ISBA is embedded in the SURFEX modeling platform. The current version is SURFEX V9.1, described in , and . ISBA uses a 14-layer scheme to solve soil physics (hydrology, thermodynamics, gas diffusion). The model includes the representation of 16 plant functional types (PFTs), rock, ice and bare soil. The ISBA scheme used here is ISBA-CC described in . This version computes carbon cycle dynamics using 6 pools to represent plants and 7 pools for the soil organic matter. Photosynthesis is represented using a semi-empirical approach based on , implemented by . The scheme was modified by for tropical vegetation. As previously stated, an implicit nitrogen limitation was implemented to regulate photosynthesis with increasing CO₂. It consists of two parameterizations: the first one acts globally to correct the model tendency to overestimate CO₂ fertilization. The second acts directly on photosynthesis by reducing the specific leaf area (SLA) with increasing CO₂, thereby constraining leaf growth and carbon assimilation .

The assimilated carbon is first allocated to the leaves. It is then reallocated to the other biomass pools using different empirical allometric relations . Each biomass carbon pool is associated with a respiration and a turnover rate. Soil litter and soil organic-carbon pools are represented within each soil layer, and their dynamics follow the CENTURY model of . Latest developments include a gas module that explicitly simulates the dynamics of O2, CO₂, and CH4 with methane related processes and vertical carbon transfers. The equations driving the carbon cycle are detailed in the Appendix .

We chose to build the nitrogen cycle consistently with the carbon cycle. Each vegetation and soil carbon pool has an associated nitrogen pool, and nitrogen decomposition fluxes follow those of carbon (Fig. ). To reduce computational cost, these N pools and fluxes are not explicitly represented, consistent with approaches used in other land models (ISAM, ; O-CN, ; ORCHIDEE, ; JULES, ). Instead carbon and nitrogen pools are linked by stoichiometric nitrogen-carbon ratios (N / C) that are prescribed for all pools except for leaves in order to adjust vegetation response to N availability . The model also explicitly describes the dynamics of a labile nitrogen pool in vegetation and a mineral nitrogen pool in soils. Soil and vegetation exchange N by an uptake flux that is a function of the mineral N availability, root distribution and plant N demand . Consequently, a limitation in the N mineral pool directly reduces plant NPP, and constrains the decomposition of organic matter. Gaseous exchanges with the atmosphere and leaching of mineral N are also represented.

The labile pool of nitrogen, Nlabile, is a storage pool that represents the nitrogen that is easily transported within the plant . N is taken up from the soil by the roots and is then redistributed to the various plant parts. Its dynamics is explicitly represented by: 1ddtNlabile(t)=Nupday(t)-Ndemand(t) where Nupday represents the nitrogen taken up by plants from the soil mineral reservoir (see Sect. ) and Ndemand is the nitrogen needed to build plant tissues. Because the C allocation scheme in ISBA is built as a cascade through the biomass pools with multiple outcomes (see Appendix ), the computation of the N needed to fulfill tissue growth is diagnosed by comparing the total biomass before and after C allocation and applying the corresponding N / C ratio. However, this diagnosed flux needs to be corrected by turnover because the change in total biomass results from both tissue growth and turnover while only growth implies a N demand. 2Ndemand*=1Δt∑x=16Bx*(t+Δt)-Bx(t)×NCBx+Nturn*(t) where NCBx is the N / C ratio of the biomass pool x and Nturn* is the N lost by turnover. To render the known N translocation of N from leaf to plant during senescence , the N turnover flux is reduced by a fraction that is directed from the leaf pool to the storage pool before leaf fall. This results in marked difference between C turnover and N turnover. This has the effect of decorrelating C and N turnover fluxes. Nturn* is expressed as: 3Nturn*(t)=∑x=161-ftrans,xMx(t)NCBx

where ftrans,x is the fraction of nitrogen from pool x that is translocated (see Table ) and Mx the turnover rate of the C pool x. ^* denotes potential fluxes before N limitation that is described in Sect. . In these last 2 equations, NCBx is time dependent for leaves and prescribed for all other pools (see Sect.). N demand can be positive: nitrogen is needed to meet carbon demand. However, the biomass cascade in the model is build so that carbon is transferred from metabolic pools (high N / C) to more ligneous pools (low N / C). As a consequence, the N demand can also be negative. In this case, the surplus of nitrogen is transferred to the labile pool. Similarly to the C allocation scheme, the dynamics of Nlabile is computed once a day.

In response to N limitation, the photosynthesis is reduced which slows down tissue growth. In addition, the plant limit N losses by readsorbing more N during senescence. In the model, both strategies are implemented sequentially. The first step is to limit C assimilation. This is implemented by computing the C allocation scheme twice. The first time, the C allocation is computed considering infinite N supply. This gives the potential Ndemand* from Eqs. () and () that is compared to the available labile N to compute the limitation parameter, ηlim,assim, following : 4ηlim,assim=min1,flabile,maxNlabileNdemand*Δt where flabile,max=0.9 is a limit to empty at most 90 % of the labile pool. This limitation is immediately applied to the daily net carbon assimilation by leaves during the second round of computation of C allocation. A1(t)=ηlim,assimA1*(t). This updates all the biomass pools and the actual N demand. 5Ndemand=1Δt∑x=16Bx(t+Δt)-Bx(t)×NCBx+Nturn*(t) The limitation may persist. The second step is then to increase retranslocation from leaves to the labile pool, as it has been done in the FUN model developed by . A correction is applied to the nitrogen turnover flux if there is no sufficient N labile to support it. The corrective factor, fcorr, is computed as the ratio of the maximum quantity that can be removed from the labile pool (flabile,maxNlabile-Ndemand) and the potential turnover flux Nturn*. 6fcorr=min1,flabile,maxNlabile-NdemandNturn* The actual turnover is then Nturn=fcorrNturn*.

The nitrogen-carbon ratio evolves during the plant development and also in response to environmental constraints . It has been observed in general that (i) structural elements such as branches, bark or heartwood contain less nitrogen than leaves. (ii) Litter is N poor compared to vegetation biomass and soil organic carbon. As a first approximation, we assumed in the model the ratio to be constant for all pools except for leaves. We prescribe a PFT-dependent value adapted from literature . The ratio associated with each carbon pool is denoted by NCBx, for biomass pool Bx and NCCi for soil carbon pool Ci. Table  summarizes values used in the model. The leaf ratio, NCB1, varies in order to adjust the system to the nitrogen availability. Initial value is taken according literature. Then, it increases when the nitrogen supply matches the potential total demand Nlabile>Ndemand*, otherwise it decreases. Minimum and maximum values are set to avoid unrealistic ratios (see Table ). Variations of NCB1 are described by Eq. (), adapted from . 7NCB1(t+Δt)=Nlabile<Ndemand*:NCB1(t)×maxNCB1,minNCB1(t),1-0.25×γNCNlabile>Ndemand*:NCB1(t)×minNCB1,maxNCB1(t),1.25-0.25×γNC where γNC dampens the variation according to: 8γNC=exp⁡-λ×NCB1,max-NCB1(t)NCB1,max-NCB1,mink. The parameters λ=1.6 and k=3.0 are chosen to adjust the dampening effect, which must allow the NC ratio to reach its boundary values.

Mineral (inorganic) N may be found as two soluble species in the soil: NH4+ and NO3- . Nitrogen enters the soil system by biological N fixation (BNF), NBNF, and by deposition, Ndepo. Both are complex processes that are simplified and supposed to directly supply the mineral pool (see Sect. ). Mineral nitrogen undergoes chemical reactions (nitrification and denitrification) during which N is lost to the atmosphere as gas, Ngas. N is also lost due to leaching towards river and oceans, Nleaching and by plants to fulfill growth, Nup. Decomposition processes are releasing nitrogen, but micro-organisms requires nitrogen to carry out their tasks. This is denoted by net mineralization, Nnetmin. We represent the two ion species as one mineral pool Nmin with associated fractions of NH4+ (fNH4) and NO3- (fNO3=1-fNH4), similarly to . The soil N mineral pool is vertically discretized and its dynamics is computed on the same vertical grid as the soil water, temperature and carbon. Mineral N dynamics is described for each soil layer l by: 9ddtNmin,l(t)=NBNFfwater,l+Ndepofwater,l-Ngas,l-Nleaching,l-Nup,l+Nnetmin,l. Variables added to represent the soil N dynamics are summarized in Table , and the fluxes are detailed in the following sections.

The model is evaluated on two Free-Air CO₂ enrichment (FACE), experiment sites located in North America: Duke and Oak Ridge forests. Figure  exhibits the mean seasonal temperature and precipitation at Duke and Oak Ridge. Both sites present a similar climate. The average annual temperature and precipitation are: 15.5 °C and 1140 mm at Duke and 13.9 °C and 1371 mm at Oak Ridge .

The Duke experiment was conducted in a pine forest in North Carolina (35°58^′ N, 79°06^′ W). The stand is composed of 92 % loblolly pine (Pinus taeda), with sub-dominant sweetgum and yellow poplar trees, and 48 other woody plant species . The forest was established in 1983 and the experiment began in 1996 . Six circular plots, each 30 m in diameter, were studied. Half were used as control plots and were exposed to ambient CO₂ concentration, (aCO₂: 350 ppm), while the other three received elevated CO₂ concentration (eCO₂: 571 ppm) .

Oak Ridge forest is composed of sweetgum (Liquidambar styraciflua L.) and is located in Tennessee (35°54^′ N, 84°20^′ W). Trees were planted in 1988, and the experiment began in 1997 . The plots have a diameter of 25 m. There are two control (aCO₂: 390 ppm) and three elevated CO₂ plots (eCO₂: 542 ppm) .

For both sites, regular measurements of annual carbon fluxes, biomass pools, and soil carbon content can be found in the literature and have been used to compare simulation results with observations.

Only the dominant tree specie is modeled: pine for Duke and sweetgum for Oak Ridge. We used the corresponding ISBA PFT: temperate evergreen needle-leaved trees for Duke and temperate broadleaved deciduous trees for Oak Ridge. Initial carbon stocks are set to 0, except for the leaf and stem pools that are initialized to a minimum value. The nitrogen stock in the plant and in the soil is initialized also to an arbitrary non 0 value to support the initial photosynthesis. The same constant nitrogen deposition rate, derived from observations (Ndepo=1.4 g_N m⁻² yr⁻¹; ) is prescribed at both sites. Following the protocol of , the soil depth is 1 m at Duke and 2 m at Oak Ridge. The discretization is shown on the y axis of Fig. . There are 8 layers at Duke and 10 at Oak Ridge. ISBA is used in offline mode, forced by meteorological forcing provided by . Two sets of simulation were run: a reference simulation with only the carbon cycle referred to as the C version, and a second set with the new implementation of the nitrogen cycle called the CN version. In both C and CN versions we deactivate the pre-existing implicit N limitation parametrizations used in ISBA to down regulate the photosynthesis (Sect. 2.5 in ). Simulation characteristics can be found in Table .

For both sites and both sets of simulation, several simulation steps have been carried out in order to better represent the site and its history. The protocol is the following. First, there is a spinup. We cycled over a spinup forcing that uses meteorological data of the FACE experiment with CO₂ concentration held constant at pre-industrial level. The criterion to end the spinup is discussed in the next section. Then, CO₂ concentration was gradually increased to simulate the industrial period. Historical meteorological forcing was used. This step lasted until the start of the forest plantation. At both sites, a clearing occurred before tree planting. Therefore, the biomass was reset to 0 and a simulation was run until the beginning of the FACE experiment. This step is referred to as plantation. There were 2 simulations run for the FACE experiment: one at ambient CO₂ and one at elevated CO₂. Table  summarizes the simulation protocol at each site.

The spinup is a critical part of the simulation process and there can be several criteria to define whether a simulation is ready to be run. Typically, spinup is considered complete when carbon pools reach a steady state, i.e., when the average total carbon stock per year stabilizes indicating system equilibrium.

A first spinup was done following this method for both sites. At Duke, equilibrium was reached after 1200 and 2400 years for C and CN version respectively. At Oak Ridge, equilibrium was reached after 1100 and 2200 years. However, this method overestimates soil carbon content compared to field observations. For the top 15 cm of soil, observed values are 1977 g_C m⁻² at Duke , and 2670 g_C m⁻² at Oak Ridge . For each set of simulation (C or CN), we compute the total below-ground litter and soil carbon in the first four soil layers to match the measurement depth. Table  summarizes the simulated values, which significantly exceed observed levels. However, letting the system reach equilibrium assumes that vegetation and soils at these sites are the result of hundreds of years of present day climate with no disturbances, which is not realistic. In addition, the land use changes are not taken into account. Both sites have an agricultural past: mowed grass at Duke and crops at Oak Ridge . Chapter 4 of special report on Climate Change and Land documents a strong reduction of soil C content in cropland and grasslands compared to forest. This may explain a large part of the discrepancies between the model and the observations.

An alternative approach is to stop the spinup once the soil C content reaches observed values. This method resulted in much shorter spinup durations: 21 and 45 years for the C and CN versions respectively, at Duke; and 21 and 87 years at Oak Ridge. The first spinup type is denoted as “eq” (equilibrium-based) and the second “real” (observation-based) in the following sections.

Then from each spinup type, industrial, plantation and FACE experiments simulations are conducted. Figure  shows the impact of the spinup on the NPP results. For both sites, the C only simulations are not impacted by the type of spinup. However for the CN simulations, discrepancies are observed due to N limitations. The initial condition defines the N status in the system, a greater C soil content leads to higher mineral N pool which supplies then the labile pool. After the equilibrium spinup, the average N in the system (Nmin+Nlabile) is of 3.24 g_N m⁻² at Duke and of 5.72 g_N m⁻² at Oak Ridge. For the spinup “real”, we found a value of 1.64 g_N m⁻² at Duke and 3.99 g_N m⁻² at Oak Ridge. Note that the NPP simulated by the CN version after equilibrium spinup is very close to the one simulated by the C version, indicating that the equilibrium spinup results in a system not limited in N. We chose the type of spinup that results in a soil carbon content equal to observations. In what follows, all simulations results originate from a spinup “real”. In this configuration, the system is not at equilibrium. This is closer to the real soil status due to the recent reforestation.

We evaluate our model by comparing it to observations and multi-model simulations from who evaluated 11 models at the Duke and Oak Ridge sites. We compare our model results with the minimum, maximum and mean of these 11 models, as well as to the observational data given by (Figs 2 and 3). Results are shown on Figs.  and .

At Duke under ambient CO₂ (Fig. , top left panel), both model versions result in annual NPPs within the 11-model range. The CN version performs better, with a smaller bias relative to observations (145 g_C m⁻² yr⁻¹ vs. 157 g_C m⁻² yr⁻¹ for the C version) and improved interannual variability (correlation of 0.66 vs. 0.64). At Oak Ridge, the C version overestimates NPP (bias of 520 g_C m⁻² yr⁻¹). Results of the CN version are within the 11-model range and better match observations (bias of 178 g_C m⁻² yr⁻¹). However, both model versions fail to capture the observed post-2003 decline in forest productivity associated with progressive nitrogen limitation , resulting in weak correlations with observations. This could be explained by an overestimation of the initial inorganic N stocks as discussed by . At elevated CO₂, the C-only version overestimates the NPP response at both sites (Fig. , bottom panels). Including N limitation (CN version) reduces this response. It is in better agreement with the observations at Duke (smaller bias), but the N limitation at Oak Ridge is excessive (strong negative bias). At Duke, the C version of the model accurately represents the inter-annual variability of the response, as indicated by a high correlation. The correlation decreases with the CN version. At Oak Ridge, both versions of the model yields weak correlation.

Figure  shows the annual N assimilation flux from soil to plant, Nup, which can only be analyzed with the CN version of the model. Under ambient CO₂ (top panel) Nup is slightly underestimated at Duke (bias of -1 g_N m⁻² yr⁻¹) and overestimated at Oak Ridge (bias of 7). At both sites, the model shows weak skill in reproducing the interannual variability. At Duke, the modeled CO₂ response is in good agreement with the observations and performs better than the multi-model mean. At Oak Ridge, the CO₂ response of the uptake flux is close to the multi-model mean but both fail to represent the inter annual variability. On average, an increase of the uptake flux due to elevated CO₂ is observed and modeled at Duke and Oak Ridge to sustain the increase in NPP. However, the underlying process differ between sites. At Duke, SOM decomposition happened faster, increasing mineralization and thus available N . At Oak Ridge, increased C allocation to fine roots led to greater root biomass and deeper roots allowing trees to access more N. This adaptive response is likely linked to the site history, a former agricultural land . Such adaptation strategies are not represented by the model. Instead, in the model, the increased Nup is due to increased available N in the mineral pool related to increased BNF mostly. Processes linked to the soil N dynamics are discussed in Sect. .

At Duke, under ambient CO₂, the C version overestimates biomass in the woody components for the year 1997 (Table ). This leads to an overestimation of the total biomass, although it underestimates fine-root biomass. Including the nitrogen cycle slightly reduces woody biomass but does not improve leaves and fine-root biomass. At Oak Ridge, the total biomass simulated for 1998 is 7097 g_C m⁻² using the C version and 5755 g_C m⁻² using the CN version. As at Duke, inclusion of the N cycle reduces C accumulation in woody biomass. No observational data are available for comparison.

At Duke under ambient CO₂, the carbon partitioning between biomass pools changed over time (Fig. ) as discussed in . The allocation to woody tissues increased, which is expected in an ageing forest. Both model versions reproduce this behavior, although the magnitude of the increase is smaller, and carbon allocation to wood is overestimated.

At Oak Ridge, no allocation shift was observed during the first 3 years, as indicated by biomass increments measured in 1998, 1999 and 2000 (Table ). The proportion of C allocated to wood (Δ(B2+B3+B5)/ΔBtot) and fine roots (ΔB4/ΔBtot) remained constant over time. On average, 60 % of the carbon increment was stocked in wood and 12 % in fine roots. Both model versions similarly show no allocation shift during the first 3 years or over the full simulation period (1998–2008). However, the modeled proportion of carbon increments allocated to wood is higher than observed (84 % in average) while it is underestimated for fine roots (-1 % in average). Inclusion of the nitrogen cycle does not affect the partitioning of carbon in the biomass, neither its evolution during the three years.

Under elevated CO₂ treatment, total biomass at Duke increased by 6204 g_C m⁻² between 1997 and 2004 , corresponding to a 34 % relative to ambient plots. During the same time period, the C version simulates a 74 % increase in response to elevated CO₂, whereas the CN version a 47 % increase. At Oak Ridge, between 1998 and 2008, we find a 37 % increase according to the C version and 15 % for the CN version. No data are available for comparison. Overall, the CN version limits the modeled carbon sink, which is an improvement at the Duke site. CO₂ enrichment has no effect on the partitioning of carbon in biomass at Duke (Fig. ), a feature that is well represented by both model versions. As mentioned earlier, an increase in fine root biomass was observed at Oak Ridge , from 11 % in 1998 to 22 % in 2000 (Table ). Both model versions fail to represent this shift as the model does not include a dynamic allocation scheme. The N cycle does not have an impact on the partitioning of biomass.

Soil carbon content observations are only available for the upper layers of the soil. Table  summarizes SOC content in the soil between 0 and 15 cm measured at Duke and Oak Ridge together with simulation results. Both the model versions overestimate the SOC content, but the addition of the nitrogen cycle improves the results.

In response to elevated CO₂, contrasting dynamics were observed at Duke and Oak Ridge. At Duke, the forest floor mass (litter and fine roots) increased under elevated CO₂, but little SOM accumulation was observed . Conversely, at Oak Ridge, there was no accumulation in the forest floor , while SOM accumulation occurred due to increased fine root production rapidly decomposed (see Table , accumulation of C in the first soil layers is 3 times higher at elevated CO₂). These contrasting dynamics in SOC and forest floor are not well represented by the model. There is an increase in SOC content modeled in response to elevated CO₂ at both sites. This accumulation is stronger at Duke than at Oak Ridge. The C version models an increase in SOC accumulation of 210 % at Duke and 56 % at Oak Ridge while the CN version results in 1279 % increase at Duke and 18 % at Oak Ridge. Both model versions simulate an increase of C in the forest floor (computed as surface litter Lsurf and fine-roots B4) in response to elevated CO₂ at both sites. The increase is smaller with the CN version.

This study points out the limitations of the carbon cycle model in ISBA. The allocation pattern is not flexible, therefore adaptions to environmental changes cannot be captured. This impacts carbon partitioning within the soil and the representation of decomposition processes. Vertical soil discretization is important to improve the modeling of C and N dynamics . However this is not sufficient to represent the response to elevated CO₂ as shown here. Other processes are lacking such as a dynamical root profile or the effect of microbial communities .

This section focuses on the CN version of the model to evaluate the new implementation. Figure  shows the dynamics of nitrogen in the vegetation and Fig.  its dynamics as bulk in the soil. The vegetation labile pool and the soil mineral pool are coupled through the uptake flux (shown in Fig. ) that determines N availability for plant growth. In early spring, photosynthesis is mainly sustained by the labile pool. Progressively, when the labile pool empties around April or May, the N / C ratio of leaves starts to decrease. This triggers an increase in uptake flux that is able to sustain NPP through the summer. Figure  shows that the N / C ratio evolves as a function of the nitrogen demand. The ratio decreases as the labile pool is depleted. There is no observation to compare these results with, but the model behaves as expected.

The main source of mineral N at Duke and at Oak Ridge is net mineralization. BNF is of the same order of magnitude at both sites (see Table ), which is consistent with the similar magnitude of NPP at the two sites, as BNF is proportional to NPP. A new global BNF estimate suggests that the BNF rate used in this study overestimates this flux . They evaluate a BNF flux of 0.35 g_N m⁻² yr⁻¹ for evergreen needleleaf forests such as Duke and of 0.61 g_N m⁻² yr⁻¹ for deciduous broadleaf forests such as Oak Ridge. As NBNF varies with NPP, it peaks in summer. Ndepo is prescribed and identical at both sites. Net mineralization however is twice as high at Oak Ridge as at Duke, especially in winter. As a result, the mineral N pool is larger at Oak Ridge for most of the year. This drives soil N dynamics, as all output fluxes are proportional to Nmin. Nleaching, Ngas, and Nup are hence greater at Oak Ridge.

Few measurements are available for comparison. At Duke, measured in 1998 on ambient plots an annual N2O flux of 0.0070 g_N m⁻² yr⁻¹, and an annual leaching flux < 0.001 g_N m⁻² yr⁻¹. For the same year, the model simulates an N2O flux that is twice as high (0.0162 g_N m⁻² yr⁻¹) and overestimates by several orders of magnitude the leaching flux (3.39 g_N m⁻² yr⁻¹). Reasons for this higher leaching are related to the vertical profile of the soil discussed further down. Calibration of the gaseous outputs is difficult due to the limited number of observations available at these sites. A multi-site analysis carried out by provides estimates of the N2O fluxes. In temperate evergreen coniferous forests, the average flux is of 0.0568 g_N m⁻² yr⁻¹. As a comparison, the model yields on average at Duke on ambient plots 0.0142 g_N m⁻² yr⁻¹. For temperate deciduous forests, the observed value is 0.0470 g_N m⁻² yr⁻¹ and at Oak Ridge the average flux on the ambient plots is 0.0267 g_N m⁻² yr⁻¹. Gas losses will be studied in the future on agricultural surfaces where more N2O data are available.

To better understand the dynamics of the net mineralization flux, Fig.  depicts the mineralization and immobilization fluxes. Mineralization due to respiration of SOC pools, FSOC, dominates the net mineralization flux at both sites (purple line). The mean annual amount of carbon decomposition is higher at Duke than Oak Ridge, as indicated by heterotrophic respiration rates of 357 g_C m⁻² yr⁻¹ at Duke and 324 g_C m⁻² yr⁻¹ at Oak Ridge. This results in higher FSOC at Duke. Inputs from surface biomass, FBx,Lsurf result from the balance between the N / C ratio of biomass and that of surface litter. This balance is controlled by the N / C ratio of leaves, the only one flexible in the model. Therefore FBx,Lsurf is greater during winter, when nitrogen demand is low and leaf N / C ratio is high. This leads to an accumulation of nitrogen near the soil surface as exhibited by Figs.  and . FBx,Lsurf and, to a lesser extent, FBx,Lsoil, are greater at Oak Ridge because the imposed N / C ratios of biomass pools in broadleaf deciduous trees are higher than those of needleleaf evergreen trees (Table ). Although annual biomass turnover is greater at Duke (688 g_C m⁻² yr⁻¹) than at Oak Ridge (615 g_C m⁻² yr⁻¹), the higher N / C ratios of biomass pools at Oak Ridge result in greater N release at that site. Around March at Duke, net mineralization is dominated by immobilization associated with surface litter decomposition that depletes the mineral pool (Fig. ). The immobilization flux from litter decomposition is stronger at Duke, again due to the lower N / C ratios.

As mentioned in Sect. , the current version of the model does not represent the vertical movement of N in the soil. Therefore, to avoid unrealistic accumulation of N, we imposed a vertical profile of some input and output fluxes along the soil depth. N resulting from N deposition for instance would otherwise accumulate in the upper layer of the soil. Both NBNF and Ndepo are distributed according to the soil water profile (Eq.  and Fig. ). Therefore, deeper soil layers are more enriched in N because they contain more water (Figs.  and ). This is a model artifact that will be addressed in a future version of the model through an explicit representation of vertical nitrogen transport in the soil. The imposed vertical profiles of gas loss and leaching follow the vertical profile of mineral N in the soil. N uptake follows the root profile and is proportional to mineral N. Because net mineralization provides a high supply of N near the soil surface, uptake fluxe is greatest in the upper soil layers.

In response to elevated CO₂, the BNF which is strongly tied to the NPP, is enhanced on both sites. At Duke, the increase of litter enhances the immobilization flux, thereby reducing net mineralization, whereas at Oak Ridge, there is little change in net mineralization. This is not coherent with observations: the increase in forest floor at Duke stimulated microbial activity, accelerating SOM decomposition and mineralization, thereby increasing N availability . At Oak Ridge, it is the increase in fine roots that increased the SOC content due to fast root turnover, leading to higher immobilization and reduced N availability . These discrepancies originate from differences in the simulated soil carbon dynamics. Moreover, measurements show that N / C ratios are important parameters that control the net mineralization flux. Plants can adapt to N shortage by decreasing their N / C ratio. This dampens N-limitation effects but affects the litter quality: immobilization is increased resulting in less N available . However implementing flexible N / C ratios in models is not straightforward as identified by multi model analysis. Without appropriate constraints, such flexibility can lead to unrealistic stoichiometric ratios .

In the simulations, the main source of new N is the BNF, proportional to NPP that increases under elevated CO₂ conditions. The newly available N is used by plants (increase of Nup). BNF is an important external source of nitrogen and can alleviate the N limitation . However, external nitrogen inputs (mostly ammonia) are known to directly regulate BNF activity in cells , as well as in diverse soil and forest organism (e.g., in moss soil carpet, in coastal sediment). The current parametrization does not take into account the N status of the soil. We have implemented a straightforward BNF parametrization as it has been done in other land surface models. However, some works are critical about the pertinence of using NPP to model BNF and its validity is questioned . In particular, for future predictions, the NPP dependent parametrization is sensitive to CO₂ increase and is probably not realistic . Following the work of , next steps will be dedicated to implement a more process-based parametrization of BNF. First, it is important to differentiate symbiotic from asymbiotic BNF as it does not involve the same processes . On one hand, symbiotic BNF is directly linked to plant needs and is another direct N source in addition to the root N uptake. A resource optimization framework such as proposed by integrates the C cost of each process and improves the model response to elevated CO₂ and increase in N deposition . On the other hand, free living BNF plays a crucial role in providing mineral N needed for specific environmental functionalities such as litter decomposition. This pathway dominates some ecosystems where N fixer species are scarce . Moreover, both symbiotic and asymbiotic processes are temperature dependent but with contrasting optimums. Due to the predicted rising temperature, this is an important aspect to consider .