Depressional storage for Markov‐Gaussian surfaces

Abstract

Processes during rain events, such as infiltration, runoff, soil erosion, and crust formation, are influenced in part by depressional storage and surface roughness. If the surface topography is known, its potential depressional storage can be calculated. The objective of this paper was to relate the statistical parameters for quantifying surface roughness to depressional storage. Analysis of topographic data sets digitized at millimeter grids by a laser scanner showed that soil roughness can be quantified by a Markov‐Gaussian (M‐G) type random process. A Monte Carlo simulation procedure was used to find the mean ponding characteristics from simulated M‐G surfaces. Depressional storages were found to be functions of two M‐G parameters, two sample length scales, and the slope steepness. The Markov parameters are the global variance (σ2) and the correlation length scale (L), and the sample length scales are grid spacing (Δx) and side length (Ls). After proper scaling, all storage functions collapsed into two nondimensional relationships: (1) storage at zero slope as a function of relative sample length scale, and (2) storage as a function of scaled slope. When L = 0, simulated surfaces followed the random Gaussian model and the nondimensional storage was only a function of scaled slope. Storages calculated from digitized elevation data sets with M‐G type statistics agreed well with results obtained from simulated surfaces.