The Multiple Time Scales Of Hydrological Drought Frequency In Fenhe River Upper Reaches Based On Copula

Drought is the second most important natural disaster in the world, it is also one of the most important meteorological disasters in China. Over the past few years, the drought had been showing a rising frequency and increasing the loss,which had seriously restricted the economic development of our country. Water resource was a kind of dynamic resource which had a certain periodicity. But water resource was affected by such as atmospheric circulation, solar radiation,human activities, physical geography and many other uncertain factors in the process of circulation. Thus water resource also showed a certain multiple time scales characteristics. Therefore hydrologic drought which based on the monthly runoff data also showed a certain periodicity and multiple time scales characteristics. This paper attempts to combine the ensemble empirical mode decomposition method with Copula function theory, and apply it to the frequency and characteristics analysis of hydrological drought. Subsequently,the regulations of drought occurrences in the basin were analyzed, which has great significance and guidance to water resources rational allocation, theplanning and design of water conservancy project, as well as to drought control and disaster mitigation. The main conclusions drawn from this study are as follows:(1) In Shangjingyou, Fenhe reservoir, Zhaishang and Lancun hydrological station, the evolution of the nature monthly runoff contains 8 IMF components and a trend term. From the IMFs, the nature monthly runoff of Shangjingyou may exist several cycles such 2.83 months, 5.24 months, 7.50 months, 14.80 months, 27.23 months, 55.53 months, 85.81 months, 259.65 months; the nature monthly runoff of Fenhe reservoir may exist several cycles such 2.85 months,5.91 months, 7.80 months, 18.56 months, 29.32 months, 52.99 months, 80.47 months, 231.92 months; the nature monthly runoff of Zhaishang may exist several cycles such 2.81 months, 5.60 months, 7.06 months, 18.37 months,27.75 months, 55.42 months, 85.99 months, 214.33 months; the nature monthly runoff of Lancun may exist several cycles such 2.74 months, 5.17 months, 7.43 months, 16.66 months, 24.94 months, 67.34 months, 87.14 months, 96.55 months.(2) 11 probability distribution functions were adopted to analyze the drought duration(D), drought severity(S) and drought severity peak(M)variables probability behaviors and then through the Kolmogorov-Smirnov(K-S)test to obtain the optimal marginal distributions. The results show that: most of the drought durations are subjected to extreme value type Ⅰ distribution, while most of the drought severity and drought severity peaks are subjected togeneralized extreme value distribution.(3) Through the correlation coefficient calculation between drought variables, the results show that: there are certain relationships between the drought duration(D), drought severity(S) and drought severity peak(M). The correlation between the drought severity(S) and severity peak(M) is the highest,the correlation between the drought duration(D) and severity(S) is in the middle, while the correlation between the drought duration(D) and severity peak(M) is the lowest.(4) Clayton Copula, GH Copula, AMH Copula and Nelson NO.2 Copula the four symmetric Archimedean Copulas were applied to construct the two-dimensional joint distribution of drought variables. The correlation index method was applied to the parameter estimation. Take RMSE, AIC and BIC as goodness-of-fit assessment indicators to select the optimal two-dimensional joint distribution. The results show that: Clayton Copula was revealed to have the best fit results for the four hydrological stations in Fenhe river upper reaches; while AMH Copula was revealed to have the worst fit results.(5) Clayton Copula, GH Copula, AMH Copula and Frank Copula the four symmetric Archimedean Copulas were applied to construct the threedimensional joint distribution of drought variables. The fitting curve method was applied to the parameter estimation and RMSE was taken as the curve fitting criteria. Take AIC and BIC as goodness-of-fit assessment indicators to select the optimal three-dimensional joint distribution. The results show that: ClaytonCopula was revealed to have the best fit results among the drought variables of the four hydrological stations in Fenhe river upper reaches; while AMH Copula was revealed to have the worst fit results.(6)The drought return periods of four stations in Fenhe upper reaches exhibit a certain rules: under drought characteristic variables constant, the threedimensional co-occurrence return periods is larger than the two-dimensional co-occurrence return periods; the two-dimensional co-occurrence return periods is larger than the univariate return periods; univariate return periods is greater than the two-dimensional joint return periods; the two-dimensional joint return periods is larger than three-dimensional joint return periods.