Evapotranspiration estimates are paramount for understanding climatology and better water management, especially in regions notorious for recurrent droughts, high evapotranspiration losses and basins with overspilling. This study adds new dimensions to the adjustment of the Hargreaves-Samani model (HS) against the standard FAO Penman-Monteith method for estimating reference evapotranspiration. The original coefficient (C = 0.0023) and the overall exponent (E = 1.0) in HS are calibrated and validated while splitting and exchanging of odd and even years' datasets. Sudan and South Sudan are selected as a case of least studied and data-scarce countries though encompassing the largest part of the Nile basin with diverse hydroclimate zones. Implications of the proposed dimensions for the results and their usage in water management are discussed. Data splitting in the present manner reveals variation in the results between the different datasets, depending on the geographical location and the associated climate as well as the season. Thus, data splitting avoids bias towards certain mode of climate in a changing world and subsequent misinterpretation. Both C and E increase linearly with latitude from the dry sub-humid to the hyper-arid zone. The resulting latitude dependence offers interpolation and extrapolation of the constants across this large yet understudied region. Least calibration characterized the wettest months whereas largest calibration distinguished the transitional months towards the dry/cool season. Adjusting C is more suitable for the hyper-arid and semi-arid zones as well as for the hot and wet seasons. Calibrating E suits better the arid and dry sub-humid zones in addition to the dry/cool season. The present results (mis)match results reported in the literature for similar climate zones, thus opening venues for further studies elsewhere.