Enhanced soil organic carbon estimation via hybrid modeling: A data-driven solution to carbon inputs

Soil organic carbon (SOC) is a key component of the global carbon cycle, yet reliable SOC stock prediction remains constrained by uncertainties in carbon inputs (Cinputs). Conventional process-based models, such as RothC, typically rely on empirical estimates of Cinputs, limiting their applicability across heterogeneous environmental and management conditions. Here, we develop a hybrid modeling framework that integrates the RothC model with a data-driven parameter estimator. The carbon input modifier (α) is first inferred through a probabilistic inversion using Markov Chain Monte Carlo (MCMC) and subsequently generalized to the regional scale by training machine learning models on environmental covariates. The framework was evaluated using the European LUCAS dataset, which includes SOC stock measurements for the top 20 cm of soil from more than 7000 sites collected between 2009 and 2018. The hybrid framework substantially outperformed the RothC model, reducing the RMSE of SOC stock predictions from 25.22 to 16.31 t C ha−1, with a corresponding relative RMSE from about 46% to 30%, and increasing the R2 from 0.43 to 0.70 across diverse European ecosystems. SHapley Additive exPlanations (SHAP) analysis identified initial SOC, bulk density, precipitation, and land-use type as dominant regulators of α. Importantly, α exhibited compelling ecological plausibility, as evidenced by a negative correlation with baseline SOC consistent with carbon saturation theory, as well as systematic variations across land-use types reflecting anthropogenic management and vegetation influences on carbon partitioning. This study demonstrates the potential of hybrid approaches to reconcile mechanistic interpretability with data-driven adaptability, providing a scalable tool for soil carbon monitoring and sustainable land management policy development.