Calibration of empirical equations for estimating reference evapotranspiration in different climates of Iran

Abstract

The accurate estimation of reference evapotranspiration (ETref) is a crucial component for modeling hydrological and ecological cycles. The goal of this study was the calibration of 32 empirical equations used to determine ETref in the three classes of temperature-based, solar radiation–based, and mass transfer–based evapotranspiration. The calibration was based on measurements taken between the years 1990 and 2019 at 41 synoptic stations located in very dry, dry, semidry, and humid climates of Iran. The performance of the original and calibrated empirical equations compared to the PM-FAO56 equation was evaluated based on model evaluation techniques including the coefficient of determination (R2), the root mean square error (RMSE), the average percentage error (APE), the mean bias error (MBE), the index of agreement (D), and the scatter index (SI). The results show that the calibrated Baier and Robertson equation for temperature-based models, the Jensen and Haise equation for solar radiation–based models, and the Penman equation for mass transfer–based models performed better than the original empirical equations. The calibrated equations had, respectively, an average R2 = 0.73, 0.67, and 0.78; RMSE = 35.14, 35.02, and 30.20 mm year-1; and MBE = − 5.6, − 3.89, and 2.57 mm year-1. The original empirical equations had values of average R2 = 0.60, 0.37, and 0.65; RMSE = 68.34, 66.98, and 52.62 mm year-1; and MBE = − 5.75, 4.26, and 8.99 mm year-1, respectively. The calibrated empirical equations for very dry climate (e.g., Zabol, Zahedan, Bam, Iranshahr, and Chabahar stations) also significantly reduced the SI value from SI > 0.3 (poor class) to SI < 0.1 (excellent class). Therefore, the calibrated empirical equations are highly recommended for estimating ETref in different climates.