Precipitation Monitoring Network Optimization Based On Spatial Information Balancing Model And Integrated Entropy-Copula Model

Precipitation monitoring networks provide fundamental data for hydrometeorological research and hydraulic engineering,which is of vital importance for water resources management,reservoir operation and flood forecast.In order to improve the information collecting efficiency,it is necessary to scientifically design and optimize the network.Entropy can quantify the information transferred by monitoring stations,which has been widely used for network optimization.Copula functions,as a method for multivariable joint distribution fitting,can be integrated with entropy for entropy index estimation,which avoids the uncertainty caused by previous discretization methods.This study focused on the improvement of entropy-based optimization models and the computation of entropy indexes.Currently,several entropy-based network optimization criterions with varying standards have been presented,and there is a lack of a comparative study under identical geographical conditions.This study summarized four typical entropy criterions,and applied them to the precipitation network of the Zhexi area in the Taihu Lake basin;then compared the ranking and frequency of prioritized stations under different criterions as well as their distribution,and discussed the effect of the discretization method.Most prioritized stations were located at the edge area,which was adverse to the observation of rainfall with large spatial-temporal variation in the mountains,especially rainstorms.Therefore,it is necessary to improve the current optimization approaches to obtain more reasonable network schemes.By combining entropy-based criterions with the network layout,this paper established a spatial information balancing(SIB)model for precipitation monitoring network optimization.First,the area was divided and recombined through Thiessen polygons.Then with the “node-station group” as a basic unit,the information efficiency coefficient(IEC)in different sub-areas was evaluated according to their information capacity and redundancy,and the “peak/valley nodes” were identified.Finally,optimization schemes were formed by adding or removing stations around the identified nodes.SIB model was applied to the precipitation network of the Zhexi area.The generated optimization schemes could allocate more stations in the mountainous area with large spatial-temporal precipitation variation and areas with sparse existing stations,which was effective for spatial information balancing.The number and location of added and removed stations varied with the IEC threshold as well as the discretization method.To improve the computation of entropy indexes,this paper proposed an entropycopula integrated approach,which estimates the information capacity and redundancy indexes through the principle of maximum entropy(POME)and copula-based joint distribution fitting.Accordingly,optimization models HI-TI and H-T were established and applied to precipitation monitoring networks of the Zhexi area and the Beijing city.Among the 5 copula families used,Gumbel,Frank and Normal copula could better fit the joint distribution of the precipitation series.Prioritized stations performed well in restoring the spatial rainfall distribution of typical precipitation events,and more stations were required for the restoration of heavy rainfall events;prioritized stations derived from flood season data performed better for rainstorm events.The innovation points of this study can be concluded as:(1)The study established an optimization model based on the idea of spatial information balancing,and proposed the information efficiency coefficient index(IEC),the concept of “peak/valley node”,and corresponding schemes of adding/removing stations.Compared with the current “multi-objective criterion + Prato solution” mode,SIB model integrated the network layout,which could intuitively present the optimization process,and remained space for decision-making participation.(2)The study proposed an entropy-copula integrated approach for entropy index computation and established corresponding network optimization models.POME was adopted to obtain marginal entropy under the maximum entropy distribution;copulas were introduced to fit the dependence structure of precipitation series to obtain stable mutual information estimates.The approach could avoid the subjectivity and uncertainty of current discretization methods.