Abstract. Following the Budyko framework, soil wetting ratio (the ratio between soil wetting and precipitation) as a function of soil storage index (the ratio between soil wetting capacity and precipitation) is derived from the SCS-CN method and the VIC type of model. For the SCS-CN method, soil wetting ratio approaches one when soil storage index approaches infinity, 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, soil wetting ratio equals soil storage index when soil storage index is lower than a certain value, due to the finite upper bound of the power distribution function of storage capacity. In this paper, a new distribution function, supported on a semi-infinite interval x ∈ [0, ∞), is proposed for describing the spatial distribution of storage capacity. From this new distribution function, an equation is derived for the relationship between soil wetting ratio and storage index. In the derived equation, soil wetting ratio approaches zero as storage index approaches zero; when storage index tends to infinity, soil wetting ratio approaches a certain value (≤ 1) depending on the initial storage. Moreover, the derived equation leads to the exact SCS-CN method when initial water storage is zero. 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 SCS-CN method and VIC type of model.