The joint distribution of reference crop evapotranspiration and irrigation water in the irrigation district

For the irrigation district, irrigation water is the manual water supply for the farmland while reference crop evapotranspiration (ET0) reflects water demand. Thus, the joint distribution of irrigation water and ET0 can reveal water shortage risk under the condition of the manual water supply. In order to understand their relationships and overcome the drawbacks of different marginal distributions of hydrological variables, Archimedean copulas are introduced. Based on the data series of ET0 and irrigation water in the Luhun irrigation district of China, the univariate marginal distributions of ET0 and irrigation water are first selected. Then, with the Gumbel-Hougaard copula in the Archimedean copulas, the joint distribution of ET0 and irrigation water is proposed. The results show that the best-fitting marginal distributions of ET0 and irrigation water are generalized extreme values and normal distributions, respectively, but for their joint distribution, the Gumbel-Hougaard copula is the best-fitting one. The water shortage risks with different encounter situations of ET0 and irrigation water are better revealed using the proposed copula-based joint distribution.