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Precision pollution control relies on accurate spatial interpolation and quantitative source apportionment. This study addresses key methodological gaps by developing two novel tools: a non-negative constrained biharmonic spline interpolation algorithm (v4r) for handling non-stationary data and outliers, and an adaptive pollution source-constrained nonnegative matrix factorization (APSC-NMF) model that incorporates prior source profiles to reduce interpretation subjectivity. Validated on heavy metals in mining-impacted agricultural soils, v4r reduced the root mean square error by 73.66% and 24.57% relative to Ordinary Kriging and Inverse Distance Weighting, respectively. APSC-NMF achieved an 11.87% lower factorization error than unconstrained Positive Matrix Factorization, yielding more interpretable source signatures. Spatial-risk analysis identified severe thallium and cadmium pollution, significant ecological risks from mercury, and heightened health risks for children from thallium and copper ingestion, designating specific zones for priority remediation. Together, v4r and APSC-NMF provide a robust analytical framework for precise spatial mapping and source quantification, informing environmental management.
Yu et al. (Fri,) studied this question.