Comparison of artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration estimation in the Basque Country (Northern Spain)

Reference evapotranspiration (ETo) determination is a key factor for water balance and irrigation scheduling. Evapotranspiration can be measured directly by high-cost micrometeorological techniques, or estimated by mathematical models. The combination equation of Penman–Monteith, modified by Allen et al. [Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration. Guidelines for computing crop water requirements. FAO Irrigation and Drainage, Paper no. 56. FAO, Rome] (PM56), is the reference equation for ETo estimation. This method is also appropriate for the calibration of other ETo estimation equations. The utilization of these calibrated ETo equations is recommended in the absence of data of any of the meteorological parameters necessary for the application of PM56. In addition to the use of classic ETo equations, the adoption of artificial neural network (ANN) models for the estimation of daily ETo has been evaluated in this study. ANNs are mathematical models, whose architecture has been inspired by biological neural networks. They are highly appropriate for the modelling of non-linear processes, which is the case of the evapotranspiration process. Seven ANNs (with different input combinations) have been implemented and compared with ten locally calibrated empirical and semi-empirical ETo equations and variants of these equations (with estimated meteorological parameters as inputs). The comparisons have been based on statistical error techniques, using PM56 daily ETo values as a reference. ANNs have obtained better results than the locally calibrated ETo equations in the three groups of evaluated methods: temperature and/or relative humidity-based methods (0.385 mm d⁻¹ of root mean square error (RMSE)), solar radiation-based methods (0.238 mm d⁻¹ of RMSE), and methods based on similar requirements to those of PM56 except for the estimation of solar radiation and/or relative humidity (0.285 mm d⁻¹ of RMSE).