Toward a metabolic theory of catchments: Scaling of water and carbon fluxes with size

Allometric scaling relations are widely used to link biological processes to body size in nature. Several studies have shown that such scaling laws hold also for natural ecosystems, including individual trees and forests, riverine metabolism, and river network organization. However, the derivation of scaling laws for catchment-scale water and carbon fluxes has not been achieved so far. Here, we focus on scaling relations of catchment green metabolism, defined as the set of ecohydrological and biogeochemical processes through which vegetation assemblages in catchments maintain their structure and react to the surrounding environment. By revising existing plant size-density relationships and integrating them across large-scale domains, we show that the ecohydrological fluxes occurring at the catchment scale are invariant with respect to the above-ground vegetation biomass per unit area of the basin, while they scale linearly with catchment size. We thus demonstrate that the sublinear scaling of plant metabolism results in an isometric scaling at catchment and regional scales. Deviations from such predictions are further shown to collapse onto a common distribution, thus incorporating natural fluctuations due to resource limitations into a generalized scaling theory. Results from scaling arguments are supported by hyperresolution ecohydrological simulations and remote sensing observations.