Upslope area – handling NaNs

Posted by Steve Eddins, October 16, 2007

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Since I originally posted my upslope toolbox to MATLAB Central back in August, I have heard from some experts about an issue related to NaNs in the DEM data. Specifically, some data sets record elevation only for DEM pixels within a particular catchment basin. Pixels outside the catchment basin typically are NaN. Some of my code doesn't handle NaN values in the DEM.

After some e-mail correspondence, I settled on this approach:

In the pixel flow direction computation, replace groups of NaN pixels that touch the border by a high value. (You can read about the technique for find such pixels in this post.) This replacement makes the flow direction on the watershed pixels point inward, toward the catchment basin.

When solving the flow matrix for upslope area, use 0 instead 1 on the right-hand side for exterior NaN pixels. This means that such pixels don't contribute any flow to the system.

Here's a simple example:

[x,y] = meshgrid(-3:3);
E = hypot(x,y);
E(abs(x) + abs(y) > 3) = NaN

E =

       NaN       NaN       NaN    3.0000       NaN       NaN       NaN
       NaN       NaN    2.2361    2.0000    2.2361       NaN       NaN
       NaN    2.2361    1.4142    1.0000    1.4142    2.2361       NaN
    3.0000    2.0000    1.0000         0    1.0000    2.0000    3.0000
       NaN    2.2361    1.4142    1.0000    1.4142    2.2361       NaN
       NaN       NaN    2.2361    2.0000    2.2361       NaN       NaN
       NaN       NaN       NaN    3.0000       NaN       NaN       NaN

R = dem_flow(E);
T = flow_matrix(E, R);
A = upslope_area(E, T)

A =

         0         0         0    1.0000         0         0         0
         0         0    1.0000    2.0000    1.0000         0         0
         0    1.0000    1.8112    4.1888    1.8112    1.0000         0
    1.0000    2.0000    4.1888   25.0000    4.1888    2.0000    1.0000
         0    1.0000    1.8112    4.1888    1.8112    1.0000         0
         0         0    1.0000    2.0000    1.0000         0         0
         0         0         0    1.0000         0         0         0

Notice that the upslope area at the lowest pixel is 25. This is the number of non-NaN pixels in the DEM.

I uploaded version 1.2 of the upslope toolbox, with these NaN-related changes, to the MATLAB Central File Exchange in early October. If you have data sets that use NaNs outside the catchment basin of interest, you might want to download the new version.

Published with MATLAB® 7.5