @@ def feature_detection_multithreshold_timestep(
                 [features_thresholds, features_threshold_i], ignore_index=True
             )
 
-        # if i_threshold>0:
-        #     print(regions_old.keys())
-
         # For multiple threshold, and features found both in the current and previous step, remove "parent" features from Dataframe
         if i_threshold > 0 and not features_thresholds.empty:
             # for each threshold value: check if newly found features are surrounded by feature based on less restrictive threshold
@@ -1061,50 +1057,6 @@ def feature_detection_multithreshold_timestep(
         elif i_threshold == 0:
             regions_old = regions_i
 
-        # print(regions_i.keys())
-        # if i_threshold>0:
-        #     print(regions_old.keys())
-
-        # if strict_thresholding:
-        #     if regions_i:
-        #         # remove data in regions where no features were detected
-        #         valid_regions: np.ndarray = np.zeros_like(track_data, dtype=bool)
-        #         region_indices: list[int] = list(regions_i.values())[
-        #             0
-        #         ]  # linear indices
-        #         valid_regions.ravel()[region_indices] = 1
-        #         if i_threshold > 2:
-        #             raise RuntimeError
-        #         # track_data[np.logical_not(valid_regions)] = threshold_i
-        #         if target=="maximum":
-        #             track_data[np.logical_not(valid_regions)] = np.minimum(track_data[np.logical_not(valid_regions)], threshold_i)
-        #         #     track_data[np.logical_not(valid_regions)] = -np.inf
-        #         elif target=="minimum":
-        #             track_data[np.logical_not(valid_regions)] = np.maximum(track_data[np.logical_not(valid_regions)], threshold_i)
-        #         #     track_data[np.logical_not(valid_regions)] = np.inf
-        #     else:
-        #         # since regions_i is empty no further features can be detected
-        #         logging.debug(
-        #             "Finished feature detection for threshold "
-        #             + str(i_threshold)
-        #             + " : "
-        #             + str(threshold_i)
-        #         )
-        #         return features_thresholds
-
-        # if i_threshold > 0 and not features_thresholds.empty and regions_old:
-        #     # Work out which regions are still in feature_thresholds to keep
-        #     # This is faster than calling "in" for every idx
-        #     keep_old_keys = np.isin(
-        #         list(regions_old.keys()), features_thresholds["idx"]
-        #     )
-        #     regions_old = {
-        #         k: v for i, (k, v) in enumerate(regions_old.items()) if keep_old_keys[i]
-        #     }
-        #     regions_old.update(regions_i)
-        # else:
-        #     regions_old = regions_i
-
         logging.debug(
             "Finished feature detection for threshold "
             + str(i_threshold)

From c21905efefd0b9ac69039cfd8e67afd55c6673b3 Mon Sep 17 00:00:00 2001
From: William Jones <william.jones@physics.ox.ac.uk>
Date: Fri, 28 Jul 2023 22:03:35 +0100
Subject: [PATCH 3/7] Add additional tests for strict_thresholding

---
 tobac/tests/test_feature_detection.py | 78 +++++++++++++++++++++++++++
 1 file changed, 78 insertions(+)

diff --git a/tobac/tests/test_feature_detection.py b/tobac/tests/test_feature_detection.py
index 4eb0784a..37b6b586 100644
--- a/tobac/tests/test_feature_detection.py
+++ b/tobac/tests/test_feature_detection.py
@@ -1,7 +1,9 @@
+import tobac
 import tobac.testing as tbtest
 import tobac.feature_detection as feat_detect
 import pytest
 import numpy as np
+import xarray as xr
 from pandas.testing import assert_frame_equal
 
 
@@ -745,6 +747,82 @@ def test_strict_thresholding():
     assert len(features) == 1
     assert features["threshold_value"].item() == thresholds[0]
 
+    # Repeat for minima
+    test_data_iris = tbtest.make_dataset_from_arr(10 - test_data, data_type="iris")
+    # All of these thresholds will be met
+    thresholds = [9, 5, 2.5]
+
+    # This will detect 2 features (first and last threshold value)
+    features = feat_detect.feature_detection_multithreshold_timestep(
+        test_data_iris,
+        0,
+        dxy=1,
+        threshold=thresholds,
+        n_min_threshold=n_min_thresholds,
+        strict_thresholding=False,
+        target="minimum",
+    )
+    assert len(features) == 1
+    assert features["threshold_value"].item() == thresholds[-1]
+
+    # Since the second n_min_thresholds value is not met this will only detect 1 feature
+    features = feat_detect.feature_detection_multithreshold_timestep(
+        test_data_iris,
+        0,
+        dxy=1,
+        threshold=thresholds,
+        n_min_threshold=n_min_thresholds,
+        strict_thresholding=True,
+        target="minimum",
+    )
+    assert len(features) == 1
+    assert features["threshold_value"].item() == thresholds[0]
+
+    # Test example from documentation
+    input_field_arr = np.zeros((1, 101, 101))
+
+    for idx, side in enumerate([40, 20, 10, 5]):
+        input_field_arr[
+            :,
+            (50 - side - 4 * idx) : (50 + side - 4 * idx),
+            (50 - side - 4 * idx) : (50 + side - 4 * idx),
+        ] = (
+            50 - side
+        )
+
+    input_field_iris = xr.DataArray(
+        input_field_arr,
+        dims=["time", "Y", "X"],
+        coords={"time": [np.datetime64("2019-01-01T00:00:00")]},
+    ).to_iris()
+
+    thresholds = [8, 29, 39, 44]
+
+    n_min_thresholds = [79**2, input_field_arr.size, 8**2, 3**2]
+
+    features_demo = tobac.feature_detection_multithreshold(
+        input_field_iris,
+        dxy=1000,
+        threshold=thresholds,
+        n_min_threshold=n_min_thresholds,
+        strict_thresholding=False,
+    )
+
+    assert features_demo.iloc[0]["hdim_1"] == pytest.approx(37.5)
+    assert features_demo.iloc[0]["hdim_2"] == pytest.approx(37.5)
+
+    # Now repeat with strict thresholding
+    features_demo = tobac.feature_detection_multithreshold(
+        input_field_iris,
+        dxy=1000,
+        threshold=thresholds,
+        n_min_threshold=n_min_thresholds,
+        strict_thresholding=True,
+    )
+
+    assert features_demo.iloc[0]["hdim_1"] == pytest.approx(49.5)
+    assert features_demo.iloc[0]["hdim_2"] == pytest.approx(49.5)
+
 
 @pytest.mark.parametrize(
     "h1_indices, h2_indices, max_h1, max_h2, PBC_flag, position_threshold, expected_output",

From 47212e55a9fb212b8053ca0c293545129468bfae Mon Sep 17 00:00:00 2001
From: William Jones <william.jones@physics.ox.ac.uk>
Date: Tue, 15 Aug 2023 16:52:20 +0100
Subject: [PATCH 4/7] Update version number to 1.5.1

---
 tobac/__init__.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tobac/__init__.py b/tobac/__init__.py
index 8a2da1af..2af56371 100644
--- a/tobac/__init__.py
+++ b/tobac/__init__.py
@@ -77,4 +77,4 @@
 from . import merge_split
 
 # Set version number
-__version__ = "1.5.0"
+__version__ = "1.5.1"

From e3ff4b2d7453e9464f2fa4d7f7826f5fcfc14b24 Mon Sep 17 00:00:00 2001
From: William Jones <william.jones@physics.ox.ac.uk>
Date: Tue, 15 Aug 2023 17:18:14 +0100
Subject: [PATCH 5/7] Update changelog for 1.5.1

---
 CHANGELOG.md | 17 ++++++++++++-----
 1 file changed, 12 insertions(+), 5 deletions(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 5275bab6..01811d4c 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,12 @@
 ### Tobac Changelog
 
+_**Version 1.5.1:**_
+
+**Bug fixes**
+
+- The `strict_thresholding` option in feature detection now works correctly for detecting minima, and produces the same results as without strict thresholding if the `n_min_threshold` is a scalar value [#316](https://github.com/tobac-project/tobac/pull/316)
+
+
 _**Version 1.5.0:**_
 
 **Enhancements for Users**
@@ -35,8 +42,6 @@ _**Version 1.5.0:**_
 - `scipy.interpolate.interp2d` in `add_coordinates` and `add_coordinates_3D` has been replaced with `scipy.interpolate.interpn` as `interp2d` has been deprecated. [#279](https://github.com/tobac-project/tobac/pull/279) 
 - `setup.py` updated to draw its required packages from `requirements.txt` [#288](https://github.com/tobac-project/tobac/pull/288)
 
-
-
 **Repository Enhancements**
 
 - New CI was added to automatically check the example and documentation Jupyter notebooks [#258](https://github.com/tobac-project/tobac/pull/258), [#290](https://github.com/tobac-project/tobac/pull/290)
@@ -44,7 +49,6 @@ _**Version 1.5.0:**_
 - Repository authors updated [#289](https://github.com/tobac-project/tobac/pull/289)
 - CI added to check author list formatting for Zenodo [#292](https://github.com/tobac-project/tobac/pull/292)
 
-
 **Deprecations**
 
 - All functions in `centerofgravity.py` (`calculate_cog`, `calculate_cog_untracked`, `center_of_gravity`) have been deprecated and will be removed or significantly changed in v2.0. [#200](https://github.com/tobac-project/tobac/pull/200)
@@ -54,10 +58,8 @@ _**Version 1.5.0:**_
 - `tobac.utils.combine_tobac_feats` has been renamed to `tobac.utils.combine_feature_dataframes`, and the original name has been deprecated and will be removed in a future release. [#300](https://github.com/tobac-project/tobac/pull/300)
 
 
-
 _**Version 1.4.2:**_
 
-
 **Bug fix**
 
 - Fixed a bug in the segmentation procedure that assigned the wrong grid cell areas to features in data frame  [#246](https://github.com/tobac-project/tobac/pull/246)
@@ -78,6 +80,7 @@ _**Version 1.4.1:**_
 
 - Regenerated example notebooks so that they are up to date for the present version [#233](https://github.com/tobac-project/tobac/pull/233)
 
+
 _**Version 1.4.0:**_
 
 **Enhancements**
@@ -115,12 +118,14 @@ _**Version 1.4.0:**_
 
 - Support for Python 3.6 and earlier is now deprecated and will be removed in v1.5.0 ([#193](https://github.com/tobac-project/tobac/pull/193))
 
+
 _**Version 1.3.3:**_
 
 **Bug fixes**
 
 - Added a workaround to a bug in trackpy that fixes predictive tracking [#170](https://github.com/tobac-project/tobac/pull/170)
 
+
 _**Version 1.3.2:**_
 
 **Bug fixes**
@@ -133,6 +138,7 @@ _**Version 1.3.2:**_
 - Added automatic code coverage reports [#124](https://github.com/tobac-project/tobac/pull/124)
 - Added automatic building of readthedocs documentation on pull requests
 
+
 _**Version 1.3.1:**_
 
 **Enhancements**
@@ -147,6 +153,7 @@ _**Version 1.3.1:**_
 
 - New pull request template for the repository, including a checklist to be completed for each pull request [#120](https://github.com/tobac-project/tobac/pull/120)
 
+
 _**Version 1.3:**_
 
 **Enhancements**

From 411328cc12927f3342bc6d66d5561501568309fc Mon Sep 17 00:00:00 2001
From: William Jones <william.jones@physics.ox.ac.uk>
Date: Tue, 15 Aug 2023 17:18:50 +0100
Subject: [PATCH 6/7] Update notebooks for v1.5.1 release

---
 .../feature_detection_filtering.ipynb         |  40 ++--
 .../multiple_thresholds_example.ipynb         |  64 ++---
 .../notebooks/n_min_threshold_example.ipynb   |  80 +++----
 .../position_threshold_example.ipynb          |  64 ++---
 .../Example_OLR_Tracking_model.ipynb          | 162 ++++++-------
 .../Example_OLR_Tracking_satellite.ipynb      | 172 +++++++-------
 .../Example_Precip_Tracking.ipynb             | 172 +++++++-------
 .../track_on_radar_segment_on_satellite.ipynb | 220 +++++++++---------
 .../Example_Updraft_Tracking.ipynb            | 182 +++++++--------
 9 files changed, 578 insertions(+), 578 deletions(-)

diff --git a/doc/feature_detection/notebooks/feature_detection_filtering.ipynb b/doc/feature_detection/notebooks/feature_detection_filtering.ipynb
index 6cc2500e..74c4eaa6 100644
--- a/doc/feature_detection/notebooks/feature_detection_filtering.ipynb
+++ b/doc/feature_detection/notebooks/feature_detection_filtering.ipynb
@@ -26,10 +26,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:47.195347Z",
-     "iopub.status.busy": "2023-07-11T00:01:47.195069Z",
-     "iopub.status.idle": "2023-07-11T00:01:51.687071Z",
-     "shell.execute_reply": "2023-07-11T00:01:51.686080Z"
+     "iopub.execute_input": "2023-08-15T16:14:07.185005Z",
+     "iopub.status.busy": "2023-08-15T16:14:07.184289Z",
+     "iopub.status.idle": "2023-08-15T16:14:13.774664Z",
+     "shell.execute_reply": "2023-08-15T16:14:13.773916Z"
     }
    },
    "outputs": [],
@@ -62,10 +62,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:51.691723Z",
-     "iopub.status.busy": "2023-07-11T00:01:51.691275Z",
-     "iopub.status.idle": "2023-07-11T00:01:51.919529Z",
-     "shell.execute_reply": "2023-07-11T00:01:51.918566Z"
+     "iopub.execute_input": "2023-08-15T16:14:13.779200Z",
+     "iopub.status.busy": "2023-08-15T16:14:13.778801Z",
+     "iopub.status.idle": "2023-08-15T16:14:14.029386Z",
+     "shell.execute_reply": "2023-08-15T16:14:14.028577Z"
     }
    },
    "outputs": [
@@ -101,10 +101,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:51.958983Z",
-     "iopub.status.busy": "2023-07-11T00:01:51.958706Z",
-     "iopub.status.idle": "2023-07-11T00:01:52.324795Z",
-     "shell.execute_reply": "2023-07-11T00:01:52.323887Z"
+     "iopub.execute_input": "2023-08-15T16:14:14.072818Z",
+     "iopub.status.busy": "2023-08-15T16:14:14.072541Z",
+     "iopub.status.idle": "2023-08-15T16:14:15.125350Z",
+     "shell.execute_reply": "2023-08-15T16:14:15.123554Z"
     }
    },
    "outputs": [],
@@ -135,10 +135,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:52.329156Z",
-     "iopub.status.busy": "2023-07-11T00:01:52.328875Z",
-     "iopub.status.idle": "2023-07-11T00:01:56.341645Z",
-     "shell.execute_reply": "2023-07-11T00:01:56.335837Z"
+     "iopub.execute_input": "2023-08-15T16:14:15.129205Z",
+     "iopub.status.busy": "2023-08-15T16:14:15.128939Z",
+     "iopub.status.idle": "2023-08-15T16:14:16.832504Z",
+     "shell.execute_reply": "2023-08-15T16:14:16.828647Z"
     }
    },
    "outputs": [
@@ -196,10 +196,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:56.348391Z",
-     "iopub.status.busy": "2023-07-11T00:01:56.346681Z",
-     "iopub.status.idle": "2023-07-11T00:01:57.961544Z",
-     "shell.execute_reply": "2023-07-11T00:01:57.960460Z"
+     "iopub.execute_input": "2023-08-15T16:14:16.838887Z",
+     "iopub.status.busy": "2023-08-15T16:14:16.838617Z",
+     "iopub.status.idle": "2023-08-15T16:14:18.821986Z",
+     "shell.execute_reply": "2023-08-15T16:14:18.821111Z"
     }
    },
    "outputs": [
diff --git a/doc/feature_detection/notebooks/multiple_thresholds_example.ipynb b/doc/feature_detection/notebooks/multiple_thresholds_example.ipynb
index 5c548df4..8fbbde7f 100644
--- a/doc/feature_detection/notebooks/multiple_thresholds_example.ipynb
+++ b/doc/feature_detection/notebooks/multiple_thresholds_example.ipynb
@@ -19,10 +19,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:02:04.454435Z",
-     "iopub.status.busy": "2023-07-11T00:02:04.453782Z",
-     "iopub.status.idle": "2023-07-11T00:02:09.305142Z",
-     "shell.execute_reply": "2023-07-11T00:02:09.303956Z"
+     "iopub.execute_input": "2023-08-15T16:14:27.894065Z",
+     "iopub.status.busy": "2023-08-15T16:14:27.893581Z",
+     "iopub.status.idle": "2023-08-15T16:14:38.976596Z",
+     "shell.execute_reply": "2023-08-15T16:14:38.975681Z"
     }
    },
    "outputs": [],
@@ -53,10 +53,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:02:09.308788Z",
-     "iopub.status.busy": "2023-07-11T00:02:09.308421Z",
-     "iopub.status.idle": "2023-07-11T00:02:09.531767Z",
-     "shell.execute_reply": "2023-07-11T00:02:09.531142Z"
+     "iopub.execute_input": "2023-08-15T16:14:38.981371Z",
+     "iopub.status.busy": "2023-08-15T16:14:38.980828Z",
+     "iopub.status.idle": "2023-08-15T16:14:39.374743Z",
+     "shell.execute_reply": "2023-08-15T16:14:39.373872Z"
     }
    },
    "outputs": [
@@ -101,10 +101,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:02:09.567523Z",
-     "iopub.status.busy": "2023-07-11T00:02:09.567243Z",
-     "iopub.status.idle": "2023-07-11T00:02:10.044018Z",
-     "shell.execute_reply": "2023-07-11T00:02:10.040289Z"
+     "iopub.execute_input": "2023-08-15T16:14:39.462543Z",
+     "iopub.status.busy": "2023-08-15T16:14:39.462138Z",
+     "iopub.status.idle": "2023-08-15T16:14:41.054125Z",
+     "shell.execute_reply": "2023-08-15T16:14:41.053049Z"
     }
    },
    "outputs": [],
@@ -132,10 +132,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:02:10.049518Z",
-     "iopub.status.busy": "2023-07-11T00:02:10.048756Z",
-     "iopub.status.idle": "2023-07-11T00:02:10.418507Z",
-     "shell.execute_reply": "2023-07-11T00:02:10.417896Z"
+     "iopub.execute_input": "2023-08-15T16:14:41.058529Z",
+     "iopub.status.busy": "2023-08-15T16:14:41.058272Z",
+     "iopub.status.idle": "2023-08-15T16:14:41.603331Z",
+     "shell.execute_reply": "2023-08-15T16:14:41.601089Z"
     }
    },
    "outputs": [
@@ -175,10 +175,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:02:10.421989Z",
-     "iopub.status.busy": "2023-07-11T00:02:10.421706Z",
-     "iopub.status.idle": "2023-07-11T00:02:10.742500Z",
-     "shell.execute_reply": "2023-07-11T00:02:10.741720Z"
+     "iopub.execute_input": "2023-08-15T16:14:41.615868Z",
+     "iopub.status.busy": "2023-08-15T16:14:41.614704Z",
+     "iopub.status.idle": "2023-08-15T16:14:41.958739Z",
+     "shell.execute_reply": "2023-08-15T16:14:41.958141Z"
     }
    },
    "outputs": [
@@ -233,10 +233,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:02:10.745804Z",
-     "iopub.status.busy": "2023-07-11T00:02:10.745543Z",
-     "iopub.status.idle": "2023-07-11T00:02:11.050430Z",
-     "shell.execute_reply": "2023-07-11T00:02:11.049631Z"
+     "iopub.execute_input": "2023-08-15T16:14:41.961925Z",
+     "iopub.status.busy": "2023-08-15T16:14:41.961671Z",
+     "iopub.status.idle": "2023-08-15T16:14:42.303716Z",
+     "shell.execute_reply": "2023-08-15T16:14:42.302472Z"
     }
    },
    "outputs": [
@@ -277,10 +277,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:02:11.054792Z",
-     "iopub.status.busy": "2023-07-11T00:02:11.054513Z",
-     "iopub.status.idle": "2023-07-11T00:02:11.464030Z",
-     "shell.execute_reply": "2023-07-11T00:02:11.463418Z"
+     "iopub.execute_input": "2023-08-15T16:14:42.307032Z",
+     "iopub.status.busy": "2023-08-15T16:14:42.306781Z",
+     "iopub.status.idle": "2023-08-15T16:14:42.846033Z",
+     "shell.execute_reply": "2023-08-15T16:14:42.844862Z"
     }
    },
    "outputs": [
@@ -314,10 +314,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:02:11.466933Z",
-     "iopub.status.busy": "2023-07-11T00:02:11.466636Z",
-     "iopub.status.idle": "2023-07-11T00:02:12.110406Z",
-     "shell.execute_reply": "2023-07-11T00:02:12.109782Z"
+     "iopub.execute_input": "2023-08-15T16:14:42.851702Z",
+     "iopub.status.busy": "2023-08-15T16:14:42.851440Z",
+     "iopub.status.idle": "2023-08-15T16:14:43.299851Z",
+     "shell.execute_reply": "2023-08-15T16:14:43.298918Z"
     }
    },
    "outputs": [
diff --git a/doc/feature_detection/notebooks/n_min_threshold_example.ipynb b/doc/feature_detection/notebooks/n_min_threshold_example.ipynb
index 83e95dbf..018dc1c6 100644
--- a/doc/feature_detection/notebooks/n_min_threshold_example.ipynb
+++ b/doc/feature_detection/notebooks/n_min_threshold_example.ipynb
@@ -19,10 +19,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:17.198085Z",
-     "iopub.status.busy": "2023-07-11T00:01:17.197646Z",
-     "iopub.status.idle": "2023-07-11T00:01:23.156772Z",
-     "shell.execute_reply": "2023-07-11T00:01:23.155547Z"
+     "iopub.execute_input": "2023-08-15T16:13:29.891899Z",
+     "iopub.status.busy": "2023-08-15T16:13:29.891559Z",
+     "iopub.status.idle": "2023-08-15T16:13:40.669735Z",
+     "shell.execute_reply": "2023-08-15T16:13:40.668454Z"
     }
    },
    "outputs": [],
@@ -53,10 +53,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:23.161526Z",
-     "iopub.status.busy": "2023-07-11T00:01:23.161099Z",
-     "iopub.status.idle": "2023-07-11T00:01:23.461685Z",
-     "shell.execute_reply": "2023-07-11T00:01:23.460771Z"
+     "iopub.execute_input": "2023-08-15T16:13:40.674527Z",
+     "iopub.status.busy": "2023-08-15T16:13:40.674100Z",
+     "iopub.status.idle": "2023-08-15T16:13:41.311564Z",
+     "shell.execute_reply": "2023-08-15T16:13:41.309098Z"
     }
    },
    "outputs": [
@@ -94,10 +94,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:23.505031Z",
-     "iopub.status.busy": "2023-07-11T00:01:23.504758Z",
-     "iopub.status.idle": "2023-07-11T00:01:23.962379Z",
-     "shell.execute_reply": "2023-07-11T00:01:23.961387Z"
+     "iopub.execute_input": "2023-08-15T16:13:41.390889Z",
+     "iopub.status.busy": "2023-08-15T16:13:41.390549Z",
+     "iopub.status.idle": "2023-08-15T16:13:42.553393Z",
+     "shell.execute_reply": "2023-08-15T16:13:42.551799Z"
     }
    },
    "outputs": [],
@@ -132,10 +132,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:23.975020Z",
-     "iopub.status.busy": "2023-07-11T00:01:23.974670Z",
-     "iopub.status.idle": "2023-07-11T00:01:24.488125Z",
-     "shell.execute_reply": "2023-07-11T00:01:24.486970Z"
+     "iopub.execute_input": "2023-08-15T16:13:42.559790Z",
+     "iopub.status.busy": "2023-08-15T16:13:42.559023Z",
+     "iopub.status.idle": "2023-08-15T16:13:43.274316Z",
+     "shell.execute_reply": "2023-08-15T16:13:43.272229Z"
     }
    },
    "outputs": [
@@ -196,10 +196,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:24.491977Z",
-     "iopub.status.busy": "2023-07-11T00:01:24.491692Z",
-     "iopub.status.idle": "2023-07-11T00:01:24.762533Z",
-     "shell.execute_reply": "2023-07-11T00:01:24.761829Z"
+     "iopub.execute_input": "2023-08-15T16:13:43.277981Z",
+     "iopub.status.busy": "2023-08-15T16:13:43.277350Z",
+     "iopub.status.idle": "2023-08-15T16:13:43.655653Z",
+     "shell.execute_reply": "2023-08-15T16:13:43.654872Z"
     }
    },
    "outputs": [
@@ -254,10 +254,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:24.765546Z",
-     "iopub.status.busy": "2023-07-11T00:01:24.765298Z",
-     "iopub.status.idle": "2023-07-11T00:01:25.031369Z",
-     "shell.execute_reply": "2023-07-11T00:01:25.029177Z"
+     "iopub.execute_input": "2023-08-15T16:13:43.658838Z",
+     "iopub.status.busy": "2023-08-15T16:13:43.658468Z",
+     "iopub.status.idle": "2023-08-15T16:13:44.274706Z",
+     "shell.execute_reply": "2023-08-15T16:13:44.273804Z"
     }
    },
    "outputs": [
@@ -312,10 +312,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:25.039594Z",
-     "iopub.status.busy": "2023-07-11T00:01:25.039160Z",
-     "iopub.status.idle": "2023-07-11T00:01:25.475666Z",
-     "shell.execute_reply": "2023-07-11T00:01:25.474359Z"
+     "iopub.execute_input": "2023-08-15T16:13:44.278747Z",
+     "iopub.status.busy": "2023-08-15T16:13:44.278223Z",
+     "iopub.status.idle": "2023-08-15T16:13:44.734689Z",
+     "shell.execute_reply": "2023-08-15T16:13:44.731120Z"
     }
    },
    "outputs": [
@@ -379,10 +379,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:25.478990Z",
-     "iopub.status.busy": "2023-07-11T00:01:25.478726Z",
-     "iopub.status.idle": "2023-07-11T00:01:25.744010Z",
-     "shell.execute_reply": "2023-07-11T00:01:25.743426Z"
+     "iopub.execute_input": "2023-08-15T16:13:44.738138Z",
+     "iopub.status.busy": "2023-08-15T16:13:44.737691Z",
+     "iopub.status.idle": "2023-08-15T16:13:45.070090Z",
+     "shell.execute_reply": "2023-08-15T16:13:45.069528Z"
     }
    },
    "outputs": [
@@ -453,10 +453,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:25.747104Z",
-     "iopub.status.busy": "2023-07-11T00:01:25.746853Z",
-     "iopub.status.idle": "2023-07-11T00:01:26.214434Z",
-     "shell.execute_reply": "2023-07-11T00:01:26.213506Z"
+     "iopub.execute_input": "2023-08-15T16:13:45.073250Z",
+     "iopub.status.busy": "2023-08-15T16:13:45.073013Z",
+     "iopub.status.idle": "2023-08-15T16:13:45.295177Z",
+     "shell.execute_reply": "2023-08-15T16:13:45.294558Z"
     }
    },
    "outputs": [
@@ -501,10 +501,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:26.219922Z",
-     "iopub.status.busy": "2023-07-11T00:01:26.218859Z",
-     "iopub.status.idle": "2023-07-11T00:01:26.916666Z",
-     "shell.execute_reply": "2023-07-11T00:01:26.915852Z"
+     "iopub.execute_input": "2023-08-15T16:13:45.298170Z",
+     "iopub.status.busy": "2023-08-15T16:13:45.297930Z",
+     "iopub.status.idle": "2023-08-15T16:13:45.783115Z",
+     "shell.execute_reply": "2023-08-15T16:13:45.782440Z"
     }
    },
    "outputs": [
diff --git a/doc/feature_detection/notebooks/position_threshold_example.ipynb b/doc/feature_detection/notebooks/position_threshold_example.ipynb
index b2ee5e36..bcfcca9e 100644
--- a/doc/feature_detection/notebooks/position_threshold_example.ipynb
+++ b/doc/feature_detection/notebooks/position_threshold_example.ipynb
@@ -19,10 +19,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:33.564694Z",
-     "iopub.status.busy": "2023-07-11T00:01:33.564103Z",
-     "iopub.status.idle": "2023-07-11T00:01:37.347390Z",
-     "shell.execute_reply": "2023-07-11T00:01:37.345947Z"
+     "iopub.execute_input": "2023-08-15T16:13:51.550382Z",
+     "iopub.status.busy": "2023-08-15T16:13:51.549721Z",
+     "iopub.status.idle": "2023-08-15T16:13:55.786150Z",
+     "shell.execute_reply": "2023-08-15T16:13:55.785491Z"
     }
    },
    "outputs": [],
@@ -53,10 +53,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:37.355980Z",
-     "iopub.status.busy": "2023-07-11T00:01:37.355486Z",
-     "iopub.status.idle": "2023-07-11T00:01:37.727584Z",
-     "shell.execute_reply": "2023-07-11T00:01:37.726861Z"
+     "iopub.execute_input": "2023-08-15T16:13:55.789899Z",
+     "iopub.status.busy": "2023-08-15T16:13:55.789509Z",
+     "iopub.status.idle": "2023-08-15T16:13:56.038627Z",
+     "shell.execute_reply": "2023-08-15T16:13:56.037050Z"
     }
    },
    "outputs": [
@@ -92,10 +92,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:37.762774Z",
-     "iopub.status.busy": "2023-07-11T00:01:37.762399Z",
-     "iopub.status.idle": "2023-07-11T00:01:38.223234Z",
-     "shell.execute_reply": "2023-07-11T00:01:38.221887Z"
+     "iopub.execute_input": "2023-08-15T16:13:56.079285Z",
+     "iopub.status.busy": "2023-08-15T16:13:56.078987Z",
+     "iopub.status.idle": "2023-08-15T16:13:56.819105Z",
+     "shell.execute_reply": "2023-08-15T16:13:56.814955Z"
     }
    },
    "outputs": [],
@@ -126,10 +126,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:38.228789Z",
-     "iopub.status.busy": "2023-07-11T00:01:38.228002Z",
-     "iopub.status.idle": "2023-07-11T00:01:38.694153Z",
-     "shell.execute_reply": "2023-07-11T00:01:38.693542Z"
+     "iopub.execute_input": "2023-08-15T16:13:56.823530Z",
+     "iopub.status.busy": "2023-08-15T16:13:56.823170Z",
+     "iopub.status.idle": "2023-08-15T16:13:57.439427Z",
+     "shell.execute_reply": "2023-08-15T16:13:57.438837Z"
     }
    },
    "outputs": [
@@ -177,10 +177,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:38.697291Z",
-     "iopub.status.busy": "2023-07-11T00:01:38.696889Z",
-     "iopub.status.idle": "2023-07-11T00:01:39.014066Z",
-     "shell.execute_reply": "2023-07-11T00:01:39.013273Z"
+     "iopub.execute_input": "2023-08-15T16:13:57.443184Z",
+     "iopub.status.busy": "2023-08-15T16:13:57.442924Z",
+     "iopub.status.idle": "2023-08-15T16:13:57.788033Z",
+     "shell.execute_reply": "2023-08-15T16:13:57.787402Z"
     }
    },
    "outputs": [
@@ -228,10 +228,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:39.017567Z",
-     "iopub.status.busy": "2023-07-11T00:01:39.017260Z",
-     "iopub.status.idle": "2023-07-11T00:01:39.380188Z",
-     "shell.execute_reply": "2023-07-11T00:01:39.379419Z"
+     "iopub.execute_input": "2023-08-15T16:13:57.791395Z",
+     "iopub.status.busy": "2023-08-15T16:13:57.791076Z",
+     "iopub.status.idle": "2023-08-15T16:13:58.180136Z",
+     "shell.execute_reply": "2023-08-15T16:13:58.179513Z"
     }
    },
    "outputs": [
@@ -279,10 +279,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:39.383505Z",
-     "iopub.status.busy": "2023-07-11T00:01:39.383259Z",
-     "iopub.status.idle": "2023-07-11T00:01:39.789260Z",
-     "shell.execute_reply": "2023-07-11T00:01:39.788365Z"
+     "iopub.execute_input": "2023-08-15T16:13:58.184217Z",
+     "iopub.status.busy": "2023-08-15T16:13:58.183962Z",
+     "iopub.status.idle": "2023-08-15T16:13:58.730361Z",
+     "shell.execute_reply": "2023-08-15T16:13:58.729542Z"
     }
    },
    "outputs": [
@@ -329,10 +329,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:39.792154Z",
-     "iopub.status.busy": "2023-07-11T00:01:39.791909Z",
-     "iopub.status.idle": "2023-07-11T00:01:41.425829Z",
-     "shell.execute_reply": "2023-07-11T00:01:41.425178Z"
+     "iopub.execute_input": "2023-08-15T16:13:58.734802Z",
+     "iopub.status.busy": "2023-08-15T16:13:58.734455Z",
+     "iopub.status.idle": "2023-08-15T16:14:00.352515Z",
+     "shell.execute_reply": "2023-08-15T16:14:00.351812Z"
     }
    },
    "outputs": [
diff --git a/examples/Example_OLR_Tracking_model/Example_OLR_Tracking_model.ipynb b/examples/Example_OLR_Tracking_model/Example_OLR_Tracking_model.ipynb
index 6f9471e5..702e548a 100644
--- a/examples/Example_OLR_Tracking_model/Example_OLR_Tracking_model.ipynb
+++ b/examples/Example_OLR_Tracking_model/Example_OLR_Tracking_model.ipynb
@@ -25,10 +25,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:46:39.016439Z",
-     "iopub.status.busy": "2023-07-10T23:46:39.015991Z",
-     "iopub.status.idle": "2023-07-10T23:46:48.957459Z",
-     "shell.execute_reply": "2023-07-10T23:46:48.955932Z"
+     "iopub.execute_input": "2023-08-15T15:56:18.818385Z",
+     "iopub.status.busy": "2023-08-15T15:56:18.818120Z",
+     "iopub.status.idle": "2023-08-15T15:56:24.853054Z",
+     "shell.execute_reply": "2023-08-15T15:56:24.851960Z"
     }
    },
    "outputs": [],
@@ -52,10 +52,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:46:48.963154Z",
-     "iopub.status.busy": "2023-07-10T23:46:48.962247Z",
-     "iopub.status.idle": "2023-07-10T23:46:53.299290Z",
-     "shell.execute_reply": "2023-07-10T23:46:53.298109Z"
+     "iopub.execute_input": "2023-08-15T15:56:24.857082Z",
+     "iopub.status.busy": "2023-08-15T15:56:24.856743Z",
+     "iopub.status.idle": "2023-08-15T15:56:25.803916Z",
+     "shell.execute_reply": "2023-08-15T15:56:25.803247Z"
     }
    },
    "outputs": [
@@ -63,7 +63,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "using tobac version 1.5.0\n"
+      "using tobac version 1.5.1\n"
      ]
     }
    ],
@@ -78,10 +78,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:46:53.338085Z",
-     "iopub.status.busy": "2023-07-10T23:46:53.337828Z",
-     "iopub.status.idle": "2023-07-10T23:46:53.341661Z",
-     "shell.execute_reply": "2023-07-10T23:46:53.341064Z"
+     "iopub.execute_input": "2023-08-15T15:56:25.848955Z",
+     "iopub.status.busy": "2023-08-15T15:56:25.847798Z",
+     "iopub.status.idle": "2023-08-15T15:56:25.853013Z",
+     "shell.execute_reply": "2023-08-15T15:56:25.851964Z"
     }
    },
    "outputs": [],
@@ -107,10 +107,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:46:53.344493Z",
-     "iopub.status.busy": "2023-07-10T23:46:53.344253Z",
-     "iopub.status.idle": "2023-07-10T23:46:53.347358Z",
-     "shell.execute_reply": "2023-07-10T23:46:53.346661Z"
+     "iopub.execute_input": "2023-08-15T15:56:25.858505Z",
+     "iopub.status.busy": "2023-08-15T15:56:25.856728Z",
+     "iopub.status.idle": "2023-08-15T15:56:25.862020Z",
+     "shell.execute_reply": "2023-08-15T15:56:25.861169Z"
     }
    },
    "outputs": [],
@@ -123,10 +123,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:46:53.350371Z",
-     "iopub.status.busy": "2023-07-10T23:46:53.350112Z",
-     "iopub.status.idle": "2023-07-10T23:46:53.360737Z",
-     "shell.execute_reply": "2023-07-10T23:46:53.359764Z"
+     "iopub.execute_input": "2023-08-15T15:56:25.866672Z",
+     "iopub.status.busy": "2023-08-15T15:56:25.866059Z",
+     "iopub.status.idle": "2023-08-15T15:56:25.877599Z",
+     "shell.execute_reply": "2023-08-15T15:56:25.876776Z"
     }
    },
    "outputs": [],
@@ -151,10 +151,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:46:53.364048Z",
-     "iopub.status.busy": "2023-07-10T23:46:53.363772Z",
-     "iopub.status.idle": "2023-07-10T23:46:53.563798Z",
-     "shell.execute_reply": "2023-07-10T23:46:53.562534Z"
+     "iopub.execute_input": "2023-08-15T15:56:25.881197Z",
+     "iopub.status.busy": "2023-08-15T15:56:25.880929Z",
+     "iopub.status.idle": "2023-08-15T15:56:26.014201Z",
+     "shell.execute_reply": "2023-08-15T15:56:26.011242Z"
     }
    },
    "outputs": [],
@@ -168,10 +168,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:46:53.566969Z",
-     "iopub.status.busy": "2023-07-10T23:46:53.566697Z",
-     "iopub.status.idle": "2023-07-10T23:46:53.570353Z",
-     "shell.execute_reply": "2023-07-10T23:46:53.569728Z"
+     "iopub.execute_input": "2023-08-15T15:56:26.019954Z",
+     "iopub.status.busy": "2023-08-15T15:56:26.019651Z",
+     "iopub.status.idle": "2023-08-15T15:56:26.023985Z",
+     "shell.execute_reply": "2023-08-15T15:56:26.023229Z"
     }
    },
    "outputs": [],
@@ -198,10 +198,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:46:53.575349Z",
-     "iopub.status.busy": "2023-07-10T23:46:53.574301Z",
-     "iopub.status.idle": "2023-07-10T23:46:54.282172Z",
-     "shell.execute_reply": "2023-07-10T23:46:54.281368Z"
+     "iopub.execute_input": "2023-08-15T15:56:26.028223Z",
+     "iopub.status.busy": "2023-08-15T15:56:26.027953Z",
+     "iopub.status.idle": "2023-08-15T15:56:26.410040Z",
+     "shell.execute_reply": "2023-08-15T15:56:26.408680Z"
     }
    },
    "outputs": [],
@@ -215,10 +215,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:46:54.285636Z",
-     "iopub.status.busy": "2023-07-10T23:46:54.285272Z",
-     "iopub.status.idle": "2023-07-10T23:46:54.289653Z",
-     "shell.execute_reply": "2023-07-10T23:46:54.288813Z"
+     "iopub.execute_input": "2023-08-15T15:56:26.413393Z",
+     "iopub.status.busy": "2023-08-15T15:56:26.413154Z",
+     "iopub.status.idle": "2023-08-15T15:56:26.416678Z",
+     "shell.execute_reply": "2023-08-15T15:56:26.416033Z"
     }
    },
    "outputs": [],
@@ -237,10 +237,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:46:54.293087Z",
-     "iopub.status.busy": "2023-07-10T23:46:54.292647Z",
-     "iopub.status.idle": "2023-07-10T23:46:58.617811Z",
-     "shell.execute_reply": "2023-07-10T23:46:58.617268Z"
+     "iopub.execute_input": "2023-08-15T15:56:26.419253Z",
+     "iopub.status.busy": "2023-08-15T15:56:26.418989Z",
+     "iopub.status.idle": "2023-08-15T15:56:30.852287Z",
+     "shell.execute_reply": "2023-08-15T15:56:30.850799Z"
     }
    },
    "outputs": [
@@ -274,10 +274,10 @@
    "execution_count": 11,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:46:58.620713Z",
-     "iopub.status.busy": "2023-07-10T23:46:58.620475Z",
-     "iopub.status.idle": "2023-07-10T23:46:58.623927Z",
-     "shell.execute_reply": "2023-07-10T23:46:58.623283Z"
+     "iopub.execute_input": "2023-08-15T15:56:30.855774Z",
+     "iopub.status.busy": "2023-08-15T15:56:30.855499Z",
+     "iopub.status.idle": "2023-08-15T15:56:30.859576Z",
+     "shell.execute_reply": "2023-08-15T15:56:30.859002Z"
     }
    },
    "outputs": [],
@@ -294,10 +294,10 @@
    "execution_count": 12,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:46:58.627603Z",
-     "iopub.status.busy": "2023-07-10T23:46:58.627046Z",
-     "iopub.status.idle": "2023-07-10T23:47:05.723372Z",
-     "shell.execute_reply": "2023-07-10T23:47:05.722474Z"
+     "iopub.execute_input": "2023-08-15T15:56:30.862384Z",
+     "iopub.status.busy": "2023-08-15T15:56:30.862115Z",
+     "iopub.status.idle": "2023-08-15T15:56:39.418399Z",
+     "shell.execute_reply": "2023-08-15T15:56:39.417181Z"
     }
    },
    "outputs": [
@@ -334,10 +334,10 @@
    "execution_count": 13,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:47:05.726702Z",
-     "iopub.status.busy": "2023-07-10T23:47:05.726409Z",
-     "iopub.status.idle": "2023-07-10T23:47:05.732236Z",
-     "shell.execute_reply": "2023-07-10T23:47:05.730333Z"
+     "iopub.execute_input": "2023-08-15T15:56:39.422149Z",
+     "iopub.status.busy": "2023-08-15T15:56:39.421868Z",
+     "iopub.status.idle": "2023-08-15T15:56:39.433881Z",
+     "shell.execute_reply": "2023-08-15T15:56:39.430626Z"
     }
    },
    "outputs": [],
@@ -360,10 +360,10 @@
    "execution_count": 14,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:47:05.735686Z",
-     "iopub.status.busy": "2023-07-10T23:47:05.735147Z",
-     "iopub.status.idle": "2023-07-10T23:47:06.969903Z",
-     "shell.execute_reply": "2023-07-10T23:47:06.969210Z"
+     "iopub.execute_input": "2023-08-15T15:56:39.440567Z",
+     "iopub.status.busy": "2023-08-15T15:56:39.438635Z",
+     "iopub.status.idle": "2023-08-15T15:56:40.612361Z",
+     "shell.execute_reply": "2023-08-15T15:56:40.610614Z"
     }
    },
    "outputs": [
@@ -393,10 +393,10 @@
    "execution_count": 15,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:47:06.973311Z",
-     "iopub.status.busy": "2023-07-10T23:47:06.972814Z",
-     "iopub.status.idle": "2023-07-10T23:47:06.976049Z",
-     "shell.execute_reply": "2023-07-10T23:47:06.975365Z"
+     "iopub.execute_input": "2023-08-15T15:56:40.615671Z",
+     "iopub.status.busy": "2023-08-15T15:56:40.615418Z",
+     "iopub.status.idle": "2023-08-15T15:56:40.618573Z",
+     "shell.execute_reply": "2023-08-15T15:56:40.617998Z"
     }
    },
    "outputs": [],
@@ -410,10 +410,10 @@
    "execution_count": 16,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:47:06.980242Z",
-     "iopub.status.busy": "2023-07-10T23:47:06.979874Z",
-     "iopub.status.idle": "2023-07-10T23:47:39.711840Z",
-     "shell.execute_reply": "2023-07-10T23:47:39.711208Z"
+     "iopub.execute_input": "2023-08-15T15:56:40.622137Z",
+     "iopub.status.busy": "2023-08-15T15:56:40.621869Z",
+     "iopub.status.idle": "2023-08-15T15:57:14.976938Z",
+     "shell.execute_reply": "2023-08-15T15:57:14.976302Z"
     }
    },
    "outputs": [
@@ -440,10 +440,10 @@
    "execution_count": 17,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:47:39.715236Z",
-     "iopub.status.busy": "2023-07-10T23:47:39.714914Z",
-     "iopub.status.idle": "2023-07-10T23:47:39.733595Z",
-     "shell.execute_reply": "2023-07-10T23:47:39.732544Z"
+     "iopub.execute_input": "2023-08-15T15:57:14.979944Z",
+     "iopub.status.busy": "2023-08-15T15:57:14.979693Z",
+     "iopub.status.idle": "2023-08-15T15:57:14.989269Z",
+     "shell.execute_reply": "2023-08-15T15:57:14.988386Z"
     }
    },
    "outputs": [],
@@ -460,10 +460,10 @@
    "execution_count": 18,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:47:39.737597Z",
-     "iopub.status.busy": "2023-07-10T23:47:39.737301Z",
-     "iopub.status.idle": "2023-07-10T23:49:11.473516Z",
-     "shell.execute_reply": "2023-07-10T23:49:11.472403Z"
+     "iopub.execute_input": "2023-08-15T15:57:14.992582Z",
+     "iopub.status.busy": "2023-08-15T15:57:14.992317Z",
+     "iopub.status.idle": "2023-08-15T15:59:21.200686Z",
+     "shell.execute_reply": "2023-08-15T15:59:21.199643Z"
     }
    },
    "outputs": [
@@ -36953,10 +36953,10 @@
    "execution_count": 19,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:11.476701Z",
-     "iopub.status.busy": "2023-07-10T23:49:11.476426Z",
-     "iopub.status.idle": "2023-07-10T23:49:11.479510Z",
-     "shell.execute_reply": "2023-07-10T23:49:11.478860Z"
+     "iopub.execute_input": "2023-08-15T15:59:21.216222Z",
+     "iopub.status.busy": "2023-08-15T15:59:21.215584Z",
+     "iopub.status.idle": "2023-08-15T15:59:21.234051Z",
+     "shell.execute_reply": "2023-08-15T15:59:21.232571Z"
     }
    },
    "outputs": [],
@@ -36972,10 +36972,10 @@
    "execution_count": 20,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:11.483140Z",
-     "iopub.status.busy": "2023-07-10T23:49:11.482901Z",
-     "iopub.status.idle": "2023-07-10T23:49:11.664382Z",
-     "shell.execute_reply": "2023-07-10T23:49:11.663445Z"
+     "iopub.execute_input": "2023-08-15T15:59:21.244852Z",
+     "iopub.status.busy": "2023-08-15T15:59:21.244134Z",
+     "iopub.status.idle": "2023-08-15T15:59:21.612905Z",
+     "shell.execute_reply": "2023-08-15T15:59:21.612265Z"
     }
    },
    "outputs": [
diff --git a/examples/Example_OLR_Tracking_satellite/Example_OLR_Tracking_satellite.ipynb b/examples/Example_OLR_Tracking_satellite/Example_OLR_Tracking_satellite.ipynb
index bdeefc09..2d7fc9db 100644
--- a/examples/Example_OLR_Tracking_satellite/Example_OLR_Tracking_satellite.ipynb
+++ b/examples/Example_OLR_Tracking_satellite/Example_OLR_Tracking_satellite.ipynb
@@ -17,10 +17,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:43:43.667323Z",
-     "iopub.status.busy": "2023-07-10T23:43:43.666898Z",
-     "iopub.status.idle": "2023-07-10T23:43:54.438976Z",
-     "shell.execute_reply": "2023-07-10T23:43:54.437693Z"
+     "iopub.execute_input": "2023-08-15T15:52:56.615715Z",
+     "iopub.status.busy": "2023-08-15T15:52:56.615426Z",
+     "iopub.status.idle": "2023-08-15T15:53:13.173267Z",
+     "shell.execute_reply": "2023-08-15T15:53:13.172545Z"
     }
    },
    "outputs": [],
@@ -43,10 +43,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:43:54.443139Z",
-     "iopub.status.busy": "2023-07-10T23:43:54.442830Z",
-     "iopub.status.idle": "2023-07-10T23:43:57.152301Z",
-     "shell.execute_reply": "2023-07-10T23:43:57.151615Z"
+     "iopub.execute_input": "2023-08-15T15:53:13.178204Z",
+     "iopub.status.busy": "2023-08-15T15:53:13.177872Z",
+     "iopub.status.idle": "2023-08-15T15:53:16.825906Z",
+     "shell.execute_reply": "2023-08-15T15:53:16.822344Z"
     }
    },
    "outputs": [
@@ -54,7 +54,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "using tobac version 1.5.0\n"
+      "using tobac version 1.5.1\n"
      ]
     }
    ],
@@ -69,10 +69,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:43:57.198066Z",
-     "iopub.status.busy": "2023-07-10T23:43:57.197766Z",
-     "iopub.status.idle": "2023-07-10T23:43:57.201852Z",
-     "shell.execute_reply": "2023-07-10T23:43:57.201085Z"
+     "iopub.execute_input": "2023-08-15T15:53:17.160077Z",
+     "iopub.status.busy": "2023-08-15T15:53:17.157291Z",
+     "iopub.status.idle": "2023-08-15T15:53:17.166798Z",
+     "shell.execute_reply": "2023-08-15T15:53:17.165473Z"
     }
    },
    "outputs": [],
@@ -98,10 +98,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:43:57.204709Z",
-     "iopub.status.busy": "2023-07-10T23:43:57.204463Z",
-     "iopub.status.idle": "2023-07-10T23:43:57.207684Z",
-     "shell.execute_reply": "2023-07-10T23:43:57.207045Z"
+     "iopub.execute_input": "2023-08-15T15:53:17.177723Z",
+     "iopub.status.busy": "2023-08-15T15:53:17.177366Z",
+     "iopub.status.idle": "2023-08-15T15:53:17.184565Z",
+     "shell.execute_reply": "2023-08-15T15:53:17.181754Z"
     }
    },
    "outputs": [],
@@ -114,10 +114,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:43:57.210475Z",
-     "iopub.status.busy": "2023-07-10T23:43:57.210196Z",
-     "iopub.status.idle": "2023-07-10T23:43:57.217272Z",
-     "shell.execute_reply": "2023-07-10T23:43:57.216473Z"
+     "iopub.execute_input": "2023-08-15T15:53:17.203441Z",
+     "iopub.status.busy": "2023-08-15T15:53:17.201987Z",
+     "iopub.status.idle": "2023-08-15T15:53:17.211804Z",
+     "shell.execute_reply": "2023-08-15T15:53:17.210240Z"
     }
    },
    "outputs": [],
@@ -149,10 +149,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:43:57.220329Z",
-     "iopub.status.busy": "2023-07-10T23:43:57.220080Z",
-     "iopub.status.idle": "2023-07-10T23:43:57.675655Z",
-     "shell.execute_reply": "2023-07-10T23:43:57.675021Z"
+     "iopub.execute_input": "2023-08-15T15:53:17.223620Z",
+     "iopub.status.busy": "2023-08-15T15:53:17.222750Z",
+     "iopub.status.idle": "2023-08-15T15:53:17.582960Z",
+     "shell.execute_reply": "2023-08-15T15:53:17.581583Z"
     }
    },
    "outputs": [],
@@ -166,10 +166,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:43:57.680426Z",
-     "iopub.status.busy": "2023-07-10T23:43:57.678901Z",
-     "iopub.status.idle": "2023-07-10T23:43:57.719079Z",
-     "shell.execute_reply": "2023-07-10T23:43:57.718494Z"
+     "iopub.execute_input": "2023-08-15T15:53:17.591095Z",
+     "iopub.status.busy": "2023-08-15T15:53:17.590268Z",
+     "iopub.status.idle": "2023-08-15T15:53:17.615811Z",
+     "shell.execute_reply": "2023-08-15T15:53:17.613548Z"
     }
    },
    "outputs": [
@@ -224,7 +224,7 @@
        "      margin-top: 7px;\n",
        "  }\n",
        "</style>\n",
-       "<table class=\"iris\" id=\"4948045840\">\n",
+       "<table class=\"iris\" id=\"4906746704\">\n",
        "    <tr class=\"iris\">\n",
        "<th class=\"iris iris-word-cell\">Olr (W m^-2)</th>\n",
        "<th class=\"iris iris-word-cell\">time</th>\n",
@@ -288,10 +288,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:43:57.721930Z",
-     "iopub.status.busy": "2023-07-10T23:43:57.721676Z",
-     "iopub.status.idle": "2023-07-10T23:43:57.725260Z",
-     "shell.execute_reply": "2023-07-10T23:43:57.724642Z"
+     "iopub.execute_input": "2023-08-15T15:53:17.628154Z",
+     "iopub.status.busy": "2023-08-15T15:53:17.623551Z",
+     "iopub.status.idle": "2023-08-15T15:53:17.634970Z",
+     "shell.execute_reply": "2023-08-15T15:53:17.633910Z"
     }
    },
    "outputs": [],
@@ -318,10 +318,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:43:57.728474Z",
-     "iopub.status.busy": "2023-07-10T23:43:57.728226Z",
-     "iopub.status.idle": "2023-07-10T23:43:57.733213Z",
-     "shell.execute_reply": "2023-07-10T23:43:57.732567Z"
+     "iopub.execute_input": "2023-08-15T15:53:17.645207Z",
+     "iopub.status.busy": "2023-08-15T15:53:17.643968Z",
+     "iopub.status.idle": "2023-08-15T15:53:17.656639Z",
+     "shell.execute_reply": "2023-08-15T15:53:17.655897Z"
     }
    },
    "outputs": [],
@@ -335,10 +335,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:43:57.736134Z",
-     "iopub.status.busy": "2023-07-10T23:43:57.735849Z",
-     "iopub.status.idle": "2023-07-10T23:43:57.740032Z",
-     "shell.execute_reply": "2023-07-10T23:43:57.739382Z"
+     "iopub.execute_input": "2023-08-15T15:53:17.661235Z",
+     "iopub.status.busy": "2023-08-15T15:53:17.660793Z",
+     "iopub.status.idle": "2023-08-15T15:53:17.668302Z",
+     "shell.execute_reply": "2023-08-15T15:53:17.666605Z"
     }
    },
    "outputs": [],
@@ -357,10 +357,10 @@
    "execution_count": 11,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:43:57.742774Z",
-     "iopub.status.busy": "2023-07-10T23:43:57.742525Z",
-     "iopub.status.idle": "2023-07-10T23:44:00.782646Z",
-     "shell.execute_reply": "2023-07-10T23:44:00.782030Z"
+     "iopub.execute_input": "2023-08-15T15:53:17.682061Z",
+     "iopub.status.busy": "2023-08-15T15:53:17.681063Z",
+     "iopub.status.idle": "2023-08-15T15:53:22.281897Z",
+     "shell.execute_reply": "2023-08-15T15:53:22.280027Z"
     }
    },
    "outputs": [
@@ -394,10 +394,10 @@
    "execution_count": 12,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:44:00.786142Z",
-     "iopub.status.busy": "2023-07-10T23:44:00.785855Z",
-     "iopub.status.idle": "2023-07-10T23:44:00.789371Z",
-     "shell.execute_reply": "2023-07-10T23:44:00.788717Z"
+     "iopub.execute_input": "2023-08-15T15:53:22.285934Z",
+     "iopub.status.busy": "2023-08-15T15:53:22.285573Z",
+     "iopub.status.idle": "2023-08-15T15:53:22.293034Z",
+     "shell.execute_reply": "2023-08-15T15:53:22.290024Z"
     }
    },
    "outputs": [],
@@ -414,10 +414,10 @@
    "execution_count": 13,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:44:00.792654Z",
-     "iopub.status.busy": "2023-07-10T23:44:00.792361Z",
-     "iopub.status.idle": "2023-07-10T23:44:03.785954Z",
-     "shell.execute_reply": "2023-07-10T23:44:03.785324Z"
+     "iopub.execute_input": "2023-08-15T15:53:22.301022Z",
+     "iopub.status.busy": "2023-08-15T15:53:22.299516Z",
+     "iopub.status.idle": "2023-08-15T15:53:27.936649Z",
+     "shell.execute_reply": "2023-08-15T15:53:27.936013Z"
     }
    },
    "outputs": [
@@ -452,10 +452,10 @@
    "execution_count": 14,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:44:03.788932Z",
-     "iopub.status.busy": "2023-07-10T23:44:03.788584Z",
-     "iopub.status.idle": "2023-07-10T23:44:03.792525Z",
-     "shell.execute_reply": "2023-07-10T23:44:03.791899Z"
+     "iopub.execute_input": "2023-08-15T15:53:27.940025Z",
+     "iopub.status.busy": "2023-08-15T15:53:27.939759Z",
+     "iopub.status.idle": "2023-08-15T15:53:27.944674Z",
+     "shell.execute_reply": "2023-08-15T15:53:27.943836Z"
     }
    },
    "outputs": [],
@@ -478,10 +478,10 @@
    "execution_count": 15,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:44:03.795920Z",
-     "iopub.status.busy": "2023-07-10T23:44:03.795665Z",
-     "iopub.status.idle": "2023-07-10T23:44:04.336480Z",
-     "shell.execute_reply": "2023-07-10T23:44:04.335469Z"
+     "iopub.execute_input": "2023-08-15T15:53:27.947947Z",
+     "iopub.status.busy": "2023-08-15T15:53:27.947541Z",
+     "iopub.status.idle": "2023-08-15T15:53:28.786759Z",
+     "shell.execute_reply": "2023-08-15T15:53:28.785369Z"
     }
    },
    "outputs": [
@@ -511,10 +511,10 @@
    "execution_count": 16,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:44:04.339863Z",
-     "iopub.status.busy": "2023-07-10T23:44:04.339617Z",
-     "iopub.status.idle": "2023-07-10T23:44:04.342516Z",
-     "shell.execute_reply": "2023-07-10T23:44:04.341904Z"
+     "iopub.execute_input": "2023-08-15T15:53:28.791455Z",
+     "iopub.status.busy": "2023-08-15T15:53:28.791030Z",
+     "iopub.status.idle": "2023-08-15T15:53:28.795197Z",
+     "shell.execute_reply": "2023-08-15T15:53:28.794193Z"
     }
    },
    "outputs": [],
@@ -528,10 +528,10 @@
    "execution_count": 17,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:44:04.345485Z",
-     "iopub.status.busy": "2023-07-10T23:44:04.345216Z",
-     "iopub.status.idle": "2023-07-10T23:44:54.438424Z",
-     "shell.execute_reply": "2023-07-10T23:44:54.437160Z"
+     "iopub.execute_input": "2023-08-15T15:53:28.799557Z",
+     "iopub.status.busy": "2023-08-15T15:53:28.799050Z",
+     "iopub.status.idle": "2023-08-15T15:54:39.184744Z",
+     "shell.execute_reply": "2023-08-15T15:54:39.183126Z"
     }
    },
    "outputs": [
@@ -558,10 +558,10 @@
    "execution_count": 18,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:44:54.446118Z",
-     "iopub.status.busy": "2023-07-10T23:44:54.445739Z",
-     "iopub.status.idle": "2023-07-10T23:44:54.459844Z",
-     "shell.execute_reply": "2023-07-10T23:44:54.458577Z"
+     "iopub.execute_input": "2023-08-15T15:54:39.280052Z",
+     "iopub.status.busy": "2023-08-15T15:54:39.279017Z",
+     "iopub.status.idle": "2023-08-15T15:54:39.317144Z",
+     "shell.execute_reply": "2023-08-15T15:54:39.316134Z"
     }
    },
    "outputs": [],
@@ -578,10 +578,10 @@
    "execution_count": 19,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:44:54.462979Z",
-     "iopub.status.busy": "2023-07-10T23:44:54.462709Z",
-     "iopub.status.idle": "2023-07-10T23:46:29.116828Z",
-     "shell.execute_reply": "2023-07-10T23:46:29.116072Z"
+     "iopub.execute_input": "2023-08-15T15:54:39.320424Z",
+     "iopub.status.busy": "2023-08-15T15:54:39.320151Z",
+     "iopub.status.idle": "2023-08-15T15:56:05.390886Z",
+     "shell.execute_reply": "2023-08-15T15:56:05.385209Z"
     }
    },
    "outputs": [
@@ -31382,10 +31382,10 @@
    "execution_count": 20,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:46:29.127886Z",
-     "iopub.status.busy": "2023-07-10T23:46:29.127607Z",
-     "iopub.status.idle": "2023-07-10T23:46:29.130522Z",
-     "shell.execute_reply": "2023-07-10T23:46:29.129868Z"
+     "iopub.execute_input": "2023-08-15T15:56:05.462534Z",
+     "iopub.status.busy": "2023-08-15T15:56:05.461912Z",
+     "iopub.status.idle": "2023-08-15T15:56:05.467340Z",
+     "shell.execute_reply": "2023-08-15T15:56:05.466401Z"
     }
    },
    "outputs": [],
@@ -31401,10 +31401,10 @@
    "execution_count": 21,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:46:29.136338Z",
-     "iopub.status.busy": "2023-07-10T23:46:29.136067Z",
-     "iopub.status.idle": "2023-07-10T23:46:29.307550Z",
-     "shell.execute_reply": "2023-07-10T23:46:29.306930Z"
+     "iopub.execute_input": "2023-08-15T15:56:05.474014Z",
+     "iopub.status.busy": "2023-08-15T15:56:05.473739Z",
+     "iopub.status.idle": "2023-08-15T15:56:05.851733Z",
+     "shell.execute_reply": "2023-08-15T15:56:05.849490Z"
     }
    },
    "outputs": [
diff --git a/examples/Example_Precip_Tracking/Example_Precip_Tracking.ipynb b/examples/Example_Precip_Tracking/Example_Precip_Tracking.ipynb
index 342b7cb5..e680afe4 100644
--- a/examples/Example_Precip_Tracking/Example_Precip_Tracking.ipynb
+++ b/examples/Example_Precip_Tracking/Example_Precip_Tracking.ipynb
@@ -25,10 +25,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:17.650385Z",
-     "iopub.status.busy": "2023-07-10T23:49:17.650101Z",
-     "iopub.status.idle": "2023-07-10T23:49:20.998252Z",
-     "shell.execute_reply": "2023-07-10T23:49:20.997648Z"
+     "iopub.execute_input": "2023-08-15T15:59:30.825108Z",
+     "iopub.status.busy": "2023-08-15T15:59:30.824571Z",
+     "iopub.status.idle": "2023-08-15T15:59:40.165002Z",
+     "shell.execute_reply": "2023-08-15T15:59:40.164069Z"
     }
    },
    "outputs": [],
@@ -52,10 +52,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:21.001357Z",
-     "iopub.status.busy": "2023-07-10T23:49:21.001050Z",
-     "iopub.status.idle": "2023-07-10T23:49:21.495919Z",
-     "shell.execute_reply": "2023-07-10T23:49:21.491558Z"
+     "iopub.execute_input": "2023-08-15T15:59:40.168463Z",
+     "iopub.status.busy": "2023-08-15T15:59:40.168204Z",
+     "iopub.status.idle": "2023-08-15T15:59:41.185384Z",
+     "shell.execute_reply": "2023-08-15T15:59:41.184726Z"
     }
    },
    "outputs": [
@@ -63,7 +63,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "using tobac version 1.5.0\n"
+      "using tobac version 1.5.1\n"
      ]
     }
    ],
@@ -78,10 +78,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:21.545997Z",
-     "iopub.status.busy": "2023-07-10T23:49:21.545718Z",
-     "iopub.status.idle": "2023-07-10T23:49:21.552166Z",
-     "shell.execute_reply": "2023-07-10T23:49:21.551076Z"
+     "iopub.execute_input": "2023-08-15T15:59:41.238788Z",
+     "iopub.status.busy": "2023-08-15T15:59:41.238358Z",
+     "iopub.status.idle": "2023-08-15T15:59:41.251172Z",
+     "shell.execute_reply": "2023-08-15T15:59:41.248179Z"
     }
    },
    "outputs": [],
@@ -108,10 +108,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:21.556314Z",
-     "iopub.status.busy": "2023-07-10T23:49:21.556028Z",
-     "iopub.status.idle": "2023-07-10T23:49:21.559216Z",
-     "shell.execute_reply": "2023-07-10T23:49:21.558513Z"
+     "iopub.execute_input": "2023-08-15T15:59:41.257101Z",
+     "iopub.status.busy": "2023-08-15T15:59:41.255810Z",
+     "iopub.status.idle": "2023-08-15T15:59:41.267158Z",
+     "shell.execute_reply": "2023-08-15T15:59:41.264854Z"
     }
    },
    "outputs": [],
@@ -124,10 +124,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:21.562165Z",
-     "iopub.status.busy": "2023-07-10T23:49:21.561932Z",
-     "iopub.status.idle": "2023-07-10T23:49:21.569480Z",
-     "shell.execute_reply": "2023-07-10T23:49:21.568262Z"
+     "iopub.execute_input": "2023-08-15T15:59:41.275531Z",
+     "iopub.status.busy": "2023-08-15T15:59:41.275055Z",
+     "iopub.status.idle": "2023-08-15T15:59:41.290408Z",
+     "shell.execute_reply": "2023-08-15T15:59:41.288101Z"
     }
    },
    "outputs": [],
@@ -159,10 +159,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:21.572701Z",
-     "iopub.status.busy": "2023-07-10T23:49:21.572453Z",
-     "iopub.status.idle": "2023-07-10T23:49:21.652101Z",
-     "shell.execute_reply": "2023-07-10T23:49:21.651047Z"
+     "iopub.execute_input": "2023-08-15T15:59:41.295565Z",
+     "iopub.status.busy": "2023-08-15T15:59:41.295313Z",
+     "iopub.status.idle": "2023-08-15T15:59:41.398732Z",
+     "shell.execute_reply": "2023-08-15T15:59:41.397395Z"
     }
    },
    "outputs": [],
@@ -175,10 +175,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:21.655632Z",
-     "iopub.status.busy": "2023-07-10T23:49:21.655379Z",
-     "iopub.status.idle": "2023-07-10T23:49:21.696796Z",
-     "shell.execute_reply": "2023-07-10T23:49:21.695963Z"
+     "iopub.execute_input": "2023-08-15T15:59:41.402076Z",
+     "iopub.status.busy": "2023-08-15T15:59:41.401830Z",
+     "iopub.status.idle": "2023-08-15T15:59:41.436081Z",
+     "shell.execute_reply": "2023-08-15T15:59:41.434224Z"
     }
    },
    "outputs": [
@@ -233,7 +233,7 @@
        "      margin-top: 7px;\n",
        "  }\n",
        "</style>\n",
-       "<table class=\"iris\" id=\"5075510544\">\n",
+       "<table class=\"iris\" id=\"4895220752\">\n",
        "    <tr class=\"iris\">\n",
        "<th class=\"iris iris-word-cell\">Surface Precipitation Average (mm h-1)</th>\n",
        "<th class=\"iris iris-word-cell\">time</th>\n",
@@ -339,10 +339,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:21.701993Z",
-     "iopub.status.busy": "2023-07-10T23:49:21.701299Z",
-     "iopub.status.idle": "2023-07-10T23:49:21.705687Z",
-     "shell.execute_reply": "2023-07-10T23:49:21.704891Z"
+     "iopub.execute_input": "2023-08-15T15:59:41.440705Z",
+     "iopub.status.busy": "2023-08-15T15:59:41.440308Z",
+     "iopub.status.idle": "2023-08-15T15:59:41.445796Z",
+     "shell.execute_reply": "2023-08-15T15:59:41.444588Z"
     }
    },
    "outputs": [],
@@ -370,10 +370,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:21.708651Z",
-     "iopub.status.busy": "2023-07-10T23:49:21.708341Z",
-     "iopub.status.idle": "2023-07-10T23:49:21.711996Z",
-     "shell.execute_reply": "2023-07-10T23:49:21.711250Z"
+     "iopub.execute_input": "2023-08-15T15:59:41.449091Z",
+     "iopub.status.busy": "2023-08-15T15:59:41.448842Z",
+     "iopub.status.idle": "2023-08-15T15:59:41.452717Z",
+     "shell.execute_reply": "2023-08-15T15:59:41.452108Z"
     }
    },
    "outputs": [],
@@ -394,10 +394,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:21.717102Z",
-     "iopub.status.busy": "2023-07-10T23:49:21.716272Z",
-     "iopub.status.idle": "2023-07-10T23:49:21.985540Z",
-     "shell.execute_reply": "2023-07-10T23:49:21.984704Z"
+     "iopub.execute_input": "2023-08-15T15:59:41.460218Z",
+     "iopub.status.busy": "2023-08-15T15:59:41.458655Z",
+     "iopub.status.idle": "2023-08-15T15:59:42.456397Z",
+     "shell.execute_reply": "2023-08-15T15:59:42.418741Z"
     }
    },
    "outputs": [],
@@ -411,10 +411,10 @@
    "execution_count": 11,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:21.988734Z",
-     "iopub.status.busy": "2023-07-10T23:49:21.988483Z",
-     "iopub.status.idle": "2023-07-10T23:49:25.659105Z",
-     "shell.execute_reply": "2023-07-10T23:49:25.658456Z"
+     "iopub.execute_input": "2023-08-15T15:59:42.503039Z",
+     "iopub.status.busy": "2023-08-15T15:59:42.500551Z",
+     "iopub.status.idle": "2023-08-15T15:59:47.694929Z",
+     "shell.execute_reply": "2023-08-15T15:59:47.694266Z"
     }
    },
    "outputs": [
@@ -451,10 +451,10 @@
    "execution_count": 12,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:25.662179Z",
-     "iopub.status.busy": "2023-07-10T23:49:25.661918Z",
-     "iopub.status.idle": "2023-07-10T23:49:25.666594Z",
-     "shell.execute_reply": "2023-07-10T23:49:25.665351Z"
+     "iopub.execute_input": "2023-08-15T15:59:47.698097Z",
+     "iopub.status.busy": "2023-08-15T15:59:47.697846Z",
+     "iopub.status.idle": "2023-08-15T15:59:47.701821Z",
+     "shell.execute_reply": "2023-08-15T15:59:47.700982Z"
     }
    },
    "outputs": [],
@@ -470,10 +470,10 @@
    "execution_count": 13,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:25.670905Z",
-     "iopub.status.busy": "2023-07-10T23:49:25.670661Z",
-     "iopub.status.idle": "2023-07-10T23:49:32.340733Z",
-     "shell.execute_reply": "2023-07-10T23:49:32.340002Z"
+     "iopub.execute_input": "2023-08-15T15:59:47.706843Z",
+     "iopub.status.busy": "2023-08-15T15:59:47.706537Z",
+     "iopub.status.idle": "2023-08-15T15:59:58.665340Z",
+     "shell.execute_reply": "2023-08-15T15:59:58.664437Z"
     }
    },
    "outputs": [
@@ -511,10 +511,10 @@
    "execution_count": 14,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:32.343761Z",
-     "iopub.status.busy": "2023-07-10T23:49:32.343498Z",
-     "iopub.status.idle": "2023-07-10T23:49:32.347537Z",
-     "shell.execute_reply": "2023-07-10T23:49:32.346846Z"
+     "iopub.execute_input": "2023-08-15T15:59:58.668467Z",
+     "iopub.status.busy": "2023-08-15T15:59:58.668237Z",
+     "iopub.status.idle": "2023-08-15T15:59:58.671976Z",
+     "shell.execute_reply": "2023-08-15T15:59:58.671336Z"
     }
    },
    "outputs": [],
@@ -538,10 +538,10 @@
    "execution_count": 15,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:32.351085Z",
-     "iopub.status.busy": "2023-07-10T23:49:32.350844Z",
-     "iopub.status.idle": "2023-07-10T23:49:32.828962Z",
-     "shell.execute_reply": "2023-07-10T23:49:32.827751Z"
+     "iopub.execute_input": "2023-08-15T15:59:58.675258Z",
+     "iopub.status.busy": "2023-08-15T15:59:58.674979Z",
+     "iopub.status.idle": "2023-08-15T15:59:59.443278Z",
+     "shell.execute_reply": "2023-08-15T15:59:59.442137Z"
     }
    },
    "outputs": [
@@ -573,10 +573,10 @@
    "execution_count": 16,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:32.832823Z",
-     "iopub.status.busy": "2023-07-10T23:49:32.832553Z",
-     "iopub.status.idle": "2023-07-10T23:49:32.835800Z",
-     "shell.execute_reply": "2023-07-10T23:49:32.835186Z"
+     "iopub.execute_input": "2023-08-15T15:59:59.447626Z",
+     "iopub.status.busy": "2023-08-15T15:59:59.447282Z",
+     "iopub.status.idle": "2023-08-15T15:59:59.451377Z",
+     "shell.execute_reply": "2023-08-15T15:59:59.450366Z"
     }
    },
    "outputs": [],
@@ -590,10 +590,10 @@
    "execution_count": 17,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:49:32.839101Z",
-     "iopub.status.busy": "2023-07-10T23:49:32.838821Z",
-     "iopub.status.idle": "2023-07-10T23:50:10.935259Z",
-     "shell.execute_reply": "2023-07-10T23:50:10.934654Z"
+     "iopub.execute_input": "2023-08-15T15:59:59.454932Z",
+     "iopub.status.busy": "2023-08-15T15:59:59.454454Z",
+     "iopub.status.idle": "2023-08-15T16:00:46.641137Z",
+     "shell.execute_reply": "2023-08-15T16:00:46.640271Z"
     }
    },
    "outputs": [
@@ -620,10 +620,10 @@
    "execution_count": 18,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:50:10.938158Z",
-     "iopub.status.busy": "2023-07-10T23:50:10.937913Z",
-     "iopub.status.idle": "2023-07-10T23:50:10.945161Z",
-     "shell.execute_reply": "2023-07-10T23:50:10.944141Z"
+     "iopub.execute_input": "2023-08-15T16:00:46.645380Z",
+     "iopub.status.busy": "2023-08-15T16:00:46.645029Z",
+     "iopub.status.idle": "2023-08-15T16:00:46.656474Z",
+     "shell.execute_reply": "2023-08-15T16:00:46.655356Z"
     }
    },
    "outputs": [],
@@ -641,10 +641,10 @@
    "execution_count": 19,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:50:10.948400Z",
-     "iopub.status.busy": "2023-07-10T23:50:10.948142Z",
-     "iopub.status.idle": "2023-07-10T23:50:56.979795Z",
-     "shell.execute_reply": "2023-07-10T23:50:56.978790Z"
+     "iopub.execute_input": "2023-08-15T16:00:46.659766Z",
+     "iopub.status.busy": "2023-08-15T16:00:46.659510Z",
+     "iopub.status.idle": "2023-08-15T16:01:48.958122Z",
+     "shell.execute_reply": "2023-08-15T16:01:48.957437Z"
     }
    },
    "outputs": [
@@ -11006,10 +11006,10 @@
    "execution_count": 20,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:50:56.984617Z",
-     "iopub.status.busy": "2023-07-10T23:50:56.984316Z",
-     "iopub.status.idle": "2023-07-10T23:50:56.987823Z",
-     "shell.execute_reply": "2023-07-10T23:50:56.986919Z"
+     "iopub.execute_input": "2023-08-15T16:01:48.963636Z",
+     "iopub.status.busy": "2023-08-15T16:01:48.963353Z",
+     "iopub.status.idle": "2023-08-15T16:01:48.966634Z",
+     "shell.execute_reply": "2023-08-15T16:01:48.965949Z"
     }
    },
    "outputs": [],
@@ -11025,10 +11025,10 @@
    "execution_count": 21,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:50:56.990929Z",
-     "iopub.status.busy": "2023-07-10T23:50:56.990689Z",
-     "iopub.status.idle": "2023-07-10T23:50:57.150630Z",
-     "shell.execute_reply": "2023-07-10T23:50:57.149951Z"
+     "iopub.execute_input": "2023-08-15T16:01:48.970034Z",
+     "iopub.status.busy": "2023-08-15T16:01:48.969796Z",
+     "iopub.status.idle": "2023-08-15T16:01:49.116044Z",
+     "shell.execute_reply": "2023-08-15T16:01:49.115481Z"
     }
    },
    "outputs": [
diff --git a/examples/Example_Track_on_Radar_Segment_on_Satellite/track_on_radar_segment_on_satellite.ipynb b/examples/Example_Track_on_Radar_Segment_on_Satellite/track_on_radar_segment_on_satellite.ipynb
index 321ac896..6fa2f820 100644
--- a/examples/Example_Track_on_Radar_Segment_on_Satellite/track_on_radar_segment_on_satellite.ipynb
+++ b/examples/Example_Track_on_Radar_Segment_on_Satellite/track_on_radar_segment_on_satellite.ipynb
@@ -23,10 +23,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:55:17.887512Z",
-     "iopub.status.busy": "2023-07-10T23:55:17.887256Z",
-     "iopub.status.idle": "2023-07-10T23:55:20.161154Z",
-     "shell.execute_reply": "2023-07-10T23:55:20.160157Z"
+     "iopub.execute_input": "2023-08-15T16:07:30.195365Z",
+     "iopub.status.busy": "2023-08-15T16:07:30.194739Z",
+     "iopub.status.idle": "2023-08-15T16:07:32.717035Z",
+     "shell.execute_reply": "2023-08-15T16:07:32.716186Z"
     }
    },
    "outputs": [],
@@ -39,10 +39,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:55:20.164600Z",
-     "iopub.status.busy": "2023-07-10T23:55:20.164274Z",
-     "iopub.status.idle": "2023-07-10T23:55:31.584021Z",
-     "shell.execute_reply": "2023-07-10T23:55:31.582839Z"
+     "iopub.execute_input": "2023-08-15T16:07:32.720563Z",
+     "iopub.status.busy": "2023-08-15T16:07:32.720256Z",
+     "iopub.status.idle": "2023-08-15T16:07:40.084995Z",
+     "shell.execute_reply": "2023-08-15T16:07:40.084124Z"
     }
    },
    "outputs": [
@@ -82,10 +82,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:55:31.588728Z",
-     "iopub.status.busy": "2023-07-10T23:55:31.588015Z",
-     "iopub.status.idle": "2023-07-10T23:55:41.581811Z",
-     "shell.execute_reply": "2023-07-10T23:55:41.580910Z"
+     "iopub.execute_input": "2023-08-15T16:07:40.088716Z",
+     "iopub.status.busy": "2023-08-15T16:07:40.088274Z",
+     "iopub.status.idle": "2023-08-15T16:07:47.177832Z",
+     "shell.execute_reply": "2023-08-15T16:07:47.176959Z"
     }
    },
    "outputs": [],
@@ -99,10 +99,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:55:41.585710Z",
-     "iopub.status.busy": "2023-07-10T23:55:41.585409Z",
-     "iopub.status.idle": "2023-07-10T23:59:01.263510Z",
-     "shell.execute_reply": "2023-07-10T23:59:01.262403Z"
+     "iopub.execute_input": "2023-08-15T16:07:47.181675Z",
+     "iopub.status.busy": "2023-08-15T16:07:47.181402Z",
+     "iopub.status.idle": "2023-08-15T16:11:22.781427Z",
+     "shell.execute_reply": "2023-08-15T16:11:22.779411Z"
     }
    },
    "outputs": [],
@@ -119,10 +119,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:59:01.266783Z",
-     "iopub.status.busy": "2023-07-10T23:59:01.266504Z",
-     "iopub.status.idle": "2023-07-10T23:59:01.273710Z",
-     "shell.execute_reply": "2023-07-10T23:59:01.273104Z"
+     "iopub.execute_input": "2023-08-15T16:11:22.799571Z",
+     "iopub.status.busy": "2023-08-15T16:11:22.799242Z",
+     "iopub.status.idle": "2023-08-15T16:11:22.807756Z",
+     "shell.execute_reply": "2023-08-15T16:11:22.807038Z"
     }
    },
    "outputs": [],
@@ -183,10 +183,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:59:01.276660Z",
-     "iopub.status.busy": "2023-07-10T23:59:01.276408Z",
-     "iopub.status.idle": "2023-07-11T00:00:28.919312Z",
-     "shell.execute_reply": "2023-07-11T00:00:28.918426Z"
+     "iopub.execute_input": "2023-08-15T16:11:22.810685Z",
+     "iopub.status.busy": "2023-08-15T16:11:22.810419Z",
+     "iopub.status.idle": "2023-08-15T16:12:40.545220Z",
+     "shell.execute_reply": "2023-08-15T16:12:40.544183Z"
     }
    },
    "outputs": [],
@@ -201,10 +201,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:00:28.926601Z",
-     "iopub.status.busy": "2023-07-11T00:00:28.926349Z",
-     "iopub.status.idle": "2023-07-11T00:00:30.692782Z",
-     "shell.execute_reply": "2023-07-11T00:00:30.691465Z"
+     "iopub.execute_input": "2023-08-15T16:12:40.552747Z",
+     "iopub.status.busy": "2023-08-15T16:12:40.551728Z",
+     "iopub.status.idle": "2023-08-15T16:12:42.505045Z",
+     "shell.execute_reply": "2023-08-15T16:12:42.503192Z"
     }
    },
    "outputs": [
@@ -242,10 +242,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:00:30.697125Z",
-     "iopub.status.busy": "2023-07-11T00:00:30.696475Z",
-     "iopub.status.idle": "2023-07-11T00:00:30.807913Z",
-     "shell.execute_reply": "2023-07-11T00:00:30.807018Z"
+     "iopub.execute_input": "2023-08-15T16:12:42.511709Z",
+     "iopub.status.busy": "2023-08-15T16:12:42.511418Z",
+     "iopub.status.idle": "2023-08-15T16:12:42.612871Z",
+     "shell.execute_reply": "2023-08-15T16:12:42.612080Z"
     }
    },
    "outputs": [],
@@ -258,10 +258,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:00:30.811340Z",
-     "iopub.status.busy": "2023-07-11T00:00:30.811082Z",
-     "iopub.status.idle": "2023-07-11T00:00:30.821276Z",
-     "shell.execute_reply": "2023-07-11T00:00:30.816825Z"
+     "iopub.execute_input": "2023-08-15T16:12:42.618504Z",
+     "iopub.status.busy": "2023-08-15T16:12:42.618076Z",
+     "iopub.status.idle": "2023-08-15T16:12:42.627004Z",
+     "shell.execute_reply": "2023-08-15T16:12:42.624961Z"
     }
    },
    "outputs": [
@@ -285,10 +285,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:00:30.825406Z",
-     "iopub.status.busy": "2023-07-11T00:00:30.825165Z",
-     "iopub.status.idle": "2023-07-11T00:00:39.729074Z",
-     "shell.execute_reply": "2023-07-11T00:00:39.728161Z"
+     "iopub.execute_input": "2023-08-15T16:12:42.632255Z",
+     "iopub.status.busy": "2023-08-15T16:12:42.631786Z",
+     "iopub.status.idle": "2023-08-15T16:12:44.193555Z",
+     "shell.execute_reply": "2023-08-15T16:12:44.192965Z"
     }
    },
    "outputs": [
@@ -312,10 +312,10 @@
    "execution_count": 11,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:00:39.732613Z",
-     "iopub.status.busy": "2023-07-11T00:00:39.732352Z",
-     "iopub.status.idle": "2023-07-11T00:00:55.407002Z",
-     "shell.execute_reply": "2023-07-11T00:00:55.406173Z"
+     "iopub.execute_input": "2023-08-15T16:12:44.196528Z",
+     "iopub.status.busy": "2023-08-15T16:12:44.196252Z",
+     "iopub.status.idle": "2023-08-15T16:12:49.522164Z",
+     "shell.execute_reply": "2023-08-15T16:12:49.521284Z"
     }
    },
    "outputs": [
@@ -323,7 +323,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/40/kfr98p0j7n30fjp2n4ljjqbh0000gr/T/ipykernel_93670/584919884.py:35: RuntimeWarning: invalid value encountered in sqrt\n",
+      "/var/folders/40/kfr98p0j7n30fjp2n4ljjqbh0000gr/T/ipykernel_91279/584919884.py:35: RuntimeWarning: invalid value encountered in sqrt\n",
       "  r_s = (-1.0 * b_var - np.sqrt((b_var**2) - (4.0 * a_var * c_var))) / (2.0 * a_var)\n"
      ]
     }
@@ -348,10 +348,10 @@
    "execution_count": 12,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:00:55.421154Z",
-     "iopub.status.busy": "2023-07-11T00:00:55.418905Z",
-     "iopub.status.idle": "2023-07-11T00:00:56.489895Z",
-     "shell.execute_reply": "2023-07-11T00:00:56.488902Z"
+     "iopub.execute_input": "2023-08-15T16:12:49.526702Z",
+     "iopub.status.busy": "2023-08-15T16:12:49.526403Z",
+     "iopub.status.idle": "2023-08-15T16:12:51.814987Z",
+     "shell.execute_reply": "2023-08-15T16:12:51.813498Z"
     }
    },
    "outputs": [],
@@ -365,10 +365,10 @@
    "execution_count": 13,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:00:56.493897Z",
-     "iopub.status.busy": "2023-07-11T00:00:56.493451Z",
-     "iopub.status.idle": "2023-07-11T00:00:56.504492Z",
-     "shell.execute_reply": "2023-07-11T00:00:56.503447Z"
+     "iopub.execute_input": "2023-08-15T16:12:51.822265Z",
+     "iopub.status.busy": "2023-08-15T16:12:51.821647Z",
+     "iopub.status.idle": "2023-08-15T16:12:51.829789Z",
+     "shell.execute_reply": "2023-08-15T16:12:51.828349Z"
     }
    },
    "outputs": [],
@@ -387,10 +387,10 @@
    "execution_count": 14,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:00:56.510119Z",
-     "iopub.status.busy": "2023-07-11T00:00:56.509843Z",
-     "iopub.status.idle": "2023-07-11T00:00:56.518563Z",
-     "shell.execute_reply": "2023-07-11T00:00:56.517948Z"
+     "iopub.execute_input": "2023-08-15T16:12:51.833676Z",
+     "iopub.status.busy": "2023-08-15T16:12:51.833338Z",
+     "iopub.status.idle": "2023-08-15T16:12:51.842044Z",
+     "shell.execute_reply": "2023-08-15T16:12:51.841405Z"
     }
    },
    "outputs": [],
@@ -406,10 +406,10 @@
    "execution_count": 15,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:00:56.521833Z",
-     "iopub.status.busy": "2023-07-11T00:00:56.521531Z",
-     "iopub.status.idle": "2023-07-11T00:00:57.623689Z",
-     "shell.execute_reply": "2023-07-11T00:00:57.622852Z"
+     "iopub.execute_input": "2023-08-15T16:12:51.845109Z",
+     "iopub.status.busy": "2023-08-15T16:12:51.844864Z",
+     "iopub.status.idle": "2023-08-15T16:12:53.100971Z",
+     "shell.execute_reply": "2023-08-15T16:12:53.099734Z"
     }
    },
    "outputs": [],
@@ -422,10 +422,10 @@
    "execution_count": 16,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:00:57.627453Z",
-     "iopub.status.busy": "2023-07-11T00:00:57.627190Z",
-     "iopub.status.idle": "2023-07-11T00:00:57.819826Z",
-     "shell.execute_reply": "2023-07-11T00:00:57.818631Z"
+     "iopub.execute_input": "2023-08-15T16:12:53.104850Z",
+     "iopub.status.busy": "2023-08-15T16:12:53.104595Z",
+     "iopub.status.idle": "2023-08-15T16:12:53.381799Z",
+     "shell.execute_reply": "2023-08-15T16:12:53.381188Z"
     }
    },
    "outputs": [],
@@ -438,10 +438,10 @@
    "execution_count": 17,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:00:57.822878Z",
-     "iopub.status.busy": "2023-07-11T00:00:57.822614Z",
-     "iopub.status.idle": "2023-07-11T00:00:57.853284Z",
-     "shell.execute_reply": "2023-07-11T00:00:57.852510Z"
+     "iopub.execute_input": "2023-08-15T16:12:53.385429Z",
+     "iopub.status.busy": "2023-08-15T16:12:53.385021Z",
+     "iopub.status.idle": "2023-08-15T16:12:53.403040Z",
+     "shell.execute_reply": "2023-08-15T16:12:53.402403Z"
     }
    },
    "outputs": [
@@ -589,17 +589,17 @@
    "execution_count": 18,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:00:57.856628Z",
-     "iopub.status.busy": "2023-07-11T00:00:57.856287Z",
-     "iopub.status.idle": "2023-07-11T00:00:58.373469Z",
-     "shell.execute_reply": "2023-07-11T00:00:58.372659Z"
+     "iopub.execute_input": "2023-08-15T16:12:53.406523Z",
+     "iopub.status.busy": "2023-08-15T16:12:53.406243Z",
+     "iopub.status.idle": "2023-08-15T16:12:53.892605Z",
+     "shell.execute_reply": "2023-08-15T16:12:53.892016Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "<matplotlib.collections.PathCollection at 0x12706e650>"
+       "<matplotlib.collections.PathCollection at 0x12664acd0>"
       ]
      },
      "execution_count": 18,
@@ -640,10 +640,10 @@
    "execution_count": 19,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:00:58.377076Z",
-     "iopub.status.busy": "2023-07-11T00:00:58.376820Z",
-     "iopub.status.idle": "2023-07-11T00:00:58.413776Z",
-     "shell.execute_reply": "2023-07-11T00:00:58.412706Z"
+     "iopub.execute_input": "2023-08-15T16:12:53.896381Z",
+     "iopub.status.busy": "2023-08-15T16:12:53.895993Z",
+     "iopub.status.idle": "2023-08-15T16:12:53.941543Z",
+     "shell.execute_reply": "2023-08-15T16:12:53.940702Z"
     }
    },
    "outputs": [],
@@ -656,10 +656,10 @@
    "execution_count": 20,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:00:58.417187Z",
-     "iopub.status.busy": "2023-07-11T00:00:58.416931Z",
-     "iopub.status.idle": "2023-07-11T00:01:01.842340Z",
-     "shell.execute_reply": "2023-07-11T00:01:01.841701Z"
+     "iopub.execute_input": "2023-08-15T16:12:53.945051Z",
+     "iopub.status.busy": "2023-08-15T16:12:53.944803Z",
+     "iopub.status.idle": "2023-08-15T16:12:57.237909Z",
+     "shell.execute_reply": "2023-08-15T16:12:57.237267Z"
     }
    },
    "outputs": [
@@ -682,10 +682,10 @@
    "execution_count": 21,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:01.846257Z",
-     "iopub.status.busy": "2023-07-11T00:01:01.845953Z",
-     "iopub.status.idle": "2023-07-11T00:01:01.849575Z",
-     "shell.execute_reply": "2023-07-11T00:01:01.848934Z"
+     "iopub.execute_input": "2023-08-15T16:12:57.241053Z",
+     "iopub.status.busy": "2023-08-15T16:12:57.240803Z",
+     "iopub.status.idle": "2023-08-15T16:12:57.243921Z",
+     "shell.execute_reply": "2023-08-15T16:12:57.243162Z"
     }
    },
    "outputs": [],
@@ -702,10 +702,10 @@
    "execution_count": 22,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:01.853325Z",
-     "iopub.status.busy": "2023-07-11T00:01:01.853049Z",
-     "iopub.status.idle": "2023-07-11T00:01:01.856767Z",
-     "shell.execute_reply": "2023-07-11T00:01:01.856087Z"
+     "iopub.execute_input": "2023-08-15T16:12:57.248224Z",
+     "iopub.status.busy": "2023-08-15T16:12:57.247961Z",
+     "iopub.status.idle": "2023-08-15T16:12:57.251558Z",
+     "shell.execute_reply": "2023-08-15T16:12:57.250886Z"
     }
    },
    "outputs": [],
@@ -718,10 +718,10 @@
    "execution_count": 23,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:01.859951Z",
-     "iopub.status.busy": "2023-07-11T00:01:01.859572Z",
-     "iopub.status.idle": "2023-07-11T00:01:01.887986Z",
-     "shell.execute_reply": "2023-07-11T00:01:01.887335Z"
+     "iopub.execute_input": "2023-08-15T16:12:57.254766Z",
+     "iopub.status.busy": "2023-08-15T16:12:57.254505Z",
+     "iopub.status.idle": "2023-08-15T16:12:57.291832Z",
+     "shell.execute_reply": "2023-08-15T16:12:57.291233Z"
     }
    },
    "outputs": [
@@ -889,10 +889,10 @@
    "execution_count": 24,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:01.890946Z",
-     "iopub.status.busy": "2023-07-11T00:01:01.890656Z",
-     "iopub.status.idle": "2023-07-11T00:01:01.894796Z",
-     "shell.execute_reply": "2023-07-11T00:01:01.894140Z"
+     "iopub.execute_input": "2023-08-15T16:12:57.310753Z",
+     "iopub.status.busy": "2023-08-15T16:12:57.310497Z",
+     "iopub.status.idle": "2023-08-15T16:12:57.314043Z",
+     "shell.execute_reply": "2023-08-15T16:12:57.313208Z"
     }
    },
    "outputs": [],
@@ -908,10 +908,10 @@
    "execution_count": 25,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:01.897990Z",
-     "iopub.status.busy": "2023-07-11T00:01:01.897726Z",
-     "iopub.status.idle": "2023-07-11T00:01:03.147520Z",
-     "shell.execute_reply": "2023-07-11T00:01:03.146421Z"
+     "iopub.execute_input": "2023-08-15T16:12:57.317304Z",
+     "iopub.status.busy": "2023-08-15T16:12:57.316895Z",
+     "iopub.status.idle": "2023-08-15T16:12:58.748731Z",
+     "shell.execute_reply": "2023-08-15T16:12:58.748008Z"
     }
    },
    "outputs": [],
@@ -924,10 +924,10 @@
    "execution_count": 26,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:03.152414Z",
-     "iopub.status.busy": "2023-07-11T00:01:03.152008Z",
-     "iopub.status.idle": "2023-07-11T00:01:03.159134Z",
-     "shell.execute_reply": "2023-07-11T00:01:03.157989Z"
+     "iopub.execute_input": "2023-08-15T16:12:58.752019Z",
+     "iopub.status.busy": "2023-08-15T16:12:58.751741Z",
+     "iopub.status.idle": "2023-08-15T16:12:58.757757Z",
+     "shell.execute_reply": "2023-08-15T16:12:58.757036Z"
     }
    },
    "outputs": [],
@@ -940,10 +940,10 @@
    "execution_count": 27,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-11T00:01:03.163762Z",
-     "iopub.status.busy": "2023-07-11T00:01:03.163371Z",
-     "iopub.status.idle": "2023-07-11T00:01:07.993007Z",
-     "shell.execute_reply": "2023-07-11T00:01:07.992330Z"
+     "iopub.execute_input": "2023-08-15T16:12:58.760868Z",
+     "iopub.status.busy": "2023-08-15T16:12:58.760567Z",
+     "iopub.status.idle": "2023-08-15T16:13:01.624999Z",
+     "shell.execute_reply": "2023-08-15T16:13:01.624376Z"
     }
    },
    "outputs": [
diff --git a/examples/Example_Updraft_Tracking/Example_Updraft_Tracking.ipynb b/examples/Example_Updraft_Tracking/Example_Updraft_Tracking.ipynb
index 5bbb76a5..053d8f36 100644
--- a/examples/Example_Updraft_Tracking/Example_Updraft_Tracking.ipynb
+++ b/examples/Example_Updraft_Tracking/Example_Updraft_Tracking.ipynb
@@ -31,10 +31,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:51:04.884573Z",
-     "iopub.status.busy": "2023-07-10T23:51:04.884253Z",
-     "iopub.status.idle": "2023-07-10T23:51:10.425277Z",
-     "shell.execute_reply": "2023-07-10T23:51:10.423875Z"
+     "iopub.execute_input": "2023-08-15T16:02:00.933399Z",
+     "iopub.status.busy": "2023-08-15T16:02:00.932858Z",
+     "iopub.status.idle": "2023-08-15T16:02:09.931166Z",
+     "shell.execute_reply": "2023-08-15T16:02:09.929721Z"
     }
    },
    "outputs": [],
@@ -56,10 +56,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:51:10.429698Z",
-     "iopub.status.busy": "2023-07-10T23:51:10.429206Z",
-     "iopub.status.idle": "2023-07-10T23:51:11.594365Z",
-     "shell.execute_reply": "2023-07-10T23:51:11.593537Z"
+     "iopub.execute_input": "2023-08-15T16:02:09.935636Z",
+     "iopub.status.busy": "2023-08-15T16:02:09.934747Z",
+     "iopub.status.idle": "2023-08-15T16:02:11.835347Z",
+     "shell.execute_reply": "2023-08-15T16:02:11.834453Z"
     }
    },
    "outputs": [
@@ -67,7 +67,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "using tobac version 1.5.0\n"
+      "using tobac version 1.5.1\n"
      ]
     }
    ],
@@ -82,10 +82,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:51:11.632146Z",
-     "iopub.status.busy": "2023-07-10T23:51:11.631887Z",
-     "iopub.status.idle": "2023-07-10T23:51:11.635682Z",
-     "shell.execute_reply": "2023-07-10T23:51:11.635094Z"
+     "iopub.execute_input": "2023-08-15T16:02:11.880430Z",
+     "iopub.status.busy": "2023-08-15T16:02:11.880023Z",
+     "iopub.status.idle": "2023-08-15T16:02:11.885297Z",
+     "shell.execute_reply": "2023-08-15T16:02:11.884620Z"
     }
    },
    "outputs": [],
@@ -111,10 +111,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:51:11.638695Z",
-     "iopub.status.busy": "2023-07-10T23:51:11.638418Z",
-     "iopub.status.idle": "2023-07-10T23:51:11.641629Z",
-     "shell.execute_reply": "2023-07-10T23:51:11.641003Z"
+     "iopub.execute_input": "2023-08-15T16:02:11.888449Z",
+     "iopub.status.busy": "2023-08-15T16:02:11.888207Z",
+     "iopub.status.idle": "2023-08-15T16:02:11.892040Z",
+     "shell.execute_reply": "2023-08-15T16:02:11.891444Z"
     }
    },
    "outputs": [],
@@ -127,10 +127,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:51:11.644677Z",
-     "iopub.status.busy": "2023-07-10T23:51:11.644381Z",
-     "iopub.status.idle": "2023-07-10T23:51:11.651547Z",
-     "shell.execute_reply": "2023-07-10T23:51:11.650571Z"
+     "iopub.execute_input": "2023-08-15T16:02:11.894872Z",
+     "iopub.status.busy": "2023-08-15T16:02:11.894612Z",
+     "iopub.status.idle": "2023-08-15T16:02:11.904233Z",
+     "shell.execute_reply": "2023-08-15T16:02:11.903396Z"
     }
    },
    "outputs": [],
@@ -162,10 +162,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:51:11.654938Z",
-     "iopub.status.busy": "2023-07-10T23:51:11.654650Z",
-     "iopub.status.idle": "2023-07-10T23:51:11.660990Z",
-     "shell.execute_reply": "2023-07-10T23:51:11.659790Z"
+     "iopub.execute_input": "2023-08-15T16:02:11.910146Z",
+     "iopub.status.busy": "2023-08-15T16:02:11.909846Z",
+     "iopub.status.idle": "2023-08-15T16:02:11.916777Z",
+     "shell.execute_reply": "2023-08-15T16:02:11.915951Z"
     }
    },
    "outputs": [],
@@ -179,10 +179,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:51:11.664313Z",
-     "iopub.status.busy": "2023-07-10T23:51:11.664031Z",
-     "iopub.status.idle": "2023-07-10T23:51:12.221115Z",
-     "shell.execute_reply": "2023-07-10T23:51:12.220139Z"
+     "iopub.execute_input": "2023-08-15T16:02:11.920661Z",
+     "iopub.status.busy": "2023-08-15T16:02:11.919937Z",
+     "iopub.status.idle": "2023-08-15T16:02:12.887087Z",
+     "shell.execute_reply": "2023-08-15T16:02:12.886210Z"
     }
    },
    "outputs": [],
@@ -196,10 +196,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:51:12.224376Z",
-     "iopub.status.busy": "2023-07-10T23:51:12.224095Z",
-     "iopub.status.idle": "2023-07-10T23:51:12.278560Z",
-     "shell.execute_reply": "2023-07-10T23:51:12.277950Z"
+     "iopub.execute_input": "2023-08-15T16:02:12.890929Z",
+     "iopub.status.busy": "2023-08-15T16:02:12.890614Z",
+     "iopub.status.idle": "2023-08-15T16:02:12.979036Z",
+     "shell.execute_reply": "2023-08-15T16:02:12.978051Z"
     }
    },
    "outputs": [
@@ -254,7 +254,7 @@
        "      margin-top: 7px;\n",
        "  }\n",
        "</style>\n",
-       "<table class=\"iris\" id=\"4878664016\">\n",
+       "<table class=\"iris\" id=\"4869081168\">\n",
        "    <tr class=\"iris\">\n",
        "<th class=\"iris iris-word-cell\">W (m s-1)</th>\n",
        "<th class=\"iris iris-word-cell\">time</th>\n",
@@ -416,7 +416,7 @@
        "      margin-top: 7px;\n",
        "  }\n",
        "</style>\n",
-       "<table class=\"iris\" id=\"4890162896\">\n",
+       "<table class=\"iris\" id=\"4897709648\">\n",
        "    <tr class=\"iris\">\n",
        "<th class=\"iris iris-word-cell\">Twc (kg kg-1)</th>\n",
        "<th class=\"iris iris-word-cell\">time</th>\n",
@@ -551,10 +551,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:51:12.281429Z",
-     "iopub.status.busy": "2023-07-10T23:51:12.281177Z",
-     "iopub.status.idle": "2023-07-10T23:51:12.284821Z",
-     "shell.execute_reply": "2023-07-10T23:51:12.284230Z"
+     "iopub.execute_input": "2023-08-15T16:02:12.981793Z",
+     "iopub.status.busy": "2023-08-15T16:02:12.981562Z",
+     "iopub.status.idle": "2023-08-15T16:02:12.985300Z",
+     "shell.execute_reply": "2023-08-15T16:02:12.984557Z"
     }
    },
    "outputs": [],
@@ -582,10 +582,10 @@
    "execution_count": 10,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:51:12.287560Z",
-     "iopub.status.busy": "2023-07-10T23:51:12.287322Z",
-     "iopub.status.idle": "2023-07-10T23:51:12.307571Z",
-     "shell.execute_reply": "2023-07-10T23:51:12.306608Z"
+     "iopub.execute_input": "2023-08-15T16:02:12.988489Z",
+     "iopub.status.busy": "2023-08-15T16:02:12.987974Z",
+     "iopub.status.idle": "2023-08-15T16:02:13.014787Z",
+     "shell.execute_reply": "2023-08-15T16:02:13.009664Z"
     }
    },
    "outputs": [],
@@ -599,10 +599,10 @@
    "execution_count": 11,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:51:12.310831Z",
-     "iopub.status.busy": "2023-07-10T23:51:12.310558Z",
-     "iopub.status.idle": "2023-07-10T23:51:12.314321Z",
-     "shell.execute_reply": "2023-07-10T23:51:12.313701Z"
+     "iopub.execute_input": "2023-08-15T16:02:13.018357Z",
+     "iopub.status.busy": "2023-08-15T16:02:13.017966Z",
+     "iopub.status.idle": "2023-08-15T16:02:13.022217Z",
+     "shell.execute_reply": "2023-08-15T16:02:13.021544Z"
     }
    },
    "outputs": [],
@@ -623,10 +623,10 @@
    "execution_count": 12,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:51:12.317148Z",
-     "iopub.status.busy": "2023-07-10T23:51:12.316909Z",
-     "iopub.status.idle": "2023-07-10T23:51:14.865962Z",
-     "shell.execute_reply": "2023-07-10T23:51:14.865311Z"
+     "iopub.execute_input": "2023-08-15T16:02:13.025605Z",
+     "iopub.status.busy": "2023-08-15T16:02:13.025358Z",
+     "iopub.status.idle": "2023-08-15T16:02:18.681129Z",
+     "shell.execute_reply": "2023-08-15T16:02:18.680509Z"
     }
    },
    "outputs": [
@@ -663,10 +663,10 @@
    "execution_count": 13,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:51:14.868954Z",
-     "iopub.status.busy": "2023-07-10T23:51:14.868693Z",
-     "iopub.status.idle": "2023-07-10T23:51:14.872146Z",
-     "shell.execute_reply": "2023-07-10T23:51:14.871506Z"
+     "iopub.execute_input": "2023-08-15T16:02:18.685190Z",
+     "iopub.status.busy": "2023-08-15T16:02:18.684887Z",
+     "iopub.status.idle": "2023-08-15T16:02:18.688609Z",
+     "shell.execute_reply": "2023-08-15T16:02:18.687871Z"
     }
    },
    "outputs": [],
@@ -681,10 +681,10 @@
    "execution_count": 14,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:51:14.875229Z",
-     "iopub.status.busy": "2023-07-10T23:51:14.874901Z",
-     "iopub.status.idle": "2023-07-10T23:53:18.824797Z",
-     "shell.execute_reply": "2023-07-10T23:53:18.823827Z"
+     "iopub.execute_input": "2023-08-15T16:02:18.693017Z",
+     "iopub.status.busy": "2023-08-15T16:02:18.692621Z",
+     "iopub.status.idle": "2023-08-15T16:05:22.195666Z",
+     "shell.execute_reply": "2023-08-15T16:05:22.192844Z"
     }
    },
    "outputs": [
@@ -720,10 +720,10 @@
    "execution_count": 15,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:53:18.829442Z",
-     "iopub.status.busy": "2023-07-10T23:53:18.829130Z",
-     "iopub.status.idle": "2023-07-10T23:53:18.833815Z",
-     "shell.execute_reply": "2023-07-10T23:53:18.833246Z"
+     "iopub.execute_input": "2023-08-15T16:05:22.261423Z",
+     "iopub.status.busy": "2023-08-15T16:05:22.207751Z",
+     "iopub.status.idle": "2023-08-15T16:05:22.274117Z",
+     "shell.execute_reply": "2023-08-15T16:05:22.273189Z"
     }
    },
    "outputs": [],
@@ -747,10 +747,10 @@
    "execution_count": 16,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:53:18.836865Z",
-     "iopub.status.busy": "2023-07-10T23:53:18.836464Z",
-     "iopub.status.idle": "2023-07-10T23:53:19.277248Z",
-     "shell.execute_reply": "2023-07-10T23:53:19.276298Z"
+     "iopub.execute_input": "2023-08-15T16:05:22.277858Z",
+     "iopub.status.busy": "2023-08-15T16:05:22.277509Z",
+     "iopub.status.idle": "2023-08-15T16:05:23.785199Z",
+     "shell.execute_reply": "2023-08-15T16:05:23.784607Z"
     }
    },
    "outputs": [
@@ -780,10 +780,10 @@
    "execution_count": 17,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:53:19.280887Z",
-     "iopub.status.busy": "2023-07-10T23:53:19.280340Z",
-     "iopub.status.idle": "2023-07-10T23:53:19.283981Z",
-     "shell.execute_reply": "2023-07-10T23:53:19.283282Z"
+     "iopub.execute_input": "2023-08-15T16:05:23.791230Z",
+     "iopub.status.busy": "2023-08-15T16:05:23.790950Z",
+     "iopub.status.idle": "2023-08-15T16:05:23.795169Z",
+     "shell.execute_reply": "2023-08-15T16:05:23.794159Z"
     }
    },
    "outputs": [],
@@ -797,10 +797,10 @@
    "execution_count": 18,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:53:19.287376Z",
-     "iopub.status.busy": "2023-07-10T23:53:19.287109Z",
-     "iopub.status.idle": "2023-07-10T23:53:43.417075Z",
-     "shell.execute_reply": "2023-07-10T23:53:43.415385Z"
+     "iopub.execute_input": "2023-08-15T16:05:23.806902Z",
+     "iopub.status.busy": "2023-08-15T16:05:23.805200Z",
+     "iopub.status.idle": "2023-08-15T16:05:49.649158Z",
+     "shell.execute_reply": "2023-08-15T16:05:49.648235Z"
     }
    },
    "outputs": [
@@ -827,10 +827,10 @@
    "execution_count": 19,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:53:43.422007Z",
-     "iopub.status.busy": "2023-07-10T23:53:43.421684Z",
-     "iopub.status.idle": "2023-07-10T23:53:43.442200Z",
-     "shell.execute_reply": "2023-07-10T23:53:43.440967Z"
+     "iopub.execute_input": "2023-08-15T16:05:49.663650Z",
+     "iopub.status.busy": "2023-08-15T16:05:49.663350Z",
+     "iopub.status.idle": "2023-08-15T16:05:49.683863Z",
+     "shell.execute_reply": "2023-08-15T16:05:49.683187Z"
     }
    },
    "outputs": [],
@@ -848,10 +848,10 @@
    "execution_count": 20,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:53:43.446476Z",
-     "iopub.status.busy": "2023-07-10T23:53:43.446169Z",
-     "iopub.status.idle": "2023-07-10T23:55:05.862538Z",
-     "shell.execute_reply": "2023-07-10T23:55:05.861377Z"
+     "iopub.execute_input": "2023-08-15T16:05:49.688107Z",
+     "iopub.status.busy": "2023-08-15T16:05:49.687855Z",
+     "iopub.status.idle": "2023-08-15T16:07:22.147607Z",
+     "shell.execute_reply": "2023-08-15T16:07:22.146521Z"
     }
    },
    "outputs": [
@@ -12533,10 +12533,10 @@
    "execution_count": 21,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:55:05.867267Z",
-     "iopub.status.busy": "2023-07-10T23:55:05.866982Z",
-     "iopub.status.idle": "2023-07-10T23:55:05.870835Z",
-     "shell.execute_reply": "2023-07-10T23:55:05.869796Z"
+     "iopub.execute_input": "2023-08-15T16:07:22.155238Z",
+     "iopub.status.busy": "2023-08-15T16:07:22.154721Z",
+     "iopub.status.idle": "2023-08-15T16:07:22.160334Z",
+     "shell.execute_reply": "2023-08-15T16:07:22.158982Z"
     }
    },
    "outputs": [],
@@ -12552,10 +12552,10 @@
    "execution_count": 22,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-07-10T23:55:05.873852Z",
-     "iopub.status.busy": "2023-07-10T23:55:05.873552Z",
-     "iopub.status.idle": "2023-07-10T23:55:06.051000Z",
-     "shell.execute_reply": "2023-07-10T23:55:06.049925Z"
+     "iopub.execute_input": "2023-08-15T16:07:22.164664Z",
+     "iopub.status.busy": "2023-08-15T16:07:22.164374Z",
+     "iopub.status.idle": "2023-08-15T16:07:22.358632Z",
+     "shell.execute_reply": "2023-08-15T16:07:22.357650Z"
     }
    },
    "outputs": [

From c7b0401a93b881aae63e91ed19db5c154cfc8a04 Mon Sep 17 00:00:00 2001
From: Sean Freeman <sean.freeman@uah.edu>
Date: Mon, 21 Aug 2023 11:37:28 -0500
Subject: [PATCH 7/7] add back standardize_track_dataset

---
 tobac/utils/__init__.py |   1 +
 tobac/utils/general.py  | 125 ++++++++++++++++++++++++++++++++++++++++
 2 files changed, 126 insertions(+)

diff --git a/tobac/utils/__init__.py b/tobac/utils/__init__.py
index e8c077a2..14e5773f 100644
--- a/tobac/utils/__init__.py
+++ b/tobac/utils/__init__.py
@@ -6,6 +6,7 @@
     combine_tobac_feats,
     combine_feature_dataframes,
     transform_feature_points,
+    standardize_track_dataset,
 )
 from .mask import (
     mask_cell,
diff --git a/tobac/utils/general.py b/tobac/utils/general.py
index 1146136d..7836a9c6 100644
--- a/tobac/utils/general.py
+++ b/tobac/utils/general.py
@@ -788,3 +788,128 @@ def transform_feature_points(
         )
 
     return ret_features
+
+
+def standardize_track_dataset(TrackedFeatures, Mask, Projection=None):
+    """
+    CAUTION: this function is experimental. No data structures output are guaranteed to be supported in future versions of tobac.
+    Combine a feature mask with the feature data table into a common dataset.
+    returned by tobac.segmentation
+    with the TrackedFeatures dataset returned by tobac.linking_trackpy.
+    Also rename the variables to be more descriptive and comply with cf-tree.
+    Convert the default cell parent ID  to an integer table.
+    Add a cell dimension to reflect
+    Projection is an xarray DataArray
+    TODO: Add metadata attributes
+    Parameters
+    ----------
+    TrackedFeatures : xarray.core.dataset.Dataset
+        xarray dataset of tobac Track information, the xarray dataset returned by tobac.tracking.linking_trackpy
+    Mask: xarray.core.dataset.Dataset
+        xarray dataset of tobac segmentation mask information, the xarray dataset returned
+        by tobac.segmentation.segmentation
+    Projection : xarray.core.dataarray.DataArray, default = None
+        array.DataArray of the original input dataset (gridded nexrad data for example).
+        If using gridded nexrad data, this can be input as: data['ProjectionCoordinateSystem']
+        An example of the type of information in the dataarray includes the following attributes:
+        latitude_of_projection_origin :29.471900939941406
+        longitude_of_projection_origin :-95.0787353515625
+        _CoordinateTransformType :Projection
+        _CoordinateAxes :x y z time
+        _CoordinateAxesTypes :GeoX GeoY Height Time
+        grid_mapping_name :azimuthal_equidistant
+        semi_major_axis :6370997.0
+        inverse_flattening :298.25
+        longitude_of_prime_meridian :0.0
+        false_easting :0.0
+        false_northing :0.0
+    Returns
+    -------
+    ds : xarray.core.dataset.Dataset
+        xarray dataset of merged Track and Segmentation Mask datasets with renamed variables.
+    """
+    import xarray as xr
+
+    feature_standard_names = {
+        # new variable name, and long description for the NetCDF attribute
+        "frame": (
+            "feature_time_index",
+            "positional index of the feature along the time dimension of the mask, from 0 to N-1",
+        ),
+        "hdim_1": (
+            "feature_hdim1_coordinate",
+            "position of the feature along the first horizontal dimension in grid point space; a north-south coordinate for dim order (time, y, x)."
+            "The numbering is consistent with positional indexing of the coordinate, but can be"
+            "fractional, to account for a centroid not aligned to the grid.",
+        ),
+        "hdim_2": (
+            "feature_hdim2_coordinate",
+            "position of the feature along the second horizontal dimension in grid point space; an east-west coordinate for dim order (time, y, x)"
+            "The numbering is consistent with positional indexing of the coordinate, but can be"
+            "fractional, to account for a centroid not aligned to the grid.",
+        ),
+        "idx": ("feature_id_this_frame",),
+        "num": (
+            "feature_grid_cell_count",
+            "Number of grid points that are within the threshold of this feature",
+        ),
+        "threshold_value": (
+            "feature_threshold_max",
+            "Feature number within that frame; starts at 1, increments by 1 to the number of features for each frame, and resets to 1 when the frame increments",
+        ),
+        "feature": (
+            "feature",
+            "Unique number of the feature; starts from 1 and increments by 1 to the number of features",
+        ),
+        "time": (
+            "feature_time",
+            "time of the feature, consistent with feature_time_index",
+        ),
+        "timestr": (
+            "feature_time_str",
+            "String representation of the feature time, YYYY-MM-DD HH:MM:SS",
+        ),
+        "projection_y_coordinate": (
+            "feature_projection_y_coordinate",
+            "y position of the feature in the projection given by ProjectionCoordinateSystem",
+        ),
+        "projection_x_coordinate": (
+            "feature_projection_x_coordinate",
+            "x position of the feature in the projection given by ProjectionCoordinateSystem",
+        ),
+        "lat": ("feature_latitude", "latitude of the feature"),
+        "lon": ("feature_longitude", "longitude of the feature"),
+        "ncells": (
+            "feature_ncells",
+            "number of grid cells for this feature (meaning uncertain)",
+        ),
+        "areas": ("feature_area",),
+        "isolated": ("feature_isolation_flag",),
+        "num_objects": ("number_of_feature_neighbors",),
+        "cell": ("feature_parent_cell_id",),
+        "time_cell": ("feature_parent_cell_elapsed_time",),
+        "segmentation_mask": ("2d segmentation mask",),
+    }
+    new_feature_var_names = {
+        k: feature_standard_names[k][0]
+        for k in feature_standard_names.keys()
+        if k in TrackedFeatures.variables.keys()
+    }
+
+    #     TrackedFeatures = TrackedFeatures.drop(["cell_parent_track_id"])
+    # Combine Track and Mask variables. Use the 'feature' variable as the coordinate variable instead of
+    # the 'index' variable and call the dimension 'feature'
+    ds = xr.merge(
+        [
+            TrackedFeatures.swap_dims({"index": "feature"})
+            .drop("index")
+            .rename_vars(new_feature_var_names),
+            Mask,
+        ]
+    )
+
+    # Add the projection data back in
+    if Projection is not None:
+        ds["ProjectionCoordinateSystem"] = Projection
+
+    return ds