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**Geoscientific Model Development**
An interactive open-access journal of the European Geosciences Union

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**Model evaluation paper**
02 Nov 2018

**Model evaluation paper** | 02 Nov 2018

Carbon–nitrogen coupling under three schemes of model representation: a traceability analysis

^{1}Zhejiang Tiantong Forest Ecosystem National Observation and Research Station, Center for Global Change and Ecological Forecasting, School of Ecological and Environmental Sciences, East China Normal University, Shanghai 200062, China^{2}Center for Climate Systems Research, Columbia University, NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025, USA^{3}Center for Ecosystem Science and Society, Northern Arizona University, AZ, USA^{4}Department for Earth System Science, Tsinghua University, Beijing 100084, China^{5}Forest Ecosystem Research and Observation Station in Putuo Island, School of Ecological and Environmental Sciences, East China Normal University, Shanghai 200062, China^{6}Shanghai Institute of Pollution Control and Ecological Security, 1515 North Zhongshan Rd, Shanghai 200437, China

^{1}Zhejiang Tiantong Forest Ecosystem National Observation and Research Station, Center for Global Change and Ecological Forecasting, School of Ecological and Environmental Sciences, East China Normal University, Shanghai 200062, China^{2}Center for Climate Systems Research, Columbia University, NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025, USA^{3}Center for Ecosystem Science and Society, Northern Arizona University, AZ, USA^{4}Department for Earth System Science, Tsinghua University, Beijing 100084, China^{5}Forest Ecosystem Research and Observation Station in Putuo Island, School of Ecological and Environmental Sciences, East China Normal University, Shanghai 200062, China^{6}Shanghai Institute of Pollution Control and Ecological Security, 1515 North Zhongshan Rd, Shanghai 200437, China

**Correspondence**: Xuhui Zhou (xhzhou@des.ecnu.edu.cn)
and Jianyang Xia (jyxia@des.ecnu.edu.cn)

**Correspondence**: Xuhui Zhou (xhzhou@des.ecnu.edu.cn)
and Jianyang Xia (jyxia@des.ecnu.edu.cn)

Abstract

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The interaction between terrestrial carbon (C) and nitrogen (N) cycles has been incorporated into more and more land surface models. However, the scheme of C–N coupling differs greatly among models, and how these diverse representations of C–N interactions will affect C-cycle modeling remains unclear. In this study, we explored how the simulated ecosystem C storage capacity in the terrestrial ecosystem (TECO) model varied with three different commonly used schemes of C–N coupling. The three schemes (SM1, SM2, and SM3) have been used in three different coupled C–N models (i.e., TECO-CN, CLM 4.5, and O-CN, respectively). They differ mainly in the stoichiometry of C and N in vegetation and soils, plant N uptake strategies, downregulation of photosynthesis, and the pathways of N import. We incorporated the three C–N coupling schemes into the C-only version of the TECO model and evaluated their impacts on the C cycle with a traceability framework. Our results showed that all three of the C–N schemes caused significant reductions in steady-state C storage capacity compared with the C-only version with magnitudes of −23 %, −30 %, and −54 % for SM1, SM2, and SM3, respectively. This reduced C storage capacity was mainly derived from the combined effects of decreases in net primary productivity (NPP; −29 %, −15 %, and −45 %) and changes in mean C residence time (MRT; 9 %, −17 %, and −17 %) for SM1, SM2, and SM3, respectively. The differences in NPP are mainly attributed to the different assumptions on plant N uptake, plant tissue C : N ratio, downregulation of photosynthesis, and biological N fixation. In comparison, the alternative representations of the plant vs. microbe competition strategy and the plant N uptake, combined with the flexible C : N ratio in vegetation and soils, led to a notable spread in MRT. These results highlight the fact that the diverse assumptions on N processes represented by different C–N coupled models could cause additional uncertainty for land surface models. Understanding their difference can help us improve the capability of models to predict future biogeochemical cycles of terrestrial ecosystems.

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How to cite.

Du, Z., Weng, E., Jiang, L., Luo, Y., Xia, J., and Zhou, X.: Carbon–nitrogen coupling under three schemes of model representation: a traceability analysis, Geosci. Model Dev., 11, 4399–4416, https://doi.org/10.5194/gmd-11-4399-2018, 2018.

1 Introduction

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Terrestrial ecosystem carbon (C) storage is jointly determined by ecosystem C input (i.e., net primary productivity, NPP) and mean residence time (MRT), both of which are strongly affected by the terrestrial nitrogen (N) availability (Vitousek et al., 1991; Hungate et al., 2003; Luo et al., 2004). Nitrogen is an essential component of enzymes, proteins, and secondary metabolites (van Oijen and Levy, 2004). Plant and microbial production requires N to meet stoichiometric demands, thus affecting the C balance and nutrient turnover of ecosystems (Cleveland et al., 2013; Wieder et al., 2015b). Since N limitation is widespread for plant growth in terrestrial ecosystems (LeBauer and Treseder, 2008; Xia and Wan, 2008), N availability is often highly correlated with key ecological processes, such as C assimilation (Field and Mooney, 1986; Du et al., 2017), allocation (Kuzyakov and Xu, 2013), plant respiration (Sprugel et al., 1995), and litter and soil organic matter (SOM) decomposition (Terrer et al., 2016). Nitrogen dynamics thus play an important role in governing the terrestrial ecosystem C storage (García-Palacios et al., 2013; Shi et al., 2015).

Given the importance of N availability on C sink projections (Hungate et al., 2003; Wang and Houlton 2009, Zaehle et al., 2015, Wieder et al., 2015b), N processes are increasingly incorporated into biogeochemical models. The representation of N cycling and its feedback to C cycling in models reflects what has been established in the ecosystem research community. Early C–N coupled models demonstrated that the N availability limited C storage capacity with associated effects on plant photosynthesis and growth in many terrestrial ecosystems (Melillo et al., 1993; Luo et al., 2004). Recent studies have largely confirmed these results by improving C–N coupling models with multiple hypotheses (Zhou et al., 2014; Zaehle et al., 2014; Thomas et al., 2015). These hypotheses include plant downregulation productivity based on the N required for cell construction or N availability for plant absorption (Thornton et al., 2007; Gerber et al., 2010), constant or flexible stoichiometry for allocation and tissue (Wang et al., 2001; Shevliakova et al., 2009; Zaehle and Friend, 2010), competition between plants and microbes for soil nutrients (Zhu et al., 2017), evapotranspiration (ET) or NPP-driven empirical functions to generate spatial estimates of biological N fixation (BNF) (Cleveland et al., 1999; Wieder et al., 2015a; Meyerholt et al., 2016), and respiration of excess C to obtain N from the environment and/or to prevent the accumulation of C beyond the storage capacity (Zaehle et al., 2010). This knowledge has significantly helped improve our understanding of the terrestrial C–N coupling and is an important basis to develop comprehensive terrestrial process-based models (Thornton et al., 2007; Thomas et al., 2013). However, simulated results of the terrestrial C cycle illustrated considerable spread among models, and much uncertainty arose from predictions of N effects on C dynamics (Arora et al., 2013; Zaehle et al., 2015). The contradictory results were largely from different representations of fundamental N processes (e.g., the degree of flexibility of the C : N ratio in vegetation and soils, plant N uptake strategies, pathways of N import, decomposition, and the representations of the competition between plants and microbes for mineral N) (Sokolov et al., 2008; Wania et al., 2012; Walker et al., 2015). Furthermore, the methodology used to derive the C–N coupling schemes among models varied largely, which might be invalid for the model intercomparisons to provide insight into the underlying mechanism of N status for terrestrial C-cycle projection.

In the past decades, terrestrial models have integrated more and more processes to improve model performance (Koven et al., 2013; Todd-Brown et al., 2013; Wieder et al., 2014). The more processes are incorporated, the more difficult it becomes to understand or evaluate model behavior (Luo et al., 2015). Traceability analysis has been developed to diagnose the simulation results within (Xia et al., 2013; Ahlström et al., 2015) and among (Rafique et al., 2016; Zhou et al., 2018) models. Based on the traceability analysis framework, key traceable elements, including fundamental properties of the terrestrial C cycle and their representations in shared structures among existing models, can be identified and characterized under different sources of variation (e.g., external forcing and uncertainty in processes). Traceability analysis enables the diagnosis of where models are clearly lacking predictive ability and evaluation of the relative benefit when more or alternative components are added to the models (Luo et al., 2015).

This study is designed to examine the effects of C–N coupling under
different schemes of model representation on ecosystem C storage in the
terrestrial ecosystem (TECO) model with the traceability analysis framework.
Three schemes of model representation were conducted mainly based on the
carbon–nitrogen coupling version of TECO (TECO-CN, SM1; Weng and Luo, 2008),
the Community Land Model version 4.5 (CLM 4.5, SM2; Koven et al., 2013;
Oleson et al., 2013), and the carbon–nitrogen coupling version of the
Organizing Carbon and Hydrology in Dynamic Ecosystems model (O-CN, SM3;
Zaehle and Friend, 2010; Zaehle and Dalmonech, 2011) (Table 1). The three
C–N schemes differ in degrees of flexibility of the C : N
ratio in vegetation and soils, plant N uptake strategies, pathways of N
import, and the representations of the competition between plants and
microbes for soil-available N. Based on the forcing data of ambient
CO_{2} concentration, N deposition, and meteorological data (i.e., air
temperature, soil temperature, relative humidity, vapor pressure deficit,
precipitation, wind speed, photosynthetically active radiation) obtained from
Duke Forest during the period of 1996–2007, we conduct three alternative
C–N coupling schemes (i.e., SM1, SM2, and SM3) as well as C-only in the TECO
model framework to compare their effects on the ecosystem C storage capacity.
The N-process sensitivity analysis was carried out to evaluate the
variability in estimated ecosystem C storage caused by the process-related
parameters at the steady state.

2 Materials and methods

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The datasets used in this study were taken from the Duke free-air CO_{2}
enrichment (FACE) experiment located in Blackwood, North Carolina, USA
(35.97^{∘} N, 79.08^{∘} W). The flux tower lies on a 15-year-old
loblolly pine (*Pinus taeda* L.) plantation. The meteorological
forcing data were downloaded from the AmeriFlux database at
http://ameriflux.lbl.gov (last access: 26 December 2016), including
ambient CO_{2} concentration ([CO_{2}]), air temperature at the top
canopy (*T*_{a}), soil temperature (*T*_{s}),
photosynthetically active radiation (PAR), relative humidity (RH), vapor
pressure deficit (VPD), precipitation, wind speed (*W*_{s}), and N
deposition. All forcing datasets are available from 1996 to 2007. To set the
initial condition for the models, we collected the related datasets from
previous studies. Standing biomass and biomass production data at each plot
for plant compartments (i.e., foliage, fine root, and woody biomass,
including branches and coarse roots) were taken from McCarthy et al. (2010).
The C and N concentration data for each plant compartment based on Finzi et
al. (2007) were used to estimate C and N stocks and fluxes. Plant N demand
and uptake were calculated from these data measured by Finzi et al. (2007).
The C and N concentrations of litter and SOM were obtained from Lichter et
al. (2008).

The terrestrial ecosystem C–N coupling model (TECO-CN) used in the present study is a variant of the TECO carbon-only version (TECO-C) incorporating additional key N processes (Fig. 1). The TECO-C model is a process-based ecosystem model designed to examine critical processes regulating interactive responses of plants and ecosystems to climate change. It has four major components: canopy photosynthesis module, plant growth module, soil water dynamic module, and soil C dynamic module. The canopy photosynthesis and soil water dynamic modules run at an hourly time step, while the plant growth and soil C dynamic modules run at the daily time step. A detailed description of the TECO-C model can be found in Weng and Luo (2008).

The N cycle added to the TECO model for this study is simplified following the structure of Luo and Reynolds (1999), Gerber et al. (2010), and Wang et al. (2010). It has a similar structure to the TECO-C model (Fig. 1). There are nine organic N pools, including plant, litter, and soil N pools, and one inorganic soil N pool. The plant N pools include leaves, wood, roots, and mineral N in plant tissues. The litter and soil N pools include metabolic and structural litter N, fast, slow, and passive soil organic N (SON), and soil mineral N pools. The total plant N demand on each time step is calculated following the NPP allocation to new tissue growth based on their C : N ratios. To meet the demand, the plant N supply is calculated from three parts, including the retranslocated N from senescing tissues, plant uptake from the soil mineral N pool, and external N sources from atmospheric deposition and biological N fixation. The N absorbed by roots enters into the mineral N pool in plant tissues and is then allocated to the remaining plant pools with plant growth. The N in leaves and fine roots is reabsorbed before senescence. Plant litters will enter metabolic or structural pools depending on their C : N ratios.

The allocation coefficients act as the key factor to determine the baseline C residence time in this study. Plant-assimilated C allocated to the leaves, stems, and roots depends on their growth rates, which vary with phenology (Luo et al., 1995; Denison and Loomis, 1989; Shevliakova et al., 2009; Weng and Luo, 2008):

$$\begin{array}{}\text{(1)}& {\displaystyle}& {\displaystyle}{b}_{\mathrm{l}}={\displaystyle \frac{\mathrm{1}}{\mathrm{1}+{c}_{\mathrm{1}}+{c}_{\mathrm{2}}}},\text{(2)}& {\displaystyle}& {\displaystyle}{b}_{\mathrm{s}}={\displaystyle \frac{{c}_{\mathrm{2}}}{\mathrm{1}+{c}_{\mathrm{1}}+{c}_{\mathrm{2}}}},\text{(3)}& {\displaystyle}& {\displaystyle}{b}_{\mathrm{r}}={\displaystyle \frac{{c}_{\mathrm{1}}}{\mathrm{1}+{c}_{\mathrm{1}}+{c}_{\mathrm{2}}}},\end{array}$$

where *b*_{l}, *b*_{s}, and *b*_{r} are the partitioning coefficient of
newly assimilated C to leaves, stems, and roots, respectively. Parameters
*c*_{1} and *c*_{2} are calculated as

$$\begin{array}{}\text{(4)}& {\displaystyle}& {\displaystyle}{c}_{\mathrm{1}}={\displaystyle \frac{{\text{bm}}_{\mathrm{l}}}{{\text{bm}}_{\mathrm{r}}}}\cdot {\displaystyle \frac{{\text{CN}}_{\mathrm{l}}^{i}}{{\text{CN}}_{\mathrm{l}}^{\mathrm{0}}}},\text{(5)}& {\displaystyle}& {\displaystyle}{c}_{\mathrm{2}}=\mathrm{0.5}\cdot \mathrm{250}{e}^{\mathrm{3}}\cdot \text{SLA}\cdot \mathrm{0.00021}\cdot {h}^{\mathrm{2}},\end{array}$$

where bm_{l} and bm_{r} are the leaf and root biomass; CN${}_{\mathrm{l}}^{i}$
and CN${}_{\mathrm{l}}^{\mathrm{0}}$ represent the C : N ratios of the leaf pool at 0 and the
current time step, respectively; SLA is specific leaf area; and *h* is plant height, which is calculated as

$$\begin{array}{}\text{(6)}& {\displaystyle}h={h}_{\mathrm{max}}\left(\mathrm{1}-\mathrm{exp}\left(-{h}_{\mathrm{1}}\cdot {\text{bm}}_{\mathrm{P}}\right)\right),\end{array}$$

where *h*_{max} is the maximum canopy height, *h*_{1} is an empirical
parameter, and bm_{P} is plant biomass.

We conducted four experiments, including three simulations with their representations of C–N coupling schemes (SM1, SM2, and SM3), and an additional C-only simulation in the TECO model framework. The three C–N interaction simulations include one original scheme in the TECO-CN model and the other two schemes represent CLM4.5-BGC and O-CN. The three C–N coupling schemes differ in the representation of the downregulation of photosynthesis, the degree of flexibility of the C : N ratio in vegetation and soils (i.e., fixed C : N ratio in SM2, flexible C : N ratio in SM1 and SM3), plant N uptake strategies, pathways of N import to the plant reserves, and the competition between plants and microbes for soil mineral N (Table 1, Fig. 2).

The N downregulation of photosynthesis in SM1 is determined by the comparison between plant N demand and the actual supply of N:

$$\begin{array}{}\text{(7)}& {\displaystyle}{f}_{\mathrm{dreg}}=\mathrm{min}\left({\displaystyle \frac{{\mathrm{N}}_{\mathrm{sup}}}{{\mathrm{N}}_{\mathrm{demand}}}},\mathrm{1}\right),\end{array}$$

where N_{sup} (g N m^{−2} s^{−1}) is the actual supply of N
obtained from retranslocated N, plant N uptake, and biological N fixation.
N_{demand} (g N m^{−2} s^{−1}) is plant N demand, which is
calculated as

$$\begin{array}{}\text{(8)}& {\displaystyle}{\mathrm{N}}_{\mathrm{demand}}={\sum}_{i=\mathrm{leaf},\phantom{\rule{0.125em}{0ex}}\mathrm{wood},\phantom{\rule{0.125em}{0ex}}\mathrm{root}}{\displaystyle \frac{{\mathrm{C}}_{i}}{{\text{CN}}_{i}^{\mathrm{0}}}},\end{array}$$

where C_{i} is the C pool size of plant tissue at the current time step,
and CN${}_{i}^{\mathrm{0}}$ is the C : N ratio of plant tissue at the
first time step.

The retranslocated N is calculated as

$$\begin{array}{}\text{(9)}& {\displaystyle}{\mathrm{N}}_{\mathrm{retrans}}={\sum}_{i=\mathrm{leaf},\phantom{\rule{0.125em}{0ex}}\mathrm{wood},\phantom{\rule{0.125em}{0ex}}\mathrm{root}}{r}_{i}\times {\text{outC}}_{i}/{\text{CN}}_{i},\end{array}$$

where *r*_{i} is the N resorption coefficient, CN_{i} is the
C : N ratio, and outC_{i} (g C m^{−2} s^{−1}) is the
value of C leaving the plant pool *i* at each time step.

The plant N uptake (g N m^{−2} s^{−1}) from the soil mineral N pool is a
function of the root biomass density (Root_{total}, g C m^{−2}) and
N demand of plants, following McMurtrie et al. (2012).

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{\mathrm{N}}_{\mathrm{uptake}}=min(max\left(\mathrm{0},{\mathrm{N}}_{\mathrm{demand}}-{\mathrm{N}}_{\mathrm{retrans}}\right),\phantom{\rule{0.125em}{0ex}}{f}_{U,\phantom{\rule{0.125em}{0ex}}\mathrm{max}}.\\ \text{(10)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\left.\times {\text{SN}}_{\mathrm{mine}}\times {\displaystyle \frac{{\text{Root}}_{\mathrm{total}}}{{\text{Root}}_{\mathrm{total}}+{\text{Root}}_{\mathrm{0}}}}\right),\end{array}$$

where N_{demand} is the N demand of plants; SN_{mine}
(g N m^{−2}) is the soil mineral N; *f*_{U, max} is the maximum
rate of N absorption per step when Root_{total} approaches infinity;
and Root_{0} (g C m^{−2}) is a constant of root biomass at which the
N uptake rate is half of the parameter *f*_{U, max}.

The biological N fixation (g N m^{−2} s^{−1}) is calculated as

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{\mathrm{N}}_{\mathrm{BNF}}=min(max\left(\mathrm{0},{\mathrm{N}}_{\mathrm{demand}}-{\mathrm{N}}_{\mathrm{retrans}}-{\mathrm{N}}_{\mathrm{uptake}}\right).\\ \text{(11)}& {\displaystyle}& {\displaystyle}.{n}_{\mathrm{fix}}\times {f}_{\mathrm{nsc}}\times \text{NSC}),\end{array}$$

where *n*_{fix}=0.0167 is the maximum N fixation ratio and
*f*_{nsc} is the nutrient-limiting factor. *f*_{nsc} is
calculated as

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{f}_{\mathrm{nsc}}\\ \text{(12)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}=\left\{\begin{array}{rl}\mathrm{0},& \text{NSC}<{\text{NSC}}_{\mathrm{min}}\\ {\displaystyle \frac{\text{NSC}-{\text{NSC}}_{\mathrm{min}}}{{\text{NSC}}_{\mathrm{max}}-{\text{NSC}}_{\mathrm{min}}}},& {\text{NSC}}_{\mathrm{min}}<\text{NSC}<{\text{NSC}}_{\mathrm{max}}\\ \mathrm{1},& \text{NSC}>{\text{NSC}}_{\mathrm{max}},\end{array}\right.\end{array}$$

where NSC_{min} (g C m^{−2}) and NSC_{max}
(g C m^{−2}) are the minimal and maximal sizes of the nonstructural C pool,
respectively.

The soil microbial immobilization (g N m^{−2} s^{−1}) is calculated as

$$\begin{array}{}\text{(13)}& {\displaystyle}{\text{Imm}}_{\mathrm{N}}=\left\{\begin{array}{l}{\sum}_{i=\mathrm{4}}^{\mathrm{8}}min\left(\left({\displaystyle \frac{{\mathrm{C}}_{i}}{{\text{CN0}}_{i}}}-{\displaystyle \frac{{\mathrm{C}}_{i}}{{\text{CN}}_{i}}}\right),\mathrm{0.1}\cdot {\text{SN}}_{min}\right)\\ \text{for}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}{\text{CN}}_{i}\ge {\text{CN0}}_{i}\\ {\sum}_{i=\mathrm{4}}^{\mathrm{8}}min\left(\left({\displaystyle \frac{{\mathrm{C}}_{i}}{{\text{CN}}_{i}}}-{\displaystyle \frac{{\mathrm{C}}_{i}}{{\text{CN0}}_{i}}}\right),\mathrm{0.1}\cdot {\text{SN}}_{min}\right)\\ \text{for}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}{\text{CN}}_{i}<{\text{CN0}}_{i},\end{array}\right.\end{array}$$

where CN0_{i} and CN_{i} ($i=\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8}$) are the
C : N ratios of metabolic litter, structural litter, and fast,
slow, and passive soil organic C pools at the first and current time step,
respectively.

Two pathways of N loss are modeled. One is gaseous loss
(N_{gas_loss}, g N m^{−2} s^{−1}) and another is leaching
(N_{leach}, g N m^{−2} s^{−1}). Both are proportional to the
availability of soil mineral N (SN_{min}, g N m^{−2}). The equations
are

$$\begin{array}{ll}\text{(14)}& {\displaystyle}& {\displaystyle}{\mathrm{N}}_{\mathrm{leach}}={f}_{\mathrm{nleach}}\times {\displaystyle \frac{{V}_{\mathrm{runoff}}}{{h}_{\mathrm{depth}}}}\times {\text{SN}}_{min}{\displaystyle}& {\displaystyle}{\mathrm{N}}_{\mathrm{gas}\mathrm{\_}\mathrm{loss}}=max\left({f}_{\mathrm{ngas}}\times {e}^{\frac{{T}_{\mathrm{soil}}-\mathrm{25}}{\mathrm{10}}}\times {\text{SN}}_{min},\right.\\ \text{(15)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}.{\mathrm{N}}_{\mathrm{BNF}}+{\mathrm{N}}_{\mathrm{depos}}-{\mathrm{N}}_{\mathrm{leaching}}),\end{array}$$

where *f*_{ngas}=0.001 and *f*_{nleach}=0.5,
*T*_{soil} (^{∘}C) is the soil temperature, *V*_{runoff}
(mm s^{−1}) is the value of runoff, *h*_{depth} (mm) is the
soil depth, and N_{depos}=0.78 g N m^{−2} yr^{−1} is the N
deposition used in this study.

The N downregulation of photosynthesis in SM2 is calculated as

$$\begin{array}{}\text{(16)}& {\displaystyle}{f}_{\mathrm{dreg}}={\displaystyle \frac{{\text{CF}}_{\mathrm{allo}}-{\text{CF}}_{\mathrm{avail}\mathrm{\_}\mathrm{alloc}}}{{\text{CF}}_{{\mathrm{GPP}}_{\mathrm{pot}}}}},\end{array}$$

where CF_{allo} (g C m^{−2} s^{−1}) is the total flux of
allocated C, which is determined by available mineral N.
CF_{avail_alloc} (g C m^{−2} s^{−1}) is the potential C
flux from photosynthesis, which can be allocated to new growth.
CF${}_{{\mathrm{GPP}}_{\mathrm{pot}}}$ (g C m^{−2} s^{−1}) is the potential gross
primary productivity (GPP) when there is no N limitation.

The retranslocated N (g N m^{−2} s^{−1}) is calculated as

$$\begin{array}{}\text{(17)}& {\displaystyle}{\mathrm{N}}_{\mathrm{retrans}}=min\left({\mathrm{N}}_{\mathrm{demand}}\times {\displaystyle \frac{{\mathrm{N}}_{{\mathrm{retrans}}_{\mathrm{ann}}}}{{\mathrm{N}}_{{\mathrm{demand}}_{\mathrm{ann}}}}},{\mathrm{N}}_{\mathrm{retrans}\mathrm{\_}\mathrm{avail}}\right),\end{array}$$

where N${}_{{\mathrm{retrans}}_{\mathrm{ann}}}$ (g N m^{−2} y^{−1}) is the previous
year's annual sum of retranslocated N obtained from senescing tissues,
and N${}_{{\mathrm{demand}}_{\mathrm{ann}}}$ (g N m^{−2} y^{−1}) is the previous year's
annual sum of plant N demand. N_{retrans_avail}
(g N m ^{−2} s^{−1}) is the available retranslocated N in senescing
tissues, which is calculated by the proportional of senescing tissues.

The plant N uptake (g N m^{−2} s^{−1}) is described as

$$\begin{array}{}\text{(18)}& {\displaystyle}{\mathrm{N}}_{\mathrm{uptake}}=\left({\mathrm{N}}_{\mathrm{demand}}-{\mathrm{N}}_{\mathrm{retrans}}\right)\times {f}_{\mathrm{plant}\mathrm{\_}\mathrm{demand}},\end{array}$$

where *f*_{plant_demand} is the fraction (from 0 to 1) of the
plant N demand, which can be met given the current soil mineral N supply and
competition with heterotrophs. *f*_{plant_demand} is set to
be equal to the fraction of potential immobilization demand
(*f*_{immob_demand}) that is calculated as

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{f}_{\mathrm{plant}\mathrm{\_}\mathrm{demand}}={f}_{\mathrm{immob}\mathrm{\_}\mathrm{demand}}\\ \text{(19)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}={\displaystyle \frac{{\text{SN}}_{min}}{{\mathrm{N}}_{\mathrm{plant}\mathrm{\_}\mathrm{demand}}+{\mathrm{N}}_{\mathrm{immob}\mathrm{\_}\mathrm{demand}}}},\end{array}$$

where N_{immob_demand} (g N m^{−2} s^{−1}) is the total
potential N immobilization demand (i.e., total potential microbial N demand).

The biological N fixation (g N m^{−2} s^{−1}) is calculated as

$$\begin{array}{}\text{(20)}& {\displaystyle}{\mathrm{N}}_{\mathrm{BNF}}=\mathrm{1.8}\left(\mathrm{1}-{e}^{-\mathrm{0.03}\times {\text{NPP}}_{\mathrm{py}}}\right)/\left(\mathrm{86}\phantom{\rule{0.125em}{0ex}}\mathrm{400}\times \mathrm{365}\right),\end{array}$$

where NPP_{py} (g C m^{−2} y^{−1}) is the previous year's NPP.

The N downregulation of photosynthesis in SM3 is calculated as

$$\begin{array}{}\text{(21)}& {\displaystyle}{f}_{\mathrm{dreg}}=a+b\times {\mathrm{N}}_{\mathrm{leaf}/\mathrm{LAI}},\end{array}$$

where *a* and *b* are empirical constants, and N_{leaf∕LAI}
(g N m^{−2}) is foliage N per unit of leaf area.

The retranslocated N (g N m^{−2} s^{−1}) is calculated as

$$\begin{array}{}\text{(22)}& {\displaystyle}{\mathrm{N}}_{\mathrm{retrans}}={\sum}_{i=\mathrm{leaf},\phantom{\rule{0.125em}{0ex}}\mathrm{root}}{\mathit{\tau}}_{i}\times {f}_{\mathrm{trans},\phantom{\rule{0.125em}{0ex}}i},\end{array}$$

where *τ* (g N m^{−2} s^{−1}) is the foliage or roots shed in each
step, and ${f}_{\mathrm{trans},\phantom{\rule{0.125em}{0ex}}\mathrm{leaf}}=\mathrm{0.5}$ and ${f}_{\mathrm{trans},\phantom{\rule{0.125em}{0ex}}\mathrm{root}}=\mathrm{0.2}$ are
the fractions of N retranslocated when the tissue dies off.

The plant N uptake (g N m^{−2} s^{−1}) is calculated as

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{\mathrm{N}}_{\mathrm{uptake}}={v}_{max}\times {\text{SN}}_{min}\times \left({k}_{{\mathrm{N}}_{\mathrm{m}}\mathrm{in}}+{\displaystyle \frac{\mathrm{1}}{{\text{SN}}_{min}\times {K}_{{\mathrm{N}}_{\mathrm{min}}}}}\right)\\ \text{(23)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\times f\left({T}_{\mathrm{soil}}\right)\times f\left({\text{NC}}_{\mathrm{plant}}\right)\times {C}_{\mathrm{root}},\end{array}$$

where ${v}_{max}=\mathrm{0.514}$ is maximum N uptake capacity per unit of fine root
mass (Zaehle and Friend, 2010; Kronzucker et al., 1995, 1996),
${k}_{{\mathrm{N}}_{\mathrm{min}}}$ is the rate of N uptake not associated with
Michaelis–Menten kinetics, and ${K}_{{\mathrm{N}}_{\mathrm{min}}}$ is the half-saturation
concentration of fine root N uptake. *f*(*T*_{soil}) is calculated as

$$\begin{array}{}\text{(24)}& {\displaystyle}f\left({T}_{\mathrm{soil}}\right)=\mathrm{exp}\left(\mathrm{308.56}\cdot \left({\displaystyle \frac{\mathrm{1}}{\mathrm{56.02}}}-{\displaystyle \frac{\mathrm{1}}{{T}_{\mathrm{soil}}+\mathrm{46.02}}}\right)\right),\end{array}$$

where *T*_{soil} (^{∘}C) is soil temperature.

C_{root} (g C m^{−2}) is fine root mass.
*f*(NC_{plant}) is the dependency of N uptake on plant N
status and is calculated as

$$\begin{array}{}\text{(25)}& {\displaystyle}f\left({\text{NC}}_{\mathrm{plant}}\right)=max\left({\displaystyle \frac{{\text{NC}}_{\mathrm{plant}}-{\text{nc}}_{\mathrm{leaf},\phantom{\rule{0.125em}{0ex}}\mathrm{max}}}{{\text{nc}}_{\mathrm{leaf},\phantom{\rule{0.125em}{0ex}}\mathrm{min}}-{\text{nc}}_{\mathrm{leaf},\phantom{\rule{0.125em}{0ex}}\mathrm{max}}}},\mathrm{0}\right),\end{array}$$

where nc_{leaf, min} and nc_{leaf, max} are the minimum and
maximum foliage N concentration, respectively. NC_{plant}
(g N g^{−1} C) is taken as the mean N concentration of foliage, fine
root, and labile N pools, representing the active and easily translocatable
portion of plant N.

$$\begin{array}{}\text{(26)}& {\displaystyle}{\text{NC}}_{\mathrm{plant}}={\displaystyle \frac{{\mathrm{N}}_{\mathrm{leaf}}+{\mathrm{N}}_{\mathrm{root}}+{\mathrm{N}}_{\mathrm{labile}}}{{\mathrm{C}}_{\mathrm{leaf}}+{\mathrm{C}}_{\mathrm{root}}+{\mathrm{C}}_{\mathrm{labile}}}}\end{array}$$

The biological N fixation (g N m^{−2} s^{−1}) is calculated as

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{\mathrm{N}}_{\mathrm{BNF}}=\mathrm{0.1}\times max\left(\mathrm{0.0234}\times \mathrm{30}\times \text{AET}+\mathrm{0.172},\mathrm{0}\right)/\\ \text{(27)}& {\displaystyle}& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\left(\mathrm{86}\phantom{\rule{0.125em}{0ex}}\mathrm{400}\times \mathrm{365}\right),\end{array}$$

where AET (mm y^{−1}) is the mean annual evapotranspiration.

The traceability analysis framework was used to evaluate the variation of the
modeled ecosystem C storage capacity under different C–N schemes (Fig. S1 in
the Supplement). According to the traceability analysis framework (Xia et
al., 2013), the modeled C storage capacity can be traced to (i) a product of
NPP and ecosystem residence time (*τ*_{E}). The latter
*τ*_{E} can be further traced to (ii) baseline C residence time
($\mathit{\tau}{{}^{\prime}}_{\mathrm{E}})$, which is usually preset in a model according to
vegetation characteristics and soil types, (iii) N scalar (*ξ*_{N}),
(iv) environmental scalars (*ξ*) including temperature (*ξ*_{T})
and water (*ξ*_{W}) scalars, and (v) the external climate forcing.
The framework for decomposing modeled C storage capacity into a few traceable
components is built upon a pool and flux structure, which is adopted in all
of the terrestrial C models. The structure can be represented well by a
matrix equation (Luo et al., 2003; Luo and Weng, 2011; Huang et al., 2018):

$$\begin{array}{}\text{(28)}& {\displaystyle \frac{\mathrm{d}\mathit{X}\left(t\right)}{\mathrm{d}t}}=\mathit{B}\mathit{U}\left(t\right)-\mathbf{A}\mathit{\xi}\mathbf{C}X\left(t\right),\end{array}$$

where $\mathit{X}\left(t\right)={\left({X}_{\mathrm{1}}\left(t\right),{X}_{\mathrm{2}}\left(t\right),\phantom{\rule{0.125em}{0ex}}\mathrm{\dots}\phantom{\rule{0.125em}{0ex}},{X}_{\mathrm{8}}\left(t\right)\right)}^{\mathrm{T}}$ is an 8×1 vector describing eight C pool sizes in
leaf, root, wood, metabolic litter, structural litter, and fast, slow, and
passive soil organic C in the TECO model (Weng and Luo, 2008). $\mathit{B}={\left({b}_{\mathrm{1}},{b}_{\mathrm{2}},{b}_{\mathrm{3}},\mathrm{0},\phantom{\rule{0.125em}{0ex}}\mathrm{\dots}\phantom{\rule{0.125em}{0ex}},\mathrm{0}\right)}^{\mathrm{T}}$ represents the
partitioning coefficients of the photosynthetically fixed C into different
plant pools. ** U**(

The C storage capacity equals the sum of C in all pools at the steady
state (*X*_{ss}), which can be obtained by making Eq. (28) equal to
zero as described in Xia et al. (2013):

$$\begin{array}{}\text{(29)}& {\displaystyle}{X}_{\mathrm{ss}}={\left(\mathbf{A}\mathit{\xi}\mathbf{C}\right)}^{-\mathrm{1}}\mathit{B}{\mathit{U}}_{\mathrm{ss}}.\end{array}$$

The vector *U*_{ss} is the ecosystem *C* influx at the steady
state. The partitioning (** B** vector), transfer coefficients
(

$$\begin{array}{}\text{(30)}& {\displaystyle}\mathit{\tau}{{}^{\prime}}_{\mathrm{E}}=(\mathbf{AC}{)}^{-\mathrm{1}}\mathit{B}\end{array}$$

The baseline C residence time ($\mathit{\tau}{{}^{\prime}}_{\mathrm{E}})$ in Eq. (30), N scalars
(*ξ*_{N}), and environmental scalars (*ξ*_{E})
together determine the C residence time (*τ*_{E}).

$$\begin{array}{}\text{(31)}& {\displaystyle}{\mathit{\tau}}_{\mathrm{E}}={\mathit{\xi}}^{-\mathrm{1}}\mathit{\tau}{{}^{\prime}}_{\mathrm{E}}={\left({\mathit{\xi}}_{\mathrm{N}}\times {\mathit{\xi}}_{\mathrm{E}}\right)}^{-\mathrm{1}}\mathit{\tau}{{}^{\prime}}_{\mathrm{E}}\end{array}$$

Thus, the C storage capacity is jointly determined by the ecosystem residence
time (*τ*_{E}) and steady-state C influx (*U*_{ss}).

$$\begin{array}{}\text{(32)}& {\displaystyle}{\mathit{X}}_{\mathrm{ss}}={\mathit{\tau}}_{\mathrm{E}}{\mathit{U}}_{\mathrm{ss}}\end{array}$$

The environmental scalar is further separated into the temperature
(*ξ*_{T}) and water (*ξ*_{W}) scalars, which can be
represented as

$$\begin{array}{}\text{(33)}& {\displaystyle}{\mathit{\xi}}_{\mathrm{E}}={\mathit{\xi}}_{\mathrm{T}}\times {\mathit{\xi}}_{\mathrm{W}}.\end{array}$$

As the respiration and decomposition rate modifier, the N scalar is given by
vector ${\mathit{\xi}}_{\mathrm{N}}={\left({\mathit{\xi}}_{{\mathrm{N}}_{\mathrm{1}}}\left(t\right),{\mathit{\xi}}_{{\mathrm{N}}_{\mathrm{2}}}\left(t\right),\phantom{\rule{0.125em}{0ex}}\mathrm{\dots}\phantom{\rule{0.125em}{0ex}},{\mathit{\xi}}_{{\mathrm{N}}_{\mathrm{8}}}\left(t\right)\right)}^{\mathrm{T}}$. The component
${\mathit{\xi}}_{{\mathrm{N}}_{i}}\left(t\right)$ quantifies the changes in N content at each time step
compared with the initial condition in the C pool *i*. It is calculated as

$$\begin{array}{}\text{(34)}& {\displaystyle}{\mathit{\xi}}_{{\mathrm{N}}_{i}}=\mathrm{exp}\left(-{\displaystyle \frac{{\text{CN}}_{i}^{\mathrm{0}}-{\text{CN}}_{i}^{n}}{{\text{CN}}_{i}^{\mathrm{0}}}}\right),\end{array}$$

where CN${}_{i}^{\mathrm{0}}$ and CN${}_{i}^{n}$ are the C : N ratio
of the pool *i* at 0 and *n* time step, respectively.

To obtain the modeled C storage capacity, we spun up the TECO model with the
C-only and three C–N coupling schemes to the steady state using the
semi-analytical solution method developed by Xia et al. (2012). In this
study, the meteorological forcings of 1996–2007 with the time step of 30 min
were used to run the models to the steady state. Once the simulations
are spun up to the steady state, C and N fluxes and state variables as well
as the matrix elements *A*, *C*, *B*, and *ξ* in Eq. (29) from all time
steps in the last recycle of the climate forcing were saved for the
traceability analysis.

The sensitivities of both NPP and mean C residence time (MRT) as well as ecosystem C storage capacity to each main N process in three schemes were calculated as

$$\begin{array}{}\text{(35)}& {\displaystyle}& {\displaystyle}{S}_{i}^{\text{NPP}}\left(P\right)={\displaystyle \frac{{\text{NPP}}_{i}^{+}\left(P\right)-{\text{NPP}}_{i}^{-}\left(P\right)}{{\text{NPP}}_{i}^{\mathrm{0}}}},\text{(36)}& {\displaystyle}& {\displaystyle}{S}_{i}^{\mathrm{MRT}}\left(P\right)={\displaystyle \frac{{\text{MRT}}_{i}^{+}\left(P\right)-{\text{MRT}}_{i}^{-}\left(P\right)}{{\text{MRT}}_{i}^{\mathrm{0}}}},\text{(37)}& {\displaystyle}& {\displaystyle}{S}_{i}^{\mathrm{ECSC}}\left(P\right)={S}_{i}^{\mathrm{NPP}}\left(P\right)\times {S}_{i}^{\mathrm{MRT}}\left(P\right),\end{array}$$

where ${S}_{i}^{\mathrm{NPP}}\left(P\right)$, ${S}_{i}^{\mathrm{MRT}}\left(P\right)$, and
${S}_{i}^{\mathrm{ECSC}}\left(P\right)$ (*i*=1, 2, 3) represent the sensitivities of
NPP, MRT, and ecosystem C storage capacity to the N process *P* in the scheme
*i*, respectively. NPP${}_{i}^{\mathrm{0}}$ and MRT${}_{i}^{\mathrm{0}}$ are the annual mean values
of NPP and MRT at the steady state in the scheme *i*. NPP${}_{i}^{+}\left(P\right)$ and
NPP${}_{i}^{-}\left(P\right)$ are the annual mean values of NPP that were simulated to
steady state again in scheme *i* based on the value of the N process *P*
(i.e., list in Table 1) by increasing 50 % and decreasing 50 %,
respectively. MRT${}_{i}^{+}\left(P\right)$ and MRT${}_{i}^{-}\left(P\right)$ are the annual mean
values of MRTs that were simulated in the same way as NPP and calculated
using Eqs. (30) and (31).

3 Results

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At the steady state, the dynamics of N fluxes and soil mineral N showed
different patterns among three C–N schemes in the TECO model (Fig. 3). The
simulated soil N mineralization and plant N uptake fluxes in SM2 displayed
the largest daily variation (1.5 and 0.86 mg N m^{−2} d^{−1},
respectively) and annual mean values (1.26 and
0.23 g N m^{−2} yr^{−1}, respectively) among the three C–N schemes. This
variation mainly resulted from both the plant N demand and the available N in
soil (Fig. 3g). The dynamic of soil mineral N also drove the variation of the
N leaching flux, for which SM1 showed the largest daily variation
(40 mg N m^{−2} d^{−1}) and annual mean value
(0.36 g N m^{−2} yr^{−1}). However, the representation of biological
N fixation (BNF) as an option when the plant uptake is not enough for growth
led to the largest daily variation (28 mg N m^{−2} d^{−1}) but with
the smallest annual value (0.04 g N m^{−2} yr^{−1}) in SM1 in
comparison with the other two C–N schemes. Both the nitrogen balance requirement
and the dynamic of soil mineral N resulted in the largest daily variation
(1.97 mg N m^{−2} d^{−1}) and annual value of gaseous N loss
(1.39 g N m^{−2} yr^{−1}) in SM3. The combined effect of the flexible
C : N ratio and soil mineral N drove the largest daily
variation of N immobilization fluxes (1.3 mg N m^{−2} d^{−1}) in SM3
and the largest annual mean value (1.15 g N m^{−2} yr^{−1}) in SM1.
The dynamics of soil mineral N in SM2 and SM3 displayed similar patterns
of daily and annual dynamics.

Compared with the TECO-C model, the three C–N coupling schemes introduced
significant signs of N limitation on forest growth at the steady state but
with varying magnitude (Fig. 4). Specifically, the three N schemes caused
significant reductions in GPP (10 %, 10 %, and 12 % for SM1, SM2,
and SM3, respectively) compared to the C-only TECO model. Similar response
patterns were also found for NPP, ecosystem respiration, and heterotrophic
respiration. Among the three schemes, SM3 had the strongest effect (45 %,
12 %, and 45 % reduction for NPP, ecosystem respiration, and
heterotrophic respiration, respectively), while SM2 had the weakest effect
(15 %, 8 %, and 13 %, respectively), and the effect of SM1 was
relatively moderate (29 %, 10 %, and 29 %, respectively). However,
by comparison with the TECO-C version, both the SM1 and SM3 schemes increased
the autotrophic respiration by 12 % and 27 %, respectively. At or
near the steady state, NEE in both TECO-C and the three C–N coupling schemes had
similarly mean values (1.37, −0.13, 0.66, and
0.84 g C m^{−2} yr^{−1}), which were approximately equal to zero but
with large variations (56, 39.4, 48.1, and 34.9).

The three C–N coupling schemes induced different effects on C and N
stoichiometric status for different pools (Figs. 5 and S2). All three schemes
had significant limitation signs on woody and structural litter as well as fast and slow
SOM pools but with different magnitudes (Fig. 5a). SM2 had the highest C
sizes for the roots (731.8 g C m^{−2}) and metabolic litter
(1252.1 g C m^{−2}), while SM1 had the highest C size for passive SOM
pool (4249.5 g C m^{−2}). SM2 had a constant C : N
ratio for all the displaying pools (Fig. 5b), while the
C : N ratios for the three displaying pools (leaf, root, and
structural litter) had no significant change in SM1 and SM3. As for both
woody and metabolic litter pools, SM1 and SM3 had higher
C : N ratios (357.2 and 357.9, respectively) compared with
SM2 (354). SM1 had the lowest C : N ratio (4.6) for the soil
passive SOM pool among the three schemes.

The divergent effects of the three C–N schemes on plant N uptake (Fig. 3),
autotrophic respiration, and NPP (Fig. 4) lead to different N use efficiency
(NUE) and carbon use efficiency (CUE) (Fig. 6). SM1 had the highest NUE
(159.1 g C g^{−1} N), mainly resulting from its low plant N uptake. In
contrast, SM3 had the lowest NUE (67.3 g C g^{−1} N) as a result of its
small NPP. Because of the hypothesis of N uptake for
free (whereby nitrogen uptake does not require the expenditure of energy in the form of carbon), SM2 had the highest CUE
(0.54) among the three C–N schemes, which was close to that in the C-only
version (0.57). However, SM3 had the lowest CUE (0.35) due to both C cost for
plant active N uptake and the assumption that increased respiration removes
the excess C.

The ecosystem C storage capacity also differed greatly among the three C–N
coupling schemes and the C-only version of the TECO model (Fig. 7). The C-only
version had the largest C storage capacity (19.5 kg C m^{−2}) among the
four simulations due to its high NPP (879.9 g C m^{−2} yr^{−1}).
The C storage capacity in SM1 (15.1 kg C m^{−2}) was close to that in
SM2 (13.7 kg C m^{−2}). The SM3 had the lowest C storage capacity
(8.9 kg C m^{−2}) among the four simulations as a result of its small
NPP (483.9 g C m^{−2} yr^{−1}) and relatively short MRT (18.6 years).
By comparison with the C-only version, the three C–N schemes all induced
different reductions in NPP (−29 %, −15 %, and −45 % for
SM1, SM2, and SM3, respectively) and further reduced their ecosystem C storage
capacity. For the MRT, SM1 exhibited positive effects (+9 %) relative
to the C-only version, while the other two schemes induced negative
ones (i.e., −16.9 % in SM2 and −16.7 % in SM3).

Ecosystem C residence time (*τ*_{E}) is collectively determined by
baseline residence time, N scalar, and environmental scalars as shown in
Eq. (31). Specifically, differences in *τ*_{E} among the three C–N
coupling schemes and the C-only TECO model are determined by baseline residence
time and the effects of the N scalar on eight plant C pools (Fig. 8). For
example, SM1 had the longest *τ*_{E} because the N scalar had very
strong control of passive SOM. The baseline residence time was further
determined by C allocation (Fig. 9). Overall, compared with the C-only
version, the additional N processes enhanced the partitioning coefficient of
NPP to roots (33 %, 82 %, and 53 % for SM1, SM2, and SM3,
respectively) but decreased the partitioning coefficient to wood
(−25 %, −45 %, and −34 %, respectively). Furthermore, the
decreased partitioning coefficient to wood regulated the variations of the
baseline residence time of wood, structural litter, and slow and passive SOM.
However, the increased partitioning coefficient to roots determined the
variations of the baseline residence time of roots and metabolic litter.

For either NPP or MRT, the N processes had different sensitivities among the three C–N schemes of the TECO model (Fig. 10). For NPP, plant C : N ratio had the highest sensitivities in both SM1 (0.32) and SM2 (0.53). However, the plant N uptake in SM3 had the highest sensitivity (0.87) for NPP. For MRT, competition between plants and microbes, downregulation of photosynthesis, and plant C : N had the highest sensitivities in SM1 (0.27), SM2 (0.19), and SM3 (0.56), respectively. As the NPP and MRT jointly determined the ecosystem C storage capacity, the plant tissue C : N ratio, downregulation of photosynthesis, and plant N uptake had the highest sensitivities for the ecosystem C storage capacity in SM1 (0.06), SM2 (0.09), and SM3 (0.26), respectively.

4 Discussion

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Gross or net primary production (i.e., GPP or NPP) is regulated by the amount of N availability for plant growth through the N demand, which is set by the relative proportion of biomass growth in the different plant components and their C : N stoichiometry (Zaehle et al., 2014; Thomas et al., 2015). The limitation of equilibrium N on plant production reflects the effects of multiple processes in the C–N interaction, mainly including downregulation of photosynthetic capacity by N availability, the ecosystem's balance of N inputs and losses (i.e., net ecosystem N exchange), plant N uptake, soil N mineralization, and the C : N stoichiometry of vegetation and soils. However, due to a lack of consensus on the nature of the mechanisms, the representation of these processes varies greatly among diverse models (Zaehle et al., 2014).

There are two common alternative assumptions for the downregulation of
photosynthesis that have been implemented in models: (1) the change in
photosynthetic capacity is directly associated with the magnitude of plant-available N (e.g., SM2), and (2) N limitation is associated with foliage N,
which feeds back to limit photosynthetic capacity (e.g., SM1 and SM3). Our
results showed that both assumptions had significant limitations with similar
effects on GPP (Fig. 4a, g). The probable reason is that the TECO model
calculates photosynthesis by light availability and the carboxylation rate based
on the Farquhar model (Farquhar et al., 1980). The effects of N stress under
the TECO framework, either associated with plant-available N or associated
with foliage N concentration, are estimated according to limiting factors of
photosynthetic biochemistry (the maximum rate of carboxylation,
${V}_{{\mathrm{c}}_{\mathrm{max}}}$, and the maximum rate of electron transport at
saturating irradiance, *J*_{max}). The two assumptions of downregulation of
photosynthesis may have different time-dependent effects on GPP in
nonsteady-state systems (Xu et al., 2012; Walker et al., 2017).

At or near the steady state, net ecosystem N exchange is driven by the
processes of N input via deposition and fixation and N loss via leaching and
volatilization (Zaehle et al., 2014; Thomas et al., 2015). Previous studies
have stated that analyzing the steady-state condition is useful to understand
N effects because the balance between external N sources and N losses
determines whether an ecosystem is N limited (Rastetter et al., 1997; Menge et
al., 2009; Thomas et al., 2015). In this study, divergent NPP responses among
the three schemes might partly result from their different representations of
BNF (Figs. 3 and 10). Specifically, SM2 and SM3 simulated BNF explicitly,
which used modified empirical relationships of BNF with NPP and
evapotranspiration (ET), respectively (Cleveland et al., 1999). These
phenomenological relationships generally captured biogeographical
observations of higher rates of BNF in humid environments with high solar
radiation (Wieder et al., 2015a). However, the highest response of NPP in
only ET-driven BNF (i.e., SM3) may illustrate that not only energetic but
also C costs of “fixing” atmospheric dinitrogen (N_{2}) into a biologically
usable form (NH_{3}) broadly affect NPP (Gutschick, 1981; Rastetter et
al., 2001). This was because SM3 considered C investments in BNF, while SM2
did not. By contrast, for the nonsteady state, the NPP-driven BNF creates a
positive feedback between BNF and NPP, possibly causing a large impact on C
dynamics and terrestrial C storage (Wieder et al., 2015a). On the other hand,
SM1 applied a different strategy, which set BNF as an option when the plant N
uptake is not enough for growth in terms of C investment, leading to the
highest plant NUE (Fig. 6a) but a lower response of BNF to NPP (Fig. 10a).
Another driving factor of the net ecosystem N exchange is N loss, which
depends on the rate of leaching and volatilization. In this study, using the
same formulation in proportion to the size of the soil mineral N pool among the
three schemes, the different annual mean magnitude of N leaching was more
correlated with soil mineral N. In the original CLM4.5 and O-CN (Oleson et
al., 2013; Zaehle et al., 2010), the soil mineral N pool is divided into two
pools (ammonium and nitrate). The N leaching is only valid on the nitrate
pool, while the ammonium pool is assumed to be unaffected by leaching. This
hypothesis may reduce the correlation between leaching and total soil mineral
N.

The processes of plant N uptake and net N mineralization determine how N moves through the plant–soil system, thereby triggering N limitation on plant growth and C storage capacity (Fig. 10). However, to our knowledge, exploring those processes exactly in models is limited by inadequate representation of aboveground and belowground interactions that control the patterns of N allocation and whole-plant stoichiometry (Zaehle et al., 2014; Thomas et al., 2015). Plant tissue, litter, and SOM are the primary sinks of N in terrestrial ecosystems, while N in these forms is not directly available for plant uptake, leading to an increase in N demand for plant growth. This N must turn over to become available for plant uptake. Therefore, the time for N to stay in these unavailable pools controls the transactional delay between the incorporation of N into the plant unavailable pool and becomes available for plant uptake. In this way, the residence time of N in SOM appears to be an important factor for governing plant growth. This N limitation mainly occurs in nonsteady state because the accumulation of N in slow-turnover-rate SOM pools reduces the N available for plant uptake (Thomas et al., 2015). At or near steady state, however, the sequestration of N in SOM mainly affects the C residence time (Figs. 8 and 10b). In this study, the different NUE among the three C–N schemes is induced by different mechanisms. SM1 had the highest NUE due to the combined effects of plant N uptake based on C investment strategy (as described above) and flexible tissue C : N ratio. Nitrogen stress increased the tissue C : N ratio (Fig. 5b), leading to a high microbial N immobilization and then a lower net N mineralization (Fig. 3), which allowed for plant cell construction with a lower N requirement. However, this was not the case for SM3 since both hypotheses of increasing respiration to remove the excess C under N stress and the higher C investment for the BNF lead to the decrease in C input and then limits the microbial immobilization for the passive SOM pool. The inclusion of flexible C : N stoichiometry appeared to be an important feature allowing models to capture responses of the ecosystem C storage capacity to climate variability through adjusting the C : N ratio of nonphotosynthetic tissues or the whole-plant allocation among tissues (Figs. 9 and 10) with different C : N ratios (Zaehle and Friend, 2010).

Ecosystem N status in models, including plant-available and unavailable N forms, is set by N inputs from N fixation and N deposition, N losses from leaching and denitrification, and N gain from the turnover of litter and SOM through tissue senescence and decomposition. As noted above, the external N cycle (i.e., N inputs and N losses) couples the N processes within the plant–litter–SOM system, being mainly associated with the limitation of plant production (Vitousek, 2004; Vicca et al., 2012; Craine et al., 2015). The effects of ecosystem N status on C mean residence time (MRT), however, has been much less studied than N limitation on the productivity of plants and soil organisms because these effects involve various impacts on C transfer among pools and C release from each pool via decomposition and respiration (Thompson and Randerson, 1999; Xia et al., 2013). Therefore, the different impacts of ecosystem N status induce oscillating N limitation on MRT (Figs. 8 and 10) due to the inherently different assumptions of C–N interactions among the three C–N coupling schemes (Zhou et al., 2012; Shi et al., 2018).

At the steady state, the different effects of N status on changes in modeled
MRT can be attributed to the different rate of soil N mineralization
dependent on the total amount of N in SOM and its turnover time,
immobilization based on the competition strategy between plants and microbes
and their stoichiometry, and different deployment of reabsorbed N. The
traceability framework in this study can trace those different effects into
three components (i.e., climate forcing, N scalar *ξ*_{N}, and
baseline MRT) based on three alternative C–N coupling schemes under the TECO
model framework. Since the forcing data are identical, we assumed the same
effects for this component in all four experiments.

In our study, the N scalar (*ξ*_{N}) was based on the dynamics of
C : N ratios (Eq. 34). Therefore, the N scalar had no
effect on MRT in SM2, resulting from the assumption of a fixed
C : N ratio in all C pools (Figs. 5b and 8c). In both SM1
and SM3, however, the N scalar had large effects on the SOM pool, which is
probably related to different mechanisms. Specifically, the N scalar in SM1
had contrasting effects on MRT of fast and passive SOM pools (i.e., negative
vs. positive, respectively), which may largely be attributed to the plant and
microbe competition strategy combining with a much larger passive SOM pool in
the TECO-CN model (Du et al., 2017; Zhu et al., 2017). Under N stress, the
competition between plants and microbes is expected to be intensified,
resulting in an increasing C : N ratio of nonphotosynthetic
tissues (e.g., wood and root) and the vegetation C : N
ratio. This effectively prevents N limitation of cell construction and
corresponds to an increase in whole-plant NUE (Thomas et al., 2015). In this
case, the higher C : N ratio in those tissues lowers
structural litter quality, leading soil microbes to immobilize more N to
maintain their stoichiometric balance (Hu et al., 2001; Manzoni et
al., 2010). However, in SM3, increased respiration acted as a mechanism to
remove the excess C, which is a stoichiometry-based implementation to prevent
the accumulation of labile C to prevent the accumulation of C beyond the
storage capacity under N stress (Zaehle and Friend, 2010; Thomas et
al., 2015). This mechanism promotes the respiration of faster-turnover pools
(fast and slow SOM pools; Fig. 5a), leading to an increased
C : N ratio and decreased MRT in these two pools (Fig. 8).

In the traceability framework, the baseline MRT is determined by the
potential decomposition rates of C pools (**C** matrix), coefficients
for the C partitioning of NPP (** B** vector), and transfer coefficients
between C pools (

5 Conclusions

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C–N coupling has been represented in ecosystem and land surface models with different schemes, generating great uncertainties in model predictions. The most difference among terrestrial C–N coupling models occurs with the degree of flexibility of the C : N ratio in vegetation and soils, plant N uptake strategies, downregulation of photosynthesis, and the representations of the pathways of N import. In this study, we evaluated alternative representations of C–N interactions and their impacts on the C cycle using the TECO model framework. Our traceability analysis showed that the different representations of C–N coupling processes lead to divergent simulations of plant production, C residence time, and thus the ecosystem C storage capacity. Plant production is mainly affected by the different assumptions on net ecosystem N exchange, plant N uptake, net N mineralization, and the C : N ratio of vegetation and soil. In comparison, alternative representations of plant and microbe competition strategy and plant N uptake, combined with the flexible C : N ratio in vegetation and soils, led to notable spread effects on C residence time. Overall, the downregulation of photosynthesis, plant tissue C : N ratio, plant N uptake, and N retranslocation are the dominant processes of ecosystem C storage capacity. Identifying representations of the main C–N processes under different schemes can help us improve the N limitation assumptions employed in terrestrial ecosystem models and forecast future C sinks in response to climate change.

Code availability

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Code availability.

The code for TECO-CN and the three C–N coupling schemes is available at https://github.com/zgdu/TECO-CN-2.0-new (last access: 20 April 2018) (Du et al., 2018).

Data availability

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Data availability.

The data for this paper are available upon request to the corresponding authors.

Supplement

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Supplement.

The supplement related to this article is available online at: https://doi.org/10.5194/gmd-11-4399-2018-supplement.

Author contributions

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Author contributions.

ZD, JX, and XZ designed the study. ZD and EW wrote the code. ZD performed the experiments. ZD wrote the paper with contributions from all coauthors.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

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Acknowledgements.

This work was financially supported by the National Key R&D Program of
China (2017YFA0604600), the National Natural Science Foundation of China
(31770559, 31722009, 41630528), National 1000 Young Talents Program of China,
and the Fundamental Research Funds for Central Universities. Zhenggang Du
also thanks the China Scholarship Council (201606140130) for scholarship
support.

Edited by: Tomomichi Kato

Reviewed by: Will Wieder and one anonymous referee

References

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Short summary

In this study, based on a traceability analysis technique, we evaluated alternative representations of C–N interactions and their impacts on the C cycle using the TECO model framework. Our results showed that different representations of C–N coupling processes lead to divergent effects on plant production, C residence time, and thus the ecosystem C storage capacity. Identifying those effects can help us to improve the N limitation assumptions employed in terrestrial ecosystem models.

In this study, based on a traceability analysis technique, we evaluated alternative...

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