To address the prominent problem of declining runoff in many rivers around the world, studying the law of runoff change and attribution analysis is very important for the planning and management of watershed water resources and has practical significance for solving the imbalance between supply and demand of watershed water resources and maintaining the healthy development of rivers. Three commonly used coupled water-energy balance equations based on Budyko hypothesis are selected to estimate the elasticity coefficient of runoff change to each driving factor, and the contribution rate of different factors to runoff change in the study area is quantified by the total differential method and the complementary method, respectively. The results show that the runoff of Huangfuchuan River basin showed a significant decreasing trend from 1954 to 2015, and the runoff mutation points were 1979 and 1996; in the alteration period I (1979–1996), precipitation was the main factor leading to the runoff reduction in Huangfuchuan River basin, followed by the influence of underlying surface; the contribution rate of underlying surface to runoff alterations ranged from 63.7% to 65.46%; the impact of potential evapotranspiration was slightly smaller. In the alteration period II (1997–2015), the underlying surface played a dominant role in runoff reduction of Huangfuchuan River basin. The contribution rate of the underlying surface to runoff change ranged from 80.21% to 86.34%, followed by precipitation, and the potential evapotranspiration had the least impact. The impact of human activities on the whole watershed increased with the passage of time. The land use change, the overall increase of NDVI (vegetation cover) and the construction of water conservation projects are important reasons for the reduction of runoff in Huangfuchuan River basin.
Exploring the relationship between runoff and sediment elements in a river basin is a prerequisite for realizing the scientific management scheme of runoff and sediment. In this study, six commonly applied probability distributions are utilized to fit the marginal distribution, and three Archimedes copulas are used to fit the joint distribution to build a joint probability distribution model of river runoff and sediment in sandy areas. The synchronous and asynchronous encounter probabilities of runoff and sediment are calculated. The uncertainties of marginal distribution, parameter estimation, and copula function in the process of constructing the joint distribution model framework are analyzed. The results indicate that: (1) The runoff and sediment series from 1954 to 2015 of the Huangfuchuan River basin are divided into three stages by using the cumulative anomaly method and the double mass curve method, and the runoff and sediment in the three stages have strong correlations. In the Ta (1954–1978) and Tb (1979–1996) stages, the optimal joint distribution functions of runoff and sediment are Gumbel, and in the Tc (1997–2015) stage the optimal joint distribution function is Clayton; (2) The synchronous probabilities of runoff and sediment series in the three stages are 69.84%, 84.82%, and 70.72%, respectively, which are much greater than the asynchronous frequencies of abundance and depletion, and this showed that the conditions of runoff and sediment in the river basin are consistent; (3) The joint distribution function is sensitive to the choice of marginal distributions, parameters, and copula functions, and the optimal marginal distribution function, optimal copula function, and the parameters selected by the maximum likelihood estimation method can better fit the runoff-sediment relationship in the river basin and reduce the process uncertainty.
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