3维干旱变量联合概率分布研究

Study on 3D Arid Variable Joint Probability Distribution

研究多变量干旱特性联合分布的推求方法。选择干旱历时、干旱烈度和烈度峰值为水文干旱特性变量。单变量的边际分布参数分别采用矩法、概率权重法、极大似然法和遗传算法进行计算和优化。应用检验、Kolmogorov-Smirnov等6种检验法进行单变量分布的拟合度检验。采用Pearson’s古典相关系数,Spearman秩相关系数,Kendall’s,Chi-Plots和K-Plots进行变量间的相依性度量。选择4种常用的3维Archimedean Copula函数进行干旱特性变量联合分布拟合。根据RMSE、AIC和BIC准则选择最优copula。在此基础上,采用基于Rosenblatt变换的Bootstrap法进行3维copula的拟合度检验。模型应用于渭河流域北洛河状头站径流序列,结果表明:Gumbel-Hougaard copula拟合效果最好,可以描述洛河状头站3维干旱变量的联合分布。

Study variables Method of Deriving the joint distribution of drought characteristics.Which select drought duration,drought intensity and the intensity peak is belong to hydrological drought characteristics variables.For univariate marginal distribution parameters,the moment method,the probability weighting method,the maximum likelihood method and genetic algorithm are applied to calculate and optimize.The article is based on application of the test,Kolmogorov-Smirnov and other 6 methods to test the single variable distribution of the goodness of fit.Application of Pearson's classical correlation coefficient,Spearman's rank correlation coefficient,Kendall's Chi-Plots and K-Plots carry on dependencies metrics between the variables.Choose four kinds of commonly used three-dimensional Archimedean Copula functions and carry on arid characteristics of variable joint distribution fitting.It is based on RMSE,AIC and BIC criteria to select the optimal copula.Bootstrap method based on the Rosenblatt transformation Square test of three-dimensional copula,the model is applied to the Beiluo shaped head station runoff series of Weihe River.The result shows Gumbel-Hougaard copula fitting effect of the best,you can describe the joint distribution of Luohe shaped head station three-dimensional arid variable.