Large‐Scale Modeling of Unsaturated Flow by a Stochastic Perturbation Approach

Abstract

Core Ideas Large‐scale equations have the same form as the Richards equation. Large‐scale parameters are expressed by the mean parameters plus correction terms. Mean parameters can substitute for the large‐scale parameters. The spatial variability of soil properties hinders the mean unsaturated flow. Based on the stochastic perturbation approach, a large‐scale unsaturated flow model was derived in which the saturated hydraulic conductivity (Ks) is assumed to be a random field. The corresponding effective parameters (i.e., the large‐scale relative diffusivity and the large‐scale relative conductivity) can be evaluated by the mean parameters and correction terms, and the latter are affected by variability of the dimensionless form of Ks and the flow process. Analytical solutions of the large‐scale parameters were derived by a spectral approach for a synthetic, one‐dimensional case. The simulated results from the large‐scale model were compared with the results from Monte Carlo simulations as well as the simulation results with mean parameters under one‐, global two,‐ and local two‐dimensional infiltration cases, respectively. Comparisons showed that the soil water content calculated using the mean parameters is smaller than that obtained by the Monte Carlo simulations, while the actual mean soil water content is smaller than the value calculated by large‐scale parameters based on the spectral approach. This study shows that the mean parameter can be an alternative to the large‐scale parameter (which is difficult to obtain) for unsaturated flow modeling. The validity of the assumptions of the large‐scale model were also tested.