Including soil depth as a predictor variable increases prediction accuracy of SOC stocks

Accurate estimates of soil organic carbon (SOC) stocks are important in understanding terrestrial carbon cycling. Based on the fundamental theorem of surfaces, an alternative method, high accuracy surface modelling (HASM) combined with soil depth information was applied to predict the spatial pattern of SOC stocks in Hebei Province, China. In this study, we collected 434 soil samples and key environmental covariates related to soil-forming factors (soil, climate, organisms, topography, and soil depth information) in the study area, and compared the accuracy of 16 spatial prediction models (including single models, hybrid models, and HASM combined with single or hybrid models) on the spatial distribution of SOC stocks. The results confirmed that the method of HASM combined with the generalized additive model (GAM) with soil depth covariate (HASM_GAMD) achieved a better performance than other methods at soil depths of 0–30, 0–100 and 0–200 cm. The root-mean-square error and coefficient of determination values of predicting the spatial pattern of SOC stocks by the HASM_GAMD model demonstrated a 43% and 49% improvement, respectively, compared with models without depth information. The prediction uncertainty of the HASM_GAMD model based on 90% prediction interval was lower than that of other models. The HASM_GAMD model excels in addressing not only the nonlinear relationship between covariates and SOC stocks, but also in incorporating point observation data that varies with soil depth. Furthermore, the model conducts modelling by integrating surface and optimal control theories. Results obtained from the HASM_GAMD demonstrated that the SOC stocks in Hebei Province amounted to 1449.08 Tg C. Our study introduces an alternative model for modelling of SOC stocks and our findings are a valuable reference for assessing carbon stocks in Hebei Province to support sustainable land management and climate change mitigation.