A geographically weighted neural network model for digital soil mapping of heavy metal copper in coastal cities

Assessing the spatial distribution of heavy metals in soil is essential for mitigating risks to human health and ensuring the sustainable use of soil resources. This study proposed a geographically weighted neural network (GWNN) model, leveraging deep learning and geographically weighted regression (GWR). The model was designed based on the GWR concept to address the spatial autocorrelation of copper (Cu) in soil and incorporated convolutional neural network (CNN) to capture the nonlinear relationships between Cu and environmental covariates. The GWNN model was compared with GWR, extreme gradient boosting (XGBoost), and artificial neural network (ANN) models. XGBoost was employed to select important environmental covariates and spatial autocorrelation of Cu concentrations was assessed using Moran’s I. The model’s performance was evaluated using 10-fold cross-validation, and prediction uncertainty was quantified with 100 bootstrap models. The results indicated that temperature covariates were the most significant predictors of soil Cu concentrations. The R 2 values for Cu prediction accuracy were 0.60 for GWNN, 0.53 for ANN, 0.49 for XGBoost, and 0.32 for GWR. The spatial distribution of Cu showed a trend of higher concentrations in the north and lower concentrations in the south, consistent with spatial clusters identified by local Moran’s I. The mean uncertainty of the 90 % confidence interval for GWNN was 16.49 %, closely aligning with XGBoost (15.44 %) and ANN (16.29 %) and significantly outperforming the GWR (18.25 %). Overall, the GWNN model demonstrated strong predictive accuracy and low uncertainty, offering an improved approach for digital soil mapping applications. • A novel hybrid statistical model was developed to predict soil Cu concentrations. • GWNN model outperformed other machine learning models. • GWNN demonstrated high predictive accuracy and low uncertainty. • Importance of environmental covariates to soil Cu prediction was analyzed.