Dynamic upscaling of decomposition kinetics for carbon cycling models

Abstract

Abstract. The distribution of organic substrates and microorganisms in soils is spatially heterogeneous at the microscale. Most soil carbon cycling models do not account for this microscale heterogeneity, which may affect predictions of carbon (C) fluxes and stocks. In this study, we hypothesize that the mean respiration rate R‾ at the soil core scale (i) is affected by the microscale spatial heterogeneity of substrate and microorganisms and (ii) depends upon the degree of this heterogeneity. To theoretically assess the effect of spatial heterogeneities on R‾, we contrast heterogeneous conditions with isolated patches of substrate and microorganisms versus spatially homogeneous conditions equivalent to those assumed in most soil C models. Moreover, we distinguish between biophysical heterogeneity, defined as the nonuniform spatial distribution of substrate and microorganisms, and full heterogeneity, defined as the nonuniform spatial distribution of substrate quality (or accessibility) in addition to biophysical heterogeneity. Four common formulations for decomposition kinetics (linear, multiplicative, Michaelis–Menten, and inverse Michaelis–Menten) are considered in a coupled substrate–microbial biomass model valid at the microscale. We start with a 2-D domain characterized by a heterogeneous substrate distribution and numerically simulate organic matter dynamics in each cell in the domain. To interpret the mean behavior of this spatially explicit system, we propose an analytical scale transition approach in which microscale heterogeneities affect R‾ through the second-order spatial moments (spatial variances and covariances). The model assuming homogeneous conditions was not able to capture the mean behavior of the heterogeneous system because the second-order moments cause R‾ to be higher or lower than in the homogeneous system, depending on the sign of these moments. This effect of spatial heterogeneities appears in the upscaled nonlinear decomposition formulations, whereas the upscaled linear decomposition model deviates from homogeneous conditions only when substrate quality is heterogeneous. Thus, this study highlights the inadequacy of applying at the macroscale the same decomposition formulations valid at the microscale and proposes a scale transition approach as a way forward to capture microscale dynamics in core-scale models.

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

“…In addition to missing critical analytical insight, not accounting for this behavior might have severe consequences for inverse modeling and estimation of the parameters governing process-based models (PBMs). The basic consequences of Jensen's Inequality for estimation of trace gas emission (CH 4 and N 2 O) were first discussed by Van Oijen et al (2017), but have not been picked up on elsewhere, until the present work (and very recently by Chakrawal et al (2019)). Chakrawal et al (2019) provide a detailed and compelling first-pass application of scale transition theory to biogeochemical modeling.…”

“…The basic consequences of Jensen's Inequality for estimation of trace gas emission (CH 4 and N 2 O) were first discussed by Van Oijen et al (2017), but have not been picked up on elsewhere, until the present work (and very recently by Chakrawal et al (2019)). Chakrawal et al (2019) provide a detailed and compelling first-pass application of scale transition theory to biogeochemical modeling. Our contribution here complements their laudable effort by providing a more generic mathematical analysis of the scale transition, equally applicable to both forward and reverse michaelismenten microbial kinetics.…”

“…However, following Chesson (2012) and Chakrawal et al (2019) we are free to approximate the solution for arbitrary distributions using a Taylor Series approximation expanded to the 2nd moment. Specifically, we take the expectation over a multivariable Taylor Series expansion, centered around the mean-field values of all parameters θ (for simplicitiy, the variables M B and C are included in the parameter vector θ):…”

“…Our contribution here complements their laudable effort by providing a more generic mathematical analysis of the scale transition, equally applicable to both forward and reverse michaelismenten microbial kinetics. As in Chakrawal et al (2019), we address the consequences of heterogeneity in both substrate/microbes ("biochemical heterogeneity") as well as in the kinetic parameters ("ecological heterogeneity"). However, we diverge from their approach in that, rather than explore detailed simulation models, we derive a completely non-dimensionalized expression for aggregating non-linear microbial kinetics over both types of heterogeneity simultaneously.…”

A framework for modelling soil structure dynamics induced by biological activity

“…Alongside the experimental research discussed in the foregoing, some detailed process-oriented models have also been developed that describe interactions between soil structure and various individual biological agents such as roots, earthworms or microorganisms (e.g. Baumert et al, 2018;Blanchart et al, 2009;Chakrawal et al, 2020;Ebrahimi & Or, 2016;Hallett et al, 2013;Monga et al, 2014;Roose et al, 2016;Ruiz et al, 2017). Although such approaches lead to valuable insights into the individual governing processes, they operate at small spatial (e.g.…”