Two‐dimensional steady state unsaturated water flow in heterogeneous soils with autocorrelated soil hydraulic properties

Abstract

The stochastic nature of soil water pressure head and vertical and horizontal flux density under two‐dimensional unsaturated steady state flow conditions was examined by using a Monte Carlo technique. Random autocorrelated scale factors were generated by a first‐order nearest neighbor model and were used to describe a stationary random field of hydraulic conductivity functions. Scale factor values were assumed to vary only in the horizontal direction, perpendicular to the mean flow. The water flow equation was numerically solved for steady state infiltration and transpiration in a two‐dimensional domain, of which the lower boundary was described by a groundwater level. Differences in results between a saturated and unsaturated soil water system were most likely caused by the direction in which the hydraulic properties are randomly autocorrelated and differences in the applied boundary conditions. In contrast to earlier findings with respect to the saturated system, the variability in fluxes for the unsaturated system decreased with an increase in the autocorrelation length, and the variation in soil water pressure head for one‐ and two‐dimensional systems tended to be equal with increasing autocorrelation lengths. When considering a two‐layer system it was found that the variability in the lateral flow component at the layer boundary was severely increased as compared to the single‐layer simulations.