Simple model of morphometric constraint on carbon burial in boreal lakes

Abstract

A geometric theory was developed to explain the empirical relationship between carbon burial and lake shape in boreal lakes. The key feature of this model is an attenuation length scale, analogous to models of marine organic carbon fluxes. This length scale is the ratio of how fast carbon is displaced vertically versus how fast it is respired and engenders a simple model with a single easily constrained free parameter. Lake depths are modeled based on fractal area–volume relationships that reflect the approximate scale invariance of Earth’s topography on idealized lake geometries. Carbon burial is estimated by applying the attenuation length scale to these depths. Using this model, we demonstrate the relationship between the dynamic ratio—a metric of lake morphometry calculated by dividing the square root of surface area by the mean depth—and carbon burial. We use scaling relationships to predict how dynamic ratio, and by extension carbon burial, varies across the lake size spectrum. Our model also provides a basis for generalizing empirical studies to the biome scale. By applying our model to a boreal lake census, we estimate boreal lake carbon burial to be 1.8 ± 0.5 g C/m2/yr or 1.1 ± 0.3 Tg C/yr among all boreal lakes.