Chapter 16 Carbon pools and components of the carbon balance
16.1 Size of carbon pools
Biomass of leaves, sapwood and fine roots is needed in the model to estimate respiratory costs and the size of the C storage pools.
16.1.1 Leaf structural, metabolic and storage biomass
The live leaf area LAlive per individual (in m2) is: LAlive=10000⋅LAIlive/N where N is the density of the cohort and LAIlive is the leaf area index. The actual (expanded) leaf area LAϕ is estimated analogously from LAIϕ: LAϕ=10000⋅LAIϕ/N Structural leaf biomass per individual (Bleaf; gdry·ind−1) is the result of dividing leaf area by SLA (m2⋅kg−1), the specific leaf area of the species: Bleaf=1000⋅LAϕ/SLA where a factor 1000 is used to convert from kg to g. Hence, only expanded leaf area has respiratory cost (i.e. winter resistance buds do not). Leaf storage volume for an individual (Vstorage,leaf; in L⋅ind−1) is: Vstorage,leaf=LAϕ⋅Vleaf where Vleaf is the water storage capacity of leaf tissue per leaf area unit (in L⋅m−2) (see A.4.5). Leaf storage volume is necessary to estimate the biomass of metabolic (sugars) or storage (starch) from the concentration of these substances in leaves (SSleaf and STleaf, which are expressed in molgluc⋅L−1), and conversely. For example: Bsugar,leaf=SSleaf⋅Vstorage,leaf⋅mgluc where mgluc is the molar mass of glucose. To estimate leaf starch storage capacity, the model assumes that up to 10% of leaf tissue volume can be occupied with starch, so that the leaf starch storage capacity (STmaxleaf; in mol⋅ind−1) is: STmaxleaf=0.1⋅1000⋅Vstorage,leaf⋅ρstarchmstarch
where ρstarch is the density of starch and mstarch is its molar mass.
16.1.2 Sapwood structural, metabolic and storage biomass
Sapwood volume (Vsapwood; in L⋅ind−1) is defined as the product of sapwood area and the sum of aboveground height and belowground coarse root length: Vsapwood=1000⋅SA⋅(H+∑sFRPs⋅Ls) where SA is sapwood area, H is plant height, FRPs is the proportion of fine roots in soil layer s and Ls is the coarse root length in layer s (all lengths expressed here in m). Sapwood structural biomass per individual (Bsapwood; gdry·ind−1) represents the sapwood biomass of sapwood of trunks, branches and coarse roots. It is defined as the product of Vsapwood and wood density (ρwood; gdry·cm−3): Bsapwood=1000⋅Vsapwood⋅ρwood While Bsapwood represents the structural sapwood biomass, it cannot be used to estimate sapwood respiration, since only xylem axial or radial parenchymatic rays (and not dead cells like tracheids or vessels) contribute to sapwood respiration. In addition, we assume that embolized parts of sapwood do not contribute to sapwood respiration. Hence, sapwood living (respiratory) biomass is estimated using: Bliving,sapwood=1000⋅(1−PLCstem)⋅Vsapwood⋅ρwood⋅(1−fconduits) where PLCstem is the current proportion of stem conductance lost and fconduits is the fraction of sapwood volume that corresponds to dead conducts, being the complement of the fraction of parenchymatic tissue. The volume available for metabolic or storage carbon within sapwood is limited by both the sapwood fraction that corresponds to parenchyma and wood porosity (i.e. (1−(ρwood/1.54))). Sapwood storage volume (Vstorage,sapwood; in L⋅ind−1) is: Vstorage,sapwood=Vsapwood⋅(1−(ρwood/1.54))⋅(1−fconduits) Analogously to leaf carbon, Vstorage,sapwood is used to estimate the biomass of metabolic (sugars) or storage (starch) from the concentration of these substances in sapwood (SSsapwood and STsapwood, which are expressed in molgluc⋅L−1), and conversely. For example: Bsugar,sapwood=SSsapwood⋅Vstorage,sapwood⋅mgluc where mgluc is the molar mass of glucose. To estimate sapwood storage capacity, the model assumes that up to 50% of volume of parenchymatic cells can be occupied with starch, so that the sapwood starch storage capacity (STmaxsapwood; in mol⋅ind−1) is: STmaxsapwood=0.5⋅1000⋅Vstorage,sapwood⋅ρstarchmstarch
16.1.3 Fine root area and biomass
The fine root compartment does not have labile carbon (i.e. the model supplies labile carbon for fine roots from sapwood compartment), so that only the structural biomass of fine roots needs to be estimated. If growth is simulated using the basic water balance model, the initial area of fine roots (FRA, m2) for layer s is estimated from leaf area using: FRA=FRPs⋅LAϕ⋅RLR where FRPs is the proportion of fine roots in layer s and RLR is the species-specific root area to leaf area ratio. Biomass of fine roots per individual for a given layer s (Bfineroot,s; gdry·ind−1) is then estimated from FRAs using: Bfineroot,s=104⋅FRAs2.0⋅√π⋅SRLρfineroot where ρfineroot is fine root tissue density (gdry⋅cm−3) and SRL (cm⋅gdry−1) is the specific root length. Fine root biomass per individual (gdry⋅ind−1) is simply the sum across layers: Bfineroot=∑sBfineroot,s If growth is simulated using the advanced water balance model, the initial fine root length per area in each soil layer (FLAs; m⋅m−2) is estimated from rhizosphere conductance, assuming a cylindrical flow geometry in the rhizosphere. The initial fine root biomass for a given layer s (gdry⋅ind−1) is then calculated using: Bfineroot,s=10000⋅FLAsN⋅0.01⋅SRL where N is the density of individuals. Finally, initial fine root area in each soil layer (FRAs) is then calculated from Bfineroot by inverting the equation presented above: FRAs=10−4⋅Bfineroot,s⋅2.0⋅√π⋅SRLρfineroot
16.1.4 Total living biomass
Total living biomass per individual (i.e. not accounting for heartwood or xylem conduits) is: Btotal=Bleaf+Bliving,sapwood+Bfineroot++Bsugar,leaf+Bstarch,leaf+Bsugar,sapwood+Bstarch,sapwood Btotal is used to express carbon balance components per dry weight of living biomass in the model output, which allows a better comparison across plant cohorts of different size and species.
16.2 Components of labile carbon balance
Here we provide the details of labile carbon balance calculations, i.e. how the components of eqs. (15.1) and (15.2) are determined.
16.2.1 Gross photosynthesis
The soil water balance submodel provides values of photosynthesis calculated at the plant cohort level, but note that the user output of function spwb
and pwb
refers to net photosynthesis (An) after accounting for an estimate of leaf respiration. In the basic water balance model there is no way to make the distinction between gross and net photosynthesis, so we will assume here that Ag=An (in gC⋅m−2) as calculated in section 6.1.6. In the advance water balance model the output is also net photosynthesis, but the distinction is possible (see section 11.1). In any case, here we start with a Ag value in units of carbon per ground area unit, i.e. gC⋅m−2, and to enter the carbon balance we need scale photosynthesis to units of glucose per individual (A; in ggluc⋅ind−1). This is done using:
A=10000⋅AgN⋅mglucmcarbon⋅6
where N is the density of individuals per hectare, mgluc is the glucose molar mass and mcarbon is the carbon molar mass.
16.2.2 Maintenance respiration
Maintenance respiration (in ggluc·ind−1) is calculated for each of the three compartments (leaves, sapwood, and fine roots) individually (Mouillot et al. 2001), and differs slightly depending on the complexity of the transpiration submodel.
When simulating growth with the basic water balance, the model uses a Q10 relationship of baseline respiration with temperature, which means that for every 10 ºC change in temperature there is a Q10 factor change in respiration: Mleaf=(Bleaf+Bsugar,leaf)⋅MRleaf⋅Q(Tmean−20)/1010⋅(LPAR)WUEdecayMsapwood=(Bliving,sapwood+Bsugar,sapwood)⋅MRsapwood⋅Q(Tmean−20)/1010Mfineroot=Bfineroot⋅MRfineroot⋅Q(Tmean−20)/1010⋅(LAi/LAlivei) where Tmean is the average daily temperature (in ºC). Baseline maintenance respiration rates per dry biomass (MRleaf, MRsapwood and MRfineroot for leaves, parenchymatic sapwood and fine roots, respectively; in ggluc⋅gdry−1⋅day−1) are can be supplied via species-specific parameters and should refer to 20 ºC. Leaf and fine root rates can also be estimated from nitrogen concentration, following Reich et al. (2008) (see section A.3.18). Factor Q10 has been found to decrease with temperature (Tjoelker et al. 2001). For example, a 10 °C increase in measurement temperature at low measurement temperatures from 5 to 15 °C results in an approximate 2.8 fold increase in respiration rate, whereas an increase in temperature from 25 to 35 °C results in a less than two-fold (1.8) increase in rate. The general temperature relationship proposed by Tjoelker et al. (2001) is used here: Q10=3.22−0.046⋅Tmean Factor (LPAR)WUEdecay is added to reduce respiration rates in leaves under shade, analogously to the reduction of water use efficiency explained in 6.1.6. Thus, it is assumed that the carbon use efficiency of the leaves is more or less constant. Factor LAi/LAlivei is added to the maintenance respiration of fine roots to reduce respiration rates during winter in winter-deciduous species, assuming a decrease in respiration rates of fine roots parallel to that of leaves.
When simulating growth with the advanced model, sub-daily leaf maintenance respiration rates are estimated as the difference between gross and net photosynthesis (see 11.1.4). Sapwood and fine root respiration rates are also estimated at sub-daily steps and, hence, sub-daily canopy temperature variation is taken into account (i.e. sub-daily canopy Tcan values are used instead of the daily temperature mean, Tmean).
16.2.3 Growth respiration
Construction costs per unit dry weight of new tissue (CCleaf, CCsapwood and CCfineroot for leaves, sapwood and fine roots; in ggluc⋅gdry−1) are specified as control parameters (i.e. they are not species-specific). These unitary costs include both the carbon used in respiration during growth and structural carbon. Given an increase in leaf area ΔLA, leaf growth respiration is: Gleaf=ΔLA⋅CCleaf⋅1000/SLA Analogously, given an increase in sapwood area ΔLA, sapwood growth respiration is: Gsapwood=ΔSA⋅CCsapwood⋅(H+∑sFRPs⋅Ls)⋅ρwood Finally, and given an increase in fine root biomass ΔBfineroot: Gfineroot=ΔBfineroot⋅CCfineroot
16.2.4 Phloem transport
When growth is simulated using the basic water balance model, phloem transport between leaf and sapwood (Fphloem) is simply modelled as the flow needed to make the concentration of metabolic carbon equal in both compartments. When the advanced water balance submodel is used, Fphloem is modelled following Hölttä et al. (2017). Specifically, the instantaneous phloem flow per leaf area basis (molgluc⋅m−2⋅s−1) depends on kphloem, i.e. the phloem conductance per leaf area basis (L⋅m−2⋅MPa−1⋅s−1), sap viscosity relative to water and the difference in turgor between the sieve cells of leaf and sapwood compartments. kphloem is estimated as linear function of stem maximum conductance, kstem,max:
kphloem=fphloem⋅kstem,max
where factor f_{phloem} is specified by the control parameter phloemConductanceFactor
. Sap viscosity is calculated following Först et al. (2002), which takes into account temperature and the average sugar concentration between the two compartments (no phloem flow can occur if temperature is below zero). Turgor in sieve cells of each compartment depends on symplastic water potential and osmotic water potential, with Van’t Hoff’s equation being used to calculate the osmotic water potential, based on temperature, sugar concentration and the concentration of other solutes (control parameter nonSugarConcentration
). Note that here leaf or sapwood sugar concentration is modulated to account for the effect of the relative water content of the compartment on osmotic water potential.
16.2.5 Sugar-starch dynamics
When growth is simulated using the basic water balance submodel, sugar-starch dynamics (SC_{leaf} and SC_{sapwood}) are simply defined as the conversion between metabolic and storage carbon needed to keep the sugar concentration equal to an equilibrium required for metabolic functioning, which is specified by control parameters equilibriumOsmoticConcentration
(including two values, for leaves and sapwood respectively) and nonSugarConcentration
. For example, if leaf osmotic equilibrium concentration is 0.8 mol\,gluc \cdot L^{-1} and non-sugar concentration is 0.3 mol\,gluc \cdot L^{-1}, the model will simulate sugar-starch dynamics to stabilize sugar concentration in leaves to 0.5 mol\,gluc \cdot L^{-1}. A lower equilibrium osmotic concentration is required for sapwood, by default 0.6 mol\,gluc \cdot L^{-1}, so that sugar equilibrium concentration is 0.1 mol\,gluc \cdot L^{-1}. That lower equilibrium concentrations are required for sapwood than for leaves is necessary to sustain the phloem transport of sugars from leaves towards sapwood.
When growth is simulated using the advanced water balance submodel, sugar-starch dynamics are similar to the previous case, in the sense that equilibrium sugar concentrations are sought for leaves and sapwood. However, instantaneous conversion rates are calculated depending on equations regulating starch synthesis (occurring when sugar concentration is higher than the equilibrium concentration) and starch hydrolysis (occurring when sugar concentration is lower than the equilibrium concentration). Synthesis is modelled as a Michaelis-Menten function, whereas hydrolysis rate is simply a linear function of starch concentration. Maximum synthesis rates and hydrolysis linear factors are larger (i.e. faster sugar-starch dynamics) in leaves than sapwood.
16.2.6 Root exudation
Whereas surplus in leaf storage capacity is relocated into sapwood storage, surplus in sapwood storage carbon is diverted towards root exudation (RE_{sapwood}). Hence, root exudation is not a process competing for metabolic carbon, but only a consequence of plant C storage capacity being surpassed (Prescott et al. 2020). Root exudation may happen in the model when growth is restricted due to sink limitations but photosynthesis continues and storage carbon levels have attained the storage capacity in the sapwood compartment (ST_{sapwood} > ST^{max}_{sapwood}).