Computation and Characterization of Surface Roughness of Catchments Extracted from Simulated Digital Elevation Models

In the past few decades, the quantitative computation of surface roughness has received increasing attention due to its importance in numerical surface study. In this paper, concepts of mathematical morphology are employed to compute and characterize the surface roughness of catchments extracted from a simulated digital elevation model (DEM). Morphological smoothing is implemented on the simulated DEM using square kernels of increasing size. The mask of pixels modified in each catchment at each kernel size is computed by performing the intersection operation between the catchment and the mask of pixels modified at each kernel size. The normalized probability functions of the catchments are computed as the ratio of the area of pixels modified in the catchment at each kernel size to the area of the catchment. The computed values of are used to compute two important grayscale granulometric complexity measures; average size of convex and concave regions in the catchments, and the surface roughness of the catchments due to the convex and concave region distribution averaged over the area of catchment. It is observed the larger the average size of the convex and concave regions in the catchment, the larger is the average roughness of the catchment. A power law relationship is also observed between the average size of convex and concave regions in the catchments and the surface roughness of the catchments. This power law arises as a consequence of the fractal properties of the surface roughness of catchments extracted from the simulated DEMs.