<p>Soil heavy metal pollution threatens environmental integrity and public health, necessitating precise spatial prediction. Traditional methods like on-site sampling and spectral inversion are labor-intensive and susceptible to disruptions from surface factors such as vegetation and moisture. While existing interpolation approaches face distinct limitations, physically driven methods like ordinary Kriging and cokriging rely on stationarity or intrinsic assumptions for physical interpretability but struggle with linearity constraints and challenges in capturing complex non-stationary and nonlinear distributions prevalent in soil data, whereas data-driven neural network-based methods, including IGNNK, often employ heuristic approximations without true variogram grounding, limiting their physical explainability despite greater flexibility. This study introduces variogram-distance graph attention Kriging (VDGAK), an innovative hybrid model that merges the physical explainability of Kriging with the adaptability of graph attention networks (GAT), to map eight heavy metals (Cd, As, Cr, Cu, Mn, Pb, Zn, Ni) across Youyang County, Southwest China, based on 466 soil samples. By incorporating variogram-derived spatial relationships and distance into GAT’s attention mechanism, VDGAK excels at modeling complex, non-stationary and nonlinear distributions. Compared to ordinary Kriging (OK), GAT, V-GAT (variogram-integrated GAT), and D-GAT (distance-integrated GAT), VDGAK consistently outperforms all models across eight metals, achieving the highest R² and the lowest errors (RMSE% and MAE%). Across all metals, OK consistently underperforms, while V-GAT and D-GAT vary depending on trend or local variation dominance. This study underscores hybrid models like VDGAK, blending physical and data-driven strengths, enhance soil heavy metal mapping, improving environmental monitoring and remediation.</p>

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Variogram-distance graph attention Kriging: an innovative hybrid approach for improving soil heavy metals interpolation

  • Ling Zeng,
  • Daichi Xu,
  • Rui Sun,
  • Meng Yuan,
  • Bin Hu

摘要

Soil heavy metal pollution threatens environmental integrity and public health, necessitating precise spatial prediction. Traditional methods like on-site sampling and spectral inversion are labor-intensive and susceptible to disruptions from surface factors such as vegetation and moisture. While existing interpolation approaches face distinct limitations, physically driven methods like ordinary Kriging and cokriging rely on stationarity or intrinsic assumptions for physical interpretability but struggle with linearity constraints and challenges in capturing complex non-stationary and nonlinear distributions prevalent in soil data, whereas data-driven neural network-based methods, including IGNNK, often employ heuristic approximations without true variogram grounding, limiting their physical explainability despite greater flexibility. This study introduces variogram-distance graph attention Kriging (VDGAK), an innovative hybrid model that merges the physical explainability of Kriging with the adaptability of graph attention networks (GAT), to map eight heavy metals (Cd, As, Cr, Cu, Mn, Pb, Zn, Ni) across Youyang County, Southwest China, based on 466 soil samples. By incorporating variogram-derived spatial relationships and distance into GAT’s attention mechanism, VDGAK excels at modeling complex, non-stationary and nonlinear distributions. Compared to ordinary Kriging (OK), GAT, V-GAT (variogram-integrated GAT), and D-GAT (distance-integrated GAT), VDGAK consistently outperforms all models across eight metals, achieving the highest R² and the lowest errors (RMSE% and MAE%). Across all metals, OK consistently underperforms, while V-GAT and D-GAT vary depending on trend or local variation dominance. This study underscores hybrid models like VDGAK, blending physical and data-driven strengths, enhance soil heavy metal mapping, improving environmental monitoring and remediation.