Earth Science Informatics

, Volume 11, Issue 3, pp 325–340 | Cite as

Calibration and spatial modelling of daily ET0 in semiarid areas using Hargreaves equation

  • Francisco Gomariz-CastilloEmail author
  • Francisco Alonso-Sarría
  • Francisco Cabezas-Calvo-Rubio
Research Article


Evapotranspiration is difficult to measure and, when measured, its spatial variability is not usually taken into account. The recommended method to estimate evapotranspiration, Penman-Monteith FAO, requires variables not available in most weather stations. Simplified but less accurate methods, as Hargreaves equation, are normally used. Several approaches have been proposed to improve Hargreaves 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 interpolate Hargreaves and Penman-Monteith-FAO ET0 on a daily basis; the Hargreaves ET0 layers and the parameter layers were used to obtain calibrated ET0 estimations. To compare 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 with 79 weather stations with data from 01/01/2003 to 31/12/2014.


Evapotranspiration Hargreaves equation Allen calibration Spatial interpolation Random forest 



This study was funded by the Segura Hydrographic Confederation, MAPAMA (Government of Spain), within the framework of the Research Project Scientific Support Activities for the Hydrological Planning and European Cooperation Process.

This study was funded in part by the Seneca Foundation, Science and Technology Agency of the Murcia Region (Ref. 19325 / PI / 2015), project The Role of Water Markets in Integrated Water Resources Management in Watersheds.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Euro-mediterranean Water InstituteMurciaSpain
  2. 2.Institute for Water and EnvironmentUniversity of MurciaMurciaSpain

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