Head and flux variability in heterogeneous unsaturated soils under transient flow conditions

A numerical model for the analysis of uncertainty propagation in flow throu gh unsaturated soils is developed. This model is based on a first-order Tay lor series expansion of the discretized Richards equation. Soil hydrologic properties (the saturated hydraulic conductivity and the pore size distribu tion parameter) are assumed to be stochastic processes in space. The surfac e boundary conditions can be considered as deterministic variables in time or stochastic time series. Spectral analysis and Monte Carlo simulations we re used to verify this numerical model for flow under both steady and trans ient conditions. The model is then used to examine the effect of uncertaint y in boundary conditions and the effect of heterogeneity on the pressure he ad and flux variance profiles at various times for one-dimensional vertical flow cases. Dependence of pressure head variance on the flow conditions (d rying or wetting) is examined. On the basis of the analysis it is found tha t the propagation of the head variance is similar to that of the concentrat ion variance for solute transport in saturated aquifers. The head variance is proportional to the mean pressure gradient, and thus large head variance s are associated with the wetting and the drying front of a moisture pulse. The peak head variance is smaller at the wetting front than it is at the d rying front. This difference is attributed to the difference in the magnitu de of mean hydraulic gradient and should not necessarily be interpreted as a hysteresis effect. Ln addition, it is shown how the variance of the flux of a moisture pulse increases with depth.