Uncertainty analysis for the data-driven model using Monte Carlo simulations to predict sodium adsorption rate: A case study, Aras, Sepid-Rud, and Karun Rivers in Iran

Water quality management requires a profound understating of future variations of surface and groundwater qualities for assessment and planning for human consumption, industrial, and irrigation purposes. In this regard, mathematical models, such as Box-Jenkins time series models, Bayesian time series models, and data-driven models are available for future prediction of water quality. However, the uncertainty associated with forecasting is one of the main problems of using these models towards water quality and future planning. In the present work, the uncertainty of the Adaptive Neuro-Fuzzy Inference System, based on Fuzzy c-means clustering, (ANFIS-FCMC) (genfis 3) model is quantified to analyze and predict Sodium Adsorption Rate(SAR) of water of Aras, Sepid-Rud, and Karun Rivers by using Monte Carlo simulations. The results indicate the combined standard and the expanded uncertainty simulated for SAR of Aras River water are 0.58 and1.16, respectively, and the gap is 2 .412 ±1.1622. Also, the combined standard and the expanded uncertainty simulated for SAR of Spid-Rud River water were1.11 and 2.22, respectively, and the gap is equal to 2 .235 ±2.22. Furthermore, the combined standard and the expanded uncertainty simulated for SAR of Aras River water are 2.063, and 4.126, respectively, and the gap is 4.79 ±4.126. Finally, the minimum uncertainty happened to predict SAR of Aras River using ANFIS-FCMC (genfis3) model and maximum SAR uncertainty belong to Karun River.