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Oscillatory behaviour of two nonlinear microbial models of soil carbon decomposition

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


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 5 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 equation in the two-pool model, and to equation 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 between 5 and 15 yr depending on other parameter values, and has smaller amplitude at soil temperatures between 0 ffiC to 15 ffiC. 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 behaviour and insensitivity of soil carbon to carbon input in the nonlinear models are 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.


Publication typeArticle
Published inBiogeosciences Discussions
PublisherEuropean Geosciences Union

Previous versions

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

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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