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Oscillatory behavior of two nonlinear microbial models of soil carbon decomposition

Y.P. Wang, B.C. Chen, W.R. Weider, M. Leite, B.E. Medlyn, M. Rasmussen, M.J. Smith, F.B. Augusto, F. Hoffman, and Y.Q. Luo

Abstract

A number of nonlinear models have recently been proposed for simulating soil carbon decomposition. Their predictions of soil carbon responses to fresh litter input and warming differ significantly from conventional linear models. Using both stability analysis and numerical simulations, we showed that two of those nonlinear models (a two-pool model and a three-pool model) exhibit damped oscillatory responses to small perturbations. Stability analysis showed the frequency of oscillation is proportional to √(ϵ−1−1) Ks/Vs in the two-pool model, and to √(ϵ−1−1) Kl/Vl in the three-pool model, where ϵ is microbial growth efficiency, Ks and Kl are the half saturation constants of soil and litter carbon, respectively, and /Vs and /Vl are the maximal rates of carbon decomposition per unit of microbial biomass for soil and litter carbon, respectively. For both models, the oscillation has a period of between 5 and 15 years depending on other parameter values, and has smaller amplitude at soil temperatures between 0 and 15 °C. In addition, the equilibrium pool sizes of litter or soil carbon are insensitive to carbon inputs in the nonlinear model, but are proportional to carbon input in the conventional linear model. Under warming, the microbial biomass and litter carbon pools simulated by the nonlinear models can increase or decrease, depending whether ϵ varies with temperature. In contrast, the conventional linear models always simulate a decrease in both microbial and litter carbon pools with warming. Based on the evidence available, we concluded that the oscillatory behavior and insensitivity of soil carbon to carbon input are notable features in these nonlinear models that are somewhat unrealistic. We recommend that a better model for capturing the soil carbon dynamics over decadal to centennial timescales would combine the sensitivity of the conventional models to carbon influx with the flexible response to warming of the nonlinear model.

Details

Publication typeArticle
Published inBiogeosciences
PublisherEuropean Geosciences Union

Newer versions

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Previous versions

Y.P.Wang, B.C.Chen, W.R.Weider, Y.Q.Luo, B.E.Medlyn, M.Rasmussen, M.J.Smith, F.B.Agusto, and F.Hoffman. Oscillatory behaviour of two nonlinear microbial models of soil carbon decomposition, Biogeosciences Discussions, European Geosciences Union, December 2013.

Matthew J. Smith, Mark C. Vanderwel, Vassily Lyutsarev, Stephen Emmott, and Drew W. Purves. The climate dependence of the terrestrial carbon cycle; including parameter and structural uncertainties, Biogeosciences Discussions, European Geosciences Union, 4 October 2012.

S. Caldararu, D. W. Purves, and P.I. Palmer. Phenology as a strategy for carbon optimality: a global model, Biogeosciences, 2014.

Wang, Y., Smith, M.J., Luo, Y., Leite, M., Augusto, F., Chen, B., Hoffman, F.M., Medlyn, B.E., Rasmiussen, and M.. Theoretical analysis of the global land carbon cycle: what determines the trajectory of future carbon uptake?, American Geophysical Union, 9 December 2013.

M. J. Smith, D. W. Purves, M. C. Vanderwel, V. Lyutsarev, and S. Emmott. The climate dependence of the terrestrial carbon cycle, including parameter and structural uncertainties, Biogeosciences, European Geosciences Union, 29 January 2013.

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