Earth Sci Inform https://doi.org/10.1007/s12145-017-0327-1 RESEARCH ARTICLE Calibration and spatial modelling of daily ET 0 in semiarid areas using Hargreaves equation Francisco Gomariz-Castillo 1,2 · Francisco Alonso-Sarr´ ıa 2 · Francisco Cabezas-Calvo-Rubio 1 Received: 5 June 2017 / Accepted: 10 October 2017 © Springer-Verlag GmbH Germany 2017 Abstract Evapotranspiration is difficult to measure and, when measured, its spatial variability is not usually taken into account. The recommended method to estimate evapo- transpiration, Penman-Monteith FAO, requires variables not available in most weather stations. Simplified but less accu- rate methods, as Hargreaves equation, are normally used. Several approaches have been proposed to improve Harg- reaves equation accuracy. In this work, 14 calibrations of the Hargreaves equation are compared. Three goodness of fit statistics were used to select the optimal, in terms of simplicity and accuracy. The best option was an annual linear regression. Its parameters were interpolated using regression-kriging combining Random Forest and Ordinary Kriging. Twelve easy to obtain ancillary variables were used as predictors. The same approach was used to interpo- late Hargreaves and Penman-Monteith-FAO ET 0 on a daily basis; the Hargreaves ET 0 layers and the parameter layers were used to obtain calibrated ET 0 estimations. To com- pare the spatial patterns of the three estimations the daily layers were integrated into annual layers. The results of the proposed calibration are much more similar to Penman- Monteith FAO results than those obtained with Hargreaves equation. The research was conducted in south-east Spain Communicated by: H. A. Babaie  Francisco Gomariz-Castillo fjgomariz@um.es 1 Euro-mediterranean Water Institute, Campus de Espinardo s/n, 30100 Murcia, Spain 2 Institute for Water and Environment, University of Murcia, Campus de Espinardo s/n, 30100 Murcia, Spain with 79 weather stations with data from 01/01/2003 to 31/12/2014. Keywords Evapotranspiration · Hargreaves equation · Allen calibration · Spatial interpolation · Random forest Introduction Evapotranspiration is one of the most important processes in the water cycle; its knowledge is essential to water resources management, planning and design, especially in semiarid regions. However, its direct measurement is very expensive, time consuming and mainly carried out in agricultural plots; it is then almost impossible to have enough observations to obtain a regional interpolation. Several models have been proposed to estimate evapotranspiration from meteorologi- cal variables (Xu and Singh 2002), specifically a reference evapotranspiration (ET 0 ) defined by Allen et al. (1998) as “the rate of evapotranspiration from an hypothetical crop with an assumed crop height (0.12 m), a fixed canopy resis- tance (70 s m-1) and albedo (0.23), such crop would closely resemble the evapotranspiration from a widespread sur- face of green grass of homogeneous height, fully growing, wholly shading the ground and not short of water”. The Penman-Monteith FAO (PMFAO) equation (Allen et al. 1989; Monteith 1965) is considered to provide the most accurate estimation of daily and monthly ET 0 in all cli- mates (Subburayan et al. 2011) and has been recommended by FAO (Allen et al. 1994). It requires several weather vari- ables that are not available in many weather stations and are also difficult to interpolate. Alternative methods using only temperature or radiation as independent variables have been proposed to overcome this issue (Xu and Singh 2000; 2001). These methods can be applied in a substantially