Enhancing total hardness forecasting in water resources: a hybrid framework integrating machine learning, TVF-EMD signal decomposition, and XGBoost feature selection

Total Hardness (TH) is a critical hydrochemical parameter influencing water quality management in industrial, potable, and agricultural systems. Accurate TH forecasting is essential for sustainable resource utilization but remains challenging due to the parameter's nonstationary dynamics and complex interactions with environmental factors. To address this challenge, this study proposes and validates a novel hybrid forecasting framework that synergistically integrates machine learning (ML) with Time-Varying Filter-Based Empirical Mode Decomposition (TVF-EMD) for signal processing and eXtreme Gradient Boosting (XGBoost) for feature selection. The framework's performance was rigorously evaluated against four standalone ML models – Generalized Regression Neural Network (GRNN), Random Forest (RF), Cascaded Forward Neural Network (CFNN), and Response Surface Methodology (RSM) – using data from hydrometric stations. Key quantitative results demonstrate the superiority of the hybrid approach. The optimal CFNN-TVF-XGBoost configuration achieved Nash-Sutcliffe Efficiency (NSE) values of 0.78 and 0.95, representing improvements of approximately 4.3% and 7.7% over the best standalone model (CFNN). Critical model insights include: (1) a single lag step suffices for robust TH forecasting, (2) XGBoost-driven feature selection enhanced computational efficiency by reducing input dimensionality by 69.0% and 79.6%, and (3) TVF-EMD effectively isolated the nonstationary components of the TH signal. Residual analysis (Q-Q plots and PDFs) confirmed the hybrid model's robustness, with reduced variance and improved error distribution. Importantly, extending beyond point forecasts, probabilistic analysis using Weibull and Normal distributions provided reliable estimates of extreme TH values, a crucial aspect for risk assessment given model behavior variability. This work presents not merely a case study but a generalizable, theoretically grounded framework that fills a research gap by unifying advanced signal decomposition, intelligent feature selection, machine learning, and extreme value analysis. The results underscore the critical synergy among these components in geoscientific data analytics, offering a powerful tool for environmental risk mitigation and operational water-quality management.HighlightsThe hybrid CFNN-TVF-XGBoost model enhances TH forecasting accuracy.TVF-EMD captures nonstationary TH dynamics effectively.Probabilistic methods assess extreme TH values via distribution functions.