A process-based insight into nonstationarity of the probability distribution of annual runoff

In this paper, a process‐based analytical derivation approach is proposed to perform a nonstationary analysis for annual runoff distribution by taking into account the information of nonstationarities in both hydrological inputs and runoff generation processes. Under the Budyko hypothesis, annual runoff is simulated as a formulation of hydrological inputs (annual precipitation and potential evaporation) using an annual runoff model based on the Fu equation with a parameter w accounting for the runoff generation processes. The nonstationarity of the runoff generation process is captured by the dynamic Fu‐equation parameter w. Then the multivariate joint probability distribution among the hydrological inputs, the Fu‐equation parameter w, and the runoff model error k is constructed based on the nonstationary analysis for both the hydrological inputs and w. Finally, the annual runoff distribution is derived by integrating the multivariate joint probability density function. The derived distribution by the process‐based analytical derivation approach performs well in fitting distributions of the annual runoffs from both the Yangtze River and Yellow River, China. For most study watersheds in these two basins, the derived annual runoff distributions are found to be nonstationary, due to the nonstationarities in hydrological inputs (mainly potential evaporation) or the Fu‐equation parameter w. VC 2017. American Geophysical Union. All Rights Reserved