The itslive_interp function interpolates ITS_LIVE velocity data to specified points.
zi = itslive_interp(region,variable,xi,yi)
zi = itslive_interp(region,variable,lati,loni)
zi = itslive_interp(..., method=InterpMethod)
zi = itslive_interp(..., year=years)
v_along = = itslive_interp(region,'along',...)
v_across = = itslive_interp(region,'across',...)zi = itslive_interp(region,variable,xi,yi) interpolates ITS_LIVE mosaic data for the specified region and variable, at the projected map coordinates xi, yi. The region is a number from 1 to 19 (type itslive_regions for a map). The variable can be 'v', 'vx', 'v_error', or any gridded variable in the ITS_LIVE v2 mosaics. Coordinates xi,yi correspond to the map units (m) in the projection of the specified region.
zi = itslive_interp(region,variable,lati,loni) as above, but using geographic coordinates.
zi = itslive_interp(..., method=InterpMethod) specifies an interpolation method. Interpolation is linear by default, except for variables 'landice', and 'floatingice', which are nearest neighbor.
zi = itslive_interp(...,'year',years) specifies years of velocity mosaics. Default year is 0000, which corresponds to climatology mosaics.
v_across = itslive_interp(region, 'across',...) calculates the across-track velocity for a path such as a grounding line lati,loni or xi,yi. This is designed for calculating the flow across a flux gate.
v_along = itslive_interp(region, 'along',...) the complement to the across track component. The value of v_along should be about the same as v
Plot a time series of annual velocities at a location near the grounding line of Byrd Glacier, Antarctica. The location is (80.38°S,158.75°E) and the region number for Antarctica is 19:
year = 2014:2022;
v = itslive_interp(19, 'v',-80.38,158.75,'year',year);
v_error = itslive_interp(19, 'v_error',-80.38,158.75,'year',year);
figure
errorbar(year,v,v_error)
xlim([2013 2023])
ylabel('Annual velocity (m yr^{-1})')
title 'Byrd Glacier, Antarctica'
exportgraphics(gcf,'itslive_interp_documentation_byrd.jpg')
In the example above, we plotted a time series of annual velocities at a single location. Now let's plot the summary mosaic values (a multi-year average) for multiple locations at Malaspina Glacier, Alaska (region 1). These are the same locations that are plotted as the default example in the ITS_LIVE widget. These locations on Malaspina are also used in the itslive_data documentation to create this map:
% Define locations and years of interest:
lat = [60.08343 60.02582 59.92546 59.83722];
lon = [-140.46707 -140.57831 -140.72388 -140.80765];
% Get velocity values:
v = itslive_interp(1, 'v', lat, lon);
figure
bar(v)
xlabel 'Data point number'
ylabel 'Summary mosaic velocity (m yr^{-1})'
exportgraphics(gcf,'itslive_interp_documentation_velocity_bar.jpg')
How certain can we be about those velocity estimates? Let's take a look at what data went into those values:
v_error = itslive_interp(1, 'v_error', lat, lon);
count = itslive_interp(1, 'count', lat, lon);
figure
plot(count, v_error, '.', markersize=50)
xlabel 'Data count'
ylabel 'Velocity error (m yr^{-1})'
exportgraphics(gcf,'itslive_interp_documentation_error_vs_count.jpg')
In the figure above, we see that the velocity error estimates are near zero. They're stored as integer values, because there's no use splitting hairs over tenths of meters per year when discussing uncertainties. Although they're stored as integer values, the itslive_interp function performs linear interpolation by default, which is why we get one value that isn't exactly an integer. Mostly what we see in the figure above is that uncertainties are low when lots of data are available, and in this case, all four points have at least 2500 velocity measurements, and the uncertainty for the point with over 5500 measurements rounds to zero.
To get velocity values for multiple locations and multiple years, just enter them into itslive_interp like this:
% Define locations and years of interest:
lat = [60.08343 60.02582 59.92546 59.83722];
lon = [-140.46707 -140.57831 -140.72388 -140.80765];
years = 2014:2022;
% Get annual velocities and error at the specified points:
v = itslive_interp(1, 'v', lat, lon, year=years);
v_error = itslive_interp(1, 'v_error', lat, lon, year=years);
figure
errorbar(years,v, v_error)
title 'Malaspina Glacier, Alaska'
xlim([2013 2023])
ylabel('Annual velocity (m yr^{-1})')
exportgraphics(gcf,'itslive_interp_documentation_malaspina_annual.jpg')
This example interpolates ITS_LIVE velocity trend data to a 50 m resolution grid.
Note that the native resolution of ITS_LIVE velocity data is 120 m, so interpolating to 50 m meets Nyquist and doesn't require lowpass filtering before interpolation to prevent aliasing. The itslive_interp function does not perform any type of antialiasing.
Below we use just base MATLAB functions until we get to the optional fancy stuff. For those steps you'll need cmocean for the colormap. Also, modismog for the background image mosaic of Greenland and scalebarpsn for the scalebar, which are both part of Arctic Mapping Tools.
% Create grid:
res = 50; % m grid resolution
x = -389350:res:-179900;
y = -813900:-res:-1128100;
[X,Y] = meshgrid(x,y);
% Get velocity trends at grid points:
dv_dt = itslive_interp(5, 'dv_dt', X, Y);
landice = itslive_interp(5, 'landice', X, Y);
figure
h = imagesc(x,y,dv_dt);
h.AlphaData = landice; % make non-ice transparent
axis xy image off
clim([-1 1]*10) % sets color axis limits
cb = colorbar;
ylabel(cb,'Velocity trend 2014-2022 m yr^{-2}')
% Optional fancy stuff:
cmocean balance % sets colormap
modismog('contrast','white') % modis mosaic of greenland
scalebarpsn('location','se') % part of Arctic Mapping Tools
exportgraphics(gcf,'itslive_interp_documentation_greenland_grid.jpg')
This example calculates total flux out of Antarctica's Pine Island Glacier basin. We'll get the basin boundaries using the basin_data function, which you can find in the Antarctic boundaries repo on GitHub. This example also uses pspath from Antarctic Mapping Tools and bedmachine_interp from the Bedmachine toolbox.
% Load a basin outline:
[lati,loni] = basin_data('imbie refined','pine island');
% Densify to 100 m spacing: (use only finite values)
isf = isfinite(lati);
[lati,loni] = pspath(lati(isf),loni(isf),100);
% Calculate ice velocity across the basin boundary:
vci = itslive_interp(19, 'across', lati, loni);
% Get corresponding ice thickness:
thi = bedmachine_interp('thickness',lati,loni,'antarctica');
% Calculate flux across each point:
Ui = vci.*thi;
figure
scatterps(lati,loni,30,Ui,'filled')
cmocean('-balance','pivot')
modismoaps('contrast','low')
cb = colorbar;
ylabel(cb,'ice flux m^2/yr')
exportgraphics(gcf,'itslive_interp_documentation_flux_map.jpg')
In the figure above, the red indicates ice mass leaving the control volume. Most of the boundary is white, because most of it sits along ice divides where velocity is near zero.
Here's another way to look at it. Below I'm using the anomaly function from Climate Data Toolbox but you can just use plot if you prefer. And if you'd like to adapt this example to your own application where pathdistps might not apply, just calculate d as a cumulative sum of distances along the flux gate.
% Calculate total volume imbalance
d = pathdistps(lati,loni); % distance along the path in meters
figure
subplot(3,1,1)
anomaly(d/1000,vci)
axis tight
ylabel 'velocity across (m/yr)'
subplot(3,1,2)
plot(d/1000,thi)
axis tight
box off
ylabel 'ice thickness (m)'
subplot(3,1,3)
anomaly(d/1000,Ui)
axis tight
ylabel 'local flow m^2/yr'
xlabel 'distance around basin boundary (km)'
exportgraphics(gcf,'itslive_interp_documentation_flux_line.jpg')
And here's the total flux across the boundary line:
dx = gradient(d); % dx is 100 m in our example, but taking the gradient is more general.
Vol = sum(Ui.*dx,'omitnan');
% Convert Volume to mass (multiply by 917 kg/m^3, then 1e-12 to get to Gt)
Mass = Vol*917*1e-12
-136.6592That is, a net 136 Gt/yr of ice flows out of Pine Island Glacier's grounded basin.
The MATLAB functions in this repo and this documentation were written by Chad A. Greene of NASA/JPL. The NASA MEaSUREs ITS_LIVE project is by Alex S. Gardner and the ITS_LIVE team.