Abstract. 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 system 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
and time guarantees that upscaled dynamics will violate mean-field
assumptions via Jensen's 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. Likewise, predictions
of CO2 efflux from models conditioned on mean-field values will also be
biased. Here we present a generic mathematical analysis of upscaling
Michaelis–Menten kinetics under heterogeneity and provide solutions in
dimensionless form. We illustrate how our dimensionless form facilitates
qualitative insight into the significance of this scale transition and argue
that it will facilitate cross-site intercomparisons of flux data. We also
identify the critical terms that need to be constrained in order to unbias
parameter estimates.