Quantitative characterization of uncertainty in the source apportionment induced by the dual spatial heterogeneity of soil heavy metals

Abstract

Source apportionment of soil heavy metals is pivotal for global pollution prevention; however, its engineering application remains constrained by spatial uncertainty in the apportionment results. This study focused on the core challenge in the engineering application of soil heavy metal source apportionment: uncertainty in the spatial application of apportionment results. Methodological research was conducted using 160 intensive sampling data points collected from 40 representative sampling areas. By synergistically combining a multi-source fingerprint database with dual spatial heterogeneity analysis, the new framework integrated of Bayesian hierarchical modeling and topological network analysis to quantify the spatial uncertainty distribution and reliability. This method controlled the impact of soil heterogeneity within the resolvable spatial range of the maximum likelihood solutions, achieving a 32.7 % enhancement in apportionment stability via support vector machine-classified fingerprint quantification. Methodological synergy elevated source apportionment reliability by 28 % on average while mitigating high-dimensional errors from multifactor correlations, an unprecedented advancement in the field. Furthermore, a computational method for evaluating source apportionment stability was developed, further demonstrating the superior performance of the proposed framework in assessing source apportionment uncertainties. The findings provide accurate information and reliable evidence for soil heavy metal pollution remediation projects and offer an engineering-applicable technical paradigm for addressing nonlinear source-sink relationships in typical mining cities.

Keywords: Heavy metals; Reliability index; Soils; Source apportionment; Uncertainty.