Abstract
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.
Highlights
A number of soil and litter carbon decomposition models based on Michaelis–Menton kinetics, or nonlinear soil carbon models, have recently been developed (Schimel and Weintraub, 2003; Allison et al, 2010; German et al, 2012)
We focus on the intrinsic oscillatory responses of the modeled system to perturbations and, do not consider the forced responses of the system to oscillations in external factors, such as through diurnal variation in soil temperature or seasonal variation in carbon input
To help explain the differences in the responses of the equilibrium carbon pools to change in Fnpp between the linear and nonlinear models, we developed a three-pool linear model that has same equilibrium pool sizes as the nonlinear model
Summary
A number of soil and litter carbon decomposition models based on Michaelis–Menton kinetics, or nonlinear soil carbon models, have recently been developed (Schimel and Weintraub, 2003; Allison et al, 2010; German et al, 2012). It is well known that a system of nonlinear ordinary differential equations, such as a nonlinear soil model, can become unstable in response to a small perturbation to its initial pool sizes (Raupach, 2007) or inputs and can switch between different equilibrium states in response to climatic variation (Manzoni and Porporato, 2007), there is presently no evidence that soil carbon dynamics exhibits such characteristics over interannual to decadal timescales. We analyze the stability of two recently published nonlinear soil carbon models in response to nonperiodic change in carbon input: the two-pool model developed by German et al (2012) and the three-pool model simplified from Wieder et al (2013), and pay particular attention to the time course of the responses to perturbation over decadal timescales. Dictions from two types of models are more consistent with empirical evidence from field and laboratory studies
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