Calibration and Modification of the Hargreaves–Samani Equation for Estimating Daily Reference Evapotranspiration in Iraq

Daily reference evapotranspiration (${\mathrm{ET}}_{\mathrm{o}}$) is an essential component of the hydrologic processes of surface water generation from precipitation. Iraq suffers from a scarcity of surface water due to the erection of many dams on the Tigris and Euphrates Rivers by neighboring countries on upstream locations along these rivers. Therefore, ${\mathrm{ET}}_{\mathrm{o}}$ values should be measured more accurately in Iraq. In this study, the Penman–Monteith (PM) equation was used as the benchmark to calculate the standard values of ${\mathrm{ET}}_{\mathrm{o}}$ for 103 stations in Iraq using a daily meteorological data set from 2010 to 2019 (5 years each for calibration and validation periods). Three forms of the Hargreaves–Samani (HS) equation were evaluated for estimating the ${\mathrm{ET}}_{\mathrm{o}}$ values. The first two equations have common and optimum coefficient sets (HSC and HSO equations, respectively). The third equation is proposed in this study and modifies the HS equation by incorporating a wind speed variable with an optimum coefficient set (HSW equation). The coefficients of the HSO and HSW equations were optimized in terms of the Nash–Sutcliffe efficiency (NSE) coefficient and the coefficient of determination ($R^2$) using the shuffled complex evolution (SCE) optimization method. The respective success rates of ${\mathrm{ET}}_{\mathrm{o}}$ estimation during the calibration and validation periods are 37% and 39% when using the HSC equation, 96% and 95% with the HSO equation, and 100% and 100% with the HSW equation. Results indicated that the HSO and HSW equations enhance the estimation of ${\mathrm{ET}}_{\mathrm{o}}$ values relative to the HSC equation, and the HSW equation performs best among the three. Therefore, incorporating the wind speed in the HS equation with the optimum coefficient set increases the robustness of its predictive capacity for all regions of Iraq, including those with high altitudes.

The applicability of the Hargreaves–Samani equation, which depends only on temperatures, was investigated using common coefficients in estimating daily evapotranspiration values for 10 years (2010–2019) in 103 regularly distributed stations covering the entire area of Iraq. It was found that the common form of the Hargreaves–Samani equation failed in most regions of Iraq except the northern and northeastern regions. Therefore, the Hargreaves–Samani equation was calibrated with new coefficients for Iraq in lieu of the common coefficients. The Hargreaves–Samani equation with the new calibration coefficients was more successful in calculating the evapotranspiration in 95% of all stations across Iraqi area; the exceptions were some stations located in northern and northeastern regions, in which the common equation succeeded. Thus, to obtain an equation that remains applicable for the entire area of Iraq, the Hargreaves–Samani equation was developed further by incorporating the wind speed and later calibrated to obtain the appropriate coefficients for Iraq. This developed Hargreaves–Samani equation was very successful in estimating the values of evapotranspiration in all regions of Iraq.