Global Self-Similar Scaling of Terrestrial Carbon With Aridity

While it is well known that water availability controls vegetation growth and soil microbial activity, how aridity affects ecosystem carbon patterns is not completely understood. Toward a more quantitative assessment of terrestrial carbon stocks, here we apply dimensional analysis and scaling to the global joint distribution of terrestrial carbon stock, obtained from international survey data and harmonized global maps. The results show a remarkable self-similar behavior of the global carbon stock with dryness index, whereby the key statistics (e.g., mean, quantiles, and standard deviation) of carbon stock tend to scale with the hydroclimatic regime (i.e., aridity) via a universal exponent. Such a scaling reflects the strong coupling between the hydrological cycle and biogeochemical process and enables robust predictions of carbon stocks as a function of aridity only. When normalized by its averages in the corresponding hydroclimatic regime, the carbon stock distributions collapse onto a single double Pareto lognormal distribution, often used in economics to describe income. The presence of this distribution in completely different physical contexts, such as biogeochemistry and economics, hints at generating mechanisms that transcend the details of the specific stock being considered.