Multivariate statistical assessment of critical and trace elements in fly ash from a municipal solid waste incineration plant in southern Poland

Municipal solid waste incineration fly ash (MSWI-FA) is both an environmentally significant residue and a potential secondary source of critical and valuable elements. This study investigated the distribution and inter-element relationships of 24 trace, critical and rare earth element variables in 30 fly ash samples collected from a municipal solid waste incineration plant in southern Poland. To address left-censored data, concentrations below analytical detection limits were treated using tobit regression prior to multivariate analysis. Hierarchical cluster analysis (HCA), principal component analysis (PCA), enrichment factor (EF) calculations and partial least squares (PLS) regression were applied to identify the main controls on element distribution. The first two principal components explained 59.8% of the total variance (PC1=47.2%, PC2=12.6%). PCA and HCA revealed distinct element associations, including a stable group comprising LREE, HREE, Sc, Li, Mg and Sr, and a separate group dominated by Sb, Zn, Bi, Tl and related elements. Enrichment factor analysis indicated very high enrichment of Sb(EF=1835), Zn(EF=1183), Pd(EF =231), Pt(EF=177) and Bi(EF=137), reflecting strong accumulation relative to crustal abundances. In contrast, Fe(EF=0.98), V(EF=0.67), HREE(EF=0.68), Sc(EF=0.41) and Nb(EF =0.008) showed little or no enrichment. PLS models further differentiated strongly interconnected element groups from elements exhibiting largely independent behaviour. The integrated application of tobit regression, multivariate statistics and enrichment factor analysis identified two principal controls on element distribution: a relatively stable mineral-associated component and thermally redistributed enriched elements. The results contribute to the assessment of MSWI fly ash as a potential secondary resource within urban mining and circular economy strategies.