A new probability density function for spatial distribution of soil water storage capacity leads to the SCS curve number method

Following the Budyko framework, the soil wetting ratio (the ratio between soil wetting and precipitation) as a function of the soil storage index (the ratio between soil wetting capacity and precipitation) is derived from the Soil Conservation Service Curve Number (SCS-CN) method and the variable infiltration capacity (VIC) type of model. For the SCS-CN method, the soil wetting ratio approaches 1 when the soil storage index approaches inline-formula∞, due to the limitation of the SCS-CN method in which the initial soil moisture condition is not explicitly represented. However, for the VIC type of model, the soil wetting ratio equals the soil storage index when the soil storage index is lower than a certain value, due to the finite upper bound of the generalized Pareto distribution function of storage capacity. In this paper, a new distribution function, supported on a semi-infinite interval inline-formula $M2inlinescrollmathmlx\in [\mathrm{normal\; 0},\mathrm{normal\; \infty })$ 49pt12ptsvg-formulamathimgce2e8821c0ea1a3bbebc52abab378af9 hess-22-6567-2018-ie00001.svg49pt12pthess-22-6567-2018-ie00001.png , is proposed for describing the spatial distribution of storage capacity. From this new distribution function, an equation is derived for the relationship between the soil wetting ratio and the storage index. In the derived equation, the soil wetting ratio approaches 0 as the storage index approaches 0; when the storage index tends to infinity, the soil wetting ratio approaches a certain value (inline-formula≤1) depending on the initial storage. Moreover, the derived equation leads to the exact SCS-CN method when initial water storage is 0. Therefore, the new distribution function for soil water storage capacity explains the SCS-CN method as a saturation excess runoff model and unifies the surface runoff modeling of the SCS-CN method and the VIC type of model.