Articles | Volume 11, issue 7
Biogeosciences, 11, 1817–1831, 2014
Biogeosciences, 11, 1817–1831, 2014

Research article 07 Apr 2014

Research article | 07 Apr 2014

Oscillatory behavior of two nonlinear microbial models of soil carbon decomposition

Y. P. Wang1, B. C. Chen2, W. R. Wieder3, M. Leite4, B. E. Medlyn5, M. Rasmussen6, M. J. Smith7, F. B. Agusto8, F. Hoffman9, and Y. Q. Luo10 Y. P. Wang et al.
  • 1CSIRO Marine and Atmospheric Research Private Bag 1, Aspendale, Vic 3195, Australia
  • 2Department of Mathematics, University of Texas, Arlington, Texas, USA
  • 3The National Center for Atmospheric Research, Boulder, Colorado, USA
  • 4Department of Mathematics and Statistics, University of Toledo, Toledo, USA
  • 5Department of Biological Sciences, Faculty of Science, Macquarie University, NSW 2109, Australia
  • 6Department of Mathematics, Imperial College, London, UK
  • 7Computational Science Laboratory, Microsoft Research, Cambridge, UK
  • 8Department of Mathematics and Statistics, Austin Peay State University, Clarksville TN37044, USA
  • 9Oak Ridge National Laboratory, Computational Earth Sciences Group, P.O. Box 2008, Oak Ridge, TN 37831, USA
  • 10Department of Microbiology and Plant Biology, University of Oklahoma, Norman, Oklahoma, USA

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.

Final-revised paper