Using artificial neural networks to predict the reference evapotranspiration

Artificial neural network models (ANNs) were used in this study to predict reference evapotranspiration (ETo) using climatic data from the meteorological station at the test station in Kafr El-Sheikh Governorate as inputs and reference evaporation values computed using the Penman-Monteith (PM) equation. These datasets were used to train and test seven different ANN models that included different combinations of the five diurnal meteorological variables used in this study, namely, maximum and minimum air temperature (Tmax and Tmin ), dew point temperature (Tdw), wind speed (u), and precipitation (P), how well artificial neural networks could predict ETo values. A feed-forward multi-layer artificial neural network was used as the optimization algorithm. Using the tansig transfer function, the final architected has a 6-5-1 structure with 6 neurons in the input layer, 5 neurons in the hidden layer, and 1 neuron in the output layer that corresponds to the reference evapotranspiration. The root mean square error (RMSE) of 0.1295 mm∙day -1 and the correlation coefficient (r) of 0.996 are estimated by artificial neural network ETo models. When fewer inputs are used, ETo values are affected. When three separate variables were employed, the RMSE test values were 0.379 and 0.411 mm∙day -1 and r values of 0.971 and 0.966, respectively, and when two input variables were used, the RMSE test was 0.595 mm∙day -1 and the r of 0.927. The study found that including the time indicator as an input to all groups increases the prediction of ETo values significantly, and that including the rain factor has no effect on network performance. Then, using the Penman-Monteith method to estimate the missing variables by using the ETo calculator the normalised root mean squared error (NRMSE) reached about 30% to predict ETo if all data except temperature is calculated, while the NRMSE reached about of 13.6% when used ANN to predict ETo using variables of temperature only.