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.