Forecasting Reference Evapotranspiration Using Non-Linear Autoregressive Artificial Neural Network

Afifi, Ahmed S.
Bateni, Sayed
Civil Engineering
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The accurate forecast of reference evapotranspiration (ETo) has a vital role in real-time decisions on water resources management by quantifying the prospective changes in agricultural and hydrological processes. The real-time decisions on irrigation scheduling are primarily made based on the agricultural water demand predictions, which themselves strongly depend on ETo. Reference evapotranspiration is a complex process driven mainly by weather variables, and thus is characterized by high non-linearity and non-stationarity. In this study, the nonlinear autoregressive (NAR) and hybrid wavelet-NAR (WNAR) neural network approaches are used to forecast ETo for 1-, 3- and 7-days-ahead at six sites (namely, Alliance, Champion, Dunning, McCook, Mead, and North Platte) in Nebraska. These sites are chosen to cover various climatic conditions. At each site, 70%, 15%, and 15% of the daily ETo measurements from 1994 to 2015 are used respectively to train, validate, and test the NAR and WNAR networks. Thereafter, the trained NAR and WNAR networks are utilized to forecast ETo in 2016. The training and transfer functions as well as the number of feedback delays, hidden layers and nodes are determined by trial-and-error to optimize performance of the networks. Three training functions (i.e., Levenberg-Marquardt backpropagation (trainlm), resilient backpropagation (trainrp), and scaled conjugate gradient (trainscg)) andthree transfer functions (i.e., Log-Sigmoid (logsig), Tan-Sigmoid (tansig), and Radial Basis (radbas)) are utilized in the networks. It is found that the trainlm training function, tansig transfer function, 15 feedback delays, and 2 hidden layers with 20 nodes in each layer generate the best results. The findings show that the NAR and WNAR approaches can accurately forecast ETo. The six-site average mean absolute error (MAE) of 1-day-ahead ETo forecasts from NAR is 0.37 mm/day. The WNAR approach decreases the corresponding MAE to 0.23 mm/day. WNAR also improves the average root mean square error (RMSE), and the average coefficient of correlation (R2) from 0.73 mm/day to 0.54 mm/day, and from 0.94 to 0.96, respectively. The six-site average MAE of 3-day-ahead ETo forecasts from NAR is 0.78 mm/day. The WNAR approach decreases the corresponding MAE to 0.47 mm/day. WNAR also improves the RMSE, and R2 from 1.09 mm/day to 0.75 mm/day, and from 0.87 to 0.92, respectively. The six-site average MAE of 7-day-ahead ETo forecasts from NAR is 1.16 mm/day. The WNAR approach decreases the corresponding MAE to 0.91 mm/day. WNAR also improves the average RMSE and R2 from 1.48 mm/day to 1.24 mm/day, and from 0.74 to 0.78, respectively. Thus, the results support an overall better accuracy of the WNAR model when compared to the NAR model. Finally, performance of NAR is compared to those of autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA).
Environmental engineering, Agriculture engineering, Atmospheric sciences, ARIMA, Forecast, NAR, Neural Network, Nonlinear Autoregressive, Reference Evapotranspiration
123 pages
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