Modeling reference evapotranspiration with calculated targets. Assessment and implications

Due to the absence of experimental reference evapotranspiration (ETo) records, data-driven models consider in most cases calculated ETo targets to train and test the models, usually according to the standard FAO56 Penman Monteith equation (FAO56-PM). This procedure is also adopted for calibrating more conventional empirical approaches like the well-known Hargreaves (HG) equation. This study aims at assessing the performance implications derived from using calculated targets instead of experimental measurements for training and testing data-driven models or calibrating empirical methods. Therefore an application of a gene expression programming (GEP) based approach for estimating ETo is presented considering calculated and lysimetric targets fed with two different input combinations and assessed through k-fold testing. The same procedure is adopted to evaluate the calibration of the HG equation. Finally, the FAO56-PM and the HG equations are compared with their corresponding GEP models bearing in mind the type of targets used. The locally trained GEP4 and GEP6 models trained using the experimental lysimetric targets are more accurate than the corresponding HG and FAO56-PM equations, assessed using lysimetric benchmarks. The external performance accuracy of GEP4 and GEP6 models decreases considerably in the cross-station approach using experimental targets. In this case, the FAO56-PM and the HG equations might be preferable. The accuracy of the GEP models trained with calculated targets decreases considerably when the performance is assessed using experimental benchmarks. The conclusions drawn when only calculated benchmarks are used might be not sound or even false. The same applies for empirical equations calibrated with calculated targets. Four new GEP-based equations (one per input combination and station) are provided to estimate ETo.