Towards a metabolic theory of catchments: scaling of water and carbon fluxes with size

Allometric scaling relations are widely used to link biological processes in nature. They are typically expressed as power laws, postulating that the metabolic rate of an organism scales as its mass to the power of an allometric exponent, which ranges between 2/3 and 3/4. Several studies have shown that such scaling laws hold also for natural ecosystems, including individual trees and forests, riverine metabolism, and river network organization. Here, we focus on allometric relations at watershed scale to investigate “catchment metabolism”, defined as the set of ecohydrological and biogeochemical processes through which the catchment maintains its structure and reacts to the environment. By revising existing plant size-density relationships and integrating them across large-scale domains, we show that the ecohydrological fluxes (representative of metabolic rates of a large and diverse vegetation assemblage) occurring at the catchment scale are invariant with respect to its average above-ground biomass, while they scale linearly with the basin size. We verify our theory with hyper-resolution ecohydrological simulations across the European Alps, which represent an ideal case study due to the large elevation gradient affecting the availability of energy and water resources. Deviations from the isometric scaling are observed and ascribable to energy limitations at high elevations. Remote sensing data from semiarid and tropical basins are also used to show that the observed scaling of water and carbon fluxes with size holds across a broad spectrum of climatic conditions.