Probabilistic Simulation Of Two-variable Monthly Streamflow Based On Copula Function

The frequency analysis of hydrological events plays a huge role in flood control and drought relief,water resources planning and management,and water conservancy project construction.However,in practice,it is often difficult to meet the requirements of hydrological event analysis because of limited observation data.Therefore,it is necessary to construct a sufficiently long hydrological sequence to provide data support for engineering management and planning design.Since the univariate hydrological event is not enough to fully consider the interrelationship between various factors of hydrological events,bas-ed on the study of univariate hydrological events,this paper uses the multivariate joint frequency calculation method to analyze the monthly streamflow.The traditional multivariate hydrological event calculation methods have certain shortcomings.Therefore,this paper uses the Copula function to construct a joint distribution of the monthly streamflow because it's flexible,suitable and simple.The two-variable joint distribution refers to a series of processes for joint distribution functions of two functions with constructed edge distribution,including parameter estimation,goodness-of-fit evaluation,error analysis,etc.The study of two-variable joint probability distribution is a special case of multivariate joint probability distribution research.It has achieved good results in drought frequency research and analysis.By using the two stations'historical daily streamflow data to simulate long-sequence monthly streamflow to make it consistent with historical data on the basis of Bengbu Station and Moniac Station.The monthly streamflow is simulated randomly based on the Archimedean Copula function combined with the Gibbs sampling method.The main conclusions this paper are:(1)The results show that most of the months obey the P-? distribution,and a few months obey other distributions.The each months' value of Kolmogorov-Smirnov does not exceed the critical value,and the P-value was greater than 0.05 by the results of fitting.(2)Using the two-variable empirical frequency formula to calculate the empirical frequency of adjacent months,three Copula functions are selected to fit the two-variable joint probability distribution.The optimal Copula function of adjacent months is selected by Visual Graph method and AIC,and the Kolmogorov-Smirnov is used to show that the selected Copula function is reasonable and effective.(3)Based on the two-variable Copula function and Gibbs sampling method,the conditional probability is used to simulate the monthly streamflow.The results show that the mean and root mean square error of the Moniac station in April,June and December are not more than 30%,and the relative errors of other months are smaller,the errors are less than 5%,and the statistical characteristics of the original data are basically maintained.The mean and root mean square errors of the BengBu station in January,May and November are not more than 30%,and the relative errors in other months are smaller,none of which exceeded 5%,and the statistical characteristics of the original data are basically maintained.And the error of the correlation coefficient of both stations are small.