| Drought affactes and restricts the economic and social development a lot in humanhistory. Because of its special geography, climate and hydrology characteristics in China,drought has hurt coutries economic development seviouly. Especially in recent years, theshortage of water resources led to unbalance between supply and demand of waterconsumption, this increasingly aggravates the conflict between human and nature in harmonywith each other. Drought has very disadvantageous effects on industry, agricultureproduction,economic construction and social development. Drought also causes the extremelyfragile ecology environment of local area. Accordingly, the theoretical analysis of drought isvery necessary in the arid and semi-arid area in China. Taking Xinjiang region and HeiheRiver basin as representations, meteorological drought variables were extracted by monthlyrainfall datas and hydrology drought variables were extracted by monthly runoff datas toconstruct multivariate joint distributions of drought variables to further do drought analysis.The related research is very important to the study of the evolution rules of drought events.Two and three-dimension joint distributions of drought variables were analyzed based onArchimedean Copulas functions for monthly precipitation at41representative weatherstations in Xinjiang province and at21weather stations in Heihe River basin. The monthlyrunoff data of3hydrologic stations, i.e., Yingluoxia, Liyuan and Zhengyixia in the upstreamregion of Heihe River basin, were also selected for hydrological drought analysis. The bestCopula function was selected by evaluations of goodness of fit to describe rules of droughtevents and to provide theoretical supports for drought prevention and control, reasonableallocation of water consumption, water resources sustainable development, waterconservancy construction project planning and construction in the locality. The followingmain conclusions were drawn:(1)Three drought variables, i.e., drought duration, drought severity and drought peak,were selected by run-length theory from long sequence of average monthly rainfall data inXinjiang region and Heihe River basin as well as average monthly runoff data in Heihe Riverbasin. Relative squared residuals minimization rule(WLS)showed that, for41weatherstations in Xinjiang and21weather stations in Heihe River basin: drought durations areexponential distributed; drought severities are Weibull distributed, while drought peaks are generally Pareto distributed. And for3hydrologic stations in Heihe River basin: droughtdurations of are Pareto distributed; drought severities are subjected to Weibull distribution,while drought peaks are subjected to Gamma distribution. The stations that have a poordegree of fitting were rejected by Kolmogorov-Smirnov (K-S) test of marginaldistributions.For Xinjiang region:Hami city,Tulufan city,Qiemo county,Hetian county andMinfeng county stations were rejected.While for Heihe River basin:Mazongshan,Yumentown,Yongchang,Alashanyouqi,Tuole,Gangcha and Menyuan stations were rejected.(2) The characteristic drought variables must be correlated between each other to useCopulas function to construct theire joint distributions. Through correlation measurement, forXinjiang region, the correlation was strongest between drought duration and drought severity,the next was drought severity and drought peak, while the correlation was weakest betweendrought duration and drought peak. For Heihe River basin based on the basic data at or the21weather stations and3hydrologic stations: the correlation was strong between droughtseverity and drought peak, the next was drought duration and drought severity, while thecorrelation was weakest between drought duration and drought peak.(3) The parameter estimation of Copulas functions for the meteorological and thehydrology drought variables for Xinjiang region and Heihe River basin was conducted.20kinds of two-dimension Archimedean Copulas, Plackett Copulas, Farlie-Gumbei-Morgenstern(FGM) Copulas functions as well as4kinds of symmetric,5kinds of asymmetricthree-dimension Archimedean Copulas functions were analyzed based on fitting curvemethod and maximum likelihood method. The standard of fitting curve method was minimumstandards of squared residuals. AIC, RMSE and Bias as goodness-of-fit assessment indiceswere taken to compare the fitting effects. The results of parameter estimation showed thatfitting curve method was better than maximum likelihood method for Xinjiang region andHeihe River basin. So it was selected to estimate the parameters of Copulas functions.(4)The best Copula function was selected by evaluation of goodness degree for fitting.For Xinjiang region: Frank Copula was the best when it was applied to two-dimension jointdistribution for drought duration-drought severity, and drought duration-drought peak.Clayton Copula was the best for drought severity-drought peak and three-dimension jointdistributions of the three drought variables. For Heihe River basin: FGM Copula was the bestwhen it was applied to two-dimension joint distributions for drought duration-droughtseverity. Nelsen No20Copula was the best for drought duration-drought peak. Nelsen No14Copula was best for drought severity-drought peak and Clayton Copula was the best forthree-dimension joint distribution of the three drought variables.While for3hydrologic stations-Yingluoxia, Liyuan and Zhengyixia in the upstream of Heihe River basin: FGMCopula was the best when it was applied to two-dimension joint distributions for droughtduration-drought severity, and drought duration-drought peak. Nelsen No20Copula wasthe best for drought severity-drought peak and Clayton Copula was the best forthree-dimension joint distribution of the three drought variables.(5)Two and three-dimension joint distribution models were constructed based on thebest Copulas functions, and the associated probability and return period of drought variableswere calculated for Xinjiang region and Heihe River basin. Two-and three-dimensional returnperiods were similar for Xinjiang region and Heihe River basin: the return period of singlevariable ranged between two-dimension joint return period and co-occurrence return period.The co-occurrence return period of the two-dimension, three-dimension was longer than jointreturn period. The co-occurrence return period of the three-dimension was longer than that oftwo-dimension, while the joint return period of the three-dimension was shorter than that oftwo-dimension.(6)Spatial distributions of drought feature variables in Xinjiang and Heihe River basinwere drawn through the conditional probabilities of two-dimensionl and three-dimensionaldrought variables: P(S≤50|D≥4), P(M≤10|D≥4), P(S≤50|M≥10) and P(S≤50|M≥10,D≥4).The spatial distribution characteristics of multivariate drought variables showed that, forXinjiang region,the conditional probabilities of drought events increased from the north to thesouth, meaning the conditional probability of drought events in southern Xinjiang were morelikely to happen than the northern Xinjiang. While for Heihe River basin, the conditionalprobabilities of drought events in the downstream region were more likely to happen than thatof upstream region. |
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