Study On Simulation Of Sediment Load In Wuding River Basin Based On Copula Function

Hydrological forecasts widely used at present are typically deterministic,which usually provide to users in the form of point estimation that ignores the uncertainty and cannot meet the demand of risk information for decision makers.Quantitative description and estimation of the inherent uncertainty of hydrological forecast in terms of probability distribution and the corresponding probabilistic hydrological forecast is not only more scientific and reasonable in theory,but also can increase economic and social benefits.Hydrological forecasting services are now trending toward providing users with probabilistic forecasts instead of traditional deterministic forecasts.Traditional hydrological frequency analysis is based on linear relationships,while the Copula function can describe linear or nonlinear relationships between variables,which get absolute advantages.Therefore,the Copula function theory can be used to explore the uncertainty prediction model.Taking the annual runoff and sediment load of the Wuding River as the research objects,the Copula joint distribution model of the runoff and sediment load characteristic variables of the six measurement stations is established,and the simulation of the sediment load value and its 50%and 90%uncertainty intervals under different runoff is analyzed based on the conditional distribution model.It is expected to provide a theoretical basis for the Wuding River Basin governance planning,water and soil conservation benefit evaluation.This article mainly draws the following conclusions:(1)The PE3 distribution,Gamma distribution and Exponential distribution are used to perform univariate fitting analysis on the runoff and sediment load of each station.The optimal marginal distribution of annual runoff at Baijiachuan,Qingyangcha and Lijiahe stationsis determined is the Gamma distribution function,and the optimal marginal distribution of annual runoff at Dingjiagou,Zhaoshiyao and Suide stations is the PE3 distribution function.The optimal marginal distribution of annual sediment load at Baijiachuan,Zhaoshiyao and Suide stations is the PE3 distribution function,the optimal marginal distribution of annual sediment load at Dingjiagou and Lijiahe stations is the Exponential distribution function,and the optimal marginal distribution of annual sediment load at Qingyang Cha station is the Gamma distribution function.(2)Determine the optimal Copula function for annual runoff and annual sediment load in the study basin.The Copula function can accurately simulate the joint distribution of annual runoff and annual sediment load.Among them,the optimal joint distribution function of annual runoff and annual sediment load at Baijiachuan station,Zhaoshiyao station,Suide station and Qingyangcha station is Frank Copula function;the optimal joint distribution function of annual runoff and annual sediment load at Dingjiagou station,Qingyangcha station is Gumbel Copula function.(3)Established a probability prediction model of annual sediment load based on the Copula function in the Wuding River Basin,simulated the results of annual sediment load under the actual measured annual runoff conditions,and simulated the 50%and 90%uncertainty interval.The simulation results show the probability prediction model which based on the Copula function are reliable,Compared with the traditional power function regression model,the CRPS values of the Copula prediction models at Baijiachuan,Dingjiagou,Zhaoshiyao,Suide,Qingyangcha and Lijiahe stations decreased by 19.37%,14.75%,30.65%,91.13%,54.97%,24.63%.(4)The four hydrological stations S75-100 increased significantly in the magnitude of sediment load delivery at Baijiachuan,Suide,Qingyangcha and Lijiahe station,showing the characteristics of"big runoff versus big sediment load".