Application Of CEM Model And KCEM Optimization Model In Hydrometric Network Design

Relatively accurate and systematic data sources is essential for the design,planning and construction of hydraulic engineering projects.The modern hydrological gauge network established should cover real-time and effective information for water resources management,reservoir operation,flood control and forecasting.A systematic gauge network is able to meet the demands of different users and alleviate the expenditures and resources for the sake of socioeconomics perspective.As a result,optimization design of hydrometric network should adopt the principle of optimal information and minimum estimation error to add and delete existing network.Different research methods can be adopted on the basis of different optimization targets of the network.The focus of this study is to establish two evaluation models of the network respectively from the perspective of information theory and estimation accuracy of the network:CEM model and KCEM model.CEM represents the copula entropy-based two phase multiobjective optimization approach.Copula entropy theory used in this paper helps to solve the core problem of high dimensional information index objectively.The proposal of copula entropy-based multiobjective hydrological net,work model aims to figure out the best choice of network design.The employed copula entropy based multiobjective optimization approach,including:(1)copula entropy-based directional information transfer(CDIT)for clustering the potential hydrometeorological network into several groups,and(2)multiobjective method for selecting the optimal combination of gauges for regionalized groups.The proposed model was applied into the optimal design of streamflow stations in Yiluo River.With the help of performance checking indices(NSC,MNCE and MNCE),results indicate that the two-phase copula entropy-based multiobjective technique is capable of evaluating the performance of regional hydrometeorological network which enables decision makers to develop strategies for water resource management.The former model is only evaluated from the perspective of the optimal total information of the station network,without considering the influence of the estimation precision of the station network.So this paper also developed a kriging and copula entropy-based model(KCEM model)for designing an optimal rain gauge network which can reduce the kriging variance for either areal or point rain estimates across the watershed and at the same time achieve the optimum rainfall information by optimally redesigning(discontinuing)some overlapping stations as well as optimizing the installation of augmented gauges.The model is actually applied in the raingauge network of Shanghai,China.This research innovatively proposed the NI-KSE criterion and take 4 usual variogram models(Exponential,Spherical,Gaussian and Matern models)into consideration.According to the results of cross validation statistics,the spatial characteristics and pattern of all the sample data in the simulated area can be achieved by the best fitted variogram model with the smallest residual sum of squares(SSERR).The proposed NI-KSE based criterion combines the spatial interpolation and information theory to choose the optimal gauge combination which can improve the estimation error based on the final station combination results.The main innovative points can be concluded as follows:(1)The two-phase copula entropy-based multi-objective network optimization model was firstly adopted.The estimation of mutual information and total correlation is beneficial from the flexibility of the copula function and the idea of two stage helps to solve the curse of dimensionality and regionalize the present stations into several groups.Before the calculation of copula entropy,semiparametric approach-based(SP)copula function selection and Cramer-von Mises Statistics is proposed to determine the appropriate Archimedean Copula,which is expanded to the high dimensional case.And the results also recommend the outstanding response.(2)The firstly proposed NI-KSE based criterion combines the spatial interpolation and information theory to choose the optimal gauge combination which can improve the estimation error,and enhance the transmitted information capacity,joint information and alleviate the redundancy in the network(i.e.optimum total net information content)at the same time.Also optimization results helps verify the reasonability of kriging and entropy combined method.