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Abstract. Prediction of mean annual runoff is of great interest but still poses achallenge in ungauged basins. The present work diagnoses the prediction inmean annual runoff affected by the uncertainty in estimated distribution ofsoil water storage capacity. Based on a distribution function, a waterbalance model for estimating mean annual runoff is developed, in which theeffects of climate variability and the distribution of soil water storagecapacity are explicitly represented. As such, the two parameters in themodel have explicit physical meanings, and relationships between theparameters and controlling factors on mean annual runoff are established.The estimated parameters from the existing data of watershed characteristicsare applied to 35 watersheds. The results showed that the model couldcapture 88.2 % of the actual mean annual runoff on average across thestudy watersheds, indicating that the proposed new water balance model ispromising for estimating mean annual runoff in ungauged watersheds. Theunderestimation of mean annual runoff is mainly caused by theunderestimation of the area percentage of low soil water storage capacitydue to neglecting the effect of land surface and bedrock topography. Higherspatial variability of soil water storage capacity estimated through theheight above the nearest drainage (HAND) and topographic wetness index (TWI)indicated that topography plays a crucial role in determining themore »actualsoil water storage capacity. The performance of mean annual runoffprediction in ungauged basins can be improved by employing better estimationof soil water storage capacity including the effects of soil, topography,and bedrock. It leads to better diagnosis of the data requirement forpredicting mean annual runoff in ungauged basins based on a newly developedprocess-based model finally.« less

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 $x\in [\mathrm{0},\mathrm{\infty })$, 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 tendsmore »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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