the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
The quasiequilibrium framework revisited: analyzing longterm CO_{2} enrichment responses in plant–soil models
Mingkai Jiang
Sönke Zaehle
Martin G. De Kauwe
Anthony P. Walker
Silvia Caldararu
David S. Ellsworth
Belinda E. Medlyn
Elevated carbon dioxide (CO_{2}) can increase plant growth, but the magnitude of this CO_{2} fertilization effect is modified by soil nutrient availability. Predicting how nutrient availability affects plant responses to elevated CO_{2} is a key consideration for ecosystem models, and many modeling groups have moved to, or are moving towards, incorporating nutrient limitation in their models. The choice of assumptions to represent nutrient cycling processes has a major impact on model predictions, but it can be difficult to attribute outcomes to specific assumptions in complex ecosystem simulation models. Here we revisit the quasiequilibrium analytical framework introduced by Comins and McMurtrie (1993) and explore the consequences of specific model assumptions for ecosystem net primary productivity (NPP). We review the literature applying this framework to plant–soil models and then analyze the effect of several new assumptions on predicted plant responses to elevated CO_{2}. Examination of alternative assumptions for plant nitrogen uptake showed that a linear function of the mineral nitrogen pool or a linear function of the mineral nitrogen pool with an additional saturating function of root biomass yield similar CO_{2} responses at longer timescales (>5 years), suggesting that the added complexity may not be needed when these are the timescales of interest. In contrast, a saturating function of the mineral nitrogen pool with linear dependency on root biomass yields no soil nutrient feedback on the verylongterm (>500 years), nearequilibrium timescale, meaning that one should expect the model to predict a full CO_{2} fertilization effect on production. Secondly, we show that incorporating a priming effect on slow soil organic matter decomposition attenuates the nutrient feedback effect on production, leading to a strong mediumterm (5–50 years) CO_{2} response. Models incorporating this priming effect should thus predict a strong and persistent CO_{2} fertilization effect over time. Thirdly, we demonstrate that using a “potential NPP” approach to represent nutrient limitation of growth yields a relatively small CO_{2} fertilization effect across all timescales. Overall, our results highlight the fact that the quasiequilibrium analytical framework is effective for evaluating both the consequences and mechanisms through which different model assumptions affect predictions. To help constrain predictions of the future terrestrial carbon sink, we recommend the use of this framework to analyze likely outcomes of new model assumptions before introducing them to complex model structures.
 Article
(2340 KB)  Fulltext XML

Supplement
(208 KB)  BibTeX
 EndNote
Predicting how plants respond to atmospheric carbon dioxide (CO_{2}) enrichment (eCO_{2}) under nutrient limitation is fundamental for an accurate estimate of the global terrestrial carbon (C) budget in response to climate change. There is now ample evidence that the response of terrestrial vegetation to eCO_{2} is modified by soil nutrient availability (FernándezMartínez et al., 2014; Norby et al., 2010; Reich and Hobbie, 2012; Sigurdsson et al., 2013). Over the past decade, land surface models have developed from Conly models to carbon–nitrogen (CN) models (Gerber et al., 2010; Zaehle and Friend, 2010). The inclusion of CN biogeochemistry has been shown to be essential to capture the reduction in the CO_{2} fertilization effect with declining nutrient availability and therefore its implications for climate change (Zaehle et al., 2015). However, it has also been shown that models incorporating different assumptions predict very different vegetation responses to eCO_{2} (Lovenduski and Bonan, 2017; Medlyn et al., 2015). Careful examination of model outputs has provided insight into the reasons for the different model predictions (De Kauwe et al., 2014; Medlyn et al., 2016; Walker et al., 2014, 2015; Zaehle et al., 2014), but it is generally difficult to attribute outcomes to specific assumptions in these plant–soil models that differ in structural complexity and process feedbacks (Lovenduski and Bonan, 2017; Medlyn et al., 2015; Thomas et al., 2015).
Understanding the mechanisms underlying predictions of ecosystem carbon cycle processes is fundamental for the validity of prediction across space and time. Comins and McMurtrie (1993) developed an analytical framework, the “quasiequilibrium” approach, to make model predictions traceable to their underlying mechanisms. The approach is based on the twotiming approximation method (Ludwig et al., 1978) and makes use of the fact that ecosystem models typically represent a series of pools with different equilibration times. The method involves the following: (1) choosing a time interval (τ) such that the model variables can be divided into “fast” pools (which approach effective equilibrium at time τ) and “slow” pools (which change only slightly at time τ); (2) holding the slow pools constant and calculating the equilibria of the fast pools (an effective equilibrium as this is not a true equilibrium of the entire system); and (3) substituting the fast pool effective equilibria into the original differential equations to give simplified differential equations for the slow pools at time τ.
In a CN model, plant net primary production (NPP) can be estimated from two constraints based on equilibration of the C balance (the “photosynthetic constraint”) and the N balance (the “nitrogen recycling constraint”) (Comins and McMurtrie, 1993). Both constraints link NPP with leaf chemistry (i.e., N : C ratio) (derivation in Sect. 3.1). The simulated production occurs at the intersection of these two constraint curves (shown graphically in Fig. 1). To understand behavior on medium and long timescales (e.g., wood and slow and passive soil organic pools in Fig. 2; 20–200 years), one can assume that plant pools with shorter equilibration times in the model (e.g., foliage, fineroot, or active soil organic pools in Fig. 2) have reached quasiequilibrium, and model dynamics are thus driven by the behavior of the longertimescale pools.
The recent era of model development has seen some significant advances in representing complex plant–soil interactions, but models still diverge in future projections of CO_{2} fertilization effects on NPP (Friend et al., 2014; Koven et al., 2015; Walker et al., 2015). A recent series of multimodel intercomparison studies has demonstrated the importance of understanding underlying response mechanisms in determining model response to future climate change (Medlyn et al., 2015), but this can be difficult to achieve in complex global models. The quasiequilibrium framework is a relatively simple but quantitative method to examine the effect of different assumptions on model predictions. As such, it complements more computationally expensive sensitivity analyses and can be used as an effective tool to provide a priori evaluation of both the consequence and mechanism through which different new model implementations affect model predictions.
Here, by constructing a quasiequilibrium framework based on the structure of the Generic Decomposition And Yield (G'DAY) model (Comins and McMurtrie, 1993), we evaluate the effects on plant responses to eCO_{2} of some recently developed model assumptions incorporated into ecosystem models, for example the Community Land Model (CLM) (Oleson et al., 2004), the Community Atmosphere–Biosphere Land Exchange (CABLE) model (Kowalczyk et al., 2006), the Lund–Potsdam–Jena (LPJ) model (Smith et al., 2001), the JSBACH model (Goll et al., 2017b), and the OCN model (Zaehle et al., 2010). Specifically, we test how different functions affecting plant N uptake influence NPP responses to eCO_{2} at various quasiequilibrium time steps. The present study is a continuation of the series of quasiequilibrium studies reviewed in Sect. 2, with a general aim of helping researchers to understand the similarities and differences of predictions made by different processbased models, as demonstrated in Sect. 3.
Many of the assumptions currently being incorporated into CN models have previously been explored using the quasiequilibrium framework; here we provide a brief literature review describing the outcomes of this work (Table 1). Firstly, the flexibility of plant and soil stoichiometry has recently been highlighted as a key assumption (Stocker et al., 2016; Zaehle et al., 2014). A key finding from early papers applying the quasiequilibrium framework was that model assumptions about the flexibility of the plant wood N : C ratio (Comins, 1994; Comins and McMurtrie, 1993; Dewar and McMurtrie, 1996; Kirschbaum et al., 1994, 1998; McMurtrie and Comins, 1996; Medlyn and Dewar, 1996) and soil N : C ratio (McMurtrie and Comins, 1996; McMurtrie et al., 2001; Medlyn et al., 2000) were critical determinants of the magnitude of the transient (10 to >100 years) plant response to eCO_{2} (Fig. 1). Different to the effect of foliar N : C ratio flexibility, which has an instantaneous effect on photosynthesis, the flexibility of the wood N : C ratio controls the flexibility of nutrient storage per unit biomass accumulated in the slow turnover pool. Therefore, a constant wood N : C ratio, such as was assumed in CLM4 (Thornton et al., 2007; Yang et al., 2009), means that effectively a fixed amount of N is locked away from the active processes such as photosynthesis on the timescale of the life span of the woody tissue. In contrast, a flexible wood N : C ratio, such as was tested in OCN (Meyerholt and Zaehle, 2015), allows variable N storage in the woody tissue and consequently more nutrients available for C uptake on the transient timescale. Similarly, flexibility in the soil N : C ratio determines the degree of the soil N cycle feedback (e.g., N immobilization and mineralization) and therefore its effect on plant response to eCO_{2}. A large response to eCO_{2} occurs when the soil N : C ratio is allowed to vary, whereas there could be little or no response if the soil N : C ratio is assumed to be inflexible (McMurtrie and Comins, 1996).
Changes in plant allocation with eCO_{2} are also a source of disagreement among current models (De Kauwe et al., 2014). The quasiequilibrium framework has been used to investigate a number of different plant C allocation schemes (Comins and McMurtrie, 1993; Kirschbaum et al., 1994; Medlyn and Dewar, 1996). For example, Medlyn and Dewar (1996) suggested that plant longterm growth responses to eCO_{2} depend strongly on the extent to which stem and foliage allocations are coupled. With no coupling (i.e., fixed allocation of C and N to stemwood), plant growth was not responsive to eCO_{2}; with linear coupling (i.e., allocation to stemwood proportional to foliage allocation), a significant longterm increase in total growth following eCO_{2} was found (Fig. S1 in the Supplement). The reason for this is similar to the argument behind wood N : C ratio flexibility: decreasing C allocation to wood decreases the rate of N removal per unit of C invested in growth. In contrast, Kirschbaum et al. (1994) found that changes in allocation between different parts of a plant only marginally changed the CO_{2} sensitivity of production at different timescales. The fundamental difference between the two allocation schemes was that Kirschbaum et al. (1994) assumed that the root allocation coefficient was determined by a negative relationship with the foliar N : C ratio, meaning that the increase in foliar N : C ratio would lead to a decreased root allocation and increased wood and foliage allocation, whereas Medlyn and Dewar (1996) investigated stem–foliage allocation coupling without introducing a feedback via the foliar N : C ratio. The comparison of the two allocation schemes is indicative of the underlying causes of model prediction divergence in recent intermodel comparisons (De Kauwe et al., 2014; Walker et al., 2015).
Another hypothesis currently being explored in models is the idea that increased belowground allocation can enhance nutrient availability under elevated CO_{2} (Dybzinski et al., 2014; Guenet et al., 2016). Comins (1994) argued that the N deficit induced by CO_{2} fertilization could be eliminated by the stimulation of N fixation. This argument was explored in more detail by McMurtrie et al. (2000), who assumed that eCO_{2} led to a shift in allocation from wood to root exudation, which resulted in enhanced N fixation. They showed that, although the increase in N fixation could induce a large eCO_{2} response in NPP over the long term, a slight decrease in NPP was predicted over the medium term. This decrease occurred because increased exudation at eCO_{2} increased soil C input, causing increased soil N sequestration and lowering the N available for plant uptake. Over the long term, however, both NPP and C storage were greatly enhanced because the sustained small increase in N input led to a significant buildup in total ecosystem N on this timescale.
The interaction between rising CO_{2} and warming under nutrient limitation is of key importance for future simulations. Medlyn et al. (2000) demonstrated that shortterm plant responses to warming, such as physiological acclimation, are overridden by the positive effects of warming on soil nutrient availability in the medium to long term. Similarly, McMurtrie et al. (2001) investigated how the flexibility of the soil N : C ratio affects predictions of the future C sink under elevated temperature and CO_{2}. They showed that assuming an inflexible soil N : C ratio with elevated temperature would mean a release of nitrogen with enhanced decomposition, leading to a large plant uptake of N to enhance growth. In contrast, an inflexible soil N : C ratio would mean that the extra N mineralized under elevated temperature is largely immobilized in the soil and there is hence a smaller increase in C storage. This effect of soil N : C stoichiometry on the response to warming is opposite to the effect on eCO_{2} described above. Therefore, under a scenario in which both temperature and CO_{2} increase, the C sink strength is relatively insensitive to soil N : C variability, but the relative contributions of temperature and CO_{2} to this sink differ under different soil N : C ratio assumptions (McMurtrie et al., 2001). This outcome may explain the results observed by Bonan and Levis (2010) when comparing coupled carbon cycle–climate simulations. The Terrestrial Ecosystem Model (TEM; Sokolov et al., 2008) and CLM (Thornton et al., 2009), which assumed inflexible stoichiometry, had a large climate–carbon feedback but a small CO_{2} concentrationcarbon feedback, contrasting with the OCN model (Zaehle et al., 2010), which assumed flexible stoichiometry and had a small climate–carbon feedback and a large CO_{2} concentration–carbon feedback. Variations among models in this stoichiometric flexibility assumption could also potentially explain the tradeoff between CO_{2} and temperature sensitivities observed by Huntzinger et al. (2017).
This section combines both methods and results together because equation derivation is fundamental to the analytical and graphic interpretation of model performance within the quasiequilibrium framework. Below we first describe the baseline simulation model and derivation of the quasiequilibrium constraints (Sect. 3.1); we then follow with analytical evaluations of new model assumptions using the quasiequilibrium framework (Sect. 3.2). Within each subsection (Sect. 3.2.1 to 3.2.3), we first provide key equations for each assumption and the derivation of the quasiequilibrium constraints with these new assumptions; we then provide our graphic interpretations and analyses to understand the effect of the model assumption on plant NPP responses to eCO_{2}.
More specifically, we tested alternative model assumptions for three processes that affect plant carbon–nitrogen cycling: (1) Sect. 3.2.1 evaluates different ways of representing plant N uptake, namely plant N uptake as a fixed fraction of mineral N pools, as a saturating function of the mineral N pool linearly depending on root biomass (Zaehle and Friend, 2010), or as a saturating function of root biomass linearly depending on the mineral N pool (McMurtrie et al., 2012); (2) Sect. 3.2.2 tests the effect the potential NPP approach that downregulates potential NPP to represent N limitation (Oleson et al., 2004); and (3) Sect. 3.2.3 evaluates root exudation and its effect on the soil organic matter decomposition rate (i.e., priming effect). The first two assumptions have been incorporated into some existing land surface model structures (e.g., CLM, CABLE, OCN, LPJ), whereas the third is a framework proposed following the observation that models did not simulate some key characteristic observations of the DukeFACE experiment (Walker et al., 2015; Zaehle et al., 2014) and therefore could be of importance in addressing some model limitations in representing soil processes (van Groenigen et al., 2014; Zaehle et al., 2014). It is our purpose to demonstrate how one can use this analytical framework to provide an a priori and generalizable understanding of the likely impact of new model assumptions on model behavior without having to run a complex simulation model. Here we do not target specific ecosystems to parameterize the model but anticipate the analytical interpretation of the quasiequilibrium framework to be of general applicability for woodydominated ecosystems. One could potentially adopt the quasiequilibrium approach to provide casespecific evaluations of model behavior against observations (e.g., constraining the likely range of wood N : C ratio flexibility).
3.1 Baseline model and derivation of the quasiequilibrium constraints
Our baseline simulation model is similar in structure to G'DAY (Generic Decomposition And Yield; Comins and McMurtrie, 1993), a generic ecosystem model that simulates biogeochemical processes (C, N, and H_{2}O) at daily or subdaily time steps. A simplified G'DAY model version that simulates plant–soil C–N interactions at a weekly time step was developed for this study (Fig. 2). In G'DAY, plants are represented by three stoichiometrically flexible pools: foliage, wood, and roots. Each pool turns over at a fixed rate. Litter enters one of four litter pools (metabolic and structural aboveground and belowground) and decomposes at a rate dependent on the litter N : C ratio, soil moisture, and temperature. Soil organic matter (SOM) is represented as active, slow, and passive pools, which decay according to firstorder decay functions with different rate constants. Plants access nutrients from the mineral N pool, which is an explicit pool supplied by SOM decomposition and an external input, which is assumed to be constant, as a simplified representation of fixation and atmospheric deposition.
The baseline simulation model further assumes the following: (1) gross primary production (GPP) is a function of a lightuse efficiency (LUE), which depends on the foliar N : C ratio (n_{f}) and atmospheric CO_{2} concentration (C_{a}) (Appendix A1); (2) carbon use efficiency (the ratio NPP : GPP) is constant; (3) allocation of newly fixed carbon among foliage (a_{f}), wood (a_{w}), and root (a_{r}) pools is constant; (4) foliage (n_{f}), wood (n_{w}), and root N : C (n_{r}) ratios are flexible; (5) wood and root N : C ratios are proportional to the foliar N : C ratio, with constants of proportionality r_{w} and r_{r}, respectively; (6) a constant proportion (t_{f}) of foliage N is retranslocated before leaves senesce; (7) active, slow, and passive SOM pools have fixed N : C ratios; and (8) an N uptake constant determines the plant N uptake rate. Definitions of the parameters and forcing variables are summarized in Table 2. For all simulations, the ambient CO_{2} concentration (aCO_{2}) was set at 400 ppm and eCO_{2} at 800 ppm.
We now summarize the key derivation of the two quasiequilibrium constraints, the photosynthetic constraint, and the nutrient cycling constraint from our baseline simulation model (details provided in Appendix A1 and A2). The derivation follows Comins and McMurtrie (1993), which is further elaborated in work by McMurtrie et al. (2000) and Medlyn and Dewar (1996) and evaluated by Comins (1994). First, the photosynthetic constraint is derived by assuming that the foliage C pool (C_{f}) has equilibrated. Following the GPP and CUE assumptions (see above) and the detailed derivations made in Appendix A1, there is an implicit relationship between NPP and n_{f}:
where I_{0} is the incident radiation, k is the canopy light extinction coefficient, and σ is the specific leaf area. This equation is the photosynthetic constraint, which relates NPP to n_{f}.
Secondly, the nitrogen cycling constraint is derived by assuming that nitrogen inputs to and outputs from the equilibrated pools are equal. Based on the assumed residence times of the passive SOM (∼400 years), slow SOM (15 years), and woody biomass (50 years) pools, we can calculate the nutrient recycling constraint at three different timescales (conceptualized in Fig. 3): very long (VL, >500 years, all pools equilibrated), long (L, 100–500 years, all pools equilibrated except the passive pool), or medium (M, 5–50 years, all pools equilibrated except slow, passive, and wood pools). In the VL term, we have
where N_{in} is the total N input into the system, and N_{loss} is the total N lost from the system via leaching and volatilization. Analytically, with some assumptions about plant N uptake (Appendix A2), we can transform Eq. (2) into a relationship between NPP and n_{f}, expressed as
where l_{n} is the fraction of N mineralization that is lost, a_{f}; a_{w} and a_{r} are the allocation coefficients for foliage, wood, and roots, respectively, and n_{fl}, n_{w}, and n_{r} are the N : C ratios for foliage litter, wood, and roots, respectively. Since n_{w} and n_{r} are assumed proportional to n_{f} (Table 2), the nutrient recycling constraint also links NPP and n_{f}. The intersection with the photosynthetic constraint yields the verylongterm equilibria of both NPP and n_{f}. Similarly, we can write the nitrogen recycling constraint in the L term and M term as a function between NPP and n_{f} (details explained in Appendix A2). Their respective interaction with the photosynthetic constraint yields the Lterm and Mterm equilibria points of both NPP and n_{f} (Figs. 1 and 3). Essentially, at each timescale, there are two unknowns (NPP and n_{f}) to be resolved via both the nitrogen recycling constraint and the photosynthetic constraint equations. Based on this set of analytical equations, one can evaluate how different assumptions affect the behavior of the model quantitatively. Below, we describe how different new model assumptions affect the predicted plant response to a doubling of the CO_{2} concentration at various timescales.
3.2 Evaluations of new model assumptions based on the quasiequilibrium framework
3.2.1 Explicit plant N uptake
We now move to considering new model assumptions. We first consider different representations of plant N uptake. In the baseline model, the mineral N pool (N_{min}) is implicit, as we assumed that all mineralized N in the soil is either taken up by plants (N_{U}) or lost from the system (N_{loss}). Here, we evaluate three alternative model representations in which plant N uptake depends on an explicit N_{min} pool and their effects on plant responses to eCO_{2}. We consider plant N uptake as (1) a fixed coefficient of the mineral N pool, (2) a saturating function of root biomass and a linear function of the mineral N pool (McMurtrie et al., 2012), and (3) a saturating function of the mineral N pool and a linear function of root biomass. The last function has been incorporated into some land surface models, for example, OCN (Zaehle and Friend, 2010) and CLM (Ghimire et al., 2016), while the first two have been incorporated into G'DAY (Corbeels et al., 2005).
A mineral N pool was made explicit by specifying a constant coefficient (u) to regulate the plant N uptake rate (i.e., $\cdot {N}_{\mathrm{U}}=u\phantom{\rule{0.125em}{0ex}}{N}_{\mathrm{min}}$). N lost from the system is a function of the mineral N pool (N_{min}) regulated by a loss rate (l_{n, rate}, yr^{−1}). For the VLterm equilibrium, we have N_{in}=N_{loss}, which means ${N}_{\mathrm{min}}=\frac{{N}_{\mathrm{in}}}{{l}_{\mathrm{n},\phantom{\rule{0.125em}{0ex}}\mathrm{rate}}}$, and hence
where n_{fl} is the foliage litter N : C ratio, which is proportional to n_{f} (Table 2). At the VL equilibrium, we can rearrange the above equation to relate NPP to n_{f}:
which indicates that the N cycling constraint for NPP is inversely dependent on n_{f}.
The second function represents plant N uptake as a saturating function of root biomass (C_{r}) and a linear function of the mineral N pool (McMurtrie et al., 2012), expressed as
where K_{r} is a constant. At the VL equilibrium, we have ${N}_{\mathrm{in}}={N}_{\mathrm{loss}}={l}_{\mathrm{n},\phantom{\rule{0.125em}{0ex}}\mathrm{rate}}{N}_{\mathrm{min}}$ and ${C}_{\mathrm{r}}=\frac{\mathrm{NPP}\cdot {a}_{\mathrm{r}}}{{s}_{\mathrm{r}}}$, where s_{r} is the lifetime of the root. Substituting for C_{r} in Eq. (6), we relate N_{U} to NPP:
Since N_{U} is also a function of NPP, we can rearrange and get
Comparing with Eq. (5), here NPP is also inversely dependent on n_{f} but with an additional negative offset of $\frac{{K}_{\mathrm{r}}{s}_{\mathrm{r}}}{{a}_{\mathrm{r}}}$. The third approach to represent N uptake (e.g., OCN and CLM) expresses N uptake as a saturating function of mineral N also linearly depending on root biomass (Zaehle and Friend, 2010), according to
where K is a constant coefficient, and V_{max} is the maximum root N uptake capacity simplified as a constant here. Since N_{U} is also a function of NPP, we get
This equation sets a limit to possible values of n_{f}. In equilibrium, for N_{min} to be nonzero, we need $\left({a}_{\mathrm{f}}{n}_{\mathrm{fl}}+{a}_{\mathrm{w}}{n}_{\mathrm{w}}+{a}_{\mathrm{r}}{n}_{\mathrm{r}}\right)<{V}_{max}\frac{{a}_{\mathrm{r}}}{{s}_{\mathrm{r}}}$. The N loss rate is still proportional to the mineral N pool, so N_{loss} is given by
The above equation provides an N_{loss} term that no longer depends on NPP but only on n_{f}. If the N leaching loss is the only system N loss, the VLterm nutrient constraint no longer involves NPP, implying that the full photosynthetic CO_{2} fertilization effect is realized. The L and Mterm nutrient recycling constraints, however, are still NPP dependent due to feedbacks from the slowly recycling wood and SOM pools (e.g., Eq. A11–A15).
The impacts of these alternative representations of N uptake are shown in Fig. 4. First, the explicit consideration of the mineral N pool with a fixed uptake constant (u) of 1 yr^{−1} has little impact on the transient response to eCO_{2} when compared to the baseline model (Figs. 4a, 1a, Table 3). Varying u does not strongly (<5 %) affect plant responses to CO_{2} fertilization at different time steps (Fig. S2). This is because u is only a scaling factor of NPP, meaning it affects NPP but not its response to eCO_{2} (Table 4), as depicted by Eq. (5).
Moreover, the approach that assumes N uptake as a saturating function of root biomass linearly depending on the mineral P pool (McMurtrie et al., 2012) has comparable eCO_{2} effects on production to the baseline and the fixed uptake coefficient models (Fig. 4b, Table 3). Essentially, if $\frac{{K}_{\mathrm{r}}{s}_{\mathrm{r}}}{{a}_{\mathrm{r}}}$ is small, we can approximate NPP by $\frac{{N}_{\mathrm{in}}}{{l}_{\mathrm{n},\mathrm{rate}}\left({a}_{\mathrm{f}}{n}_{\mathrm{fl}}+{a}_{\mathrm{w}}{n}_{\mathrm{w}}+{a}_{\mathrm{r}}{n}_{\mathrm{r}}\right)}$, which shares a similar structure to the baseline and fixed uptake coefficient models (Eqs. 8, 5, and A10). Furthermore, Eq. (8) also depicts the fact that an increase in a_{r} should lead to higher NPP, and an increase in s_{r} or K_{r} should lead to decreased NPP. However, these predictions depend on assumptions of l_{n,rate} and n_{f}. If l_{n,rate} or n_{f} is small, NPP would be relatively less sensitive to a_{r},K_{r}, or s_{r}.
By comparison, representing N uptake as a saturating function of mineral N linearly depending on root biomass (Ghimire et al., 2016; Zaehle and Friend, 2010) no longer involves the VLterm nutrient recycling constraint on production (Fig. 4c), which is predicted by Eq. (11). Actual VLterm NPP is determined only by n_{f} along with the photosynthetic constraint, meaning that the full CO_{2} fertilization effect on production is realized with the increase in CO_{2}. The magnitudes of the CO_{2} fertilization effect at other time steps are comparable to those of the baseline model (Table 3) because the N_{loss} term is smaller than the N_{w},N_{Sp}, or N_{Ss} terms, meaning it has a relatively smaller effect on NPP at equilibrium. However, steeper nutrient recycling constraint curves are observed (Fig. 4c), indicating a stronger sensitivity of the NPP response to changes in n_{f}.
3.2.2 Potential NPP
In several vegetation models, including CLMCN, CABLE, and JSBACH, potential (nonnutrientlimited) NPP is calculated from light, temperature, and water limitations. Actual NPP is then calculated by downregulating the potential NPP to match nutrient supply. Here we term this the potential NPP approach. We examine this assumption in the quasiequilibrium framework following the implementation of this approach adopted in CLMCN (Bonan and Levis, 2010; Thornton et al., 2007). The potential NPP is reduced if mineral N availability cannot match the demand from plant growth:
where P_{dem} is the plant N demand, and NPP_{pot} is the potential NPP of the plant. Writing $\left({a}_{\mathrm{f}}{n}_{\mathrm{f}}+{a}_{\mathrm{w}}{n}_{\mathrm{w}}+{a}_{\mathrm{r}}{n}_{\mathrm{r}}\right)$ as n_{plant}, the wholeplant N : C ratio, and the wholesoil N : C ratio as n_{soil}, we can calculate the immobilization N demand as
where f is the fraction of litter C that becomes soil C, C_{lit} is the total litter C pool, and s_{t} is the turnover time of the litter pool. Actual plant N uptake is expressed as
Actual NPP is expressed as
For the VL constraint, we have N_{in}=N_{loss}. We can calculate NPP_{pot} as
For an actual NPP, we need to consider the immobilization demand. Rearranging the above, we get
This equation removes the NPP_{act} dependence on NPP_{pot}. It can be shown that the fraction of ${P}_{\mathrm{dem}}/({I}_{\mathrm{dem}}+{P}_{\mathrm{dem}}$) depends only on the N : C ratios and f, not on NPP_{pot}. This means that there will be no eCO_{2} effect on NPP_{act}.
As shown in Fig. 5a, the potential NPP approach results in relatively flat nutrient recycling constraint curves, suggesting that the CO_{2} fertilization effect is only weakly influenced by soil N availability. Despite a sharp instantaneous NPP response, CO_{2} fertilization effects on NPP_{act} are small on the M, L, and VLterm timescales (Table 3). This outcome can be understood from the governing equation for the nutrient recycling constraint, which removes NPP_{act} dependence on NPP_{pot} (Eq. 17). Although in the first instance, the plant can increase its production, over time the litter pool increases in size proportionally to NPP_{pot}, meaning that immobilization demand increases to match the increased plant demand, which leads to no overall change in the relative demands from the plant and the litter. This pattern is similar under alternative wood N : C ratio assumptions (Fig. 5b, Table 3).
3.2.3 Root exudation to prime N mineralization
The priming effect is described as the stimulation of the decomposition of native soil organic matter caused by larger soil carbon input under eCO_{2} (van Groenigen et al., 2014). Experimental studies suggest that this phenomenon is widespread and persistent (Dijkstra and Cheng, 2007), but this process has not been incorporated by most land surface models (Walker et al., 2015). Here we introduce a novel framework to induce the priming effect on soil decomposition and test its effect on plant production response to eCO_{2} within the quasiequilibrium framework.
To account for the effect of priming on decomposition of SOM, we first introduce a coefficient to determine the fraction of root growth allocated to exudates, a_{rhizo}. Here we assumed that the N : C ratio of rhizodeposition is the same as the root N : C ratio. The coefficient a_{rhizo} is estimated by a function dependent on foliar N : C:
where n_{ref} is a reference foliar N : C ratio to induce plant N stress (0.04), and a_{0} and a_{1} are tuning coefficients (0.01 and 1, respectively). Within the quasiequilibrium framework, for the VL soil constraint we now have
To introduce an effect of root exudation on the turnover rate of the slow SOM pool, rhizodeposition is transferred into the active SOM pool according to a microbial use efficiency parameter (${f}_{\mathrm{cue},\phantom{\rule{0.125em}{0ex}}\mathrm{rhizo}}=\mathrm{0.3}$). The extra allocation of NPP into the active SOM is therefore
The increased active SOM pool N demand is associated with the degradation rate of the slow SOM pool, expressed as
where k_{slow} is the original decomposition rate of the slow SOM pool, and k_{m} is a sensitivity parameter. The decomposition rate of the slow SOM pool affects N_{Rs}, the amount of N released from the slow SOM pools, as
where C_{s} is the slow SOM pool, and Ω_{ss} and Ω_{ps} represent the proportion of C released through the decomposition of the slow and passive SOM pools that subsequently enters the slow SOM pool, respectively.
Root exudation and the associated priming effect result in a strong Mterm plant response to eCO_{2} when compared to the baseline model (Fig. 6a in comparison to Fig. 4a). In fact, the magnitude of the priming effect on the Mterm NPP response to eCO_{2} is comparable to its L and VLterm NPP responses, indicating a persistent eCO_{2} effect over time (Table 3). A faster decomposition rate and therefore a smaller pool size of the slow SOM pool are observed (Table 5). With a fixed wood N : C ratio assumption, the NPP response to eCO_{2} is drastically reduced in the M term compared to the model with a variable wood N : C assumption (Fig. 6b), but it is comparable to its corresponding baseline fixed wood N : C model (Table 3). Varying parameter coefficients (a_{0}, a_{1}, f_{cue, rhizo}, and k_{m}) affects the decomposition rates of the slow soil organic pool and hence could lead to variation of the priming effect on Mterm CO_{2} response (Fig. S3). Further experimental studies are needed to better constrain these parameters. Adding root exudation without influencing the slow SOM pool decomposition rate (Eq. 21) leads to a smaller predicted Mterm CO_{2} response than the model with the direct effect on the slow SOM pool. However, it also leads to a higher predicted Mterm CO_{2} response than the baseline model (Fig. 7) because a_{r} and n_{r} affect the reburial fraction of the slow SOM pool, as shown in McMurtrie et al. (2000). Finally, the model with a variable wood N : C assumption indicates that there is no increase in NUE (Table 2) in the M term compared to its L and VLterm responses (Fig. 6c). In comparison, the fixed wood N : C ratio assumption means that there is a decreased wood “quality” (reflected via a decreased N : C ratio), and therefore faster decomposition of the slow SOM pool does not release much extra N to support the Mterm CO_{2} response, leading to a significant rise of NUE in the M term (Fig. 6d).
4.1 Influence of alternative N uptake assumptions on predicted CO_{2} fertilization
The quasiequilibrium analysis of the timevarying plant response to eCO_{2} provides a quantitative framework to understand the relative contributions of different model assumptions governing the supply of N to plants in determining the magnitude of the CO_{2} fertilization effect. Here, we evaluated how plant responses to eCO_{2} are affected by widely used model assumptions relating to plant N uptake, soil decomposition, and immobilization demand under alternative wood N–C coupling strategies (variable and fixed wood N : C ratios). These assumptions have been adopted in land surface models such as OCN (Zaehle and Friend, 2010), CABLE (Wang et al., 2007), LPJGuess N (Wårlind et al., 2014), JASBACHCNP (Goll et al., 2012), ORCHIDEECNP (Goll et al., 2017a), and CLM4 (Thornton et al., 2007). In line with previous findings (Comins and McMurtrie, 1993; Dewar and McMurtrie, 1996; Kirschbaum et al., 1998; McMurtrie and Comins, 1996; Medlyn and Dewar, 1996), our results show that assumptions related to wood stoichiometry have a very large impact on estimates of plant responses to eCO_{2}. More specifically, models incorporating a fixed wood N : C ratio consistently predicted smaller CO_{2} fertilization effects on production than models using a variable N : C ratio assumption (Table 3). Examples of models assuming constant (Thornton et al., 2007; Weng and Luo, 2008) and variable (Zaehle and Friend, 2010) plant tissue stoichiometry are both evident in the literature, and therefore, assuming that all other model structures and assumptions are similar, prediction differences could potentially be attributed to the tissue stoichiometric assumption incorporated into these models, as suggested in some previous simulation studies (Medlyn et al., 2016, 2015; Meyerholt and Zaehle, 2015; Zaehle et al., 2014). Together with a more appropriate representation of the tradeoffs governing tissue C–N coupling (Medlyn et al., 2015), further tissue biochemistry data are necessary to constrain this fundamental aspect of ecosystem model uncertainty (Thomas et al., 2015).
C–N coupled simulation models generally predict that the CO_{2} fertilization effect on plant production is progressively constrained by soil N availability over time: the progressive nitrogen limitation hypothesis (Luo et al., 2004; Norby et al., 2010; Zaehle et al., 2014). Here we showed similar temporal patterns in a model with different plant N uptake assumptions (Fig. 4) and the potential NPP assumption (Fig. 5). In particular, the progressive N limitation effect on NPP is shown as a downregulated Mterm CO_{2} response after the sharp instantaneous CO_{2} fertilization effect on production is realized. However, the model incorporating a priming effect of C on soil N availability with a flexible wood N : C ratio assumption induced a strong Mterm CO_{2} response (13 % increase in NPP), thereby introducing a persistent CO_{2} effect over time (Fig. 6a). This strong Mterm CO_{2} response is due to an enhanced decomposition rate of soil organic matter, consistent with a series of recent observations and modeling studies (Finzi et al., 2015; Guenet et al., 2018; Sulman et al., 2014; van Groenigen et al., 2014). However, as a previous quasiequilibrium study showed, a significant increase in the Mterm CO_{2} response can occur via changes in litter quality into the slow SOM pool or increased N input into the system (McMurtrie et al., 2000). Our study differs from McMurtrie et al. (2000) in that we introduced an explicit effect of C priming on k_{slow} – the decomposition rate of the slow SOM pool – via extra rhizodeposition (Eq. 21). As such, a faster decomposition rate of slow SOM is observed (Table 5), equivalent to adding extra N for mineralization to support the Mterm CO_{2} response (Fig. 6c). More complex models for N uptake, incorporating a carbon cost for nitrogen acquisition, are being proposed (Fisher et al., 2010; Ghimire et al., 2016; M. Shi et al., 2015); we suggest that the likely effects of introducing these complex sets of assumptions into largescale models could usefully be explored with the quasiequilibrium framework.
Processes regulating progressive nitrogen limitation under eCO_{2} were evaluated by Liang et al. (2016) based on a metaanalysis, which bridged the gap between theory and observations. It was shown that the expected diminished CO_{2} fertilization effect on plant growth was not apparent at the ecosystem scale due to extra N supply through increased biological N fixation and decreased leaching under eCO_{2}. Here, our baseline assumption assumed fixed N input into the system, and therefore plantavailable N is progressively depleted through increased plant N sequestration under eCO_{2}, as depicted by the progressive N limitation hypothesis (Luo et al., 2004). A function that allows the N fixation parameter to vary could provide further assessment of the tightness of the ecosystem N cycle process and its impact on plant response to eCO_{2}. Furthermore, given the significant role the wood N : C ratio plays in plant N sequestration, matching the modeled range of wood tissue stoichiometry with observations can provide an additional level of evaluation of model performance. Our study provides a generalizable evaluation based on the assumption that the wood N : C ratio, when allowed to vary in a model, is proportional to the leaf N : C ratio. Casespecific, more realistic evaluations can be performed based on the quasiequilibrium framework to bridge models with observations.
A strong M term and persistent CO_{2} fertilization effects over time was also found by some models in Walker et al. (2015), but without introducing a priming effect. In models such as CLM, N losses from the system are concentration dependent, and plant N uptake is a function of both N supply and plant demand. Increased plant N demand in models in which N uptake is a function of plant N demand reduces the soil solution N concentration and therefore system N losses. This means that over time N can accumulate in the system in response to eCO_{2} and sustain an eCO_{2} response. Here, our quasiequilibrium framework considers N lost as a fixed rate that depends linearly on the mineral N pool, and the mineral N pool changes at different equilibrium time points. For example, as shown in Table S1, the Mterm N loss rate is significantly reduced under eCO_{2} compared to the VLterm N loss rate under aCO_{2}. This suggests a positive relationship between N loss and NPP, as embedded in Eq. (4).
We also showed that the magnitude of the CO_{2} fertilization effect is significantly reduced at all timescales when models incorporate the potential NPP approach (Fig. 5). Among all model assumptions tested, the potential NPP approach induced the smallest M to VLterm responses (Table 3). It can be shown from equation derivation (Eq. 17) that the fraction ${P}_{\mathrm{dem}}/({P}_{\mathrm{dem}}+{I}_{\mathrm{dem}}$) depends only on the N : C ratios and f (fraction of litter C become soil C), implying that models incorporating the potential NPP assumption should show no response of NPP to CO_{2}. Both our study and simulationbased studies showed small CO_{2} responses (Walker et al., 2015; Zaehle et al., 2014), possibly because the timing of P_{dem} and I_{dem} differs due to the fluctuating nature of GPP and N mineralization at daily to seasonal time steps such that N is limiting at certain times of the year but not at others. Additionally, models such as CLM have volatilization losses (not leaching) that are reduced under eCO_{2}, which may lead to production not limited by N availability, meaning that a full CO_{2} fertilization effect may be realized. Finally, leaching is simplified here and treated as a fixed fraction of the mineral N pool. In models such as CLM or JASBACH, it is a function of the soilsoluble N concentration, implying a dependency on litter quality (Zaehle et al., 2014).
4.2 Implications for probing model behaviors
Model–data intercomparisons have been shown as a viable means to investigate how and why models differ in their predicted response to eCO_{2} (De Kauwe et al., 2014; Walker et al., 2015; Zaehle et al., 2014). Models make different predictions because they have different model structures (Lombardozzi et al., 2015; Meyerholt et al., 2016; Shi et al., 2018; Xia et al., 2013; Zhou et al., 2018), parameter uncertainties (Dietze et al., 2014; Wang et al., 2011), response mechanisms (Medlyn et al., 2015), and numerical implementations (Rogers et al., 2016). It is increasingly difficult to diagnose model behaviors from the multitude of model assumptions incorporated into the model. Furthermore, while it is true that the models can be tuned to match observations within the domain of calibration, models may make correct predictions but based on incorrect or simplified assumptions (Medlyn et al., 2005, 2015; Walker et al., 2015). As such, diagnosing model behaviors can be a challenging task in complex plant–soil models. In this study, we showed that the effect of a model assumption on plant response to eCO_{2} can be analytically predicted by solving the photosynthetic and nutrient recycling constraints together. This provides a constrained model framework to evaluate the effect of individual model assumptions without having to run a full set of sensitivity analyses, thereby providing an a priori understanding of the underlying response mechanisms through which the effect is realized. We suggest that before implementing a new function into the full structure of a plant–soil model, one could use the quasiequilibrium framework as a test bed to examine the effect of the new assumption.
The quasiequilibrium framework requires that additional model assumptions be analytically solvable, which is increasingly not the case for complex modeling structures. However, as we demonstrate here, studying the behavior of a reducedcomplexity model can nonetheless provide real insight into model behavior. In some cases, the quasiequilibrium framework can highlight where additional complexity is not valuable. For example, here we showed that adding complexity in the representation of plant N uptake did not result in significantly different predictions of plant response to eCO_{2}. Where the quasiequilibrium framework indicates little effect of more complex assumptions, there is a strong case for keeping simpler assumptions in the model. However, we do acknowledge that the quasiequilibrium framework operates on timescales of >5 years; where finescale temporal responses are important, the additional complexity may be warranted.
The multipleelement limitation framework developed by Rastetter and Shaver (1992) analytically evaluates the relationship between shortterm and longterm plant responses to eCO_{2} and nutrient availability under different model assumptions. It was shown that there could be a marked difference in the shortterm and longterm ecosystem responses to eCO_{2} (Rastetter et al., 1997; Rastetter and Shaver, 1992). More specifically, Rastetter et al. (1997) showed that the ecosystem NPP response to eCO_{2} appeared on several characteristic timescales: (1) there was an instantaneous increase in NPP, which results in an increased vegetation C : N ratio; (2) on a timescale of a few years, the vegetation responded to eCO_{2} by increasing uptake effort for available N through increased allocation to fine roots; (3) on a timescale of decades, there was a net movement of N from soil organic matter to vegetation, which enables vegetation biomass to accumulate; and (4) on the timescale of centuries, ecosystem responses were dominated by increases in total ecosystem N, which enable organic matter to accumulate in both vegetation and soils. Both the multipleelement limitation framework and the quasiequilibrium framework provide information about equilibrium responses. These approaches also provide information about the degree to which the ecosystem replies to internally recycled N vs. exchanges with external sources and sinks. The multipleelement limitation framework also offers insight into the C–N interaction that influences transient dynamics. These analytical frameworks are both useful tools for making quantitative assessments of model assumptions.
A related model assumption evaluation tool is the traceability framework, which decomposes complex models into various simplified component variables, such as ecosystem C storage capacity or residence time, and hence helps to identify structures and parameters that are uncertain among models (Z. Shi et al., 2015; Xia et al., 2013, 2012). Both the traceability and quasiequilibrium frameworks provide analytical solutions to describe how and why model predictions diverge. The traceability framework decomposes complex simulations into a common set of component variables, explaining differences due to these variables. In contrast, quasiequilibrium analysis investigates the impacts and behavior of a specific model assumption, which is more indicative of mechanisms and processes. Subsequently, one can relate the effect of a model assumption more mechanistically to the processes that govern the relationship between the plant N : C ratio and NPP, as depicted in Fig. 1, thereby facilitating efforts to reduce model uncertainties.
Models diverge in future projections of plant responses to increases in CO_{2} because of the different assumptions that they make. Applying model evaluation frameworks, such as the quasiequilibrium framework, to attribute these differences will not necessarily reduce multimodel prediction spread in the short term (Lovenduski and Bonan, 2017). Many model assumptions are still empirically derived, and there is a lack of mechanistic and observational constraints on the effect size, meaning that it is important to apply models incorporating diverse process representations. However, use of the quasiequilibrium framework can provide crucial insights into why model predictions differ and thus help identify the critical measurements that would allow us to discriminate among alternative models. As such, it is an invaluable tool for model intercomparison and benchmarking analysis. We recommend the use of this framework to analyze likely outcomes of new model assumptions before introducing them to complex model structures.
The code repository is publicly available via DOI https://doi.org/10.5281/zenodo.2574192 (Jiang et al., 2019).
Here we show how the baseline quasiequilibrium framework is derived. Specifically, there are two analytical constraints that form the foundation of the quasiequilibrium framework, namely the photosynthetic constraint and the nitrogen cycling constraint. The derivation follows Comins and McMurtrie (1993), which is further elaborated in work by McMurtrie et al. (2000) and Medlyn and Dewar (1996) and evaluated Comins (1994).
A1 Photosynthetic constraint
Firstly, gross primary production (GPP) in the simulation mode is calculated using a lightuse efficiency approach named MATE (Model Any Terrestrial Ecosystem) (McMurtrie et al., 2008; Medlyn et al., 2011; Sands, 1995), in which absorbed photosynthetically active radiation is estimated from leaf area index (L) using Beer's law and is then multiplied by a lightuse efficiency (LUE), which depends on the foliar N : C ratio (n_{f}) and atmospheric CO_{2} concentration (C_{a}):
where I_{0} is the incident radiation, k is the canopy light extinction coefficient, and L is leaf area index. The derivation of LUE for the MATE is described in full by McMurtrie et al. (2008); our version differs only in that the key parameters determining the photosynthetic rate follow the empirical relationship with the foliar N : C ratio given by Walker et al. (2014), and the expression for stomatal conductance follows Medlyn et al. (2011).
In the quasiequilibrium framework, the photosynthetic constraint is derived by assuming that the foliage C pool (C_{f}) has equilibrated. That is, the new foliage C production equals turnover, which is assumed to be a constant fraction (s_{f}) of the pool:
where a_{f} is the allocation coefficient for foliage. From Eq. (A1), net primary production is a function of the foliar N : C ratio and the foliage C pool:
where σ is the specific leaf area. Combining the two equations above leads to an implicit relationship between NPP and n_{f},
which is the photosynthetic constraint.
A2 Nutrient recycling constraint
The nitrogen cycling constraint is derived by assuming that nitrogen inputs to and outputs from the equilibrated pools are equal. Based on the assumed residence times of the passive SOM (∼400 years), slow SOM (15 years), and woody biomass (50 years) pools, we can calculate the nutrient recycling constraint at three different timescales: very long (VL, >500 years, all pools equilibrated), long (L, 100–500 years, all pools equilibrated except the passive pool), or medium (M, 5–50 years, all pools equilibrated except slow, passive and wood pools).
In the VL term, we have
where N_{in} is the total N input into the system, and N_{loss} is the total N lost from the system via leaching and volatilization. Following Comins and McMurtrie (1993), the flux N_{in} is assumed to be a constant. The total N loss term is proportional to the rate of N mineralization (N_{m}), following
where l_{n} is the fraction of N mineralization that is lost. It is assumed that mineralized N that is not lost is taken up by plants (N_{U}):
Combining with Eq. (A6), we have
The plant N uptake rate depends on production (NPP) and plant N : C ratios, according to
where a_{f}, a_{w}, and a_{r} are the allocation coefficients for foliage, wood, and roots, respectively, and n_{fl}, n_{w}, and n_{r} are the N : C ratios for foliage litter, wood, and roots, respectively. The foliage litter N : C ratio (n_{fl}) is proportional to n_{f}, according to Table 2. Combining Eq. (A9) with Eqs. (A5) and (A8), we obtain a function of NPP that can be related to total N input, which is the nutrient recycling constraint in the VL term, expressed as
Since n_{w} and n_{r} are assumed proportional to n_{f}, the nutrient recycling constraint also links NPP and n_{f}. The intersection with the photosynthetic constraint yields the verylongterm equilibria of both NPP and n_{f}.
In the L term, we now have to consider N flows leaving and entering the passive SOM pool, which is no longer equilibrated:
where ${N}_{{\mathrm{R}}_{\mathrm{p}}}$ and ${N}_{{\mathrm{S}}_{\mathrm{p}}}$ are the release and sequestration of the passive SOM N pool, respectively. The release flux, ${N}_{{\mathrm{R}}_{\mathrm{p}}}$, can be assumed to be constant on the Lterm timescale. The sequestration flux, ${N}_{{\mathrm{S}}_{\mathrm{p}}}$, can be calculated as a function of NPP. In G'DAY, as with most carbon–nitrogen coupled ecosystem models, carbon flows out of the soil pools are directly related to the pool size. As demonstrated by Comins and McMurtrie (1993), such soil models have the mathematical property of linearity, meaning that carbon flows out of the soil pools are proportional to the production input to the soil pool, or NPP. Furthermore, the litter input into the soil pools is assumed proportional to the foliar N : C ratio, with the consequence that N sequestered in the passive SOM is also related to the foliar N : C ratio. The sequestration flux into the passive soil pool (${N}_{{\mathrm{S}}_{\mathrm{p}}}$) can thus be written as
where n_{p} is the N : C ratio of the passive SOM pool, and ${\mathrm{\Omega}}_{{\mathrm{p}}_{\mathrm{f}}}$, ${\mathrm{\Omega}}_{{\mathrm{p}}_{\mathrm{w}}}$, and ${\mathrm{\Omega}}_{{\mathrm{p}}_{\mathrm{r}}}$ are the burial coefficients for foliage, wood, and roots (the proportion of plant carbon production that is ultimately buried in the passive pool), respectively. The burial coefficients ${\mathrm{\Omega}}_{{\mathrm{p}}_{\mathrm{f}}}$, ${\mathrm{\Omega}}_{{\mathrm{p}}_{\mathrm{w}}}$, and ${\mathrm{\Omega}}_{{\mathrm{p}}_{\mathrm{r}}}$ depend on the N : C ratios of foliage, wood, and root litter (detailed derivation in Comins and McMurtrie, 1993). Combining and rearranging, we obtain the nutrient recycling constraint in the L term as
Similarly, in the M term, we have
where ${N}_{{\mathrm{R}}_{\mathrm{s}}}$and ${N}_{{\mathrm{R}}_{\mathrm{w}}}$ are the N released from the slow SOM and wood pool, respectively, and ${N}_{{\mathrm{S}}_{\mathrm{s}}}$ and ${N}_{{\mathrm{S}}_{\mathrm{w}}}$ are the N stored in the slow SOM and wood pool, respectively (Medlyn et al., 2000). The nutrient recycling constraint in the M term can thus be derived as
where n_{s} is the slow SOM pool N : C ratio, and ${\mathrm{\Omega}}_{{\mathrm{s}}_{\mathrm{f}}}$ and ${\mathrm{\Omega}}_{{\mathrm{s}}_{\mathrm{r}}}$ are foliage and root C sequestration rate into the slow SOM pool, respectively (Medlyn et al., 2000). The intersection between the nitrogen recycling constraint and the photosynthetic constraint provides an analytical solution to both NPP and n_{f} at different timescales, and we can then interpret how changing model assumptions affect the predicted plant responses to elevated CO_{2}.
The supplement related to this article is available online at: https://doi.org/10.5194/gmd1220692019supplement.
BEM and MJ designed the study; MJ, BEM, and SZ performed the analyses; APW, MGDK, and SZ designed the priming effect equations; all authors contributed to results interpretation and paper writing.
The authors declare that they have no conflict of interest.
This paper builds heavily on ideas originally developed by Ross McMurtrie and Hugh Comins (now deceased). We would like to acknowledge their intellectual leadership and inspiration.
Sönke Zaehle and Silvia Caldararu were supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (QUINCY; grant no. 647204) and the German Academic Exchange Service (DAAD; project ID 57318796). David S. Ellsworth and Mingkai Jiang were also supported by the DAAD.
This paper was edited by David Lawrence and reviewed by two anonymous referees.
Bonan, G. B. and Levis, S.: Quantifying carbonnitrogen feedbacks in the Community Land Model (CLM4), Geophys. Res. Lett., 37, L07401, https://doi.org/10.1029/2010GL042430, 2010.
Comins, H. N.: Equilibrium Analysis of Integrated Plant – Soil Models for Prediction of the Nutrient Limited Growth Response to CO_{2} Enrichment, J. Theor. Biol., 171, 369–385, 1994.
Comins, H. N. and McMurtrie, R. E.: Longterm response of nutrientlimited forests to CO_{2} enrichment; equilibrium behavior of plantsoil models, Ecol. Appl., 3, 666–681, 1993.
Corbeels, M., McMurtrie, R. E., Pepper, D. A., and O'Connell, A. M.: A processbased model of nitrogen cycling in forest plantations: Part I. Structure, calibration and analysis of the decomposition model, Ecol. Model., 187, 426–448, 2005.
De Kauwe, M. G., Medlyn, B. E., Zaehle, S., Walker, A. P., Dietze, M. C., Wang, Y.P., Luo, Y., Jain, A. K., ElMasri, B., Hickler, T., Wårlind, D., Weng, E., Parton, W. J., Thornton, P. E., Wang, S., Prentice, I. C., Asao, S., Smith, B., McCarthy, H. R., Iversen, C. M., Hanson, P. J., Warren, J. M., Oren, R., and Norby, R. J.: Where does the carbon go? A model–data intercomparison of vegetation carbon allocation and turnover processes at two temperate forest freeair CO_{2} enrichment sites, New Phytol., 203, 883–899, 2014.
Dewar, R. C. and McMurtrie, R. E.: Analytical model of stemwood growth in relation to nitrogen supply, Tree Physiol., 16, 161–171, 1996.
Dietze, M. C., Serbin, S. P., Davidson, C., Desai, A. R., Feng, X., Kelly, R., Kooper, R., LeBauer, D., Mantooth, J., McHenry, K., and Wang, D.: A quantitative assessment of a terrestrial biosphere model's data needs across North American biomes, J. Geophys. Res.Biogeo., 119, 286–300, 2014.
Dijkstra, F. A. and Cheng, W.: Interactions between soil and tree roots accelerate longterm soil carbon decomposition, Ecol. Lett., 10, 1046–1053, 2007.
Dybzinski, R., Farrior, C. E., and Pacala, S. W.: Increased forest carbon storage with increased atmospheric CO_{2} despite nitrogen limitation: a gametheoretic allocation model for trees in competition for nitrogen and light, Glob. Change Biol., 21, 1182–1196, 2014.
FernándezMartínez, M., Vicca, S., Janssens, I. A., Sardans, J., Luyssaert, S., Campioli, M., Chapin Iii, F. S., Ciais, P., Malhi, Y., Obersteiner, M., Papale, D., Piao, S. L., Reichstein, M., Rodà, F., and Peñuelas, J.: Nutrient availability as the key regulator of global forest carbon balance, Nat. Clim. Change, 4, 471–476, https://doi.org/10.1038/NCLIMATE2177, 2014.
Finzi, A. C., Abramoff, R. Z., Spiller, K. S., Brzostek, E. R., Darby, B. A., Kramer, M. A., and Phillips, R. P.: Rhizosphere processes are quantitatively important components of terrestrial carbon and nutrient cycles, Glob. Change Biol., 21, 2082–2094, 2015.
Fisher, J. B., Sitch, S., Malhi, Y., Fisher, R. A., Huntingford, C., and Tan, S. Y.: Carbon cost of plant nitrogen acquisition: A mechanistic, globally applicable model of plant nitrogen uptake, retranslocation, and fixation, Global Biogeochem. Cy., 24, GB1014, https://doi.org/10.1029/2009GB003621, 2010.
Friend, A. D., Lucht, W., Rademacher, T. T., Keribin, R., Betts, R., Cadule, P., Ciais, P., Clark, D. B., Dankers, R., Falloon, P. D., Ito, A., Kahana, R., Kleidon, A., Lomas, M. R., Nishina, K., Ostberg, S., Pavlick, R., Peylin, P., Schaphoff, S., Vuichard, N., Warszawski, L., Wiltshire, A., and Woodward, F. I.: Carbon residence time dominates uncertainty in terrestrial vegetation responses to future climate and atmospheric CO_{2}, P. Natl. Acad. Sci. USA, 111, 3280–3285, 2014.
Gerber, S., Hedin Lars, O., Oppenheimer, M., Pacala Stephen, W., and Shevliakova, E.: Nitrogen cycling and feedbacks in a global dynamic land model, Global Biogeochem. Cy., 24, GB1001, https://doi.org/10.1029/2008GB003336, 2010.
Ghimire, B., Riley William, J., Koven Charles, D., Mu, M., and Randerson James, T.: Representing leaf and root physiological traits in CLM improves global carbon and nitrogen cycling predictions, J. Adv. Model. Earth Syst., 8, 598–613, 2016.
Goll, D. S., Brovkin, V., Parida, B. R., Reick, C. H., Kattge, J., Reich, P. B., van Bodegom, P. M., and Niinemets, Ü.: Nutrient limitation reduces land carbon uptake in simulations with a model of combined carbon, nitrogen and phosphorus cycling, Biogeosciences, 9, 3547–3569, https://doi.org/10.5194/bg935472012, 2012.
Goll, D. S., Vuichard, N., Maignan, F., JornetPuig, A., Sardans, J., Violette, A., Peng, S., Sun, Y., Kvakic, M., Guimberteau, M., Guenet, B., Zaehle, S., Penuelas, J., Janssens, I., and Ciais, P.: A representation of the phosphorus cycle for ORCHIDEE (revision 4520), Geosci. Model Dev., 10, 3745–3770, https://doi.org/10.5194/gmd1037452017, 2017a.
Goll, D. S., Winkler, A. J., Raddatz, T., Dong, N., Prentice, I. C., Ciais, P., and Brovkin, V.: Carbon–nitrogen interactions in idealized simulations with JSBACH (version 3.10), Geosci. Model Dev., 10, 2009–2030, https://doi.org/10.5194/gmd1020092017, 2017b.
Guenet, B., Moyano, F. E., Peylin, P., Ciais, P., and Janssens, I. A.: Towards a representation of priming on soil carbon decomposition in the global land biosphere model ORCHIDEE (version 1.9.5.2), Geosci. Model Dev., 9, 841–855, https://doi.org/10.5194/gmd98412016, 2016.
Guenet, B., CaminoSerrano, M., Ciais, P., Tifafi, M., Maignan, F., Soong Jennifer, L., and Janssens Ivan, A.: Impact of priming on global soil carbon stocks, Glob. Change Biol., 24, 1873–1883, 2018.
Huntzinger, D. N., Michalak, A. M., Schwalm, C., Ciais, P., King, A. W., Fang, Y., Schaefer, K., Wei, Y., Cook, R. B., Fisher, J. B., Hayes, D., Huang, M., Ito, A., Jain, A. K., Lei, H., Lu, C., Maignan, F., Mao, J., Parazoo, N., Peng, S., Poulter, B., Ricciuto, D., Shi, X., Tian, H., Wang, W., Zeng, N., and Zhao, F.: Uncertainty in the response of terrestrial carbon sink to environmental drivers undermines carbonclimate feedback predictions, Sci. Rep., 7, 4765, https://doi.org/10.1038/s41598017038182, 2017.
Jiang, M., Zaehle, S., De Kauwe, M. G., Walker, A. P., Caldararu, S., Ellsworth, D. S., and Medlyn, B. E.: The quasiequilibrium framework analytical platform, Zenodo, https://doi.org/10.5281/zenodo.2574192, 2019.
Kirschbaum, M. U. F., King, D. A., Comins, H. N., McMurtrie, R. E., Medlyn, B. E., Pongracic, S., Murty, D., Keith, H., Raison, R. J., Khanna, P. K., and Sheriff, D. W.: Modeling forest response to increasing CO_{2} concentration under nutrientlimited conditions, Plant Cell Environ., 17, 1081–1099, 1994.
Kirschbaum, M. U. F., Medlyn, B. E., King, D. A., Pongracic, S., Murty, D., Keith, H., Khanna, P. K., Snowdon, P., and Raison, R. J.: Modelling forestgrowth response to increasing CO_{2} concentration in relation to various factors affecting nutrient supply, Glob. Change Biol., 4, 23–41, 1998.
Koven, C. D., Chambers, J. Q., Georgiou, K., Knox, R., NegronJuarez, R., Riley, W. J., Arora, V. K., Brovkin, V., Friedlingstein, P., and Jones, C. D.: Controls on terrestrial carbon feedbacks by productivity versus turnover in the CMIP5 Earth System Models, Biogeosciences, 12, 5211–5228, https://doi.org/10.5194/bg1252112015, 2015.
Kowalczyk, E. A., Wang, Y. P., Law, R. M., Davies, H. L., McGregor, J. L., and Abramowitz, G.: The CSIRO Atmosphere Biosphere Land Exchange (CABLE) model for use in climate models and as an offline model, CSIRO, Australia, 2006.
Liang, J., Qi, X., Souza, L., and Luo, Y.: Processes regulating progressive nitrogen limitation under elevated carbon dioxide: a metaanalysis, Biogeosciences, 13, 2689–2699, https://doi.org/10.5194/bg1326892016, 2016.
Lombardozzi, D. L., Bonan, G. B., Smith, N. G., Dukes, J. S., and Fisher, R. A.: Temperature acclimation of photosynthesis and respiration: A key uncertainty in the carbon cycleclimate feedback, Geophys. Res. Lett., 42, 8624–8631, 2015.
Lovenduski, N. S. and Bonan, G. B.: Reducing uncertainty in projections of terrestrial carbon uptake, Environ. Res. Lett., 12, 044020, https://doi.org/10.1088/17489326/aa66b8, 2017.
Ludwig, D., Jones, D. D., and Holling, C. S.: Qualitative Analysis of Insect Outbreak Systems: The Spruce Budworm and Forest, J. Anim. Ecol., 47, 315–332, 1978.
Luo, Y., Su, B., Currie, W. S., Dukes, J. S., Finzi, A., Hartwig, U., Hungate, B., McMurtrie, R. E., Oren, R., Parton, W. J., Pataki, D. E., Shaw, R. M., Zak, D. R., and Field, C. B.: Progressive Nitrogen Limitation of Ecosystem Responses to Rising Atmospheric Carbon Dioxide, BioScience, 54, 731–739, 2004.
McMurtrie, R. and Comins, H. N.: The temporal response of forest ecosystems to doubled atmospheric CO_{2} concentration, Glob. Change Biol., 2, 49–57, 1996.
McMurtrie, R. E., Dewar, R. C., Medlyn, B. E., and Jeffreys, M. P.: Effects of elevated [CO_{2}] on forest growth and carbon storage: a modelling analysis of the consequences of changes in litter quality/quantity and root exudation, Plant Soil, 224, 135–152, 2000.
McMurtrie, R. E., Medlyn, B. E., and Dewar, R. C.: Increased understanding of nutrient immobilization in soil organic matter is critical for predicting the carbon sink strength of forest ecosystems over the next 100 years, Tree Physiol., 21, 831–839, 2001.
McMurtrie, R. E., Norby, R. J., Medlyn, B. E., Dewar, R. C., Pepper, D. A., Reich, P. B., and Barton, C. V. M.: Why is plantgrowth response to elevated CO_{2} amplified when water is limiting, but reduced when nitrogen is limiting? A growthoptimisation hypothesis, Funct. Plant Biol., 35, 521–534, 2008.
McMurtrie, R. E., Iversen, C. M., Dewar, R. C., Medlyn, B. E., Näsholm, T., Pepper, D. A., and Norby, R. J.: Plant root distributions and nitrogen uptake predicted by a hypothesis of optimal root foraging, Ecol. Evol., 2, 1235–1250, 2012.
Medlyn, B. E. and Dewar, R. C.: A model of the longterm response of carbon allocation and productivity of forests to increased CO_{2} concentration and nitrogen deposition, Glob. Change Biol., 2, 367–376, 1996.
Medlyn, B. E., McMurtrie, R. E., Dewar, R. C., and Jeffreys, M. P.: Soil processes dominate the longterm response of forest net primary productivity to increased temperature and atmospheric CO_{2} concentration, Can. J. For. Res., 30, 873–888, 2000.
Medlyn, B. E., Robinson, A. P., Clement, R., and McMurtrie, R. E.: On the validation of models of forest CO_{2} exchange using eddy covariance data: some perils and pitfalls, Tree Physiol., 25, 839–857, 2005.
Medlyn, B. E., Duursma, R. A., Eamus, D., Ellsworth, D. S., Prentice, I. C., Barton, C. V. M., Crous, K. Y., De Angelis, P., Freeman, M., and Wingate, L.: Reconciling the optimal and empirical approaches to modelling stomatal conductance, Glob. Change Biol., 17, 2134–2144, 2011.
Medlyn, B. E., Zaehle, S., De Kauwe, M. G., Walker, A. P., Dietze, M. C., Hanson, P. J., Hickler, T., Jain, A. K., Luo, Y., Parton, W., Prentice, I. C., Thornton, P. E., Wang, S., Wang, Y.P., Weng, E., Iversen, C. M., McCarthy, H. R., Warren, J. M., Oren, R., and Norby, R. J.: Using ecosystem experiments to improve vegetation models, Nat. Clim. Change, 5, 528–534, 2015.
Medlyn, B. E., De Kauwe Martin, G., Zaehle, S., Walker Anthony, P., Duursma Remko, A., Luus, K., Mishurov, M., Pak, B., Smith, B., Wang, Y. P., Yang, X., Crous Kristine, Y., Drake John, E., Gimeno Teresa, E., Macdonald Catriona, A., Norby Richard, J., Power Sally, A., Tjoelker Mark, G., and Ellsworth David, S.: Using models to guide field experiments: a priori predictions for the CO_{2} response of a nutrient and waterlimited native Eucalypt woodland, Glob. Change Biol., 22, 2834–2851, 2016.
Meyerholt, J. and Zaehle, S.: The role of stoichiometric flexibility in modelling forest ecosystem responses to nitrogen fertilization, New Phytol., 208, 1042–1055, 2015.
Meyerholt, J., Zaehle, S., and Smith, M. J.: Variability of projected terrestrial biosphere responses to elevated levels of atmospheric CO_{2} due to uncertainty in biological nitrogen fixation, Biogeosciences, 13, 1491–1518, https://doi.org/10.5194/bg1314912016, 2016.
Norby, R. J., Warren, J. M., Iversen, C. M., Medlyn, B. E., and McMurtrie, R. E.: CO_{2} enhancement of forest productivity constrained by limited nitrogen availability, P. Natl. Acad. Sci. USA, 107, 19368–19373, 2010.
Oleson, K. W., Dai, Y. J., Bonan, G. B., Bosilovich, M., Dichinson, R., Dirmeyer, P., Hoffman, F., Houser, P., Levis, S., Niu, G.Y., Thornton, P. E., Vertenstein, M., Yang, Z. L., and Zeng, X.: Technical description of the Community Land Model (CLM), National Center for Atmospheric Research, Boulder, Colorado, USA, 2004.
Rastetter, E. B. and Shaver, G. R.: A Model of MultipleElement Limitation for Acclimating Vegetation, Ecology, 73, 1157–1174, 1992.
Rastetter, E. B., Ågren, G. I., and Shaver, G. R.: Responses Of NLimited Ecosystems To Increased CO_{2}: A BalancedNutrition, CoupledElementCycles Model, Ecol. Appl., 7, 444–460, 1997.
Reich, P. B. and Hobbie, S. E.: Decadelong soil nitrogen constraint on the CO_{2} fertilization of plant biomass, Nat. Clim. Change, 3, 278–282, https://doi.org/10.1038/NCLIMATE1694, 2012.
Rogers, A., Medlyn Belinda, E., Dukes Jeffrey, S., Bonan, G., Caemmerer, S., Dietze Michael, C., Kattge, J., Leakey Andrew, D. B., Mercado Lina, M., Niinemets, Ü., Prentice, I. C., Serbin Shawn, P., Sitch, S., Way Danielle, A., and Zaehle, S.: A roadmap for improving the representation of photosynthesis in Earth system models, New Phytol., 213, 22–42, 2016.
Sands, P.: Modelling Canopy Production. II. From SingleLeaf Photosynthesis Parameters to Daily Canopy Photosynthesis, Funct. Plant Biol., 22, 603–614, 1995.
Shi, M., Fisher, J. B., Brzostek, E. R., and Phillips, R. P.: Carbon cost of plant nitrogen acquisition: global carbon cycle impact from an improved plant nitrogen cycle in the Community Land Model, Glob. Change Biol., 22, 1299–1314, 2015.
Shi, Z., Xu, X., Hararuk, O., Jiang, L., Xia, J., Liang, J., Li, D., and Luo, Y.: Experimental warming altered rates of carbon processes, allocation, and carbon storage in a tallgrass prairie, Ecosphere, 6, 1–16, 2015.
Shi, Z., Crowell, S., Luo, Y., and Moore, B.: Model structures amplify uncertainty in predicted soil carbon responses to climate change, Nat. Communi., 9, 2171, https://doi.org/10.1038/s41467018045269, 2018.
Sigurdsson, B. D., Medhurst, J. L., Wallin, G., Eggertsson, O., and Linder, S.: Growth of mature boreal Norway spruce was not affected by elevated [CO_{2}] and/or air temperature unless nutrient availability was improved, Tree Physiol., 33, 1192–1205, 2013.
Smith, B., Prentice, I. C., and Sykes, M. T.: Representation of vegetation dynamics in the modelling of terrestrial ecosystems: comparing two contrasting approaches within European climate space, Global Ecol. Biogeogr., 10, 621–637, 2001.
Sokolov, A. P., Kicklighter, D. W., Melillo, J. M., Felzer, B. S., Schlosser, C. A., and Cronin, T. W.: Consequences of Considering Carbon–Nitrogen Interactions on the Feedbacks between Climate and the Terrestrial Carbon Cycle, J. Climate, 21, 3776–3796, 2008.
Stocker, B. D., Prentice, I. C., Cornell, S. E., DaviesBarnard, T., Finzi, A. C., Franklin, O., Janssens, I., Larmola, T., Manzoni, S., Näsholm, T., Raven, J. A., Rebel, K. T., Reed, S., Vicca, S., Wiltshire, A., and Zaehle, S.: Terrestrial nitrogen cycling in Earth system models revisited, New Phytol., 210, 1165–1168, 2016.
Sulman, B. N., Phillips, R. P., Oishi, A. C., Shevliakova, E., and Pacala, S. W.: Microbedriven turnover offsets mineralmediated storage of soil carbon under elevated CO_{2}, Nat. Clim. Change, 4, 1099, https://doi.org/10.1038/NCLIMATE2436, 2014.
Thomas, R. Q., Brookshire, E. N. J., and Gerber, S.: Nitrogen limitation on land: how can it occur in Earth system models?, Glob. Change Biol., 21, 1777–1793, 2015.
Thornton, P. E., Lamarque, J. F., Rosenbloom Nan, A., and Mahowald, N. M.: Influence of carbonnitrogen cycle coupling on land model response to CO_{2} fertilization and climate variability, Global Biogeochem. Cy., 21, GB4018, https://doi.org/10.1029/2006GB002868, 2007.
Thornton, P. E., Doney, S. C., Lindsay, K., Moore, J. K., Mahowald, N., Randerson, J. T., Fung, I., Lamarque, J.F., Feddema, J. J., and Lee, Y.H.: Carbonnitrogen interactions regulate climatecarbon cycle feedbacks: results from an atmosphereocean general circulation model, Biogeosciences, 6, 2099–2120, https://doi.org/10.5194/bg620992009, 2009.
van Groenigen, K. J., Qi, X., Osenberg, C. W., Luo, Y., and Hungate, B. A.: Faster Decomposition Under Increased Atmospheric CO_{2} Limits Soil Carbon Storage, Science, 344, 508–509, https://doi.org/10.1126/science.1249534, 2014.
Walker, A. P., Hanson, P. J., De Kauwe, M. G., Medlyn, B. E., Zaehle, S., Asao, S., Dietze, M., Hickler, T., Huntingford, C., Iversen, C. M., Jain, A., Lomas, M., Luo, Y. Q., McCarthy, H., Parton, W. J., Prentice, I. C., Thornton, P. E., Wang, S. S., Wang, Y. P., Warlind, D., Weng, E. S., Warren, J. M., Woodward, F. I., Oren, R., and Norby, R. J.: Comprehensive ecosystem modeldata synthesis using multiple data sets at two temperate forest freeair CO_{2} enrichment experiments: Model performance at ambient CO_{2} concentration, J. Geophys. Res.Biogeo., 119, 937–964, 2014.
Walker, A. P., Zaehle, S., Medlyn, B. E., De Kauwe, M. G., Asao, S., Hickler, T., Parton, W., Ricciuto, D. M., Wang, Y.P., Wårlind, D., and Norby, R. J.: Predicting longterm carbon sequestration in response to CO_{2} enrichment: How and why do current ecosystem models differ?, Global Biogeochem. Cy., 29, 476–495, 2015.
Wang, Y. P., Houlton, B. Z., and Field, C. B.: A model of biogeochemical cycles of carbon, nitrogen, and phosphorus including symbiotic nitrogen fixation and phosphatase production, Global Biogeochem. Cy., 21, GB1018, https://doi.org/10.1029/2006GB002797, 2007.
Wang, Y. P., Kowalczyk, E., Leuning, R., Abramowitz, G., Raupach, M. R., Pak, B., van Gorsel, E., and Luhar, A.: Diagnosing errors in a land surface model (CABLE) in the time and frequency domains, J. Geophys. Res.Biogeo., 116, G01034, https://doi.org/10.1029/2010JG001385, 2011.
Wårlind, D., Smith, B., Hickler, T., and Arneth, A.: Nitrogen feedbacks increase future terrestrial ecosystem carbon uptake in an individualbased dynamic vegetation model, Biogeosciences, 11, 6131–6146, https://doi.org/10.5194/bg1161312014, 2014.
Weng, E. and Luo, Y.: Soil hydrological properties regulate grassland ecosystem responses to multifactor global change: A modeling analysis, J. Geophys. Res.Biogeo., 113, G03003, https://doi.org/10.1029/2007JG000539, 2008.
Xia, J. Y., Luo, Y. Q., Wang, Y.P., Weng, E. S., and Hararuk, O.: A semianalytical solution to accelerate spinup of a coupled carbon and nitrogen land model to steady state, Geosci. Model Dev., 5, 1259–1271, https://doi.org/10.5194/gmd512592012, 2012.
Xia, J. Y., Luo, Y., Wang, Y.P., and Hararuk, O.: Traceable components of terrestrial carbon storage capacity in biogeochemical models, Glob. Change Biol., 19, 2104–2116, 2013.
Yang, X., Wittig, V., Jain, A. K., and Post, W.: Integration of nitrogen cycle dynamics into the Integrated Science Assessment Model for the study of terrestrial ecosystem responses to global change, Global Biogeochem. Cy., 23, GB4029, https://doi.org/10.1029/2009GB003474, 2009.
Zaehle, S. and Friend, A. D.: Carbon and nitrogen cycle dynamics in the OCN land surface model: 1. Model description, sitescale evaluation, and sensitivity to parameter estimates, Global Biogeochem. Cy., 24, GB1005, https://doi.org/10.1029/2009GB003521, 2010.
Zaehle, S., Friend, A. D., Friedlingstein, P., Dentener, F., Peylin, P., and Schulz, M.: Carbon and nitrogen cycle dynamics in the OCN land surface model: 2. Role of the nitrogen cycle in the historical terrestrial carbon balance, Global Biogeochem. Cy., 24, GB1006, https://doi.org/10.1029/2009GB003522, 2010.
Zaehle, S., Medlyn, B. E., De Kauwe, M. G., Walker, A. P., Dietze, M. C., Hickler, T., Luo, Y. Q., Wang, Y. P., ElMasri, B., Thornton, P., Jain, A., Wang, S. S., Warlind, D., Weng, E. S., Parton, W., Iversen, C. M., GalletBudynek, A., McCarthy, H., Finzi, A. C., Hanson, P. J., Prentice, I. C., Oren, R., and Norby, R. J.: Evaluation of 11 terrestrial carbonnitrogen cycle models against observations from two temperate FreeAir CO_{2} Enrichment studies, New Phytol., 202, 803–822, 2014.
Zaehle, S., Jones, C. D., Houlton, B., Lamarque, J.F., and Robertson, E.: Nitrogen Availability Reduces CMIP5 Projections of TwentyFirstCentury Land Carbon Uptake, J. Climate, 28, 2494–2511, 2015.
Zhou, S., Liang, J., Lu, X., Li, Q., Jiang, L., Zhang, Y., Schwalm, C. R., Fisher, J. B., Tjiputra, J., Sitch, S., Ahlström, A., Huntzinger, D. N., Huang, Y., Wang, G., and Luo, Y.: Sources of Uncertainty in Modeled Land Carbon Storage within and across Three MIPs: Diagnosis with Three New Techniques, J. Climate, 31, 2833–2851, 2018.