Comparison of Box–Jenkin Time Series and Radial Basis Function for Sodium Adsorption Rate Forecasting; a Case Study Aras, Sepidrud, Karun, and Mond Rivers

Desalination and Water Treatment 218 (2021) 193–209 www.deswater.com April

doi: 10.5004/dwt.2021.26987

Comparison of Box–Jenkin time series and radial basis function for sodium adsorption rate forecasting; a case study Aras, Sepidrud, Karun, and Mond Rivers

Elham Rahnamaa, Omolbanin Bazrafshana, Gholamreza Asadollahfardib,*, S. Yaser Samadic aDepartement of Natural Resources Engineering, Faculty of Agricultural Engineering and Natural Resources, Hormozgan University, Bandar Abbas, Iran, emails: [email protected] (E. Rahnama), [email protected] (O. Bazrafshan) bCivil Engineering Department, Faculty of Engineering, Kharazmi University, Tehran, Iran, email: [email protected] cSchool of Mathematical and Statistical Sciences, Southern Illinois University, Carbondale, IL, USA, email: [email protected]

Received 13 July 2020; Accepted 24 Decexmber 2020

abstract Regarding water consumption for various usage, water quality management is a significant part of water management. Future prediction of water quality parameters is necessary for the plan- ning of water quality management. Sodium adsorption rate (SAR) is a parameter, which has a significant role in irrigation. In the present study, we compared the forecasting of SAR of water in Aras, Sepidrud, Karun, and Mond Rivers, Iran, using autoregressive integrated moving average (ARIMA) time series and radial basis functions (RBF) neural network. We found ARIMA (0,1,1) × (0,1,1)12, ARIMA (0,1,1) (0,1,1)12, ARIMA (0,1,1), and ARIMA (0,1,2) × (1,1,1)12 with minimum Akaike’s Information Criterion (AIC) of –1.7127, –1.8177, 2.9317, and 12.44 for SAR prediction of Aras, Sepidrud, Karun, and Mond Rivers, respectively. The residual of the mentioned ARIMA models was independent (p-value > 0.05). Using RBF neural network for SAR forecasting of Aras, Sepidrud, Karun, and Mond Rivers with normalized data, we obtained proper training and testing. Mean squared error (MSE are between 0.00026 and 0.0255) and mean bias error (MBE are between 0.01566 and 0.0612) for training is very low. Likewise, coefficient of determination (R2 are between 0.907 and 0.960), index of agreement (IA are between 0.981 and 0.999), and the Nash–Sutcliffe effi- ciency (E are between 0.964 and 0.999) approach to 1, which describes the reliability of the model’s performance. Thirty-six months RBF neural network and 12 months of ARIMA time series of SAR forecasting for Aras River comparatively match to the measured data and forecast error of both RBF and ARIMA were comparable. We compared forecast errors of the ARIMA time series and RBF neural network for SAR forecasting of Sepidrud, Karun, and Mond Rivers; the results presented that RBF neural network is more reliable than ARIMA for the predicting of SAR. Keywords: Sodium adsorption rate forecasting; Autoregressive integrated moving average; Radial basis function neural network

* Corresponding author.