%AWang, Dingbao%BJournal Name: Hydrology and Earth System Sciences; Journal Volume: 22; Journal Issue: 12 %D2018%I %JJournal Name: Hydrology and Earth System Sciences; Journal Volume: 22; Journal Issue: 12 %K %MOSTI ID: 10106188 %PMedium: X; Size: 6567 to 6578 %TA new probability density function for spatial distribution of soil water storage capacity leads to the SCS curve number method %X

Abstract. Following the Budyko framework, the soil wetting ratio (the ratio betweensoil wetting and precipitation) as a function of the soil storage index (theratio between soil wetting capacity and precipitation) is derived from theSoil Conservation Service Curve Number (SCS-CN) method and the variableinfiltration capacity (VIC) type of model. For the SCS-CN method, the soilwetting ratio approaches 1 when the soil storage index approaches ,due to the limitation of the SCS-CN method in which the initial soil moisturecondition is not explicitly represented. However, for the VIC type of model,the soil wetting ratio equals the soil storage index when the soil storageindex is lower than a certain value, due to the finite upper bound of thegeneralized Pareto distribution function of storage capacity. In this paper,a new distribution function, supported on a semi-infinite interval $x\in \left[\mathrm{0},\mathrm{\infty }\right)$, is proposed for describing the spatial distribution of storagecapacity. From this new distribution function, an equation is derived for therelationship between the soil wetting ratio and the storage index. In thederived equation, the soil wetting ratio approaches 0 as the storage indexapproaches 0; when the storage index tends to infinity, the soil wettingratio approaches a certain value (≤1) depending on the initial storage.Moreover, the derived equation leads to the exact SCS-CN method when initialwater storage is 0. Therefore, the new distribution function for soil waterstorage capacity explains the SCS-CN method as a saturation excess runoffmodel and unifies the surface runoff modeling of the SCS-CN method and theVIC type of model.

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