Abiotic environment

A voxel space, with a resolution of 1 m³, is used to explicitly model the abiotic environment. For each tree crown, leaf area density is calculated on tree geometry assuming a uniform distribution across voxels occupied by the crown. Leaf area density is computed within each voxel summing all tree crowns inside the voxel v, and is denoted LAD(v) (leaf area per voxel in m².m⁻³). The vertical sum of LAD from voxel v to the ground level defines LAI(v) (leaf area per ground area in m².m⁻² commonly called leaf area index):

$LAI(v) = \sum _{v'=v} ^\infty LAD(v')$

Daily variations in light intensity (photosynthetic photon flux density PPFD in μmol_photons.m⁻².s⁻¹), temperature (T in degrees Celsius), and vapour pressure deficit (VPD in kPA) are computed to assess carbon assimilation within each voxel of the canopy and for a representative day per month (see Appendix 1 from @Li for further details). Variation of PPFD Within the canopy is calculated as a local Beer-Lambert extinction law:

PPFD_max, month(v) = PPFD_{top, max, month} * e^{−k * LAI(v)}

The daily maximum incident PPFD at the top of canopy PPFD_{top, max, month} is given as input. The extinction rate k is assumed as constant, besides its variation with zenith angle and species leaf inclination angle (Meir, 2000). Moreover only vertical light diffusion is considered ignoring lateral light diffusion, which can have an important role especially in logging gaps. Finally, intra-day variation at half hour time steps t for a representative day every month are used to compute PPFD_month(v, t), T_month(v, t) and VPD_month(v, t). Water and nutrient processes both in soil and inside trees are not simulated.

Photosynthesis

Autotrophic respiration

A large fraction of plants carbon uptake is actually used for plant maintenance and growth respiration. The autotrophic respiration can represent up to 65% of the gross primary productivity but varies strongly among species, sites, and environments.

TROLL uses Atkin et al. (2015) database of mature leaf dark respiration and associated leaf traits to compute leaf maintenance respiration:

R_{leaf − M} = 8.5431 − 0.1306 * N − 0.5670 * P − 0.0137 * LMA + 11.1 * V_{cmax − M} + 0.1876 * N * P

R_{leaf − M} is the dark respiration rate per leaf dry mass at a temperature of 25^∘C (nmolCO₂.g⁻¹.s⁻¹). TROLL assumes leaf respiration during daylight to be 40% of leaf dark respiration, and computes total leaf respiration by accounting for the length of daylight.

TROLL model stem respiration (R_stem in μmolC.s⁻¹) with a constant respiration rate per volume of sapwood:

R_stem = 39.6 * π * ST * (dbh − ST) * (h − CD)

dbh, h, CD and ST are tree diameter at breast height, height, crown depth and sapwood thickness, respectively (m). TROLL assumes ST = 0.04 m when dbh > 30 cm and an increasing ST for lower dbh.

Finally, TROLL computes both fine root maintenance respiration, as half of the leaf maintenance respiration. Whereas coarse root and branch maintenance respiration is computed as half of the stem respiration. And growth respiration (R_growth) is assumed to account for 25% of the gross primary productivity minus the sum of maintenance respiration.

Net carbon uptake

Net primary production of carbon for one individual NPP_ind (gC) is computed by the balance between gross primary production GPP_ind and respiration R:

NPP_ind = GPP_ind − R_maintenance − R_growth

TROLL partitions individuals’ total leaf area LA into three pools for different leaf age classes corresponding to different photosynthesis efficiency (young, mature and old leaves with LA_young, LA_mature, and LA_old respectively). Consequently we can compute growth primary production for one individual as:

$GPP_{ind} = 189.3 * \Delta t * \sum _{l= \lfloor h-CD \rfloor +1} ^{\lfloor h \rfloor} [A_l] * (\frac{LA_{young}}{2} + LA_{mature} + \frac{LA_{old}}{2})$

h and CD are tree height and crown depth, respectively (m). ⌊x⌋ is the rounding function. Δt is the duration of a timestep (year).

Thus, TROLL can compute carbon allocation to wood into an increment of stem volume ΔV (m³):

$\Delta V = 10^{-6} * \frac{f_{wood}*NPP_{ind}}{0.5*wsg}*Senesc(dbh)$

f_wood is the fixed fraction of NPP allocated to stem and branches. wsg is the wood specific gravity (g.cm⁻³, see @ref(tab:traits)). TROLL assume large trees less efficient to convert NPP as growth by using a size-related growth decline with function Senesc after a specific diameter at breast height threshold dbh_thresh:

$Senesc(dbh) = max(0;3-2*\frac{dbh}{dbh_{thresh}})$

Finally, TROLL can compute carbon allocation to canopy with canopy NPP fraction denoted f_canopy and decomposed into leaf, twig and fruit production. Carbon allocation to leaf results in a new young leaf pool, whereas other leaf pools are updated as follow:

$\begin{array}{c} \\ \Delta LA_{young} = \frac{2*f_{leaves}*NPP_{ind}}{LMA}-\frac{LA_{young}}{\tau_{young}} \\ \Delta LA_{mature} = \frac{LA_{young}}{\tau_{young}} - \frac{LA_{mature}}{\tau_{mature}}\\ \Delta LA_{old} = \frac{LA_{mature}}{\tau_{mature}} - \frac{LA_{old}}{\tau_{old}} \end{array}$

τ_young, τ_mature, and τ_old are species’ residence times in each leaf pool (years). The sum of residency time thus defined the leaf lifespan LL = τ_young + τ_mature + τ_old (years). τ_young is set to one month and τ_mature is set to a third of leaf lifespan LL. Belowground carbon allocation is not simulated inside TROLL.

Tree growth

Once the increment of stem volume ΔV is calculated, TROLL converts it into an increment of tree diameter at breast height denoted Δdbh. TROLL infer tree height from dbh using a Michaelis-Menten equation:

$h = h_{lim}*\frac{dbh}{dbh + a_h}$

On the other hand, we have the trunk volume $V = C * \pi * (\frac{dbh}{2})^2*h$, thus:

$\begin{array}{c} \\ \Delta V = C*\frac{1}{2}*\pi*h*dbh*\Delta dbh + C * \pi * (\frac{dbh}{2})^2*h \\ \Delta V = V*\frac{\Delta dbh}{dbh}*(3-\frac{dbh}{dbh + ah})\end{array}$

Next, TROLL used the new trunk dimension (dbh and h) to update tree crown geometry using allometric equations (Chave et al. 2005):

$\begin{array}{c} \\ CR = 0.80 + 10.47*dbh - 3.33*dbh^2\\ CD = -0.48 + 0.26*h~;~CD = 0.13 + 0.17*h~(h<5~m)\end{array}$

Finally, TROLL computes the mean leaf density within the crown (LD in m².m⁻³) assuming a uniform distribution:

$LD = \frac{LA_{young}+LA_{mature}+LA_{old}}{\pi*CR^2*CD}$

Mortality

Mortality is partitioned in two factors inside TROLL: background death d_b and treefall death d_t.

Chave et al. (2009) advocated for a wood economics spectrum opposing fast growing light wood species with high risk of mortality to slow growing dense wood species with reduced risk of mortality. Hence, background mortality is derived from wood specific gravity wsg inside TROLL:

$d_b = m*(1-\frac{wsg}{wsg_{lim}})+d_n$

m (events.year⁻¹) is the reference background death rate for lighter wood species (pioneers). d_n represents death by carbohydrates shortage. If the number of consecutive days with NPP_ind < 0 is superior to tree leaf lifespan d_n is set to 1 and remains null in other cases.

Mortality by treefall inside TROLL depends on a specific stochastic threshold θ:

θ = h_max * (1 − v_T * |ζ|)

h_max is the maximal tree height. v_T is the variance term set to 0.3. |ζ| is the absolute value of a random centred and scaled Gaussian. If the tree height h is superior to θ then the tree may fall with a probability 1 − θ/h (Chave 1999). The treefall direction is random (drawn from a uniform law (𝒰[0, 2π]). All trees in the trajectory of the falling tree will be hurted through a variable denoted hurt, incremented by fallen tree height h. If a tree height is inferior than its hurt values then it may die with a probability $1-\frac{1}{2}\frac{h}{hurt}$. hurt variable is reset to null at each timestep (month).

Recruitment

Once the tree becomes fertile they will start to disperse seeds. TROLL consider tree as fertile after a specific height threshold h_mature (Wright et al. 2005):

h_mature = −11.47 + 0.90 * h_max

But TROLL is not considering seed directly through a seedbank, instead seed might be interpreted as a seedling recruitment opportunity. The number of reproduction opportunities per mature tree is denoted n_s and set to 10 for all species. This assumption originates from a trade-off between seed number and seed size resulting in equivalent survival and recruitment probability. All n_s events are dispersed with a distance randomly drawn from a Gaussian distribution. Additionally, TROLL model consider external seedrain through n_ext events of seed immigration:

n_ext = N_tot * f_reg * n_ha

N_tot is the external seedrain per hectare (number of reproduction opportunities). f_reg is the species’ regional frequency. n_ha is the simulated plot size in ha.

Finally, a bank of seedlings to be recruited is defined for each pixel. If the ground-level light reaches a species light compensation point LCP the species will be recruited:

$LCP = \frac{R_{leaf}}{\phi}$

R_leaf is the leaf respiration for maintenance. ϕ is the quantum yield (μmolC.μmol photon) set to 0.06. If several species reach their LCP, one is picked at random. Seedlings are recruited with following initial geometry:

$\begin{array}{c} \\ dbh = \frac{a_h}{h_{max} - 1}\\ h = 1~m\\ CR = 0.5~m\\ CD = 0.3~m\\ LD = 0.8~m^2.^{-3} \end{array}$

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