Superlinear scaling of riverine biogeochemical function with watershed size

Abstract

River networks are a crucial component of the earth system because they regulate carbon and nutrient exchange between continents, the atmosphere, and oceans. Quantifying the role of river networks at broad spatial scales must accommodate spatial heterogeneity, discharge variability, and upstream-downstream connectivity. Allometric scaling relationships of cumulative biogeochemical function with watershed size integrate these factors, providing an approach for understanding the role of fluvial networks in the earth system. Here we demonstrate that allometric scaling relationships of cumulative river network function are linear (power exponent ~ 1) when biogeochemical reactivity is high and river discharges are low, but become increasingly superlinear (power exponent > 1) as reactivity declines or discharge increases. Superlinear scaling indicates that biogeochemical function of entire river networks within a watershed is an emergent property that increases disproportionately with increasing watershed size. Expanding observation networks will increase precision in riverine fluxes of carbon and nutrients estimated by allometric scaling functions.

The Ecology of River Ice

“…In addition, there can be a wide degree of variation among watersheds within a given biome based on factors such as elevation or land use, making it difficult to define a general set of principles for the role of winter in rivers. River or watershed size is often used to conceptualize river function as it can exert broad-scale controls on fundamental physical features of rivers such as light availability (Finlay, 2011) and flow (Poff et al, 1997) and is linked to changes in metabolic regimes (Bernhardt et al, 2018), nutrient processing rates (Creed et al, 2015;Marinos et al, 2020;Wollheim et al, 2021), and energy flow through food webs (Thorp & Delong, 1994;Vannote et al, 1980). Importantly, size is also correlated with patterns in ice formation and duration (Turcotte & Morse, 2013), indicating that there may be general patterns in winter ecological processes that also scale with river size.…”