A stochastic unsaturated flow theory and a numerical simulation model have been coupled in order to estimate the large-scale mean behavior of an unsaturated flow system in a spatially variable soil. On the basis of the theoretical developments of Mantoglou and Gelhar (1987a, b, c), the theory assumes that the local hydraulic soil properties are realizations of three-dimensional random fields, and it derives the large-scale flow structure by averaging the local governing flow equation over the ensemble. The resulting mean model representation is in the form of a partial differential equation, similar to the local flow equation. in which effective model parameters occur (e.g., effective hydraulic conductivity). Further, the theory predicts the variance (prediction error) of the capillary tension head due to the spatial variability of the local hydraulic soil properties. The governing unsaturated flow equation representing the mean system behavior is solved using a finite difference numerical solution technique. The effective parameters are evaluated from the stochastic theory formulas before entering them into the numerical solution for each iteration. The stochastic model is applied to a field site in Denmark, where information is available on the spatial variability of soil parameters and variables. Numerical simulations have been carried out, and predictions of the mean behavior and the variance of the capillary tension head and the soil moisture content have been compared to field observations. The stochastic model predicts the average system behavior reasonably well. Reasonable results are also obtained for the range of variation of the capillary tension head, despite the limited number of measurements and corresponding statistical inference issues. The stochastic model presented here seems to offer a rational framework for modeling large-scale unsaturated flow and estimating areal averages of soil-hydrological processes in spatially variable soils.
|Journal||Water Resources Research|
|Publication status||Published - 1992|