Predicting the Spatial Distribution and Regional Averages of Soil Heavy Metals Based on Stratification

The significant spatial stratified heterogeneity of soil heavy metal concentrations is a critical characteristic, and effectively capturing this feature can improve the accuracy of spatial interpolation and the reliability of regional mean estimations. This study used 412 soil sampling points in Shunyi District, Beijing, to predict the spatial distribution and regional means of soil heavy metals using a supervised learning-based stratified random forest ordinary Kriging (SRFOK) model. Spatial stratification information of soil heavy metals was extracted via supervised learning and incorporated into the spatial interpolation process. In addition, 21 environmental factors were integrated to enhance the model's ability to characterize spatial heterogeneity. The spatial distributions of the three soil heavy metals cadmium (Cd), chromium (Cr), and copper (Cu) were predicted, and their regional means were estimated. The performance of the SRFOK model was compared with those of ordinary Kriging (OK) and random forest ordinary Kriging (RFOK). Regional mean concentrations were calculated based on the interpolation results and further assessed using the sandwich estimator as a reference. The results demonstrated that the SRFOK model achieved the best prediction performance for all three heavy metals, with coefficients of determination (R2) of 0.619 (Cd), 0.635 (Cr), and 0.498 (Cu), representing improvements of 26% to 100% compared to the OK and RFOK models, as well as the lowest root mean square error (RMSE) and mean absolute error (MAE). Regional means obtained from the different models were generally consistent, and the overall concentrations of Cd, Cr, and Cu in the study area were higher than their background values in Beijing. The findings indicate that incorporating supervised learning-based stratification information into spatial interpolation enhances both the accuracy of spatial interpolation and the stability of regional mean estimation for soil heavy metals, so it is an effective approach for high-precision mapping and regional pollution risk assessment.