Comparative Study of Time Series Models, Support Vector Machines, and GMDH in Forecasting Long-Term Evapotranspiration Rates in Northern Iran Afshin Ashrafzadeh 1 ; Ozgur Kişi 2 ; Pouya Aghelpour 3 ; Seyed Mostafa Biazar 4 ; and Mohammadreza Askarizad Masouleh 5 Abstract: 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 refer- ence 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. DOI: 10.1061/(ASCE)IR.1943-4774.0001471. © 2020 American Society of Civil Engineers. Author keywords: Evapotranspiration; Seasonal autoregressive integrated moving average (SARIMA); Support vector machine; Machine learning. Introduction Reliable estimates of reference evapotranspiration (ET 0 ) rate are essential for managing agricultural water, especially in countries where water scarcity is a matter of concern. The process of evapotranspiration is a very complex natural phenomenon affected by various factors, mainly meteorological conditions; soil and land properties; and the interaction among water, soil, and plant. Numer- ous methods have been proposed for evaporation and reference evapotranspiration estimation, which can be categorized into water balance, empirical, and physical methods (Gallego-Elvira et al. 2012). Selection and implementation of a method highly depends on data availability and the purpose of the project. The FAO-56 Penman–Monteith (FAO-PM) equation (Allen et al. 1989) is rec- ognized as a standard method for estimating reference and actual evapotranspiration. The implementation of the FAO-PM method in many regions could be limited by factors such as meteorological data quantity and quality; however, several successful applications of this method in Iran can be found in the literature (e.g., Nouri and Homaee 2018; Taherparvar and Pirmoradian 2018; Mokhtari et al. 2018; Biazar et al. 2019). The Guilan Plain is a fertile rice-producing humid region situ- ated in northern Iran. The irrigation water for paddy fields of the Guilan Plain has always been supplied directly from the Sefidroud River. However, due to an increasing demand for surface water in recent years, the Guilan Plain is now experiencing serious water scarcity issues. It is believed that climate change could worsen these water issues. Senatore et al. (2019) projected an overall de- crease of 20% in precipitation and an overall increase of 2.4°C in mean annual temperature over Iran. Some studies (e.g., Hadinia et al. 2017; Pirmoradian and Davatgar 2019) also suggested that climate change would considerably affect the demand for 1 Associate Professor, Faculty of Agricultural Sciences, Dept. of Water Engineering, Univ. of Guilan, Khalij-e-Fars Blvd., Rasht 41996-13776, Iran (corresponding author). ORCID: https://orcid.org/0000-0002-9417 -6431. Email: ashrafzadeh@guilan.ac.ir 2 Professor, Faculty of Natural Sciences and Engineering, Ilia State Univ., Kakutsa Cholokashvili Ave. 3/5, Tbilisi 0162, Georgia. Email: ozgur.kisi@iliauni.edu.ge 3 Ph.D. Student, Agricultural Meteorology, Faculty of Agricultural Engineering and Technology, College of Agriculture and Natural Resources, Dept. of Irrigation and Reclamation Engineering, Univ. of Tehran, Karaj 77871-31587, Iran. ORCID: https://orcid.org/0000-0002 -5640-865X. Email: aghelpoor_p68@yahoo.com 4 Ph.D. Candidate, Dept. of Water Engineering, Univ. of Tabriz, 29 Bahman St., Tabriz 51666-16471, Iran. ORCID: https://orcid.org /0000-0002-8596-2051. Email: seyedmostafa.b@gmail.com 5 M.Sc. Student, Dept. of Computer Engineering, Sharif Univ. of Technology, Azadi St., Tehran 11155-11365, Iran. ORCID: https://orcid .org/0000-0001-7754-0273. Email: arian.askarizad@gmail.com Note. This manuscript was submitted on December 20, 2018; approved on January 2, 2020; published online on March 30, 2020. Discussion period open until August 30, 2020; separate discussions must be submitted for individual papers. This paper is part of the Journal of Irrigation and Drai- nage Engineering, © ASCE, ISSN 0733-9437. © ASCE 04020010-1 J. Irrig. Drain. Eng. J. Irrig. Drain Eng., 2020, 146(6): 04020010 Downloaded from ascelibrary.org by Afshin Ashrafzadeh on 03/30/20. Copyright ASCE. For personal use only; all rights reserved.