Estimating monthly wet sulfur (S) deposition flux over China using an ensemble model of improved machine learning and geostatistical approach

The wet S deposition was treated as a key issue because it played the negative on the soil acidification, biodiversity loss, and global climate change. However, the limited ground-level monitoring sites make it difficult to fully clarify the spatiotemporal variations of wet S deposition over China. Therefore, an ensemble model of improved machine learning and geostatistical method named fruit fly optimization algorithm-random forest-spatiotemporal Kriging (FOA-RF-STK) model was developed to estimate the nationwide S deposition based on the emission inventory, meteorological factors, and other geographical covariates. The ensemble model can capture the relationship between predictors and S deposition flux with the better performance (R² = 0.68, root mean square error (RMSE) = 7.51 kg ha⁻¹ yr⁻¹) compared with the original RF model (R² = 0.52, RMSE = 8.99 kg ha⁻¹ yr⁻¹). Based on the improved model, it predicted that the highest and lowest S deposition flux were mainly concentrated on the Southeast China (69.57 kg S ha⁻¹ yr⁻¹) and Inner Mongolia (42.37 kg S ha⁻¹ yr⁻¹), respectively. The estimated wet S deposition flux displayed the remarkably seasonal variation with the highest value in summer (22.22 kg S ha⁻¹ sea⁻¹), follwed by ones in autumn (18.30 kg S ha⁻¹ sea⁻¹), spring (16.27 kg S ha⁻¹ sea⁻¹), and the lowest one in winter (14.71 kg S ha⁻¹ sea⁻¹), which was closely associated with the rainfall amounts. The study provides a novel approach for the S deposition estimation at a national scale.