The Application Of Copula Function In The Stochastic Hydrologic Analysis In Jinsha River

Sediment deposition of river and reservoir are the key problems of reservoir operation in rivers with water control projects,so it's important to consider the change regulation of water and sediment in the plan and design of reservoir.This article focuses on the runoff flow and sediment discharge of a hydrologic station in Jinsha river watershed.Based on Copula theory and time series techniques,conducting research on the stochastic hydrological processes with runoff and sediment discharge separately and mutually.The main research contents and conclusions are as follows:(1)For random variables,the marginal distribution functions and Copula joint distribution functions are not unique.The optimal marginal distribution function and the joint distribution function can be selected according to the statistical characteristics of the function as well as hydrological data.The research chose five kinds of marginal distribution functions of annual runoff flow and annual sediment discharge and three Copula joint distribution functions to build joint distribution of annual runoff flow and sediment discharge.The optimal marginal distribution functions of annual runoff flow and annual sediment discharge are Gen.extreme value distribution and Gamma distribution,the optimal joint distribution function is Frank Copula function.Calculating the marginal distribution functions of monthly runoff flow and monthly sediment discharge,using three kinds of Copula functions to build joint distributions of corresponding monthly runoff flow and monthly sediment discharge,djacent monthly runoff flow and adjacent monthly sediment discharge to obtain the optimal joint distribution functions.The results show that when the correlation is high,the optimal joint distribution is Frank copula.(2)Analyzing the abundant and dry encounter situations of annual runoff flow and annual sediment discharge based on Frank Copula.Choosing 25%,75% as abundant and dry boundary,then the runoff flow and sediment discharge can be divided into abundant,flat and dry states separately and nine encounter situations totally.Among them,the synchronous probability is greater than asynchronous probability,situation with flat runoff flow and flat sediment discharge is the highest probability,situations with abundant runoff flow and dry sediment discharge,dry runoff flow and abundant sediment discharge flat sediment discharge are the lowest probability.The results show that water-sediment relationship is in good consistency,Copula function can describe the analysis of multi variables.(3)Using Copula theory and time series techniques to build multivariate and univariate models.Monthly water-sediment Copula Function and monthly watersediment time series can describe the non-stationary statistical properties and autocorrelation and cross-correlation properties of water and sediment,but single monthly runoff flow Copula,monthly sediment discharge Copula,monthly runoff flow time series,monthly sediment discharge time series can only describe the non-stationary statistical properties and autocorrelation characteristics of a single variable,but not the correlation between two variables.Multivariate model is more objective and comprehensive in describing stochastic hydrological processes.(4)According to that the essence of hydrologic stochastic model is conditional probability,using inverse function method with Copula joint distribution to get conditional probability and then carry out Copula stochastic simulation.At the same time,using time series model to carry out stochastic simulation.Calcuting the mean,variance,C_v,C_s,autocorrelation and cross-correlation of simulation sequence by Copula and time series and comparing with the measured values.The results show that the characteristic values simulated by Copula are reasonable,even better than that of time series simulation.