Importance and strength of environmental controllers of soil organic carbon changes with scale

Spatial heterogeneity in environmental factors on the land surface moderates exchanges of water, energy, and greenhouse gases between the land and the atmosphere. However, appropriately representing this heterogeneity in earth system models remains a critical scientific challenge. We used a large dataset of environmental factors (n = 31) representing soil-forming factors, field observations of soil organic carbon (SOC) (n = 6213), and a machine-learning algorithm (Cubist) to analyze the scaling behavior of SOC across the conterminous United States. We found that various environmental factors are significant predictors of SOC stocks at different spatial scales. Out of the 31 environmental factors we investigated, only 13 were significant predictors of SOC stocks at spatial scales ranging from 100 m to 50 km. Overall, topographic variables had higher influence at finer scales, whereas climatic variables were more important at coarser scales. The model performance worsened with increasing scale or the spatial resolution of prediction (R-2 = 0.38-0.65). The strength of environmental controls (median regression coefficient) on SOC weakened with scale, and we represented them using mathematical functions (R-2 = 0.38-0.98). Both the mean and variance of SOC stocks decreased linearly with increasing the scale in soils of the conterminous United States. Fitted linear functions accounted for 81% and 82% of the variability in the mean and variance of SOC, respectively. We also found linear relationships among mean and high-order moments of SOC (R-2 = 0.51-0.97). Improved understanding of the scaling behavior of SOC stocks and their environmental controllers can improve earth system model benchmarking and may eventually improve representation of the spatial heterogeneity of land surface biogeochemistry.