Abstract Groundwater in the Densu Basin is increasingly threatened by heavy metal contamination, yet conventional assessment methods struggle to capture the statistical complexity and spatial heterogeneity of pollution indicators. A critical challenge lies in modelling the Heavy Metal Pollution Index (HPI), which is typically skewed and influenced by correlated contaminants, leading to biased predictions when modelled without transformation. This study develops a predictive framework that integrates response transformations with nested cross-validated ensemble machine learning to address these limitations. Three transformations; raw, log, and Gaussian copula, were applied to HPI and evaluated across six learners: support vector regression (SVM), k-nearest neighbours (k-NN), CART, Elastic Net, kernel ridge regression, and a stacked Lasso ensemble. Diagnostic evaluation showed that raw-scale models produced deceptively high fits, with Elastic Net and the stacked ensemble reporting <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R^2\)</EquationSource> </InlineEquation> values close to 1.0, raising concerns of over-optimism and potential information leakage. The log transformation stabilised variance, improving prediction for SVM (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(R^2 = 0.93\)</EquationSource> </InlineEquation>, RMSE <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(= 0.18\)</EquationSource> </InlineEquation>) and k-NN (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(R^2 = 0.92\)</EquationSource> </InlineEquation>, RMSE <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(= 0.20\)</EquationSource> </InlineEquation>), though the performance of Elastic Net deteriorated. The Gaussian copula transformation yielded the most reliable outcomes: the stacked ensemble achieved <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(R^2 = 0.96\)</EquationSource> </InlineEquation> with RMSE <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(= 0.19\)</EquationSource> </InlineEquation>, while other learners such as SVM (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(R^2 = 0.86\)</EquationSource> </InlineEquation>, RMSE <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(= 0.25\)</EquationSource> </InlineEquation>) and k-NN (<InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(R^2 = 0.85\)</EquationSource> </InlineEquation>, RMSE <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(= 0.26\)</EquationSource> </InlineEquation>) maintained high accuracy. Importantly, copula-based models improved residual behaviour and produced spatially plausible prediction maps, reinforcing their potential for groundwater quality management. Clustering analysis using DBSCAN further revealed the dominance of Fe, followed by Mn, as the primary contributors to HPI, consistent with regional hydrogeochemical processes. Limitations include the reliance on random rather than spatial cross-validation and the basin-specific nature of the analysis, which may constrain transferability. Future research should explore spatially explicit validation schemes and extend the framework to diverse hydrogeological settings. Overall, the study advances predictive hydrogeochemistry by demonstrating that distribution-aware ensembles, complemented by clustering diagnostics, can provide robust and interpretable assessments of groundwater contamination. Graphical Abstract The graphical abstract illustrates the workflow for predicting groundwater heavy metal pollution in the Densu Basin using a nested cross-validated stacked ensemble learning framework. It begins with the acquisition and preprocessing of data on six key metals (As, Pb, Mn, Fe, Cd, Ni), highlighting the land-use and geogenic activities that influence contamination. Correlation and cluster dominance analyses reveal Fe and Mn as the major contributors to the Heavy Metal Pollution Index (HPI). The predictive framework integrates multiple machine learning models (SVR, CART, KNN, Elastic Net, Kernel Ridge) combined through stacking and nested cross-validation to ensure unbiased performance estimation. Comparative transformation of the HPI (raw, log, and Gaussian copula) demonstrates that the Gaussian copula approach improves normality and predictive accuracy. The concluding section summarizes that this framework effectively enhances model reliability and interpretability for groundwater quality prediction, providing a structured, data-driven approach for assessing heavy metal contamination in hydrogeochemical systems.

Smart Ensemble Learning Framework for Predicting Groundwater Heavy Metal Pollution

期刊论文
发表日期：

2026年5月14日

查看全文

Theophilus Ansah-Narh,
George Y. Afrifa,
Joseph B. Tandoh,
Kofi Asare,
Martin Addi,
Kow A. Essel-Yorke,
Daniel M. A. Akpoley,
Kenneth Aidoo,
Samuel K. Fosuhene

摘要

Abstract

Groundwater in the Densu Basin is increasingly threatened by heavy metal contamination, yet conventional assessment methods struggle to capture the statistical complexity and spatial heterogeneity of pollution indicators. A critical challenge lies in modelling the Heavy Metal Pollution Index (HPI), which is typically skewed and influenced by correlated contaminants, leading to biased predictions when modelled without transformation. This study develops a predictive framework that integrates response transformations with nested cross-validated ensemble machine learning to address these limitations. Three transformations; raw, log, and Gaussian copula, were applied to HPI and evaluated across six learners: support vector regression (SVM), k-nearest neighbours (k-NN), CART, Elastic Net, kernel ridge regression, and a stacked Lasso ensemble. Diagnostic evaluation showed that raw-scale models produced deceptively high fits, with Elastic Net and the stacked ensemble reporting \(R^2\) values close to 1.0, raising concerns of over-optimism and potential information leakage. The log transformation stabilised variance, improving prediction for SVM ( \(R^2 = 0.93\) , RMSE \(= 0.18\) ) and k-NN ( \(R^2 = 0.92\) , RMSE \(= 0.20\) ), though the performance of Elastic Net deteriorated. The Gaussian copula transformation yielded the most reliable outcomes: the stacked ensemble achieved \(R^2 = 0.96\) with RMSE \(= 0.19\) , while other learners such as SVM ( \(R^2 = 0.86\) , RMSE \(= 0.25\) ) and k-NN ( \(R^2 = 0.85\) , RMSE \(= 0.26\) ) maintained high accuracy. Importantly, copula-based models improved residual behaviour and produced spatially plausible prediction maps, reinforcing their potential for groundwater quality management. Clustering analysis using DBSCAN further revealed the dominance of Fe, followed by Mn, as the primary contributors to HPI, consistent with regional hydrogeochemical processes. Limitations include the reliance on random rather than spatial cross-validation and the basin-specific nature of the analysis, which may constrain transferability. Future research should explore spatially explicit validation schemes and extend the framework to diverse hydrogeological settings. Overall, the study advances predictive hydrogeochemistry by demonstrating that distribution-aware ensembles, complemented by clustering diagnostics, can provide robust and interpretable assessments of groundwater contamination.

Graphical Abstract

The graphical abstract illustrates the workflow for predicting groundwater heavy metal pollution in the Densu Basin using a nested cross-validated stacked ensemble learning framework. It begins with the acquisition and preprocessing of data on six key metals (As, Pb, Mn, Fe, Cd, Ni), highlighting the land-use and geogenic activities that influence contamination. Correlation and cluster dominance analyses reveal Fe and Mn as the major contributors to the Heavy Metal Pollution Index (HPI). The predictive framework integrates multiple machine learning models (SVR, CART, KNN, Elastic Net, Kernel Ridge) combined through stacking and nested cross-validation to ensure unbiased performance estimation. Comparative transformation of the HPI (raw, log, and Gaussian copula) demonstrates that the Gaussian copula approach improves normality and predictive accuracy. The concluding section summarizes that this framework effectively enhances model reliability and interpretability for groundwater quality prediction, providing a structured, data-driven approach for assessing heavy metal contamination in hydrogeochemical systems.