Explicit Solution of Horton’s Equation for Infiltration Capacity

Horton’s infiltration capacity is often used to separate rainfall excess from a rainfall hyetograph in watershed modeling. Nevertheless, this infiltration capacity is an implicit function of cumulative infiltration in soil, which is inconvenient in practical applications. This study found an explicit expression of infiltration capacity that is the sum of a steady-state term and a transitional term. The steady-state term is the critical infiltration rate or minimum infiltration capacity, and the transitional term is represented by a Lambert W function that tends to zero as time (or cumulative infiltration in soil) tends to infinity. The proposed method can be easily used, together with a unit hydrograph model, for direct runoff in watershed modeling.