Investigating the probabilistic behavior of reference evapotranspiration using Vine tree sequence

Reference evapotranspiration, which includes the contribution of climatic conditions in potential evapotranspiration, is considered as an important and strategic criterion in water resources management and irrigation designs. Therefore, it is necessary to determine and predict its changes in each region. In this study, using copula functions, the behavior and changes of this component were investigated in the west of Iran. For this purpose, the meteorological information of nine synoptic stations including Tmax, Tmin, WS, Rs, RHmax, and RHmin were used. This research aims to explore multivariate simulation based on vine tree sequences. Among these parameters, wind speed had the least effect on ET₀, and in all the studied stations, there was the highest correlation between ET₀-Tmax pair variable, which was equal to 0.90, 0.87, 0.89, 0.88, 0.86, 0.85, 0.88, and 0.81 in Aligudarz, Azna, Borujerd, Dorud, Khorramabad, Kuhdasht, Nurabad, and Poldakhter stations, respectively, based on Kendall's Tau statistics. The tree sequence of vine copulas including C-, D-, and R-vine was examined according to the input variables based on AIC and logarithm of likelihood evaluation criteria. According to the results, it was found that based on the evaluation criteria, the D-vine tree sequence has the best performance in the joint probability analysis of the studied variables. In addition, the results showed that the D-vine tree sequence, unlike the two R and C type sequences, has maintained the correlation between the studied pair variables until the last tree. The results of this study showed that copula functions could analyze evapotranspiration in different climates with high capability, which can be used in predicting the behavior of non-linear variables.