Estimation of Reference Evapotranspiration Using Neural Networks and Cuckoo Search Algorithm

The ability to optimize an artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) in reference evapotranspiration (${\mathrm{ET}}_0$) estimation using the cuckoo search algorithm (CSA) is studied in this paper. The monthly series of climatic data (minimum and maximum air temperatures, actual vapor pressure, sunshine hours, and wind speed at height of 2.0 m) from twelve meteorological stations in Serbia during the period 1983–2010 were used as inputs to the soft computing models. As the reference ${\mathrm{ET}}_0$ equation, the FAO-56 Penman-Monteith equation was selected. Statistical indicators such as the root-mean-square error (RMSE), mean absolute error (MAE), and coefficient of determination ($R^2$) were used as comparing criteria for the evaluation of the models’ performances. The obtained results show that the proposed $\mathrm{ANFIS}+\mathrm{CSA}$ model can be used for ${\mathrm{ET}}_0$ estimation with high reliability ($\mathrm{RMSE}=0.2650\mathrm{mm}{\mathrm{day}}^{-1}$, $\mathrm{MAE}=0.1843$ and $R^2=0.9695$). The selected soft computing models were compared with the results of two empirical models (adjusted Hargreaves and Priestley-Taylor) and their calibrated versions. Priestley-Taylor method had the highest RMSE ($0.5420\mathrm{mm}{\mathrm{day}}^{-1}$). The lowest RMSE of $0.1883\mathrm{mm}{\mathrm{day}}^{-1}$ has the ANN model. The calibrated adjusted Hargreaves model performs better than the calibrated Priestley-Taylor model. The $\mathrm{ANN}+\mathrm{CSA}$, ANFIS, and $\mathrm{ANFIS}+\mathrm{CSA}$ had better characteristics than the two estimated empirical equations and their calibrated versions.