Generalized Horton Model for Low-Intensity Rainfall

Abstract

The Horton equation, which is widely used to predict infiltration of water into soil, is inapplicable when the rainfall intensity is less than the initial infiltration capacity of the soil, especially during the early stages of a storm event. This study modifies the Horton equation to satisfy this condition by considering the rainfall intensity as an independent variable in addition to the other physical parameters used in the original model. The modification is based on dividing the entire infiltration relation into two curves intersecting each other at the ponding time. The two curves are then matched asymptotically into a composite relation that does not require implementing the ponding time parameter explicitly. The proposed relation satisfies the infiltration capacity of the soil such that, when ponding occurs, the difference between the potential and cumulative infiltration becomes zero. This agreement suggests that the proposed relation would be valid for describing the infiltration process within a wide range of rainfall intensities greater or less than the infiltration capacity. The proposed relation will be useful to extend our ability for understanding hydrologic processes related to rainfall infiltration in arid and semiarid environments.