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

Catchments are heterogeneous ecosystems involving several abiotic and biotic processes, where the mutual interactions among water, vegetation, and biogeochemical fluxes take place at different scales. Many biological processes in nature are characterized by allometric scaling relationships (Brown, 2004), which postulate that a biological variable B (e.g., the metabolic rate of an organism) scales with its mass M to the power of a scaling exponent ranging between 3/4 and 2/3 (West, 1997; da Silva, 2006). Few studies adopted scaling laws to describe the metabolism of ecosystems including forests (Enquist, 2017) and river basins (Rodriguez-Iturbe, 2011), although at the catchment and regional scales these dynamics remain largely unexplored. Our analysis goes towards this direction, with the aim of finding a feasible reduced-order framework relating key water and carbon fluxes to the catchment’s physical and geometrical properties. Supported by hyper-resolution ecohydrological simulations covering the whole European Alps (Mastrotheodoros, 2020) and remote sensing data, we identify allometric scaling relationships linking water and carbon dynamics (e.g., transpiration, gross primary productivity, carbon use efficiency) to topographic catchment properties (e.g., contributing area), respectively acting as proxies for the catchment metabolic rate B and mass M. These results reveal that drainage basins can be seen as complex biological systems whose dynamics follow similar scaling relations.