Prediction of Subsurface Stormflow in Heterogeneous Sloping Aquifers

An ensemble-averaged prediction equation system for transient subsurface stormflow on sloping impermeable beds in heterogeneous hillslopes is derived by means of the regular perturbation method. The covariance of hydraulic conductivity and flow depth, which emerges during the derivation of the mean flow depth, causes a closure problem. To close the equation system, a second equation is derived for this covariance term. The overall set of ensemble-averaged prediction equations then is solved numerically and their validity is tested by comparing the results against those obtained from a Monte-Carlo simulation for different values of slope and variance of hydraulic conductivity. The comparison of the results suggests that the system of prediction equations gives satisfactory results for coefficient of variation of hydraulic conductivity as high as 1.12 for slopes as steep as 0.3.