Two-Dimensional Probabilistic Infiltration Analysis in a Hillslope Using First-Order Moment Approach

A first-order moment analysis method is introduced to evaluate the pore-water pressure variability within a hillslope due to spatial variability in saturated hydraulic conductivity (K_s ) during rainfall. The influences of the variance of the natural logarithm of K_s (ln K_s ), spatial structure anisotropy of ln K_s , and normalized vertical infiltration flux (q) on the evaluations of the pore-water pressure uncertainty are investigated. Results indicate different responses of pressure head variability in the unsaturated region and the saturated region. In the unsaturated region, a larger variance of ln K_s , a higher spatial structure anisotropy, and a smaller q lead to a larger variability in pressure head, while in the saturated region, the variability in pressure head increases with the increase of variance of ln K_s , the decrease of spatial structure anisotropy, or the increase of q. These variables have great impacts on the range of fluctuation of the phreatic surface within the hillslope. The influences of these three variables on the variance of pressure head within the saturated region are greater than those within the unsaturated region, and the variance of ln K_s has the greatest impact. These results yield useful insight into the effects of heterogeneity on pressure head and uncertainty associated with predicted flow field.