Application of a two-pool model to soil carbon dynamics under elevated CO₂

Introduction

Soils contain about twice as much C as the atmosphere and three times as much C as live vegetation, and soil respiration forms a principle component of the global C cycle (Cias et al., 2013). The soil C pool may therefore play a key role in modulating climate change, but its response to future atmospheric conditions is uncertain. We previously synthesized data on soil C contents, soil respiration, and soil C inputs from CO₂ enrichment experiments to determine whether the decomposition rate (k) of soil organic C changed under elevated atmospheric CO₂ (Van Groenigen et al., 2014). We offered two possible explanations for the observed increase in decomposition: priming (i.e., increased decomposition of soil organic matter due to increased soil C inputs), or a CO₂-induced increase in soil water content which in turn stimulated microbial activity. Georgiou et al. (2015) offer another possible explanation: the increase in k may have been an artifact resulting from fitting a one-pool model to data from a multi-pool system. In this alternative explanation, actual decomposition rates may not have changed; rather the size of the labile (hereafter, ‘fast’) C pool may have increased relative to that of the recalcitrant (i.e., ‘slow’) pool, giving the impression of a change in k. To determine whether this mechanism could explain our results, we here estimate parameters in a two-pool model using data from our original meta-analysis.

Application of a two-pool soil C model

For our new analysis, we used a two-pool model which was introduced by Andrén & Kätterer (1997) (Fig. 1). It is the same model that was used by Georgiou et al. (2015) to illustrate the theoretical possibility of the artifact described above. Unlike the models used in Van Groenigen et al. (2014), this model includes pools with different turnover rates and it allows for C transfer from the fast pool to the slow pool; these properties are essential for the alternative hypothesis proposed by Georgiou et al. (2015).

To estimate model parameters, we followed the data assimilation approach outlined by Van Groenigen et al. (2014). Briefly, the two-pool model was fitted to the observed soil C data for both the ambient and the increased CO₂ treatments for each experimental site in our dataset. We constructed a joint probability density function (PDF) for the model parameters using probabilistic inversion (Xu et al., 2006). Samples were taken from the joint PDF using a Markov chain Monte Carlo technique and were then used to construct marginal distributions for model parameters. We calculated a cost function J expressing the difference between modeled and observed soil C data (Luo et al., 2003):

(1)

where n is the total number of sampling dates, each of which occurred t_i years after the start of CO₂ enrichment, and C_m and C_o are the modeled and observed soil C pool at time t_i, respectively. The cost function was minimized with a Metropolis-Hastings algorithm, combined with a convergence test.

The prior distributions of model parameters I, k₁ and k_2, and CUE₁ were chosen to be uniform between a lower and upper limit (Table 1). These limits represent constraints based upon prior knowledge about the approximate ranges of soil C input (Raich & Schlesinger, 1992), decomposition rates of fast and slow soil C pools (Trumbore, 2000; Six & Jastrow, 2002; Manzoni et al., 2012a), and carbon use efficiency of soil microbes (Andrén & Kätterer, 1997; Manzoni et al., 2012a,b). The application of a two-pool model requires data on the initial distribution of soil C among the pools, information that was not available for any of the studies in our dataset (Van Groenigen et al., 2014). We solved this issue by introducing an additional model parameter in our analysis: f, the fraction of the initial soil C stock presents in the fast soil C pool (Table 1). The lower and upper limits of the prior distribution of f were based on the partitioning of soil C between labile and recalcitrant pools used in conceptual models (Andrén & Kätterer, 1997; Trumbore, 1997). We assumed that within each experiment, f was the same for ambient and elevated CO₂ treatments. We further constrained model parameters by observations on soil or microbial respiration and plant growth, see Van Groenigen et al. (2014) for details. All analyses were performed in matlab r2012b (Mathworks, Natick, MA, USA).

The model parameters were estimated as the mean of the sampling distribution generated by the Metropolis–Hastings algorithm. We then used meta-analysis to summarize the CO₂ effects on model parameters across our dataset (e.g., Osenberg et al., 1999), using the natural log of the response ratio as the effect size (Hedges et al., 1999). metawin 2.1 was used to generate mean effect sizes and 95% bootstrapped CIs (4999 iterations) (Rosenberg et al., 2000). Effect sizes were weighted by replication (to give more weight to better estimates), adjusted by the number of comparisons per experimental site (to downweight studies with multiple effect sizes and thus avoid pseudoreplication: Van Groenigen et al., 2014). Treatment effects were considered significant if the 95% CI of the effect size did not overlap with 0.

Applying our two-pool approach to the 53 studies in our original dataset, we found that elevated CO₂ increased the decomposition rates of both the fast and slow C pools (Fig. 2). Elevated CO₂ increased the decomposition of slow C, the dominant C pool, to almost the same extent as it did the single decomposition rate, k, in the one-pool model (Van Groenigen et al., 2014). In addition, CUE₁ decreased under elevated CO₂, a response that further limits soil C storage (because low CUE₁ values cause more C to be respired during transfer from the fast to the slow pool). Averaged across all experiments in our dataset, f (the initial allocation of C to the fast pool) equaled 0.05 (results not shown).

In general, simple models fit to complex dynamics can yield parameters that are inconsistent with the inferred mechanistic controls (e.g., Ågren, 2000; Davidson & Janssens, 2006). Thus, in theory, our previous finding that elevated CO₂ induced an increase in the decomposition rate k (Van Groenigen et al., 2014) could have been an artifact of applying a one-pool model to a two-(or multi-) pool system (Georgiou et al., 2015). However, further analysis (Fig. 2) suggests this was not the case: decomposition rates in a two-pool model also increased with elevated CO₂. The fact that our one-pool and two-pool analyses yield similar results further suggests that adding more pools with even faster decomposition rates (representing labile material such as fine-root necromass and root exudates) would not greatly affect the outcome either. The significant drop in CUE₁ values under elevated CO₂ could possibly be an indication of increased C expense for N priming, but may also indicate C overflow respiration due to increased C availability to soil microbes (Craine et al., 2007; Manzoni et al., 2012a).

Georgiou et al. (2015) described the possible bias in applying a one-pool model by estimating k by dividing soil respiration by the size of the soil C stock. However, our data assimilation method used a fundamentally different approach (Luo et al., 2011); we directly estimated k from the change in soil C contents over time and constrained these estimates based on the observed responses of plant growth and microbial respiration. The two approaches yield different results; for example, simply dividing respiration rates by soil C stocks yield an apparent average CO₂ effect on k of +21% for the studies in our dataset, larger than that reported by Van Groenigen et al. (2014). This suggests that much of the artifact arises from the estimation methods, and not necessarily, from the application of a one-pool model.

Consistent with our results, numerous empirical studies indicate that decomposition rates are not fixed. For example, meta-analyses show that despite increased soil C input under elevated CO₂, sites with low N availability accumulate little or no soil C (Hungate et al., 2009), a result that strongly suggests an increase in decomposition rates. A large body of scientific evidence also shows an increase in soil organic matter decomposition following the addition of organic substrate (Kuzyakov, 2010). Collectively, these data provide strong support for the interpretation that increased CO₂ leads to an increase in decomposition rates. Trying to fit models with fixed decomposition rates to these results may therefore lead to incorrect conclusions, just as fitting oversimplified models may yield erroneous inferences.

What microbial response caused the increase in decomposition rates under elevated CO₂? Recent studies suggest that multiple mechanisms might be responsible. For instance, elevated CO₂ has been shown to increase the activity of enzymes associated with decomposition of recalcitrant soil organic matter (Carney et al., 2007; Phillips et al., 2011) and to increase decomposition of soil organic matter by stimulating the growth of mycorrhizae (Cheng et al., 2012). Our two-pool analysis does not explicitly represent these or other microbial responses; rather, it assesses the resulting effect of such responses on decomposition rates (i.e., k₁ and k₂). As such, our approach provides no new insights in microbial mechanisms involved in decomposition processes. It builds upon the approach in which time series of soil C data are used to estimate how k-values vary with environmental conditions (e.g., Andrén & Kätterer, 1997; Luo et al., 2001, 2003). We fully agree with Georgiou et al. (2015) that models explicitly representing the relation between microbial dynamics and decomposition rates may increase predictive power. Such models may also provide mechanistic insight in the role of microbes in mediating the effect of CO₂ on decomposition rates (e.g., Sulman et al., 2014; Tang & Riley, 2014; Wieder et al., 2015). Indeed, earth system models will best capture the response of decomposition to elevated CO₂, if the mechanisms that alter decomposition rates are known and incorporated into the models.

Conclusion

Our analyses suggest that decomposition rates of soil organic matter change after a step increase in atmospheric CO₂, for both a one-pool model (Van Groenigen et al., 2014) and a two-pool model (Fig. 2). Both types of models are used in earth system models to simulate soil C changes with climate change (Friedlingstein et al., 2006), but these models assume that decomposition rates (k's) are invariant and do not change with CO₂. This could lead to serious problems with predictions about long-term soil C storage; constant k's mean that increased inputs to soil will lead to proportionate increases in soil C, whereas increases in k will reduce the C storage potential of soils and thus the ability of soil to buffer the Earth from releases of CO₂ into the atmosphere.

What can be done to improve predictions of soil C dynamics under elevated CO₂? We suggest that data assimilation efforts on soil C dynamics make use of multi-pool models with flexible decomposition rates. We also support the suggestion of Georgiou et al. (2015) to inform models with the use of isotopic data, and we agree that models that explicitly represent microbial dynamics may yield important insights. Several of these models include equations that can capture priming effects (e.g., Wutzler & Reichstein, 2013). However, as the models become more complicated, they must also be better constrained by empirical data. For instance, future experiments should include measurements that can be used to estimate CUE (e.g., microbial specific respiration) and the decomposition rates of labile vs. recalcitrant organic matter pools (e.g., activity of enzymes associated with the decomposition of labile or recalcitrant pools). That said, many long-term CO₂ enrichment experiments have already finished and can no longer contribute data. As such, estimation methods (like ours) will be needed that can deal with the limited data streams. Incorporating diverse types of data and approaches will be essential for progress. This integration of models of different complexity with data of different dimensionality poses a significant challenge for the global change research community.