A hybrid modelling framework for spatiotemporal prediction of soil organic carbon stock in Dutch agricultural soils

Accurate modelling and mapping of soil organic carbon (SOC) stocks across space and time is essential for climate change mitigation and sustainable land management. Machine learning models often achieve high predictive performance for digital soil mapping, but their data-driven nature may limit their ability to represent temporal SOC dynamics in a physically consistent way. To address this, integrating process-based models may provide additional process information to improve temporal consistency, while it may also improve predictive performance. This study focused on investigating whether integrating the Rothamsted carbon model (RothC) with a Random Forest (RF) model can improve spatiotemporal modelling of SOC stocks (0–30 cm) in Dutch agricultural mineral soils between 1986 and 2022. Specifically, two hybrid strategies were developed, where Hybrid 1 incorporates RothC outputs as additional covariates in the RF model, and Hybrid 2 applies RF to the residuals of RothC simulations and then adds the predicted residuals back to the RothC-simulated SOC stocks. Model performance was evaluated using both random and nearest neighbour distance matching (NNDM) cross-validation. The results indicate that Hybrid 1 achieved the best performance (ME = −1.19 t C ha −1 , RMSE = 26.8 t C ha −1 , MEC = 0.47), improving the MEC by 20.5% compared to RF under NNDM cross-validation. Spatiotemporal analysis showed that spatial and temporal patterns predicted by Hybrid 1 closely aligned with those of the RF model, whereas Hybrid 2 showed greater similarity to RothC. Hence, integrating process-based knowledge into digital soil mapping frameworks improved the accuracy of SOC stock predictions and reduced unrealistic temporal fluctuations. This study provides a flexible methodology for SOC stock prediction. The framework allows users to prioritize predictive performance or physical consistency, particularly in intensive agricultural systems.