This study aims to model the joint probability distribution of periodic hydrologic data using meta-elliptical copulas. Monthly precipitation data from a gauging station (410120) in Texas, US, was used to illustrate parameter estimation and goodness-of-fit for univariate drought distributions using chi-square test, Kolmogorov-Smirnov test, Cramer-von Mises statistic, Anderson-Darling statistic, modified weighted Watson statistic, and Liao and Shimokawa statistic. Pearson's classical correlation coefficient r n , Spearman's q n , Kendall's s, Chi-Plots, and K-Plots were employed to assess the dependence of drought variables. Several meta-elliptical copulas and Gumbel-Hougaard, Ali-Mikhail-Haq, Frank and Clayton copulas were tested to determine the best-fit copula. Based on the root mean square error and the Akaike information criterion, meta-Gaussian and t copulas gave a better fit. A bootstrap version based on Rosenblatt's transformation was employed to test the goodness-of-fit for meta-Gaussian and t copulas. It was found that none of meta-Gaussian and t copulas considered could be rejected at the given significance level. The metaGaussian copula was employed to model the dependence, and these results were found satisfactory.

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Based on ten indices of extreme precipitation and one drought index (composite index, CI), the trends in extreme events were investigated using a Mann-Kendall non-parametric method at 39 stations in the Songhua River Basin (SHB) during 1960-2013. The regionally averaged wet-day precipitation (PRCPTOT) increased at a rate of 1.65 mm/year (R 2 = 0.28, P = 0.13), in which 82% of the stations experienced increases, but only 4 stations showed significant positive trends. The annual R95 and R99 exhibited slight upward trends at rates of 1.37 (R 2 = 0.21, P = 0.27) and 1.28 mm/year (R 2 = 0.23, P = 0.23) over the last 54 years; however, there were not significant trends in R95 and R99 at the 0.05 level. PRCPTOT, R95 and R99 showed similar spatial trends, in which positive trends mainly occurred in the northern and southeastern basins. The trends in the maximum 1-day precipitation (RX1day) and maximum 5-day precipitation (RX5day) do not show a prevalent trend (approximately 50% of the stations have a positive trend and the remaining stations have a negative trend). The simple daily intensity index (SDII) significantly decreased at an annual rate of 0.02 mm/d during 1960-2013 (R 2 = 0.66, P b 0.01); spatially, 49% of the stations experienced statistically significant decreases at the 0.05 level based on the Mann-Kendall non-parametric test. The regionally averaged heavy (R10mm) and very heavy precipitation days (R20mm) and consecutive wet days (CWD) showed no significant trends during the past 54 years; however, several individual extreme precipitation events, such as the flood of 1998 in the SHB, were well detected by these indices. The regionally averaged consecutive dry days (CDD) significantly increased (R 2 = 0.79, P b 0.01) at a rate of 0.22 days/year from 1960 to 2013. All of the stations exhibited statistically significant increases in CDD, excluding the Tongyu station in the western basin. The monthly RX5day values were highest in summer, from June to August, in the SHB; a peak occurred in July (67.5 mm) in the SHB during 1960-2013. The CI peaked in July, with the highest value of 0.2 in the SHB during 1960-2013. However, the two lowest CI values occurred in spring and fall, with values of −0.56 and −0.41, respectively. During April and May, when most of the spring drought events occur, a prevalent trend does not exist; moreover, almost no stations have statistically significant CI increases. In August and September, respectively 79% and 97% of the stations exhibited a CI negative trend, but only 2 and 6 stations showed significant decreases at the 0.05 level. The increasing extreme climate events present a challenge for local water resources management.

This study aims to model the joint probability distribution of drought duration, severity and inter-arrival time using a trivariate Plackett copula. The drought duration and inter-arrival time each follow the Weibull distribution and the drought severity follows the gamma distribution. Parameters of these univariate distributions are estimated using the method of moments (MOM), maximum likelihood method (MLM), probability weighted moments (PWM), and a genetic algorithm (GA); whereas parameters of the bivariate and trivariate Plackett copulas are estimated using the log-pseudolikelihood function method (LPLF) and GA. Streamflow data from three gaging stations, Zhuangtou, Taian and Tianyang, located in the Wei River basin, China, are employed to test the trivariate Plackett copula. The results show that the Plackett copula is capable of yielding bivariate and trivariate probability distributions of correlated drought variables.

This study aims to investigate the changing properties of drought events in Weihe River basin, China, by modeling the multivariate joint distribution of drought duration, severity and peak using trivariate Gaussian and Student t copulas. Monthly precipitations of Xi'an gauge are used to illustrate the meta-elliptical copula-based methodology for a single-station application. Gaussian and Student t copulas are found to produce a better fit comparing with other six symmetrical and asymmetrical Archimedean copulas, and, checked by the goodness-of-fit tests based on a modified bootstrap version of Rosenblatt's transformation, both of them are acceptable to model the multivariate joint distribution of drought variables. Gaussian copula, the best fitting, is employed to construct the dependence structures of positively associated drought variables so as to obtain the multivariate joint and conditional probabilities of droughts. A Kendall's return period (KRP) introduced by Salvadori and De Michele (2010) is then adopted to assess the multivariate recurrent properties of drought events, and its spatial distributions indicate that prolonged droughts are likely to break out with rather short recurrence intervals in the whole region, while drought status in the southeast seems to be severer than the northwest. The study is of some merits in terms of multivariate drought modeling using a preferable copula-based method, the results of which could serve as a reference for regional drought defense and water resources management.