Analysis On The Risk Of Water Shortage In Irrigation District Based On The Copula

With Luhun irrigation area in Henan selected as the research area,in order to improve irrigation water security,from the perspective of water resources shortage casued by the mismatch between water resources supply and demand in irrigation district under changing environments,the joint distribution models of water resources supply and demand are constructed and applied to analyze risk of irrigation water shortage,which provides an important theoretical value and practical significance for optimization of irrigation water structure and drought resisting and disaster alleviation.Based on the annual measured rainfall(P)and irrigation water capacity(IR)and reference crop evapotranspiration(ET0)data series from 1970 to 2013 at the Luhun irrigation district,the correlation between P and ET0 and IR is measured and the univariate marginal distributions of P and ET0 and IR are evaluated by hydrological statistics.The copula-based joint probability distribution(JPD)of pair(P,ET0)and pair(ET0,IR)and pair(P,ET0,IR)are established and applied to calculate and analyze frequency of wetness-dryness encountering,conditional probability distribution and conditional return period of P and ET0 and IR under conditions of the natural water supply,the manual water supply and the natural-manual water supply,respectively.The following are main results.(1)The consequence of the K-S test employed to identify the assumed marginal distributions reveals that P and IR both obeys the normal distribution and ET0 follows generalized extreme value distribution.(2)The results of correlation analysis indicates there is positive correlation between pair(ET0,IR),negative correlation between both pair(P,ET0)and pair(P,IR).Thus,the five kinds of bivariate copulas are employed to construct the bivariate JPD of pair(P,ET0)and pair(ET0,IR),with their parameter ? estimated by the relations between ? and Kendall's rank coefficient ?.Moreover,the five kinds of ternary copulas are developed to construct JPD of pair(P,ET0,IR)to describe their associated dependence structure,with maximum likelihood method applied to the parameter estimation.The adaptive copula functions are identified by K-S test.The minimum deviation square(OLS)and the akaike information criterial(AIC)are employed to evaluate the goodness-of-fit of copula function.The results indicates that the student t-copula copula function gives a better fit than the other four copulas,when employed to construct not only the bivariate JPD of pair(P,ET0)and pair(ET0,IR),but also the trivariate JPD of pair(P,ET0,IR).(3)The two categories of joint probability of different combination events between P and ET0 and that between ET0 and IR can be qualified by the application of JPD of pair(P,ET0)and pair(ET0,IR),respectively.Additionally,the same joint probability can correspond to different composite events.The analysis of transient joint probability of wetness-dryness encountering of P and ET0 and that of ET0 and IR shows among the encounter probabilities of rich-poor state between P and ET0 and that between ET0 and IR,the subtotal value of the asynchronous encounter probability(AEP)is greater than the three-fold of the synchronous encounter probability(SEP).An analysis of conditional probability and return period of P and ET0 reveals compared with other states,the higher conditional probability and the shorter conditional return period exist in either poor P or rich ET0.An analysis of conditional probability and return period of ET0 and IR reveals that larger conditional probability and shorter conditional return period arise in either rich IR or poor ET0 compared with other states.(4)The three-demensional joint probability of different combination events among P,ET0,and IR can be qualified by the application of JPD of pair(P,ET0,IR).Additionally,the same joint probability can correspond to different composite events.An analysis of transient joint probability of wetness-dryness encountering of rainfall and ET0 and IR shows among the encounter probabilities of rich-poor state,AEP is slightly greater than SEP.Under conditions of natural-manual irrigation water supply,an analysis on the two-dimensional conditional probability and the corresponding recurrence period reflecting water shortage indicates for a specific poor IR(or poor P,or rich ET0),the encounter probability of composite events of P and ET0(or IR and ET0,or IR and P)can be obtained.An analysis on the one-dimensional conditional probability and the corresponding recurrence period reflecting water shartage shows the relatively low conditional probability and fairly long conditional recurrence period arise in extreme water shortage events(P and IR are poor and ET0 is rich).