Reference grass evapotranspiration with reduced data sets: parametrization of the FAO Penman-Monteith temperature approach and the Hargeaves-Samani equation using local climatic variables

The computation of the grass reference evapotranspiration with the FAO56 Penman-Monteith equation (PM-ETo) requires data on maximum and minimum air temperatures (Tmax, Tmin), actual vapour pressure (ea), shortwave solar radiation (Rs), and wind speed at 2m height (u2). Nonetheless, related datasets are often not available, are incomplete, or have uncertain quality. To overcome these limitations, several alternatives were considered in FAO56, while many other procedures were tested and proposed in very numerous papers. The present study reviews the computational procedures relative to predicting the missing variables from temperature, i.e., the PM temperature approach (PMT), and estimating ETo with the Hargreaves-Samani (HS) equation. For the PMT approach, procedures refer to predicting: (a) the dew point temperature (Tdew) from the minimum or the mean air temperature; (b) shortwave solar radiation (Rs) from the air temperature difference (TD=Tmax-Tmin) combined with a calibrated radiation adjustment coefficient (kRs); and (c) wind speed (u2) using a default value or a regional or local average. The adequateness of computing Tdew from air temperature was reassessed and the preference for using an average u2 has been defined. To ease the estimation of Rs, for the PMT approach and the coefficient of the HS equation, multiple linear regression equations for predicting kRs were developed using local averages of the temperature difference (TD), relative humidity (RH) and wind speed as independent variables. All variables were obtained from the Mediterranean set of CLIMWAT climatic data. Two types of kRs equations were developed: climate-focused equations specific to four climate types - humid, sub-humid, semi-arid, and hyper-arid and arid -, and a global one, applicable to any type of climate. The usability of the kRs equations for the PMT and HS methods was assessed with independent data sets from Bolivia, Inner Mongolia, Iran, Portugal and Spain, covering a variety of climates, from hyper-arid to humid. With this purpose, ETo estimated with PMT and HS (ETo PMT and ETo HS) were compared with PM-ETo computed with full data sets to evaluate the usability of the kRs equations. Adopting the climate-focused kRs equations with ETo PMT, the RMSE averaged 0.59, 0.64, 0.65 and 0.72mm d−1 for humid, sub-humid, semi-arid, and arid and hyper-arid climates, respectively, while the RMSE values relative to ETo HS when using the respective climate-focused kRs equations averaged 0.58, 0.60, 0.60 and 0.69mm d−1 for the same climates. These results are similar to those obtained with the kRs global equation. The accuracy of the PMT approach when using the kRs equations was also evaluated when one, two, or all three Tdew, Rs and u2 variables are missing and the resulting goodness-of-fit indicators demonstrated the advantage of the combined use of observed and estimated weather variables. The usability of the kRs equations for an efficient parameterization of both the PMT approach and the HS equation is demonstrated with similar performance of PMT and HS procedures for a variety of climates. Because the ETo HS results depend almost linearly on temperature, the PMT approach, using estimates of the weather variables, is able to mitigate those temperature impacts, which trends may be contrary to those of other variables that determine ETo. The clear advantage of the PMT approach is that it allows using the available weather data in combination with estimates of the missing variables, which provides for more accurate ETo computations