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Stochastic modeling of unsaturated flow in heterogeneous media with water uptake by plant roots: Tests of the parallel columns model under two‐dimensional flow conditions
Author(s) -
Or Dani,
Rubin Yoram
Publication year - 1993
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 - 10.1029/93wr02339
Subject(s) - covariance function , mathematics , smoothing , covariance , spatial variability , hydraulic conductivity , flow (mathematics) , vadose zone , mathematical analysis , kriging , spatial dependence , soil science , geometry , soil water , geology , statistics
In the first paper of this series (Rubin and Or, 1993) we developed a stochastic model predicting spatial moments of soil water matric potential ψ and saturation S under conditions of unsaturated steady state flow as function of the spatial moments of log saturated hydraulic conductivity Y , capillarity index α, and plant rooting depth δ. In this study, we investigate the ability of the proposed parallel columns model to reconstruct two‐dimensional flow solutions, and apply the model to spatial estimation using the geostatistical formalism. A finite difference numerical scheme was developed to solve the two‐dimensional Richards equation in heterogeneous flow domain and obtain detailed images of the spatial distribution of ψ and S and their moments. Two‐dimensionally‐based images representing “true” distributions of ψ and S in a vertical cross section ( x‐z plane) of laterally heterogeneous soil were used in a synthetic spatial estimation problem for comparison with the one‐dimensionally‐based solution and with kriging estimates. The results show that (1) the means of ψ and S were practically identical for the one‐ and two‐dimensional solutions; (2) ψ variance obtained from the two‐dimensional solution was smaller than the one‐dimensional, whereas S variance was larger in the two‐dimensional case; (3) a smoothing of ψ under two‐dimensional flow regime resulted in spatial covariance function of a Bessel type, whereas two‐dimensional spatial covariance of S exhibited a steep decay near its origin denoting spatial discontinuity; (4) the least smoothing of ψ was observed near the surface where nearly one‐dimensional conditions exist; (5) during transient flow, spatial covariances assume their steady state form quite rapidly; (6) spatial covariances predicted by the parallel columns model provided good estimates at unmeasured locations with conservative confidence regions for ψ estimation and less conservative for S estimation; and (7) analytically predicted spatial covariances provide a means for network design.