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The potential of the copula method to construct the joint probability distribution of three hydrological variables characterizing water supply and demand (WSD) is explored for the Luhun irrigation district of China. The marginal distributions of rainfall, reference crop evapotranspiration (ET0) and irrigation water are simulated by the corresponding best-fitting cumulative distribution functions. Furthermore, the correlations between every pair of variables are quantified. On this basis, the two-dimensional joint distributions of rainfall and (ET0) (representing natural WSD), and irrigation water and (ET0) (representing man-made WSD), and the three-dimensional joint distribution of rainfall, irrigation water, and (ET0) (representing natural–man-made WSD) are established. The results reveal that the best-fitting marginal distributions for rainfall and (ET0) and irrigation water are the normal distribution and the Weibull distribution. Moreover, for rainfall and (ET0), the Student's t copula is applied to obtain the joint distribution, while the corresponding copula for (ET0) and irrigation water is the Clayton copula. Finally, the three-dimensional Student's t copula is selected to explore the dependence structure among rainfall, irrigation water, and (ET0). Therefore, these joint distributions provide an efficient approach to assess water shortage risks in the irrigation district.

Copula-based joint probability distribution of water supply and demand in Luhun irrigation district