Reformulating and testing Temesgen-Melesse's temperature-based evapotranspiration estimation method

The use of FAO-56 Penman–Monteith (PM) equation is the recommended equation to estimate potential evapotranspiration. However, when data that satisfy the PM equation is not available or incomplete, the use of PM equation is not an option. In this study, one such method known as Temesgen-Melesse's (TM) method was assessed in relation to the PM equation using data of eight class-I meteorological stations in Ethiopia. In the study, first the problems with this method were identified and the TM equation was modified. The modifications made were replacement of the average maximum temperature at the denominator of the equation varying with time with the average of Tmax for each location (which is a constant for a given location). The Second consideration was calibrating the power of the maximum temperature at the numerator using PM data instead of taking it as a constant 2.5 suggested by the authors in their original equation. Then the three (the original TM, the modified TM with constant power of 2.5 and the modified TM with the power calibrated) methods were fitted against PM equation. Thereafter tests using statistical parameters, model tendency parameters and model performances were carried out. The results indicate the modified TM equation to be better than the original TM equation in terms of percent slope (0.8–12.3 against 1.3–15.1) and the correlation coefficient (R(2)) and the slope (100% good or satisfactory against 25%). The modified and calibrated equation gave best results in terms of percent error by slope (0.5–2.3), by coefficient of efficiency (100% good or satisfactory), by R(2) and slope (100% good or satisfactory) and by mean percent error (5.7–13.6%). Therefore, whenever data that satisfy PM equation are available (even if for limited years), it is better to calibrate the power of the maximum temperature and to consider more decimal places rather than taking 2.5 as suggested by the authors. When data is not available it is better to use the modified TM equation rather than using the original TM equation. The study would benefit those who want to study long-term climate changes and drought patterns, which involve the use of evapotranspiration with limited data that satisfy the PM equation, but have long-term data of temperature.