Application Of Pair-copulas Functions In Drought Characteristics Analysis

Based on the stochastic theory, mathematical statistics and copula theory, the monthlyrainfall of90Gauging stations in Wei River Basin were selected and analyzed. Apply Frank,Clayton, Gumbel-Houggard and Ali-Mikhail-Haq copula functions to construct jointdistribution of two dimensional drought characteristics, and construct joint distribution ofthree-dimensional drought characteristics by the pair-copula decomposition. These functionswere used to analyze the drought statistical properties and occurrence patterns of regionaldrought characteristics, which Expected to provide practical guidance meaning to the regionalwater resources allocation, the water conservancy project planning and design andmanagement, the industrial and agricultural economy development. The main conclusions ofthis paper are as follows:(1) Applying the run-length theory, and use the average monthly rainfall as threshold, weselect drought duration(LS), drought intensity(LD) and intensity peak(FZ) for droughtvariables. Pearson linear correlation coefficient, Spearman correlation coefficient and Kendallrank correlation coefficient were used to analyze the dependencies of LS-LD, LS-FZ, andLD-FZ, the results showed that the positive correlation ts are displayed among variables ofdrought characteristic, the correlation of LD-FZ is the highest, LS-LD is following, the worstis LS-FZ.(2) The optimal distribution may be different from each site of Studied regional. Foroverall consideration, drought duration is followed exponential distribution, drought intensityis obeyed gamma distribution with two parameters, and generalized Pareto distribution hasthe most optimal simulation of intensity peak.(3) Using maximum likelihood estimate, Frank, Clayton and Gumbel were constructed tothe pair-copula functions, which could fitted empirical probability well, except for AMHcopula. At the confidence level is0.05, under Rosenblatt transformation based on Bootstrapmethod, we used A-D test, K-S test and C-M to test joint distribution of two-dimensional andthree-dimensional drought characteristic variables, the results show that, the selectedpair-copula function can be accepted.(4) Through Using the RMSE, AIC and BIC evaluation, the results show that, for theentire basin sites, Frank copula constructed the pair-copula has a better fitting. The secondbest copulas are Clayton and Gumbel copulas, while the fitting effects have no obvious difference. Beside AMH copula, thethree pair-copulas are all may be the optimal copulafunction for one site.(5) The results of multivariate joint (conditional) return period show that, the jointexceedance (non exceedance) return period is less than co-occurrence exceedance (nonexceedance) return period. In two dimensional joint distribution, given a variable is less thanor equal to a constant value, the conditional not exceeding probability are greater than thatwhen there has one variable is greater than a certain value, while the conditional exceedingprobability is the opposite. In the three-dimensional joint distribution, co-occurrence returnperiod is greater than the joint return period; given a variable is greater than a certain value,the other two variables' co-occurrence conditional surpassed return period is greater than thatwhen there has one variable is less than a certain value, joint conditional surpassed returnperiod is also has this property; given two variables are less than or equal to certain values,the conditional return period is less than that when there have two variables are greater thancertain values.(6) Based on the ArcGIS software, using Frank copula function as an example, weanalyze spatial distribution of the co-occurrence probability (LS>3, LD>120) andco-occurrence not exceeding probability (LS <3, LD <120), as well as study spatialdistribution of three dimensional probability (LS <3, LD <100, FZ <40), and return period(LS>3, LD>100, FZ>40),(FZ>40, LD>100|LS>3),(FZ>40or LD>100|LS>3),(FZ>40|LS>3, LD>120),(FZ>40|LS <3, LD>120), to aim to made more intuitiveunderstanding of drought characteristics for further study in regional drought.(7) Based on the Matlab software, application interface modules of drought variablesintercept, correlation analysis, marginal distribution study,2D joint characteristic analysis and3D joint characteristics analysis were devloped, realized the visual operation of the dataprocessing, simplified data analysis process, given convenience to the related study.