Abstract:Two negative exponential difference functions were introduced to estimate the probability distribution of rainfall for describing the spatial variability of rainfall over the basin. Then calculation formula of probability distribution of total runoff was conducted by a vertically-mixed runoff yield model. The joint distribution of rainfall and infiltration capability was deduced to calculate surface runoff according to the infiltration excess mechanism. Furthermore, the groundwater runoff was estimated with mean value of infiltration according to the saturation excess mechanism to improve the practicability. Thus, the probability distribution function of total runoff could be deduced. In the flow concentration calculation, the basin was generalized to a linear reservoir, and the probability function of discharge at any time interval could be obtained according to the stochastic differential equation theory. Therefore, a complete stochastic runoff model was developed. As an example, this model was applied to flood simulation in the Huangnizhuang Basin locating at a tributary of Huaihe River. Results showed that the model could provide the probabilistic flood forecasts for the risk analysis of flood control. Meanwhile, the deterministic result (i.e., the mathematical expectation of discharge probability distribution function) had a high forecast accuracy.