Scaling impacts on environmental controls and spatial heterogeneity of soil organic carbon stocks

The spatial heterogeneity of land surfaces affects energy, moisture, and greenhouse gas exchanges with the atmosphere. However, representing the heterogeneity of terrestrial hydrological and biogeochemical processes in Earth system models (ESMs) remains a critical scientific challenge. We report the impact of spatial scaling on environmental controls, spatial structure, and statistical properties of soil organic carbon (SOC) stocks across the US state of Alaska. We used soil profile observations and environmental factors such as topography, climate, land cover types, and surficial geology to predict the SOC stocks at a 50m spatial scale. These spatially heterogeneous estimates provide a data set with reasonable fidelity to the observations at a sufficiently high resolution to examine the environmental controls on the spatial structure of SOC stocks. We upscaled both the predicted SOC stocks and environmental variables from finer to coarser spatial scales (s = 100, 200, and 500m and 1, 2, 5, and 10 km) and generated various statistical properties of SOC stock estimates. We found different environmental factors to be statistically significant predictors at different spatial scales. Only elevation, temperature, potential evapotranspiration, and scrub land cover types were significant predictors at all scales. The strengths of control (the median value of geographically weighted regression coefficients) of these four environmental variables on SOC stocks decreased with increasing scale and were accurately represented using mathematical functions (R-2 = 0.83-0.97). The spatial structure of SOC stocks across Alaska changed with spatial scale. Although the variance (sill) and unstructured variability (nugget) of the calculated variograms of SOC stocks decreased exponentially with scale, the correlation length (range) remained relatively constant across scale. The variance of predicted SOC stocks decreased with spatial scale over the range of 50m to similar to 500 m, and remained constant beyond this scale. The fitted exponential function accounted for 98% of variability in the variance of SOC stocks. We found moderately accurate linear relationships between mean and higher-order moments of predicted SOC stocks (R-2 similar to 0.55-0.63). Current ESMs operate at coarse spatial scales (50100 km), and are therefore unable to represent environmental controllers and spatial heterogeneity of high-latitude SOC stocks consistent with observations. We conclude that improved understanding of the scaling behavior of environmental controls and statistical properties of SOC stocks could improve ESM land model benchmarking and perhaps allow representation of spatial heterogeneity of biogeochemistry at scales finer than those currently resolved by ESMs.