Bivariate simulation and joint analysis of reference evapotranspiration using copula functions

The aim of the present study was to analyze the correlation and simulation of the values of reference evapotranspiration of meteorological stations in the Lut Desert (Bam, Birjand, and Tabas) in the period 1984-2019 using common copulas and corresponding wind speed on a monthly scale. By examining the correlation between the pair-variables of wind speed and reference evapotranspiration in Bam, Birjand, and Tabas stations, the correlation was evaluated about 0.7, 0.76, and 0.80, respectively. By examining the structure of two-dimensional copulas and their conditional density based on different criteria, the Galambos copula was selected as the best copula for all stations. By selecting the best marginal distribution and the best copula, the frequency analysis, joint return period and copula-based simulation were presented. By presenting the joint probability curves, the probabilities of both wind speed and reference evapotranspiration at each station were presented simultaneously in the form of typical curves, which can provide very useful information about the probabilistic behavior of the studied data. Finally, the reference evapotranspiration values were simulated using a copula-based model and wind speed values. The simulation results of the mentioned values showed that the correlation of the pair-variables was appropriate. The accuracy, efficiency and error rate of simulating the values of reference evapotranspiration values were evaluated using various statistical tests. Successful simulation of this parameter is in fact a reason for accurate selection of the copula structure, which indicated a maximum error rate (RMSE) of 0.1 mm per day and 98% efficiency for all stations. By application of this algorithm in simulating the values of reference evapotranspiration and presenting its estimated relationship in the region, the amount of reference evapotranspiration can be easily simulated with available meteorological data and without much computational complexity.