Insight into biogeochemical models from Scale Transition Theory: a dimensionless, scale-free approach

Leading an effective response to the accelerating crisis of anthropogenic climate change will require improved understanding of global carbon cycling. A critical source of uncertainty in Earth Systems Models (ESMs) is the role of microbes in mediating both the formation and decomposition of soil organic matter, and hence in determining patterns of CO2 efflux. Traditionally, ESMs model carbon turnover as a first order process impacted primarily by abiotic factors, whereas contemporary biogeochemical models often explicitly represent the microbial biomass and enzyme pools as the active agents of decomposition. However, the combination of non-linear microbial kinetics and ecological heterogeneity across space guarantees that upscaled dyamics will violate mean-field assumptions via Jensens Inequality. Violations of mean-field assumptions mean that parameter estimates from models fit to upscaled data (e.g. eddy covariance towers) are likely systematically biased. Here we present a generic mathematical analysis of upscaled michaelis-menten kinetics, grounded in Scale Transition Theory. We advance the framework by providing solutions in dimensionless form, and illustrate how this approach facilitates qualitative insight into the significance of this scale transition, and argue that it will facilitate future cross site intercomparisons of scale transition effects from flux data. We also discuss the critical terms that need to be constrained in order to unbias parameter estimates.