Comparative Study of Time Series Models, Support Vector Machines, and GMDH in Forecasting Long-Term Evapotranspiration Rates in Northern Iran

Evapotranspiration estimation and forecasting is a key step in water management projects, especially in water-scarce countries such as Iran. Seasonal autoregressive integrated moving average (SARIMA), support vector machine (SVM), and group method of data handling (GMDH) models were developed and assessed to find an appropriate model for short and long-term forecasting of monthly reference evapotranspiration in the Guilan Plain, northern Iran. Monthly meteorological data gathered from four weather stations (Anzali, Astara, Manjil, and Rasht) were used to calculate monthly reference evapotranspiration in the period of 1993–2014 using the FAO-56 Penman–Monteith (FAO-PM) equation. The evapotranspiration data from 1993 to 2012 were used to fit SARIMA models and calibrate SVM and GMDH models, and the monthly evapotranspiration rates for the years 2013 and 2014 were forecasted using the calibrated models. The developed models were assessed using RMS error (RMSE), the Pearson correlation coefficient (R), the Nash–Sutcliffe model efficiency coefficient (NS), and percent bias. Taylor diagrams also were used to compare the accuracy of forecasts produced by the models. For the whole forecasting period (2013–2014), the RMSE of the calibrated SARIMA, SVM, and GMDH models were, respectively, 8.796, 9.830, and 9.547 mm/month for Anzali weather station; 8.136, 9.057, and 7.808 mm/month for Astara weather station; 9.454, 8.947, and 8.876 mm/month for Manjil weather station; and 9.301, 10.509, and 10.138 mm/month for Rasht weather station. In other words, in two weather stations under study (Anzali and Rasht), the best results were obtained from SARIMA; however, for Astara and Manjil weather stations, GMDH generated the best forecasts. Furthermore, at different forecasting horizons (1–24 months), the SARIMA models generally outperformed the SVM and GMDH models.