Analysis Of Water Encounters Of Multi-reservoirs In The Middle And Lower Reaches Of The Yellow River Based On Copula Function

With the acceleration of economic development,the demand for water resources in the Yellow River Basin is increasing continuously,while the amount of water resources in the Yellow River is decreasing.Considering the uneven distribution of incoming water in the Yellow River basin,for years,Luhun Reservoir,Guxian Reservoir,Xiaolangdi Reservoir and Hekou Village Reservoir have been built in the middle and lower reaches of the Yellow River in succession.The reservoirs' regulation and storage function make the incoming water used more efficiently.However,the incoming water data used in the study of the four reservoirs joint dispatching schemes are almost multi-year average runoff or a certain frequency characteristic value,which fails to reflect the long-term variation of the incoming water and the related characteristics among the four reservoirs.The synchronous-asynchronous analysis of the water inflow of the four reservoirs can provide a reference for the formulation of joint dispatching water supply scheme and further improve the utilization efficiency of water resources.However,in the current hydrological analysis,there are few studies on the joint distribution of higher dimensions.This paper,firstly,uses the twodimensional Copula model to analyze the encounter of incoming water of single tributary reservoir and main stream reservoir.Then according to the results obtained and the characteristics of different structural modes of R-Vine Copula model,the CVine structural mode is used to analyze the four-dimensional combined water encounters of the four reservoirs in the middle and lower reaches of the Yellow River.The main research work and achievements are as follows:(a)Based on the collected data,the inflow changes curve and trend lines of Xiaolangdi Reservoir,Guxian Reservoir,Luhun Reservoir and Hekoucun Reservoir from 1987 to 2016 are drawn,to analyze the inflow regularity of the whole year,flood season and non-flood season.Then the change of each reservoir and the relationship between reservoirs are obtained,which can provide the background for the following.(b)Four reservoirs were fitted with different marginal distributions in the whole year,flood season and non-flood season.Then AIC criterion and RMSE method are used to determine the optimal edge distribution function.By substituting the edge distribution function into common Copula function,using K-S test method for fitting test,using AIC criterion method and OLS minimum criterion method for optimum selection,the optimum two-dimensional Copula function of tributary reservoir and main stream reservoir incoming water encounter in annual,flood and non-flood is determined.By obtaining values from optimal Copula distribution maps,and substituting the values into the deduced formula for calculating the probability of encounters,the probabilities of 9 types of encounters of each combination in the whole year,flood season and non-flood season are obtained.Based on the analysis of the probability,the correlation between the incoming water of three tributary reservoirs and that of mainshtream Xiaolangdi reservoir is obtained.(c)According to the characteristics of the common structure modes of R-Vine Copula model and the relationship among the four reservoirs,the C-Vine structure is determined to be used.Based on the two-dimensional Copula method and C-Vine construction steps,the joint distribution models of four reservoirs' incoming water in the whole year,flood season and non-flood season are established.The maximum likelihood estimation method and PIT test method are used to estimate the parameters and to test the fitting.By substituting the values obtained from the model into the fourdimensional probability calculation formula,the probability of 81 kinds of encounters in the whole year,flood season and non-flood season are obtained,and the corresponding inflow quantity.By classifying and analyzing the results,we can know four-reservoirs' incoming water: having how much probability of the risk of water shortage in the whole research system,having a good complementarity,having advantages for tributary reservoirs to supply water to the main stream,having advantages to replenish water in flood season to non-flood season.In this paper,the R-Vine Copula modeling method is proved to be feasible in hydrological four-dimensional joint frequency analysis by an example study.