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中文摘要：
应用椭圆copulas描述干旱多变量间的相依性结构。采用Pearson＇sγn、Spearman＇sρn、Kendall＇sτn、秩相关图、Chi-plot和K-plot度量2变量相依性;根据极大似然法估计3维copulas的参数,并以AIC、BIC和RMSE进行copulas拟合效果评价;运用基于Rosenblatt变换的Bootstrap法进行Gaussian copula和Student t copula的拟合度检验;选择Gaussiancopula描述干旱历时D、烈度S、和峰值P的联合概率分布,探讨渭河流域干旱重现期的空间分布规律。研究表明：①3维Gaussian copula和Student t copula均适合用来描述干旱多变量联合概率分布,且前者拟合效果优于后者;②渭河流域发生较长时期持续干旱的频率高、重现期短,应加强干旱预报与管理。
英文摘要：
This study aims to model the dependence structures of multivariate drought variables using elliptical copulas.Bivariate dependence was estimated with Pearson′s classical correlation coefficient γn,Spearman′s ρnand Kendall′s τn,together with rank scatter plot and Chi-plot and K-plot,while parameters of trivariate copulas were estimated with the maximum likelihood method.For best-fitting of these copulas,Akaike information criterion（AIC）,Bayesian information criterion（BIC） and RMS error（RMSE） were used,and a bootstrap version of Rosenblatt′s transformation was used to test goodness-of-fit for Gaussian copula and student t copula.In application to the Wei River basin for determination of its spatial distribution of drought return periods,Gaussian copula was selected for modeling the multivariate joint probability distribution of its drought duration,drought severity and severity peak.The results show that both Gaussian and student t copulas are applicable,but Gaussian copula gives better fitting.In the basin,prolonged droughts had frequently broken out with rather short return periods and thus more emphases should be placed on drought forecast and management in the future.
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