珠江三角洲Copula径流模型及西水东调缺水风险分析

基于两变量Copula函数模拟、变点识别和均值平移时序重构方法，构建珠江三角洲西水东调工程受水区东江和水源区西江的枯水径流联合分布模型。以生态环境流量及最小流量管理目标为设计阈值，研究区域联合缺水风险特征及对变化环境的响应。结果表明：Archimedean copula的Clayton、Frank和GH模型，均能较好地模拟两区域枯水径流联合分布特征。变化环境下特别是流域内水利工程径流调节作用，东江枯水径流时序非一致性显著，均值跳跃明显，变点时间为1972年，最枯月径流量增加了65.5%。若要满足最小下泄流量管理目标，东江缺水风险率较高，为37.7%。与东江天然径流（还原系列）相比，在东江流域内水利工程影响下（还现系列），东、西江同时缺水风险率由35.8%下降到16.7%。但由于2江枯水径流的正相关性，西江有水可调保证率也由54.8%下降到21.0%。在已知东江缺水情形下，西江有水可调保证率（55.8%）仅略高于西江缺水风险率（44.2%）。因此，珠江三角洲西水东调工程运行，需要科学设计更为精细的水资源调度规则。

Copula runoff model and risk of water shortage in west-to-east water transfer of Pearl River Delta, China

Abstract: In the implement of water transfer project, it is essential to build the joint distribution model of low flow between the inflow and outflow region and to analyze the risk of water shortage or the assurance of water resources in the outflow region when water shortage occurs in the inflow region. In the paper, the goodness-of-test approach based on the Cramervon Mises statistics of the Rosenblatt transfer was applied for modeling bivariate joint distribution. The analysis of change point and the method of mean shift were used for reconstruction of time series of low flow. Joint distribution modeling of low flow between the inflow and outflow regions of the Project of West-to-East Water Transfer of the Pearl River Delta was built. According to the predefined thresholds set by the instream ecological flow and the lowest flow of water demand, individual and joint risks of water shortage in the inflow and outflow regions and their alterations under changing environment were investigated. Results demonstrated that Archimedean copulas, i.e. Clayton, Frank and Gumbel-Houggard models were better for modeling the joint distribution of low flow between the inflow and outflow regions. The change point of the low flow in the inflow region occurred in 1972, but there was no difference in the selection of copulas and their parameters on modeling the joint distribution of the inflow and outflow regions, regardless of using any one of the reconstructive time series, namely the forward and backward returned series. The lowest monthly stremflow in terms of mean value increased by 65.5% under changing environment, in particular the regulations of water reservoirs in the inflow region. In consequence, individual risks of water shortage in the inflow region and joint risks between the inflow and outflow regions remarkably decreased. However, the risk rate still accounted for 37.7% provided that the instream flow fulfilled the water demand in the inflow region. Though the joint risk rate decreased from 35.8% to 16.7% associated with the regulation of water reservoirs in the inflow region, the assurance rate decreased from 54.8% to 21.0% due to the positive dependence of low flow between the inflow and outflow regions. As water shortage in the inflow region was known, the assurance rate of water resources by 55.8% in the outflow region was slightly greater than its risk rate of water shortage (44.2%). In addition, the risk rate of water shortage in the outflow region accounted for 38.2% in case of maintaining its instream flow. Thus, it needs to be poured more attention how the specific regime of water resources regulation is put forward for the operation of the Project of West-to-East Water Transfer of the Pearl River Delta in the future, even though much more water in the outflow region than in the inflow region.