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

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 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 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. 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.

Multiple distinct, scale‐dependent links between fungi and decomposition

“…Significant challenges remain because while microbial communities are diverse both functionally and taxonomically, successful modelling requires simplification and it is not yet clear which axes of microbial community variation demand focus. Furthermore, upscaled estimates from even the simplest mechanistic models are certain to violate mean‐field assumptions if they do not account for fine‐scale variability (Wilson & Gerber, 2020), which is of particular concern in microbial communities because ecologically impactful interactions occur at microscopic scales (e.g. Boddy, 2000).…”

Uniting the scales of microbial biogeochemistry with trait‐based modelling

“…Starting with a model at a finer scale—(a) ecosystem, (b) community or (c) physiological—we attempt to predict the system's behaviour at a broader scale by naively reapplying lower‐level traits. In each case, such extrapolation fails due to emergent processes (Bradford et al., 2017; Wilson & Gerber, 2020) that must be explicitly included in order to make accurate predictions.…”

“…A related approach (Barbier et al., 2018) uses techniques from statistical physics to predict community properties from average interactions within a community; here, traits are not fixed parameters but rather statistical distributions. Indeed, application of such techniques to global microbial biogeochemistry has demonstrated that they might be used in Earth system contexts to capture local‐scale heterogeneity (Wilson & Gerber, 2020).…”

“…uses techniques from statistical physics to predict community properties from average interactions within a community; here, traits are not fixed parameters but rather statistical distributions. Indeed, application of such techniques to global microbial biogeochemistry has demonstrated that they might be used in Earth system contexts to capture local-scale heterogeneity(Wilson & Gerber, 2020).Another potential solution, termed targeted simulation, is used elsewhere in Earth system modelling to simplify physical processes that are too computationally expensive to explicitly model at a global scale. Used, for example, to represent cloud dynamics(Grabowski & Wang, 2013), targeted simulation uses high-resolution mechanistic simulations to determine a value for a parameter that approximates the process in a lower-resolution model.…”