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

Abstract

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.

Separating runoff change by the improved Budyko complementary relationship considering effects of both climate change and human activities on basin characteristics

“…To identify the necessity to improve the original BCR method, both the BCR method and the IBCR method are applied to separate long-term runoff change in a specific basin whose basin characteristics relate to both climate change and human activities. Since the BCR and the IBCR methods are derived based on the one-parameter Budyko equation, Fu-Equation (Fu, 1981), which is widely used and has shown good results in many steady-state and unsteady-state basins across China, is chosen in the study (Jiang et al, 2015;Jiang et al, 2017). Fu-Equation is expressed as:…”

“…The assumption that w is related to human activities alone in the BCR is not completely true since other studies indicate that there are basins whose physical characteristics are also related to climate change (Jiang et al, 2015;Jiang et al, 2017).…”

“…The BCR method has the ability to deal with the non-closure problems caused by the approximate calculations of the difference equation in the conventional sensitivity method, however, it is not true to assume that the Budyko parameter reflecting basin characteristics is related to human activities alone in certain areas, as some studies indicate that the Budyko parameter may relate to both climate change and human activities (Jiang et al, 2015). For example, Jiang et al (2017) has used covariate analysis of the Budyko parameter to identify the influential factors, and results show that in some areas of China, the basin characteristics parameter is also related to climate change. In these specific areas, climate change affects runoff in two ways, one is the direct effect by input climate data, and the other is the indirect effect by altering the basin characteristics parameter.…”

Stochastic modeling of interannual variation of hydrologic variables

“…However, Zanardo et al [2012] did not address serial correlation of the hydrograph, thus limiting generality of the analysis. Additionally, because many families of probability distributions are uniquely defined by their mean and standard deviation, we also demonstrate how "moment matching" can be used to obtain approximate probability distributions of seasonal and annual variables [e.g., Jiang et al, 2017]. These distributions could provide relevant management-oriented information, such as estimates of annual flow return intervals.…”

Statistical Analysis of Extreme Events in Precipitation, Stream Discharge, and Groundwater Head Fluctuation: Distribution, Memory, and Correlation

“…Understanding how the subtle properties of one system's extreme events can affect the other interconnected systems requires more in-depth analysis and use of advanced statistical techniques. Second, these basic statistical techniques often rely on assumptions or major simplifications of properties for water systems, such as stationarity in both space and time, which may not always be valid for real world dynamics [13][14][15]. These issues motivated this study.One example of the assumption/simplification used by basic statistical studies in hydrological extremes is the well-known Gumbel distribution.…”