Encounter probability analysis of irrigation water and reference crop evapotranspiration in irrigation district

Based on the data series of the annual reference crop evapotranspiration (ET0) and the amount of irrigation water (IR) from 1970 to 2013 in the Luhun irrigation district, the joint probability distribution of ET0 and IR is established using the Gumbel-Hougaard copula function. Subsequently, the joint probability, the conditional joint probability, and the conditional return period of rich-poor encounter situations of ET0 and IR are analysed. The results show that: (1) For the joint probabilities of rich-poor encounter situations of ET0 and IR, the asynchronous encounter probability is slightly larger than the synchronous encounter probability. (2) When IR is in rich state or ET0 is in poor state, the conditional joint probability is larger, and the conditional return period is smaller. (3) For a certain design frequency of ET0, if the design frequency decreases, the conditional joint probability of the amount of irrigation water will decrease, therefore the encounter probability of them will decrease. (4) For a certain design frequency of the amount of irrigation water, if the design frequency decreases, the conditional joint probability of ET0 will increase, thus the encounter probability of them will increase.