Introduction

Model slope and curvature from a digital elevation model (DEM) [1]. The surface is modeled as a six-term polynomial.

The surface is F(x,y) = ax² + by² + cxy + dx + ey + f,

curvature (C) is

C = 2a + 2b,

which is equivalent to the 2D Laplacian of the surface.

slope (S) is

S = sqrt(d² + e²),

and elevation (E) predicted by the surface model is

E = F(x_c,y_c) = ax_c² + by_c² + cx_cy_c + dx_c + ey_c + f

where x_c is the x index of the focal cell and y_c is the y index of the focal cell.

Use the side length (L), also called scale, to specify the area of the moving window (L x L) focused on each cell that is used for computing elevation, slope and curvature.

Dependecies

numpy, GDAL

Example

Unix like system

On Mac or Linux set surface.py to be executable at the command line using Terminal:

chmod u+x surface.py

Create a directory to store output.

mkdir output

Then to calculate the elevation, slope, and curvature using a 9 x 9 window with the sample dem ("dem-example.tif") from within the directory containing surface.py type

./surface.py -d dem-example.tif -o output -l 9 -v

Windows

On Windows you do not need to make the program executable - it already will be. Just make a directory (here called "output") to store the output files. Then run surface.py

python surface.py -d dem-example.tif -o output -l 9 -v

Try opening up the output rasters in QGIS or your favorite GIS.

For additional information run

./surface.py -h on Mac or Linux

or

python surface.py -h on Windows.

References

[1] Hurst MD, Mudd SM, Walcott R, Attal M, Yoo K (2012) Using hilltop curvature to derive the spatial distribution of erosion rates. J Geophys Res Earth Surf 117:F0217. doi:10.1029/2011JF002057

Notes

For help on getting GDAL up and running see the GDAL cookbook.