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

Abstract

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.

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Related concepts (35)

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Allometry

Allometry is the study of the relationship of body size to shape, anatomy, physiology and finally behaviour, first outlined by Otto Snell in 1892, by D'Arcy Thompson in 1917 in On Growth and Form and by Julian Huxley in 1932. Allometry is a well-known study, particularly in statistical shape analysis for its theoretical developments, as well as in biology for practical applications to the differential growth rates of the parts of a living organism's body. One application is in the study of various insect species (e.

Kleiber's law

Kleiber's law, named after Max Kleiber for his biology work in the early 1930s, is the observation that, for the vast majority of animals, an animal's metabolic rate scales to the power of the animal's mass. Symbolically: if q0 is the animal's metabolic rate, and M is the animal's mass, then Kleiber's law states that q0~M3/4. Thus, over the same time span, a cat having a mass 100 times that of a mouse will consume only about 32 times the energy the mouse uses.

Power law

In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to a power of the change, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four.

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