Daily reference evapotranspiration estimates by artificial neural networks technique and empirical equations using limited input climate variables

•Empirical equations of ETo compared to Penman-Monteith method.•ANNs model based on daily meteorological data estimate accurate ETo.•ANNs models estimate with slightly lower accuracy ETo with less input variables.•Different years training datasets give different testing results of ETo.

The artificial neural networks (ANN) and the empirical methods of Priestley-Taylor, Makkink, Hargreaves and mass transfer were used to estimate the reference evapotranspiration with daily meteorological data. These datasets consisted of daily meteorological measurements from a station in northern Greece, covering a period of five years (2009-2013). The daily values of the reference evapotranspiration were calculated using the Penman-Monteith equation. Those datasets were used for training and testing the ANN. The algorithm that was used is of the multi-layer feed forward artificial neural networks and of the back-propagation for optimization. The architecture that was finally chosen has the 4-6-1 structure, with 4 neurons in the input layer, 6 neurons in the hidden layer and 1 neuron in the output layer which corresponds to the reference evapotranspiration, using a sigmoid transfer function. The ANNs models estimate ETo with an accuracy of a root mean square error (RMSE) ranged from 0.574 to 1.33 mm d−1, and correlation coefficient (r) from 0.955 to 0.986. Using limited input variables (3 or 2) for training the ANNs result in ETo values with slightly lower accuracy. The RMSE ranged from 0.598 to 0.954 mm d−1 and r ranged from 0.952 to 0.978 when 3 inputs variables were used, and RMSE of 0.846 to 1.326 mm d−1 and r of 0.910 to 0.956 when 2 input variables were used. The Priestley-Taylor and Makkink methods correlated very well with the Penman-Monteith method followed by the Hargreaves method which overestimates the higher values of ETo. The mass transfer method also correlated satisfactorily but it underestimated the ETo values.