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.

中文翻译：

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河流系统月度 SAR 时间序列预测的发展：基于多元数据分解的混合方法


钠吸附比（SAR）是评估水资源质量的关键变量，准确预测其时间序列具有操作价值。本研究开发了一种混合方法，使用用于信号分析的多元变分模式分解 (MVMD) 模型、用于特征选择的 Boruta 模型、纯线性神经网络 (PLNN)、支持向量回归 (SVR)、Lasso 回归和 Elman 神经网络 (ENN) ) 模型来预测河流的每月 SAR 时间序列。使用两条河流的数据来提高结果的可靠性，并将开发的模型与相应的基本模型进行比较，以评估其影响。数字和图形标准表明所开发的模型相对于基本模型具有显着的优越性。在基本模型中，ENN模型表现出最高的精度，而MVMD-Boruta-ENN模型超越了所有研究的模型。这一发现表明ENN模型的结构比其他基本模型更适合SAR时间序列预测。分析模型的残差揭示了所开发模型的均值、标准差、偏度和误差范围较低，表明它们在预测 SAR 时间序列方面具有稳健的行为。值得注意的是，预测 SAR 极端值比其他值更重要。 Anderson-Darling 和 Kolmogorov-Smirnov 检验确定了 SAR 时间序列中广义 Logistic 和对数 Logistic（3 参数）函数的主导地位。使用概率分布函数来估计极值，并且与基本模型相比，所研究的模型表现出更准确的估计，表明其弹性增强。 在比较整个系列的开发模型和基本模型以及两条调查河流的极值和残差时观察到的一致模式强调了结果的可靠性。