Development of forecasting of monthly SAR time series in river systems: A multivariate data decomposition-based hybrid approach

The sodium adsorption ratio (SAR) is a critical variable in assessing the quality of water resources, and accurately forecasting its time series is operationally valuable. This study developed a hybrid approach using the multivariate variational mode decomposition (MVMD) model for signal analysis, Boruta model for feature selection, pure linear neural network (PLNN), support vector regression (SVR), Lasso regression, and Elman neural network (ENN) models to forecast monthly SAR time series for rivers. Data from two rivers were used to enhance result reliability, and the developed models were compared with corresponding basic models to evaluate their impact. Numerical and graphical criteria demonstrated the significant superiority of the developed models over the basic ones. Among the basic models, the ENN model exhibited the highest accuracy, while the MVMD-Boruta-ENN model surpasses all investigated models. This finding suggested that the ENN model's structure is more suitable for SAR time series forecasting than other basic models. Analyzing the models' residuals revealed lower mean, standard deviation, skewness, and error range in the developed models, indicating their robust behavior in forecasting the SAR time series. Notably, forecasting extreme SAR values holds greater importance than other values. Anderson-Darling and Kolmogorov-Smirnov tests identified the dominance of the generalized logistic and log-logistic (3-parameters) functions in SAR time series. Probability distribution functions were used to estimate extreme values, and the studied models exhibited more accurate estimations compared to the basic models, indicating their enhanced resilience. The consistent patterns observed in comparing developed and basic models for the entire series, as well as extreme values and residuals across the two investigated rivers, emphasized the reliability of the results.