Dependence of hillslope moisture content on downhill saturation

Abstract

We derive steady equilibria for lateral downslope moisture flow in an idealized thin closed layer as a solution to the 1D Richards' Equation. The equilibria are determined by two free parameters: the downslope flux and a boundary condition. Solutions exhibit a constant downslope flow speed and moisture content for the constant equilibrium flux, which is the product of the two. However where an isolated zone of fixed saturation degree exists representing a boundary condition, the flow speed immediately upslope is reduced and the moisture content correspondingly increased to preserve the constant equilibrium flux. The capillary head jump at the saturated zone produces a blockage that gives a high moisture content back upslope through a pooling distance determined by the equilibrium condition that the downslope flux is constant. In our numerical integrations, the vertically projected pooling height is more than 10 km for a fully saturated zone in mixed silty or clay soils, but decreases by about an order of magnitude with every 10% decrease in the boundary-zone saturation degree. The drying of downhill saturated zones with the increased speed of mountain moisture outflow and corresponding decreased mountain moisture content gives a viable explanation for the mysterious ~69% unaccounted drop seen in the spring outflow in the La Luz / Fresnal Watershed at Alamogordo's upstream spring-box diversions in the semiarid southeastern New Mexico USA.