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Depressional storage for Markov‐Gaussian surfaces
Author(s) -
Huang Chihua,
Bradford Joe M.
Publication year - 1990
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr026i009p02235
Subject(s) - ponding , surface roughness , gaussian , surface runoff , surface finish , soil science , hydrology (agriculture) , mathematics , geology , geotechnical engineering , engineering , materials science , physics , mechanical engineering , ecology , quantum mechanics , drainage , composite material , biology
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 (σ 2 ) and the correlation length scale ( L ), and the sample length scales are grid spacing (Δ x ) 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.