Characteristics of drought risk in southern China based on the Copula function

For accurate understanding and analysis of drought characteristics associated with drought hazard, based on the monthly precipitation data of 96 weather stations in southern China from 1961 to 2012, five candidate Copula models of Frank, Clayton, Galambos, Gumbel and Plackett Copula, were used for constructing the joint distribution function of drought characteristics, namely duration and severity. The drought duration follows the Weibull distribution and the drought severity follows the Lognormal distribution.It is found that for the study region, the Frank Copula is the best fitted Copula model compared to the others. Subsequently the conditional probability, conditional return period and spatial joint return period of droughts were also investigated, based on the derived Copula-based joint distribution. The results indicated that, the conditional drought severity distribution is decreased if the drought duration exceeds various thresholds, and so does the conditional drought duration distributions if the drought severity exceeds various thresholds. Both imply that the conditional drought severity distribution and the conditional drought duration distribution are decreased with the increasing drought duration and drought severity, respectively.The conditional return period of drought severity is directly proportional to the duration thresholds, the conditional return period of drought duration is directly proportional to the severity thresholds.Given that the drought duration is 6 months with a drought severity of 6, the primary "and" (viz., both drought duration and drought severity are larger than prescribed thresholds) average joint return period is 4.8 a, the primary "or" (viz., either drought duration or drought severity exceed given thresholds) average joint return period is 2.6 a, and the second "or" average joint return period is 3.5 a.Given that the drought duration is 9 months with a drought severity of 13.5, the primary "and" average joint return period is 12.6 a, the primary "or" average joint return period is 4.7 a, and the second "or" average joint return period is 7.7 a. A high risk can be detected in the Sichuan Basin, the northeastern Guizhou Province, northern Guangxi Province, western Guangdong Province and a larger part of Yunnan Province, and a relative lower drought risk is observed in the northwest of Sichuan Province, the junction of Sichuan with Yunnan and Guizhou Provinces, and the middle parts of Guangdong Province.