Dependence of mountain moisture retention on downstream saturation

We derive 1D steady equilibria for partially saturated downslope flow as a solution to the reposed vadose-zone problem. The equilibria are determined by two free parameters: a mean flow and a downstream saturation. Where there is no downstream saturation, a uniform outflow of constant saturation is obtained, but if an isolated zone of excess downstream saturation exists, the upstream flow speed is reduced and saturation increased. The saturated zone produces a capillary head jump that blocks the downward percolation. With a fully saturated downstream zone in medium clay mixtures, flow backs up more than 20 km projected vertically, but with 90% downstream saturation, the back up is reduced to less than a km. The drying of downstream saturated zones with the increased rate of mountain moisture outflow gives a viable quantitative explanation for the mysterious 56% unaccounted drop seen in the output of the southern NM La Luz / Fresnal Watershed at Alamogordo's upstream spring-box diversions.