Regional calibration of Hargreaves equation for estimating reference ET in a semiarid environment

The Hargreaves equation provides reference evapotranspiration (ETo) estimates when only air temperature data are available, although it requires previous local calibration for acceptable performance. This equation has been evaluated under semiarid conditions in Southern Spain using data from 86 meteorological stations, comparing daily estimates against those from the FAO-56 Penman–Monteith equation, which was used as standard. Variability of results among location was clearly apparent, with MBE ranging from 0.74 to −1.13 mm d−1 and RMSE from 0.46 to 1.65 mm d−1. Maxima under- and overestimation amounted to 24.5 and 22.5%, respectively. In general, larger under- and overestimations occurred in stations located close to the coast and at inland areas, respectively. Yearly means of windspeed (V) and daily temperature range (ΔT) fairly influenced the accuracy of the equation. It was more accurate for windy locations with large ΔT, and for locations with light wind conditions combined with low to moderate values of ΔT. According to the values taken by V and ΔT, the stations were represented by points on the ΔT–V coordinate plane, in which four regions were delimited. A regional calibration was carried out considering only temperature and wind conditions. Correction was not necessary for stations located within two of them; for the other two regions, new values for the empirical coefficient of the equation are suggested (0.0027 and 0.0021). After correction, average RMSE and maximum and minimum MBE decreased substantially (12, 24 and 41%, respectively), and 74 out of the 86 locations gave quite accurate results, with relative values of MBE lower than 10% in most cases. Alternatively, another method based on kriging interpolation was proposed to obtain, for each individual station, locally adjusted values for the empirical coefficient as a function of the same variables. This second correction procedure behaved even better than the first one. There was a 15% improvement in the average RMSE, and maximum and minimum MBE values decreased 50 and 70%, respectively. At all locations, relative values of MBE were less than 10% and in 70% of them were lower than 5%. Validation was done by using data from 14 meteorological stations for other Spanish regions, and the consequences from the application of the corrections proposed for an irrigation district are discussed.