where I is the inﬁltration rate (mm/hour), t is the current simulation time step, is an effective hydraulic conductivity in which land cover impact (curve number) is considered (mm/hour; Nearing et al., 1996), ψ is the wetting front matric potential (mm), and ∆Φ is a change in soil water content (mm/mm). is the saturated water content (or porosity) (mm/mm). is the residual water content and approximated to the wilting point (mm/mm).
To consider unsaturated soil conditions in the calculation of inﬁltration rate, using effective hydraulic conductivity instead of saturated hydraulic conductivity . When soil is saturated, becomes equal to the saturated hydraulic conductivity .
Cumulative volume of water inﬁltrated after ponding ( in mm) is calculated using the following equation:
When the soil is not saturated, a hydraulic conductivity is estimated using the van Genuchten equation (van Genuchten, 1980) based on soil water content, ﬁeld capacity, and wilting point:
where is the saturated hydraulic conductivity (mm/hour), is the effective (or relative) saturation (mm/mm), m is coefﬁcient. The effective saturation is calculated based on the hydraulic features of soil:
where θ is the current water content (mm/mm), is the residual water content and approximated to the wilting point (mm/mm) for the simplicity, and is the saturated water content (or porosity) (mm/mm).