1The carbon and nitrogen cycle¶

1.1DONE: Vegetation phenology¶

1.1.1DONE: Classification of plant status¶

To accurately simulate seasonal ecosystem cycles it is essential to represent the biological life cycle of plants Lieth, 1974Piao et al., 2019. The timing of each of the plant phenological phases is dependent on a combination of physiological characteristics and climatic conditions. In ORCHIDEE, each PFT can progress through the following phases: establishment, bud presence, leaf onset, canopy presence, wood growth cessation (pre-senescence), senescence, dormancy, and death. The phenology models in ORCHIDEE control the timing of leaf onset and senescence. There are no leaf onset or senescence modules associated with evergreen ecosystems where leaf turnover is simply a function of climate and leaf age (equation 245).

1.1.2DONE: Leaf onset¶

There are four different modules to determine leaf onset (Table 4), where leaf onset is determined by moisture conditions, or temperature conditions (including the number of growing days, the occurrence of chilling days, and growing degree days), or both temperature and moisture conditions.

Within the number of growing days (NGD) module, which was originally proposed by Botta et al. (2000) for arctic and boreal biomes, the onset of leaves occurs when the number of growing days exceeds a PFT-specific critical value:

where $G^{n,grow}$ refers to the number of growing days with a mean daily temperature above a threshold, 268.15 K in ORCHIDEE, calculated from the start of the midwinter (shortest day of the year) where, $c_0$ (days) represents a PFT-specific critical value (23.9 days for boreal needleleaf deciduous forests). To ensure it’s spring, temperatures must also be increasing:

where $T^{w}$ (K) and $T^{m}$ (K) represent the weekly and monthly mean temperatures, respectively.

The growing degree days - number of chilling days (GDD-NCD) module follows the general GDD model Chuine, 2000, which is designed to simulate the accumulation of warm temperatures in the spring needed for budburst and is a common model applied to satisfy temperature conditions for leaf onset to occur Hänninen & Kramer, 2007. As in the number of growing days model, temperatures must also be increasing (i.e., the weekly temperature must be greater than the monthly temperature - equation 239). GDD is calculated as a sum of the mean daily temperatures for days that have a mean daily temperature above a given threshold, starting from a given time point. Leaf onset occurs once the GDD value has crossed a defined threshold. In the GDD-NCD module the GDD is calculated from midwinter (as for the NGD module) but the general GDD module described above is further adapted to account for PFTs that require a period of cold temperatures to trigger budburst Orlandi et al., 2004 by modifying the GDD threshold to account for the number of chilling days. Thus, in the GDD-NCD module the start of the growing season occurs when the growing degree days since midwinter exceeds a calculated GDD threshold:

where $G^{deg,grow}$ (K) represents the growing degree days since midwinter and $G^{thres}$ (K) is a negative exponential that accounts for the number of chilling days with an additional three fixed parameters, following Botta et al., 2000:

where $c_1$ (-), $c_2$ (-) and $c_3$ (-) are non PFT-specific model parameters that have been calibrated against satellite data, and are 964, 0.0058, and 12.8, respectively Botta et al., 2000. $G^{n,chill}$ is the number of chilling days since midwinter, where chilling days are defined as the number of days with a mean daily temperature below a PFT-specific threshold (278.15 K and 273.15 K for temperate and boreal broadleaved deciduous forests, respectively) following Cannell & Smith (1986), Murray et al. (1989), and Chuine (2000).

Within the moisture module, the conditions determining the onset of leaf growth depend on either a soil moisture availability criterion (if hydraulic architecture is not used) or a vegetation stress proxy (if hydraulic architecture is used). This means that the growing season can begin if the last moisture minimum was a sufficiently long time ago (equation 242) and either the soil moisture availability (or vegetation stress proxy) is increasing (equation %s) or if the monthly moisture availability (or monthly vegetation stress proxy) is high enough (equation %s).

where $f^{Vst,w}$ (-) and $f^{Vst,m}$ (-) are proxies for weekly and monthly vegetation water stress, respectively, with values ranging from 0 (high moisture stress) to 1 (low moisture stress). $M^{nsm}$ (days) represents the number of days since the last moisture minimum, and $c_4$ (days) and $c_5$ (-) represent PFT-specific threshold parameters. For tropical broadleaf raingreen trees, $c_4$ and $c_5$ are 50 days and 1.0, respectively.

Vegetation water stress is calculated using the soil moisture availability criterion (essentially root profile weighted plant available relative soil moisture) that varies linearly from zero at wilting point to 1 at field capacity:

where $M^{sm}_{i}$ (kg $m^{-2}$) is the soil moisture of the $i$-th (m) soil layer (liquid phase), $M^{smf}_{i}$ (kg $m^{-2}$) soil moisture of each layer at field capacity, $M^{smw}_{i}$ (kg $m^{-2}$) is the soil moisture of each layer at wilting point, and $f^{root,fun}_{i}$ (-) is the normalized root mass/length fraction in each soil layer (0 - 1) Krinner et al., 2005. The moisture availability criterion (equation 242 - equation %s) correspond to Model 4b in Botta et al. (2000), which assumes that leaf onset in the dry tropics and semi-arid ecosystems occurs only after a certain amount of water has accumulated in the soil.

Within the moisture-growing degree day module (MOI-GDD), both the moisture conditions described above and a GDD threshold criterion must be met for leaf onset to occur. For the moisture conditions parameter $c_4$ is set to 35 days for grasses and 75 days for crops, and parameter $c_5$ is set to 0.98 for C3 grasses and 0.6 for C4 grasses and crops. The GDD test is similar to the general GDD module, described above, where the growing degree days since midwinter must exceed a calculated GDD threshold (i.e. equation 240). In this version of the GDD model $G^{deg,grow}$ represents the growing degree days calculated using days with a mean daily temperature above 278.15 K since midwinter and the $G^{thres}$ (° C) is calculated using a second-degree polynomial using the long term mean annual air surface temperature MacBean et al., 2015:

where $c_6$ (° C), $c_7$ (° C) and $c_8$ (° C) represent GDD PFT-specific parameters and $T^{3year}$ (° C) is the 3-year average 2 m air temperature. It is not possible to convert GDD between ° C and K and because these PFT parameters are used in ORCHIDEE in ° C, we have also written this relationship here in ° C. Where $c_6$ is 640 ° C, 400 ° C, 400 ° C, 450 ° C for c3 grasslands, c4 grasslands, c3 croplands, and c4 croplands. $c_7$ is 32.0 ° C, 0.0 ° C, 6.25 ° C, and 0.0 ° C for c3 grasslands, c4 grasslands, c3 croplands, and c4 croplands. $c_8$ is 0.1 ° C, 0.0 ° C, 0.0315 ° C, and 0.0 ° C for c3 grasslands, c4 grasslands, c3 croplands, and c4 croplands. As in the NGD and GDD-NCD models, temperatures must also be increasing (equation 239). An alternative to the GDD threshold is that the monthly mean temperature must be above a certain PFT dependent threshold (defined as 283.15 K for all PFTs). Finally, for c4 grasses the monthly mean temperature must also exceed a pre-set temperature of 295.15 K.

1.1.3DONE: Senescence¶

Leaf senescence occurs due to age, the cessation of the growing season, or the occurrence of crop harvests (Table 5). Leaf senescence can also trigger fruit, root, or stem senescence. In the occurrence of leaf and root senescence, the nitrogen stored in leaves and roots is transferred into the labile nitrogen pool. Evergreen species do not experience seasonal senescence. Furthermore, if there is very low leaf mass during senescence, all leaves are lost.

Even if the meteorological conditions are favorable for leaf maintenance, plants, and in particular, evergreen trees, must renew their leaves simply because the old leaves become inefficient. Therefore, the old leaves of all PFTs fall off regardless of climatic conditions, following.

where $M^{k}_{l}$ is the carbon (g C m$^{-2}$ day$^{-1}$) and nitrogen (g N m$^{-2}$ day$^{-1}$) biomass of organs, $k$ (leaves, roots, fruits, and stems), of circumference class $l$. $\Delta M$ is the fraction of carbon and nitrogen biomass lost, $\Delta t$ is the timestep (1 day), $a^{leaf}_{i}$ (days) is the age of the leaf mass in age class $i$, and $S^{crit}$ (days) is the location-specific leaf longevity, dependent on the long-term temperature:

where $c_1$ (days) is the PFT-specific leaf longevity and is 180 days for raingreen trees, summergreen trees, and grasses, 730 days for broad-leaved evergreen trees, 910 days for temperate needleleaf trees, 2000 days for boreal needleleaf evergreen trees, and 200 days for crops. $c_2$ (-), $c_3$ (-), and $c_4$ (-) are PFT specific parameters linking leaf longevity to the reference temperature. $c_2$ is 1.5 for grasses and crops, 2.0 for boreal needleleaf evergreen trees, and 1.0 for all other PFTs. $c_3$ is 0.365 for boreal needleleaf evergreen trees, and 0.75 for grasses and crops, and 1.0 for all other PFTs. $c_4$ is 120 for boreal needleleaf evergreen trees, 10 for grasses and crops, and 0 for all other PFTs. $c_5$ (K) is a PFT-specific reference temperature for the calculation of leaf longevity and is 298.15K for tropical trees, 293.15K for temperate broad-leaved evergreen trees, C4 grasses and crops; 288.15K for temperate needleleaf evergreen trees, temperate broad-leaved summergreen trees, C3 grasses and crops; and 278.15K for boreal trees.

This means that older leaves fall more frequently than younger leaves and therefore the leaf age distribution must be recalculated after leaf senescence. The fraction of biomass in each leaf age class is updated using the following equation:

where $f^{leaf}_{i,t}$ is the new leaf carbon and nitrogen fraction of leaf biomass in leaf age class $i$, $f^{leaf}_{i,t-1}$ is the old leaf fraction, $M^{leaf}_{l,t}$ is the new total leaf biomass of circumference class $l$, and $M^{leaf}_{t-1}$ is the old total leaf biomass. $\Delta M^{k}_{l}$ is the change in leaf carbon and nitrogen biomass in the considered class due to senescence.

Senescence at the end of the growing season, can be triggered by cooling temperatures, water availability limitations, or both. In the case of senescence at the end of the growing season, leaf senescence is only possible if leaves have reached a certain age (equation 248).

where $a^{l,mean}$ (days) is the mean leaf age and $c0$ (days) is the PFT-specific parameter for the minimum leaf age for senescence. $c0$ is 90 days for tropical and temperate trees, 60 days for boreal trees, and 30 days for grasses and crops.

Leaf senescence due to cool temperatures at the end of the growing season is triggered by decreasing temperatures (equation 250) and the fall of the monthly air temperature below a threshold temperature ($T^{m} < S^{T}$). The threshold temperature is defined using a second order polynomial of the long-term mean annual air surface temperature:

where $S^{T}$ (K) is the critical temperature for leaf senescence, $T^{3year}$ (K) is the long term annual mean temperature and $c_6$ (-), $c_7$ (-) and $c_8$ (-) are PFT-specific empirical constants in the quadratic temperature senescence equation. $c_6$ and $c_7$ are 0.00375 and 0.1, respectively, for C3 grasses, and 0 for all other PFTs. $c_8$ is 16.0 for temperate broad-leaved summergreen, 14.0 for boreal broad-leaved summergreen, 13.0 for boreal needleleaf summergreen trees, 5.0 for grasses, 12.0 for C3 crops and 13.0 for C4 crops. In addition, temperature must be decreasing, following:

where $T^{2w}$ (K) and $T^{m}$ (K) refer to the mean daily temperatures calculated over the past fortnight and the past month, respectively. Alternatively, leaf senescence due to cooling temperatures is also triggered if the ratio of plant respiration to photosynthesis is above a PFT-specific threshold (equation 251).

where $F^{rm,1week}$ ($gC m^{-2} day^{-1}$) represents the mean of daily maintenance respiration and $F^{gpp,1week}$ ($gC m^{-2} day^{-1}$) represents the mean of daily photosynthesis calculated for the past week, respectively. $c_9$ represents the unitless PFT-specific minimum senescence ratio parameter and is set to 0.75 for C3 grasses, 0.89 for boreal needleleaf summergreen trees, 0.87 for boreal broad-leaved summergreen trees and 1.0 for all other PFTs.

Leaf senescence due to a lack of water availability is triggered by low soil moisture availability. As occurs in leaf onset (sect. 1.1.2), this can be calculated using either the soil moisture availability criterion, if hydraulic architecture is not used, or as a ratio between a proxy for stressed and unstressed ecosystem functioning if hydraulic architecture is used. Leaf senescence is triggered if either the weekly moisture availability (or vegetation stress) falls below a critical threshold ($V^{st,w} < V^{st,thres}$) or the ratio of plant respiration to photosynthesis is sufficient (equation 251). The critical moisture availability is calculated as a function of last year’s soil moisture (or vegetation stress) minimum and maximum (or vegetation stress) using the following equation:

where $f^{Vst,thres}$ is the critical moisture availability threshold, $f^{Vst,min1y}$ and $f^{Vst,max1y}$ are the minimum and maximum moisture availabilities over the past year, $c_{10}$ is a critical relative moisture availability for phenology, $c_{11}$ is the PFT-specific critical moisture availability for senescence, and $c_{12}$ is the PFT-specific relative soil moisture availability above which there is no humidity-related senescence. $c_10$, $c_{11}$ and $c_{12}$ are 0.5, 0.3, and 0.8 for tropical broadleaf raingreen trees, respectively.

For grasses, senescence occurs if the ratio of plant respiration to photosynthesis is sufficient (equation 251).

For crops, the moment of leaf senescence equates to the actual harvest and the entire plant is made senescent. To identify the harvest moment for crops, a second order polynomial of the long-term mean annual air surface temperature is used:

where $S^{crit}$ (days) represents the harvest time threshold, and $c_{12}$ (K) and $c_{13}$ (days) represent PFT-specific parameters. $c_{12}$ is 282K and $c_{13}$ is 160 days for all crop PFTs. For senescence to occur, the length of the growing season (number of days) must exceed $H^{crit}$. In addition, the growing degree days since the initiation of the growing season must be sufficient ($G^{init} > c_{14}$) where $G^{init}$ (° C) represents the growing degree days since the start of the growing season and $c_{14}$ (° C) represents the PFT-specific minimum number of growing degree days. $c_{14}$ is 2500 ° C for all crop PFTs.

For grasses, senescence at the end of the growing season is further extended to the whole plant (i.e. all carbon and nitrogen pools) except the carbohydrate reserve. For trees, senescence at the end of the growing season extends to the fine roots at the same rate as they lose their leaves. The rate of biomass loss of both fine roots and leaves (for trees) and leaves, roots, and fruits (for grasses) is prescribed through the equation:

where $M$ is the carbon and nitrogen biomass, $\Delta M$ is the fraction of carbon and nitrogen biomass lost, $\Delta{t}$ is the times step, $c_{15}$ (days) is the PFT-specific time constant of meteorological determined turnover parameter. Where $c_{15}$ is 25 days for boreal trees, 15 days for temperate broad-leaved summergreen trees, and 5 days for temperate needleleaf evergreen trees and grasses.

All remaining leaves are shed when leaf biomass falls too low (below a PFT-specific parameter). For deciduous trees not only leaves but also fruits and fine roots are lost at this moment.

1.2DONE: Photosynthesis¶

The $CO_2$ assimilation rate ($F^A$, $\mu mol CO_2 m^{-2} s^{-1}$), stomatal conductance ($g_s$) and leaf intercellular $CO_2$ partial pressure ($p^{C_i}$) are calculated for each leaf layer, by jointly solving a set of three equations (see below). Both for c3 and c4 plants, these three equations can be manipulated into the form of a standard cubic equation for $F^A$, for which Yin & Struik (2009) proposed an analytical solution.

We implemented this analytical solution and the overall formalism for both c3 (Appendix B in Yin & Struik (2009)) and c4 photosynthesis (Appendix C in Yin & Struik (2009)).

1.2.1DONE: C3 photosynthesis¶

The Farquhar–von Caemmerer–Berry model farquhar1980 predicts the net $CO_2$ assimilation rate as the minimum of the Rubisco-limited rate ($F^{A_c}$) and electron (e$^-$) transport-limited rate ($F^{A_j}$):

These two parts of the model can be written in a single equation as:

where for the Rubisco-limited part $\chi_1= k^{V_{cmax25}}$ and $\chi_2=k^{K_{mC}}(1+p^{C_o}/k^{K_{mO}})$, for the e$^-$ transport-limited part $\chi_1=F^J_i/4$ and $\chi_2=2p^{\Gamma_*}$. $p^{C_c}$ and $p^{C_o}$ are the carbon dioxide and oxygen partial pressures at the carboxylation sites, $p^{\Gamma_*} = 0.5 p^{C_o}/c$1, is the $CO_2$ compensation point in the absence of dark respiration ($F^{R_d}$). This latter case assumes a purely linear e$^-$ transport. $c_1$ is a constant representing the relative CO₂/O₂ specificity factor for Rubisco.

Following Farquhar & Wong (1984), the rate of e$^-$ transport ($F^J$) is described as a non-rectangular hyperbolic function of irradiance:

where $c^{\alpha_\mathsf{LL}}$ is the conversion efficiency of absorbed light into $J$ at strictly limiting light, $k^{J_\mathsf{max}}$ is the maximum capacity of e$^-$ transport, and $c^{\theta}$ is the convexity factor for response of $J$ to absorbed irradiance.

The leaf photosynthesis is coupled with the stomatal conductance as follows (Yin & Struik (2009)):

were $c^{g_0}$ is the residual stomatal conductance $(molCO_{2} m^{-2} s^{-1})$, $F^{R_{d}}$ $(\mu molCO_{2} m^{-2} s^{-1})$ is the dark respiration, $k^{g_m}$ is the mesophyll conductance and $G^{hum}$ is a function describing the sensitivity of the stomata to either vapour pressure deficit ($g^{VPD}$) or leaf water potential ($g^{\psi}$), depending on the selected drought scheme (see 1.3).

According to the first diffusion law of Fick, the $CO_2$ transfer from $p^{C_a}$ (ambient $CO_2$ partial pressure) to $p^{C_c}$ can be written as:

where $c^{g_b}$ is the leaf boundary-layer conductance.

The three equations 257, 259 and 260 with the three unknowns $F^A$, $g_s$ and $p^{C_{int}}$ form the system to be solved for c3 plants.

1.2.2DONE: C4 photosynthesis¶

For c4 plants, CO₂ is fixed by phosphoenolpyruvate (PEP) carboxylase in the mesophyll cell into a c4 compound, which then goes into a bundle-sheath cell, where it is decarboxylated to provide CO₂ to Rubisco. The CO₂ concentration in the bundle-sheath is high, thus preventing photorespiration.

where $F^{V_p}$ is the rate of PEP carboxylation, $F^{R_m}$ is the mitochondrial respiration in the mesophyll and fixed to $0.5F^{R_d}$ and $F^L$ is the leakage of $CO_2$ from the bundle-sheath to the mesophyll through the bundle-sheath conductance $c^{g_{bs}}$:

$F^{V_p}$ can be limited by the PEP carboxylation rate or the e$^-$ transport rate. In the former case, we have:

where $c^{k_p}$ is the initial carboxylation efficiency of the PEP carboxylase, and $k^{V_{pmax}}$ is the maximum rate of PEP carboxylation at the saturated $p^{C_{int}}$.

For the e$^-$ transport-limited case for c4 plants, we use:

where $F^{J_2}_i$ is the rate of all e$^-$ transport through photosystem II (PSII), $k^{f_{cyc}}$ is a fraction of electrons that follows a cyclic e$^-$ transport (CET) around photosystem I (PSI), and $c^{f_{pseudo}}$ is a fraction of electrons at PSI that follow a pseudocyclic e$^-$ transport (PET). Both are not used for carbon reduction and photorespiration (which is negligible in c4 plants). Similarly, $c^{f_Q}$, a fraction of electrons at reduced plastoquinone that follow the Q-cycle, is not transferred to the plastocyanin. $c^{f_{pseudo}}$ and $c^{f_Q}$ are PFT-specific parameters. For $k^{f_{cyc}}$ we use:

where $c^{\chi}$ is the fraction of e$^-$ transport rate partitioned to the mesophyll reactions, which is set at 0.4, and $c^h$ is the number of protons required to produce one ATP, which is set at 4.

As for c3 plants, the Rubisco-based assimilation of $CO_2$ in c4 plants can be limited by either Rubisco activity or by e$^-$ transport rate (equation 256) following the equivalent to equation 257:

where $p^{O_{bs}}$ is the oxygen partial pressure in the bundle-sheath, $\gamma_*=0.5/c^{S_{c/o}}$, $c^{S_{c/o}}$ is the relative CO₂/O₂ specificity factor for Rubisco. For the Rubisco-limited rate, we have: $\chi_1=k^{V_{cmax}}$, $\chi_2=k^{K_{mC}}/k^{K_{mO}}$, $\chi_3=k^{K_{mC}}$, and for the e$^-$ transport-limited rate: $\chi_1=(1-c^{\chi})F^{J_2}_i c^z/3$, $\chi_2=7p^{\Gamma_*}/3$, $\chi_3=0$.

The oxygen partial pressures between intercellular air-space and bundle-sheath are linked through the following equation:

where $c^\alpha$ is the fraction of PSII activity in the bundle-sheath and 0.047 accounts for the diffusivities for O₂ and CO₂ in water and their respective Henry constants.

To enable an analytical solution Yin & Struik, 2009 propose an equation for c4 stomatal conductance that is slightly different than for c3:

with $C_{s}$, the $CO_2$ level at leaf surface and $p^{C_{s*}}$ the $C_{s}$-based $CO_2$ compensation point in the absence of $F^{R_d}$.

The three equations 266, 268 and 262 with the three unknowns $F^A$, $g_s$ and $p^{C_c}$ form the system to be solved for c4 plants.

1.2.3DONE: Parameter dependency on temperature, nitrogen and water¶

To account for the nitrogen dependency of $k^{V_{cmax25}}$ we use the nitrogen use efficiency (NUE, defined as $k^{V_{cmax25}}$ per leaf nitrogen content) as derived from observations by Kattge2009:

where $k^{NUE}$ is NUE scaled with $f^{sugarload}_{t}$ (1.4.5, 321) and leaf efficiency weighted for the fraction of leaves in each age class. Leaf efficiency is scaled by the leaf age of each leaf age class.

Most of the photosynthetic parameters are temperature-dependent and their temperature dependency in ORCHIDEE follows either an Arrhenius function ($F^{R_d}$, $p^{\Gamma_*}$, $k^{K_{mC}}$, $k^{K_{mO}}$, $c^{S_{c/o}}$) or a modified Arrhenius function, accounting for a decrease at high temperatures ($k^{J_{\max}}$, $k^{V_{c\max}}$, Medlyn et al. (2002)). In addition, for c3 plants, we account for an acclimation term on the two entropy factors that are involved in the temperature function for $k^{V_{c\max}}$ and $k^{J_{\max}}$ and the ratio between $k^{J_{\max}}$ and $k^{V_{c\max}}$ (kattge2007). These parameters are all function of the monthly temperature. Based on Kattge et al (2009), $k^{J_{\max}}$ is directly inferred from $k^{V_{c\max}}$ (scaled with the temperature dependency of $k^{J_{\max}}$) and the monthly temperature. There is no acclimation term on any of the parameters used for c4 plants.

The water limitation function $G^{hum}$ is impacting photosynthesis through $g_{s}$ ($G^{hum}$, see 1.3), but it is also limiting $k^{V_{c\max}}$, $k^{J_{\max}}$, $k^{g_m}$ and $F^{R_d}$.

$F^A$ is scaled from leaf to canopy level by multiplying with $d^{LAI}_{i}$ (see 1.5.7). Apart from the $I_{abs}$, the other environmental parameters that drive the photosynthesis (temperature, ambient CO₂, air humidity) are held constant along the canopy depth. We only account for a leaf nitrogen-related reduction of $k^{V_{c\max}}$ and $F^{R_d}$ along the canopy depth, depending on the fraction of absorbed light $f_{light}$, as calculated in the radiation transfer scheme (see 1.3.2).

The photon flux density absorbed by leaf photosynthetic pigments at canopy level $i$ ($I_{abs,i}$) is calculated as:

where $c^{Wtomol}$ is a conversion factor between units from $\mathsf{W m^{-2}}$ to $\mathrm{\mu mol\ photons\ m^{-2} s^{-1}}$, and $c^{RGtoPAR}$ is the fraction (=0.5) of $SW_{down}$ that is photosynthetically active.

1.3DONE: Maintenance respiration¶

Maintenance respiration refers to the carbon cost that occurs in living plant tissue to maintain a healthy and living state, e.g., resynthesis of enzymes and membrane lipids, maintenance of ion gradients across membranes, and acclimation to environmental changes Amthor, 1984. ORCHIDEE does not distinguish the underlying processes and instead uses a bulk approach ruimy1996 in which maintenance respiration of a specific PFT within a grid cell ($F^{rm}$; g C m$^{-2}$ s$^{-1}$) is the sum of maintenance respiration of the different plant organs. It is calculated as a function of biomass modulated by the temperature and nitrogen content of the vegetative and reproductive plant organs:

where $o$ denotes the plant organ, $norgan$ denotes the total number of plant organs (see 1.4), $c_1$ (s$^{-1}$) is a PFT-specific maintenance respiration coefficient prescribing the fraction of biomass that is lost during each time step and $M^{o}$ (g C m$^{-2}$) is the stand level nitrogen biomass of plant organ $o$. $c_1$ is set to zero for the above-ground and below-ground heartwood as well as the carbohydrate reserves as ORCHIDEE assumes that these organs have no maintenance respiration.

$m^{o,rm,T}$, is a temperature modulator (unitless) calculated for each plant organ $o$ as:

where $T^{3year}$ (K) represents the mean air temperature above freezing over the 3 years preceding the time step under consideration. $c_2$, $c_3$, and $c_4$ are PFT-specific parameters. For the above-ground plant organs, the 2-meter air temperature ($T^{air}$; K) is used for $T^{o}$. For below-ground plant organs, $T^{o}$ represents the root-zone temperature $T^{soil,weighted}$ (K) calculated as the vertical profile of soil temperature (see 1.7.1) weighted by the vertical profile of the root biomass (see 1.5.10). When $T^{o}$ drops below 273.15 K, $m^{o,rm,T}$ is set to one, implying that maintenance respiration continues but levels off when freezing.

In equation 271, $m^{o,rm,N}$ (unitless) is a modulator for the N concentration of organs $o$ and is calculated as:

where $c_6$ is a global parameter, ${c_5}^{cn}_{k}$ is the reference carbon-to-nitrogen ratio for organ $o$, i.e., 45 for leaves, 52 for roots and fruits, and 517 for the sapwood and carbohydrates reserves. $f^{cn}_{k}$ (unitless) is the actual carbon-to-nitrogen ratio for organ $o$ which is truncated at 200 if the calculated carbon-to-nitrogen ratio exceeds this threshold.

The parameters $c_1$, $c_2$, $c_3$, $c_4$, but not $c_5$, have been tuned at the PFT-level and $c_6$ at the global level to simulate biomass production efficiencies within the ranges observed by Vicca et al. (2012) and Campioli et al. (2015). Given that ORCHIDEE v4.2 does not simulate the carbon fluxes from the vegetation to the mycorrhizae, the latter is included in $F^{rm}$. The simulated maintenance respiration flux ($F^{rm}$) should, therefore, not be compared against observed fluxes as their definitions are not identical.

1.4DONE: Allocation and growth respiration¶

1.4.1DONE: Allocatable carbon and nitrogen¶

Following bud burst, photosynthesis produces carbon compounds that are added to the labile carbon pool as long as the plant passed bud burst and is not in presenescence yet (see 1.1):

where $M^{lab,C}_{t}$ (g C m$^{-2}$) is the labile carbon pool at the current time step $t$, $M^{lab,C}_{t-1}$ (g C m$^{-2}$) is the labile carbon pool at time step $t-1$, $F^{gpp}_{t}$ (g C m$^{-2}$ s$^{-1}$) is the photosynthetic carbon flux at the current time step, and $\Delta{t}$ is the length of the current time step which is one day given in seconds (s). If the plant is in presenescence or senescence (see 1.1), the photosynthetic flux is added to the reserve pool:

where $M^{res,C}_{t}$ and $M^{res,C}_{t-1}$ are the carbon contained in the reserve pool at time step $t$ and $t-1$ (g C m$^{-2}$), respectively. The labile carbon pool is then split into an active and none-active pool. The size of the active pool is calculated as a function of plant phenology and temperature. If the plant passed bud break and is not in presenescence yet, the active part of the labile pool was formalized following Ryan (1991), Sitch et al. (2003), and Zaehle & Friend (2010):

where $c_1$, $c_2$ and $c_3$ are PFT-specific parameters representing respectively a growth temperature coefficient, the reference temperature above which all carbon in the labile pool is allocated to growth, and the minimum temperature for allocation. The parameters $c_1$, $c_2$ and $c_3$ were set such that no carbon is available for plant growth below -2 ° C, only 3 % of the labile pool is available for allocation at 0 ° C, and at 5 ° C, 100 % of the labile pool is available for allocation. $T^{air}$ is the 2-m air temperature at $t$, and $M^{totinc}$ (g C m$^{-2}$) is the total biomass increment at the current time step. If the plant passed presenescence, the active part of the labile pool is set to zero.

Prior to allocating, $M^{totinc}$ is used to sustain the maintenance respiration flux ($F^{rm}$; g C m$^{-2}$ s$^{-1}$; see 1.3) up to a maximum of 100 % of $M^{totinc}$. A first estimate of the growth respiration, i.e., the cost for producing new tissue excluding the carbon required to build the tissue itself Amthor, 1984, is set aside. This first estimate assumes that all the available carbon will be allocated and is calculated as:

where $F^{rg,est}$ (g C m$^{-2}$ s$^{-1}$) is the estimated growth respiration and $c_4$ is the fraction of carbon respired to grow one unit of carbon, which is set to 28 % McCree, 1974. Hence, the amount of carbon that is available for biomass growth is:

where $\Delta{t}$ is the length of the time step for the calculation of biomass allocation (see table 7). Once allocation is finalized, $F^{rg,est}$ will be recalculated (section 1.4.4) to obtain the exact growth respiration for the actual biomass increment.

Whether all of the available carbon can be allocated or not depends on the nitrogen availability. The labile N pool is calculated as:

where $M^{lab,N}_{t}$ and $M^{lab,N}_{t-1}$ (g N m$^{-2}$) are the labile nitrogen pools at $t$ and $t-1$, respectively, and $F^{root,N}_{t}$ (g N m$^{-2}$ s$^{-1}$) is the nitrogen uptake by the plants at the current time step. Subsequently, $M^{totinc}$ is adjusted for the available nitrogen after estimating the nitrogen that would be required to allocate $M^{totinc}$ entirely. This estimate assumes that all tissue has the carbon-to-nitrogen ratio of leaves:

where $f^{cn,leaf}$ (unitless) is the actual carbon-to-nitrogen ratio of leaves for the PFT and grid cell under consideration and $c_5$ is the PFT-specific minimal carbon-to-nitrogen ratio for leaves. The maximal elasticity of the carbon-to-nitrogen ratio of leaves $b_{2}$ (unitless) is calculated as:

where $c_6$ is the PFT-specific maximal carbon-to-nitrogen ratio for leaves. Assuming all newly grown biomass has the actual carbon-to-nitrogen ratio of leaves, $b_{3}$ (g C m$^{-2}$) represents the maximum amount of carbon that could be allocated at time step $t$, given the available amount of nitrogen:

If there is enough nitrogen (thus $M^{totinc} < b_{3}$), $M^{totinc}$ can be allocated. If, however, there is not enough nitrogen to allocate the allocatable carbon entirely (thus $M^{totinc} > b_{3}$), the elasticity of the carbon-to-nitrogen ratio of leaves is used to adjust $M^{totinc}$:

where $c_7$ is the maximal elasticity of foliage N concentrations and set to 0.25 and $M^{totinc}$ is the carbon that will be allocated either for restoring plant allometry or for plant growth as described in the following sections.

1.4.2DONE: Plant allometry¶

Biomass is allocated to leaves, roots, sapwood, heartwood, and fruits. Allocation to leaves, roots and wood respects the pipe-model theory Shinozaki et al., 1964 and thus assumes that producing one unit of leaf mass requires a proportional amount of sapwood to transport water from the roots to the leaves as well as a proportional fraction of roots to take up the water from the soil.

The scaling parameter between leaf and sapwood mass is derived from:

where $d^{leaf}$ (m$^{2}$) is the one-sided leaf area of an individual plant, $d^{sap}$ (m$^{2}$) is the sapwood area of an individual plant, $k^{ls}$ a calculated parameter (unitless) linking leaf area to sapwood area and, $m^{water}$ (unitless) is the water stress as calculated in section 1.1. Alternatively, leaf area can be written as a function of leaf mass ($M^{leaf}$) and the specific leaf area ($k^{sla}$; m$^{2}$ g C$^{-1}$):

Sapwood mass $M^{sap}$ can be calculated from the sapwood area $d^{sap}$ as follows:

where $d^{h}$ is the tree height (m) and $c_8$ is the sapwood density (g C m$^{-3}$). Following substitution of equations 285 and 286 into equation 284, leaf mass can be written as a function of sapwood mass:

where

where $k^{ls}$ is calculated as a function of the gap fraction as supported by site-level observations Simonin et al., 2006:

$c_9$ is the minimum observed leaf area to sapwood area ratio, $c_{10}$ is the maximum observed leaf area to sapwood area ratio and $f^{Pgap}$ is the actual gap fraction of the canopy (see 1.5.8). By using the gap fraction as a driver of $k^{ls}$ more carbon will be allocated to the leaves until canopy closure is reached.

Following Magnani et al. (2000), sapwood mass and root mass ($M^{root}$) relate as follows:

where the parameter $c_{11}$ (m$^{-1}$) is calculated according to Magnani et al. (2000) (their equation (17)):