Performance Evaluation of Reference Evapotranspiration Equations across a Range of Indian Climates

Reference crop evapotranspiration $\left({\mathrm{ET}}_0\right)$ is a key variable in procedures established for estimation of evapotranspiration rates of agricultural crops. In recent years, there is growing evidence to show that the more physically based FAO-56 Penman–Monteith (PM) combination method yields consistently more accurate ${\mathrm{ET}}_0$ estimates across a wide range of climates and is being proposed as the sole method for ${\mathrm{ET}}_0$ computations. However, other methods continue to remain popular among Indian practitioners either because of traditional usage or because of their simpler input data requirements. In this study, we evaluated the performances of several ${\mathrm{ET}}_0$ methods in the major climate regimes of India with a view to quantify differences in ${\mathrm{ET}}_0$ estimates as influenced by climatic conditions and also to identify methods that yield results closest to the FAO-56 PM method. Performances of seven ${\mathrm{ET}}_0$ methods, representing temperature-based, radiation-based, pan evaporation-based, and combination-type equations, were compared with the FAO-56 PM method using historical climate data from four stations located one each in arid (Jodhpur), semiarid (Hyderabad), subhumid (Bangalore), and humid (Pattambi) climates of India. For each location, ${\mathrm{ET}}_0$ estimates by all the methods for assumed hypothetical grass reference crop were statistically compared using daily climate records extending over periods of 3–4 years. Comparisons were performed for daily and monthly computational time steps. Overall results while providing information on variations in FAO-56 PM ${\mathrm{ET}}_0$ values across climates also indicated climate-specific differences in ${\mathrm{ET}}_0$ estimates obtained by the various methods. Among the ${\mathrm{ET}}_0$ methods evaluated, the FAO-56 Hargreaves (temperature-based) method yielded ${\mathrm{ET}}_0$ estimates closest to the FAO-56 PM method both for daily and monthly time steps, in all climates except the humid one where the Turc (radiation-based) was best. Considering daily comparisons, the associated minimum standard errors of estimate (SEE) were 1.35, 0.78, 0.67, and 0.31 mm/day, for the arid, semiarid, subhumid, and humid locations, respectively. For monthly comparisons, minimum SEE values were smaller at 0.95, 0.59, 0.38, and 0.20 mm/day for arid, semiarid, subhumid, and humid locations, respectively. These results indicate that the choice of an alternative simpler equation in a particular climate on the basis of SEE is dictated by the time step adopted and also it appears that the simpler equations yield much smaller errors when monthly computations are made. In order to provide simple ${\mathrm{ET}}_0$ estimation tools for practitioners, linear regression equations for preferred FAO-56 PM ${\mathrm{ET}}_0$ estimates in terms of ${\mathrm{ET}}_0$ estimates by the simpler methods were developed and validated for each climate. A novel attempt was made to investigate the reasons for the climate-dependent success of the simpler alternative ${\mathrm{ET}}_0$ equations using multivariate factor analysis techniques. For each climate, datasets comprising FAO-56 PM ${\mathrm{ET}}_0$ estimates and the climatic variables were subject to factor analysis and the resulting rotated factor loadings were used to interpret the relative importance of climatic variables in explaining the observed variabilities in ${\mathrm{ET}}_0$ estimates. Results of factor analysis more or less conformed the results of the statistical comparisons and provided a statistical justification for the ranking of alternative methods based on performance indices. Factor analysis also indicated that windspeed appears to be an important variable in the arid climate, whereas sunshine hours appear to be more dominant in subhumid and humid climates. Temperature related variables appear to be the most crucial inputs required to obtain ${\mathrm{ET}}_0$ estimates comparable to those from the FAO-56 PM method across all the climates considered.