Research On Multivariate Hydrological Drought In Heihe Basin Based On Copulas Function

Hydrological drought refers to the sharp decrease of available water in land circulation,which is reflected in the decrease of runoff in hydrological variables and the decrease of lake water level,reservoir water level and underground water level.As an important type of natural drought,hydrological drought affects the process of water cycle.At present,most of the hydrological drought indexes take runoff as drought variable and do not consider groundwater,these can not fully reflect the actual hydrological drought,especially in the northern region where groundwater is an important source of water.The construction of multi-factor hydrological drought index based on runoff and groundwater and the analysis of the evolution characteristics of hydrological drought play an important role in regional drought control and drought relief.This paper takes Heihe river basin,the second largest inland river in China,as the research object.The variation characteristics of runoff and groundwater level were analyzed.The optimal distribution function of the variables series of runoff in different months and groundwater level difference at different observation wells were fitted using 61 distribution functions.The standard runoff drought index and the groundwater drought index were calculated and the comprehensive hydrological drought index which is taken into account runoff and groundwater was structured using the weight method in the midstream.According to the run-length theory,three drought characteristic variables were identified.The evolution characteristics of the hydrological drought were analyzed from three aspects of the drought index,the drought level and the drought characteristic variable.The multivariable joint distribution of the hydrological drought was constructed by using Copulas function,and the probability and recurrence period of drought characteristic variables were analyzed.The following main conclusions were reached:(1)The midstream runoff shows an increasing trend as a whole,and the annual runoff changes greatly.The downstream annual runoff decrease continuously before 1990 but shows an increasing trend after 1990.And both of them are in a high concussion after 2005.The annual average groundwater level shows an extremely obvious decreasing trend as a whole,in which the annual average groundwater level continue to decline before 2005 but shows an upward trend after 2005.The conversion of surface water and groundwater is frequent in the midstream.Therefore,it is necessary to construct a comprehensive droughtindex considering runoff and groundwater for the study of hydrological drought in the midstream.(2)The optimal distribution of monthly runoff in Yingluoxia is Burr with 3 or 4parameters while in Zhengyixia is Weibull with 2 parameters.The optimal distribution of groundwater level difference is mainly Burr and Cauchy.The hydrological drought index in the midstream shows a significant increasing trend and has a sudden change around 2006,while the hydrological drought index in the downstream shows a significant decreasing trend and has a sudden change around 1975.The major period of hydrological drought index changes in the midstream is the time scale of 2 years.The first major period of hydrological drought index changes in the downstream is 2 years time scale,and the second major period is 18 years time scale.(3)Both in the midstream and the downstream,there are little difference in the proportion of each month in a certain drought grade.The main drought occurred in the midstream is light drought,the proportion of moderate drought is relatively small,serious drought and special drought are basically not occurred.While the main drought occurred in the downstream are light drought and moderate drought,the proportion of serious drought is relatively small,special drought is basically not occurred.The probability of drought occurred in the midstream increases first and then decreases and reaches its maximum in the1990 s,in which the proportion of light drought changes the most.There is an overall increase in the probability of drought in the downstream,the ratios of light and moderate drought increase greatly,while the proportion of serious drought decrease but the range is small.There is little difference in the duration of drought between the midstream and the downstream,but the drought intensity and the peak intensity of downstream are larger than those of the midstream.The duration of drought events in the midstream is mostly less than5 months,and the drought that last more than 5 months has occurred only 2 times.The degree of drought occurred in the downstream is more seriously than that in the midstream,mainly characterized by long duration and high intensity.(4)There is a significant correlation between the drought characteristic variables in the midstream and downstream.The optimal Copula function for the joint distribution of D-S,D-M,S-M and D-S-M in the midstream is Joe,Gumbel,Frank and Frank Copula respectively.In the downstream,the optimal Copula function is Joe,Frank,Clayton and Frank Copula respectively.And the fitting effects are all better.The recurrence period of the light drought event which last about 4 months is about 10 years in the midstream,and the recurrence period of the serious drought event which last about half a year is about 11 yearsin the downstream.Compared with the midstream,the downstream drought events are mainly characterized by long duration and high intensity.