Wavelet-fuzzy machine learning framework for robust prediction of sodium adsorption ratio

Proper assessment of sodium adsorption ratio (SAR) in groundwater is an important component for controlling the quality of irrigation water in semiarid areas. Traditional approaches based on direct physicochemical measurements are less sophisticated in capturing nonlinear threshold behaviour as well as the multiscale temporal dynamics. This paper presents a hybrid wavelet-fuzzy-random forest framework employing a sequential integration strategy, where discrete wavelet transform first extracts multiscale temporal features from groundwater variables, fuzzy inference generates uncertainty-aware membership features, and the combined original, wavelet-derived, and fuzzy-derived feature set is subsequently used for ensemble machine learning prediction. The preprocessing of groundwater samples from hydrogeochemical domains in Gujarat retained three key features: sodium, sulphate, and fluoride. Complementary feature engineering was then applied: base measurements (Level 1:3 features), fuzzy membership functions (Level 2:12 features), and wavelet decomposition (Level 3:21 features). Although SAR was calculated using the conventional hydrochemical formulation involving Na+, Ca2+, and Mg2+ ions, the feature engineering framework emphasized sodium, sulphate, and fluoride due to their stronger statistical variability and predictive significance within the investigated groundwater dataset. Random forest, extra gradient boosting, and light gradient boosting machine ensemble models were all optimized using grid search and five-fold cross-validation on a dataset comprising 601 groundwater samples, which was divided into 481 training samples (80%) and 120 independent testing samples (20%) for model development and evaluation. The best Level 3 hybrid model was the one that performed well with a coefficient of determination = 0.8442, root mean squared error = 0.9014, and mean absolute error = 0.5252. The feature importance analysis showed that fuzzy functions (59.54%) ranked higher than raw measurements (30.57%). This indicates that multiperspective feature engineering is more effective than single-method approaches for accurate groundwater quality prediction and sustainable irrigation in water-scarce regions.