Study on Markov Joint Transition Probability and Encounter Probability of Rainfall and Reference Crop Evapotranspiration in the Irrigation District

<Para ID="Par1">Based on the markov theory, the first-order markov joint transition probability of rainfall and reference crop evapotranspiration is analyzed to reveal their joint transition laws. Then using copula function, the joint probability distribution of rainfall and reference crop evapotranspiration is built, and the conditional probabilities of rainfall and reference crop evapotranspiration are also presented. The results show that the first-order markov joint transition probability to rich-rich state and rich-poor state of rainfall and reference crop evapotranspiration is larger. The joint encounter frequency of rainfall and reference crop evapotranspiration in synchronous encounter situation is different with that in asynchronous encounter situation. The selected frank copula showing the joint probability distribution characteristics of rainfall and reference crop evapotranspiration is reasonable. When reference crop evapotranspiration is less than 1,865 mm, the sort of its conditional probability in different rainfall states is rich rainfall>normal rainfall>poor rainfall, which presents an opposite to the conditional probability of rainfall in different reference crop evapotranspiration states when rainfall is less than 1,105 mm. Copyright Springer Science+Business Media Dordrecht 2014