Application Research Of Nonparametric Kernel Density Estimation And Entropy-copula Model In Streamflow Simulation

Streamflow stochastic simulation aims to describe the relationship among the hydrological system elements,predict the hydrological regime and analyze the evolution trend of the hydrological and water resources system by establishing a stochastic hydrological model.How to accurately describe the complex relationship between streamflow sequence,maintain the statistical characteristics of observed sequence and improve the simulation accuracy is of great significance to the planning,design,operation,management and utilization of watershed water resources.The nonparametric model based on kernel density estimation overcomes the deficiency of the parametric model assuming the probability distribution and dependence form of streamflow sequence,and can capture the dependence structure of historical data and reproduce the nonlinearity,state dependence and multi-modal characteristics of streamflow sequence.However,the existing nonparametric simulation methods will produce values that are too close to the historical sequence and may generate negative values which also exist in parametric models.The streamflow stochastic simulation method based on maximum entropy and Copula theory can avoid the generation of negative values in the simulation sequence without linear assumption and normal transformation.However,the correlation between monthly runoff is complex and changeable,and the joint distribution based on a single Copula function can not accurately and comprehensively describe the non-linear correlation between monthly streamflow sequence.To solve the above problems,based on the theory of nonparametric kernel density estimation,this paper summarizes the principle and algorithm of nonparametric kernel density estimation model(NP)and NPL model.According to the principle and modeling idea of the nonparametric disaggregation model,an improved nonparametric disaggregation model is developed,and synthetic simulation of monthly streamflow sequence is carried out with the natural annual and monthly runoff data of four hydrological stations in the Yellow River Basin(Lanzhou station,Minhe station,Longmen station and Baimasi Station)as the research object.On the other hand,the entropy-mixed Copula model is proposed on the basis of the existing maximum entropy-single Copula model.Taking the natural annual and monthly runoff data of four hydrological stations in Heihe River Basin(Yingluoxia station)and Weihe River Basin(Huaxian Station,Lintong station and Zhantou Station)as research objects,the applicability of the two models in monthly runoff simulation are discussed.The main conclusions are as follows:(1)Nonparametric kernel density estimation model(NP)can better maintain the statistical characteristics of mean,standard deviation,maximum value and skewness coefficient of observed streamflow sequence.Because of the introduction of aggregation variables,NPL model performs better in describing long-term dependence and reproducing the skewness and flat-top characteristics of probability density distribution of original streamflow sequence.(2)The improved nonparametric disaggregation model(GJNPDM)and traditional nonparametric disaggregation model(NPDM)have a satisfactory simulation effect when describing the statistical characteristics of mean,standard deviation,variation coefficient and correlation between monthly runoff.Based on the comprehensive consideration of the total and component values on the variables,using the variable kernel correction bandwidth,the boundary impact is reduced.The mean values of the four stations in the improved nonparametric disaggregation model are kept under one mean square deviation standard.By analogy to the standard deviation and first-order autocorrelation coefficient(R1),They are control under the two mean square error criteria in up to 100%.The improved nonparametric disaggregation model is superior to NPDM model in terms of reproducing state-related statistical characteristics and correlation between monthly runoff.(3)In the study area,nonparametric disaggregation model and its improved model can better preserve statistical parameters of monthly streamflow sequence than non-parametric kernel density estimation model or NPL model for each site,which is suitable for the Synthetic simulation of monthly streamflow.(4)The conjugate gradient method,which is based on super-linear convergence,simple formula and small amount of calculation,can be used to solve the Lagrange multiplier of the maximum entropy marginal distribution without making any assumptions,and can be used to simulate non-normal data.Compared with Weibull,GEV and Log-Logistic distribution,the maximum entropy distribution has a better fitting effect upon the marginal probability distribution of the observed monthly streamflow.Additionally,there is no need to make linear assumptions to reflect the statistical characteristics of the actual observed data.Compared with the single Copula function(Clayton Copula,Gumbel Copula and Frank Copula),the mixed Copula function is a better distribution and can fully describe the complicated correlation between monthly streamflow at Yingluoxia station,Huaxian Station,Lintong station and Xiangtou station.In the construct of the maximum entropy-individual copula method,the maximum entropy-mixed copula method performs better regarding preserving the statistical characteristics of the mean,standard deviation and Pearson,Kendell and Spearman correlation coefficients.It can basically reproduce the linear and nonlinear dependences of each month and can be applied to random simulation of the monthly streamflow.