Correcting <scp>Hargreaves‐Samani</scp> formula using geographical coordinates and rainfall over different timescales

Abstract The United Nations Food and Agricultural Organization (FAO) approved the Hargreaves‐Samani formula (HAR‐85) as an alternative to the standard Penman‐Monteith method (FAO‐PM) for estimating grass reference evapotranspiration (ETo). With much less data demand, HAR‐85 is unequivocally useful where meteorological variables are often scarce, incomplete or unavailable. Herein, we evaluate HAR‐85 against FAO‐PM across 2.505 million km 2 , representing Sudan and South Sudan and encompassing wide hydroclimate domains including the Nile River. We further propose simple year‐round and seasonal adjustment models to correcting HAR‐85 across the entire study area. The models express HAR‐85's error in multiple linear regressions in terms of latitude, longitude, altitude and/or monthly rainfall. Varying data periods, including odd, even and all years, are used in the evaluation and the adjustment models development and validation processes to investigate the influence of changing data period. A suit of eight performance indicators shows dependency of the original bias of HAR‐85 on the geographical location, monthly rainfall amount, season of the year and data period. All error indicators amplify southward from the hyper‐arid region to the dry sub‐humid zone. For example, the mean bias error (MBE) ranges from −0.51 to 1.29 mm/day, respectively. Study area‐wide, HAR‐85 least represents FAO‐PM during the hottest month and the transitional month (between the wet and dry‐cool seasons) with MBE of 0.65 and 0.70 mm/day, respectively. Conversely, it represents FAO‐PM the most in the wettest month, with smallest MBE of 0.32 mm/day. Beholding this spatiotemporal trait, the final yearly and seasonal adjustment models developed herein enormously moderate the predominant overestimation of the original HAR‐85. The former model explains 46.7% of the error variance whereas 36.9% to 62.3% of the variation in the error is explainable by the latter models. These adjustment models narrow the monthly MBE among the stations from −0.71‐2.17 to −0.80‐1.20 and −0.65‐0.99 mm/day, respectively. Without undermining the accuracy, the year‐round adjustment model can still be feasibly recommended for general use across the study area.