The Sodium Adsorption Ratio (SAR) is a widely used variable in water quality research, particularly in agriculture and environmental studies. In many cases, the key variables required for SAR calculation, namely Na+, Mg+2, and Ca+2, are not available. Consequently, the potential to calculate SAR using a limited number of water quality variables becomes critically important. The study implemented the Multilayer Perceptron Neural Network (MLPNN), Support Vector Regression (SVR), and K-Nearest Neighbors (KNN) models at level-0 for prediction purposes, along with the Boruta model for variable selection. A stacked ensemble learning model at level-1 enhanced the prediction accuracy. The discharge and water quality dataset from the Zarrin-Gol River in northern Iran was utilized to implement the modeling procedure. Results obtained from the variable selection process using the Boruta model revealed that using a limited number of water quality variables can effectively predict SAR even without the principal variables. Further investigation of the input combinations for the level-0 models demonstrated that, for the MLPNN, KNN, and SVR models, 4, 3, and 1 input variables, respectively, yielded optimal predictions. Among the level-0 models, the MLPNN model exhibited the highest accuracy, with RMSE = 0.54, MBE = 0.26, MAE = 0.44, R = 0.84, IA = 0.67, and KGE = 0.79. Implementing the stacked ensemble learning model at level-1 significantly improved the SAR prediction compared to the level-0 models. The ensemble-NN model yielded the best performance in estimating SAR within the range of recorded data, with RMSE = 0.53, MBE = 0.29, MAE = 0.41, R = 0.87, IA = 0.70, and KGE = 0.82. Residual analysis further confirmed the superior predictive capability of the level-1 models compared to the level-0 models. The generalized-logistic probability distribution function is used to estimate the extreme values data. The Ensemble-KNN model best predicted extreme values data, with RMSE = 0.69, MBE = −0.61, MAE = 0.61, R = 0.61, IA = 0.26, and KGE = 0.37. The findings underscore the substantial advancements achieved through stacked ensemble methods in enhancing the modeling of SAR across various aspects, including total data, extreme values, and models' residuals.

钠吸附比 (SAR) 是水质研究中广泛使用的变量，特别是在农业和环境研究中。在许多情况下，SAR 计算所需的关键变量，即 Na+、Mg+2 和 Ca+2 并不可用。因此，使用有限数量的水质变量计算 SAR 的潜力变得至关重要。该研究在 0 级实现了多层感知器神经网络 (MLPNN)、支持向量回归 (SVR) 和 K 最近邻 (KNN) 模型以用于预测目的，以及用于变量选择的 Boruta 模型。1 级堆叠集成学习模型提高了预测准确性。利用伊朗北部扎林戈尔河的流量和水质数据集来实施建模程序。使用 Boruta 模型的变量选择过程获得的结果表明，即使没有主变量，使用有限数量的水质变量也可以有效地预测 SAR。对 0 级模型的输入组合的进一步研究表明，对于 MLPNN、KNN 和 SVR 模型，分别使用 4、3 和 1 个输入变量产生最佳预测。在0级模型中，MLPNN模型的准确率最高，RMSE = 0.54，MBE = 0.26，MAE = 0.44，R = 0.84，IA = 0.67，KGE = 0.79。与 0 级模型相比，在 1 级实现堆叠集成学习模型显着改善了 SAR 预测。集成神经网络模型在估计记录数据范围内的 SAR 方面表现最佳，RMSE = 0.53、MBE = 0.29、MAE = 0.41、R = 0.87、IA = 0.70 和 KGE = 0.82。残差分析进一步证实了 1 级模型相对 0 级模型的优越预测能力。广义逻辑概率分布函数用于估计极值数据。Ensemble-KNN 模型对极值数据的预测效果最好，RMSE = 0.69，MBE = -0.61，MAE = 0.61，R = 0.61，IA = 0.26，KGE = 0.37。研究结果强调了通过堆叠集成方法在增强 SAR 建模的各个方面（包括总数据、极值和模型残差）方面取得的重大进展。