Using the copula method, the joint probability distribution of irrigation water volume and efficiency is constructed, and their joint return period is also described to reveal the encounter probability of irrigation water volume and efficiency. Furthermore, the conditional probability of irrigation water efficiency with different water volumes is built to show the quantitative effects of flow on irrigation water efficiency. The results show that the copula-based function can present the encounter risk and conditional probability of irrigation water volume and efficiency at their different magnitudes.

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