Statistical analysis of modified Hargreaves equation for precise estimation of reference evapotranspiration

There are a lot of meteorological stations around the world, like Pakistan, where all the meteorological parameters are not accessible to analyze Penman-Monteith (PM) method for the estimation of Reference Evapotranspiration (ETo ). So ablative methods such as Hargreaves Samani (HS) equation are therefore a potential solution to this problem, which required small numbers of meteorological parameters to estimate ETo . But, simplification brings imprecision and the need for regional calibration of the HS equation's constant. In this study, fuzzy logic based calibration of the constants in the HS equation at the various climatic locations of Pakistan for the period of 1980 - 2019 is performed. The precision of HS and Modified HS (MHS) against standard PM method for the approximation of ETo was evaluated and compared the calibration process of HS equation by adjusting the coefficients of the equation gradually. The performance of the MHS is evaluated based on the statistical indicators such as Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Performance Index (PI). The statistical assessment of the study revealed that the MHS equation performed better as compared to the conventional HS equation and simultaneous adjustment of all the empirical parameters "ah", "bh","ch" and "dh" was the best alternative for calibration of the HS equation. Furthermore, the change point detection analysis has been carried out on ETo (estimated by MHS) using Pettitt's test, Buishand's range test and Buishand's U test. Results of the change point analysis indicated different change points from year 1980 to 2019, mainly due to the industrialization and urbanization during this time period.