A linearized solution of the slope crest infiltration problem

Abstract

It was found recently that the long‐slope ponded infiltration solution applies also to a wide range of nonplanar topographies. The long‐slope solution neglects any slope crest effect, and a careful analysis of this is needed. The present work reassesses the previous primitive estimate of the crest effect. We solve the problem of linearized infiltration into a symmetrical ridge with 45° slope angles. The integral matching of flow behavior gives results of ample accuracy for our purpose. The 45° slope is very steep in nature, but yields a simple product solution. We use this to calibrate the previous long‐slope criterion for arbitrary slope angle. The primary slope crest effect is increase of moisture content and decrease of capillary potential gradients near the crest. The affected region propagates downslope but its influence on infiltration dynamics tends to dissipate because the relative importance of capillarity diminishes as time increases. We find that the previous criterion for applicability of long‐slope infiltration dynamics was too conservative by a factor ranging from 2 at very small infiltration times to 100 at large times. The solution gives details of both downslope and inslope unsaturated flows. The ponded infiltration rate is least at the crest and increases downslope: This result is independent of linearization or slope angle.