Abstract
The relationship between rainfall and reference crop evapotranspiration (ET0) can be complex in an irrigation district. To reveal such complex and possibly a nonlinear relationship, rainfall and ET0 data were collected at the Xinxiang irrigation experiment station from the years 1961 to 2010. Marginal distributions of the two variables derived from fitting the Pearson Type III distribution were incorporated for the development of the joint probability distribution using a copula model. Subsequently, the joint probability as well as the return period of given specific rainfall and ET0 values can be computed. For the analysis of the variations in drought conditions over the 50 years, the copula-based joint probability is further decomposed into several subcomponents using the empirical mode decomposition method. The variations under distinct frequencies and over different time periods were observed. Our results showed that the joint probability distribution of rainfall and ET0 can facilitate the planning for drought resistance in an irrigation district.
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