Rainfall (P, mm) is a model input. It is assumed that the total daily rainfall corresponds to a single event of rain per day (one storm, as in e.g. Rodriguez-Iturbe et al., 1999; Laio et al., 2001; Fischer et al., 2014; Gutiérrez et al., 2014).

Rainfall interception by the canopy is simulated using a model where interception depends on LAI, as proposed by Liang et al. (1994): 11I=min⁡P,K×LAI, where K=0.2 mm and LAI corresponds to the leaf area index at ground level, averaged across the ground-level aboveground voxels that contribute to a single belowground voxel (typically 625 = 25² aboveground voxels contribute to one belowground voxel). Similar simple formulations of canopy interception have been used elsewhere (e.g. Liu et al., 2017), and this choice is justified by the lack of relevant data to properly parameterize more complex formulations at most field sites. More complex models of rainfall interception also exist, however (Rutter and Morton, 1977; Gash, 1979; Gash et al., 1995).

As in most bucket models coupled with a forest dynamics model, the temporal propagation of the wetting front into the soil is not explicitly simulated here because of the daily time step and the vertically lumped representation of soil moisture dynamics (e.g. Laio et al., 2001; Guimberteau et al., 2014). When the soil top layer has enough available storage to absorb the totality of the throughfall (i.e. when throughfall is smaller than the layer water content at field capacity minus the current soil water content), it is assumed that the increment in soil water content of that top layer is equal to the throughfall. Otherwise, the excess water percolates to the next layer below (L1→2 in Eq. 10a). In the absence of an explicit wetting front, run-off occurs only when the superficial layer is already saturated, which is similar to Dunne run-off (Dunne and Black, 1970). More complex formulations of run-off exist (d'Orgeval et al., 2008; Guimberteau et al., 2014; Horton, 1933), but because of the high porosity of many tropical forest soils (Hodnett and Tomasella, 2002; Sander, 2002) and the lack of explicit topography in this version, our choice is parsimonious.

We assumed that water evaporates from the topsoil layer only, a reasonable assumption if the topsoil layer is not too thin. We followed Sellers et al. (1992) under which evaporation from the soil is expressed as (see Merlin et al., 2016 for a review of alternatives) 12E=MwRTs×es-earsoil+raero, where E is in kg m⁻² s⁻¹, Mw is the molar mass of water vapour (Mw=18 kg mol⁻¹), R is the ideal gas constant (R=8.31 J mol⁻¹ K⁻¹), Ts is the temperature at the soil surface in Kelvin computed using Eq. (4) at ground level, es is the vapour pressure of the soil surface in Pa, ea is the vapour pressure of air above the soil surface in Pa, rsoil is the soil surface resistance in s m⁻¹, and raero is the aerodynamic resistance to heat transfer in s m⁻¹. Soil water pressure es is a function of the water potential of the topsoil belowground voxel (ψsoil,top – MPa; Jones, 2013, Eq. 5.14 therein): 13es=esatTs×exp⁡VwRTs×ψsoil,top=esatTs×exp⁡2.17×ψsoil,topTs, where Vw is the partial molal volume of water (Vw=18×10-6 m³ mol⁻¹), and esatTs is the saturated vapour pressure at Ts computed following the Buck equation (Jones, 2013, Appendix 4 therein). ea is by definition equal to esatTs-VPDground, where the latter is the VPD at ground level in Pa. rsoil is computed following Sellers et al. (1992, Eq. 19 therein, see also Merlin et al., 2016, Eq. 12): 14rsoil=exp⁡8.206-4.255×θtopθfc,top, where θtop is the water content of the topsoil belowground voxel and θfc,top is its water content at field capacity (in m³). Aerodynamic resistance raero is computed as follows (Merlin et al., 2016, Eq. B10 therein): 15raero=1κ2×uZln⁡ZZm2, with κ again being the von Kármán constant (κ=0.40), uZ the wind seed (in m s⁻¹) at reference height Z, here taken at 1 m above ground, and Zm the momentum soil roughness in metres, set to 0.001 m.

Trees transpire soil water from the belowground voxel they are rooted in (see Sect. 2.4.3). For a given tree, the total daily soil water uptake is the sum of the water transpired by leaves across its crown and across daytime half-hours (see Sect. 2.5.2). Soil layers contribute to water uptake as a function of tree-dependent weights, wl (see Eq. 21, Sect. 2.4.3), which depend on root biomass and on the soil hydraulic state in each layer.

For each belowground voxel in layer l, the soil water potential (ψl) and the soil hydraulic conductivity (Kl) are computed at each time step from the soil water content in the focal voxel using the van Genuchten–Mualem soil characteristic and hydraulic conductivity curves (Mualem, 1976; van Genuchten, 1980; see Table 1 in Marthews et al., 2014). Parameters of these curves are estimated using regression models (pedotransfer functions) for tropical soils (Hodnett and Tomasella, 2002), except the saturated hydraulic conductivity, which is computed following Cosby et al. (1984; see Table 2 in Marthews et al., 2014). In practice, when only soil texture data are available, TROLL 4.0 contains a default option to apply the texture-based-only pedotransfer function provided by Tomasella and Hodnett (1998), coupled to the soil characteristic and hydraulic conductivity curves of Brooks and Corey (1964) (see Tables 1 and 2 in Marthews et al., 2014).

In TROLL 4.0, each tree (and seed) is attributed a botanical species defined by a taxonomic binomial. It is assumed that the user has sufficiently good knowledge of the tree species growing in the study area so that a list of species-specific mean plant functional trait values can be provided as input. These are the leaf mass per area (LMA, in g m⁻²), the leaf area (LA, cm²), the leaf nitrogen content per dry mass (N, in mg g⁻¹), the leaf phosphorous content per dry mass (P, in mg g⁻¹), the wood specific gravity (wsg, in g cm⁻³), the leaf water potential at turgor loss point (πtlp, in MPa), and three allometric parameters (dbh_thres, hlim, ah, all in metres; see Sect. 2.4.2). The number of species provided as input is not limited. In addition to mean plant functional trait values, it is possible to input individual trait values from which a trait variance–covariance matrix is computed (alternatively the trait variance–covariance matrix can be prescribed). With this option, for each recruited tree, the trait values are drawn from a distribution rather than attributed the species-specific mean value. For each trait i and tree j, the species-specific mean value is multiplied by a factor eεi,j, where εi,j∼N(0,σi) and σi is the trait-specific standard deviation on a logarithmic scale (lognormal variation). The sole exception is wood specific gravity, which we assume to be normally distributed around the mean with εwsg,j∼N(0,σwsg). Trait covariance is only considered for leaf N, leaf P, and LMA, and other traits are assumed to be decoupled (Baraloto et al., 2010b). Note that with this implementation, intraspecific variation is not heritable or structured in space or time, and it is thus a surrogate for variability emerging from genetic variation or plasticity (Girard-Tercieux et al., 2023, 2024). A more realistic representation of the latter, especially light-driven trait plasticity along the vertical canopy gradient (Lamour et al., 2023b; Lloyd et al., 2010), is left for a future version.

Above ground, the tree geometry is represented as a three-dimensional object within the voxelized space and consists of a trunk and a crown filled with leaves. The trunk is assumed to be a cylinder characterized by its total height and its diameter (dbh, for diameter at breast height, by analogy with forest inventories). The aboveground dimensions of trees are predicted from their dbh via scaling rules. For tree j with dbh_j, we calculate its height hj, its crown radius cr_j, and its crown depth cd_j as follows. 16hj=hlim×dbhjah+dbhj×eεh,j17crj=eacr×dbhbcr×eεcr,j18cdj=minhj2,(acd+bcd×hj)×eεcd,j Here, hlim and ah are species-specific coefficients of the Michaelis–Menten function, and acr, bcr, acd, and bcd are allometric coefficients that are species-independent. εh,j, εcr,j, and εcd,j are tree-level variance terms to simulate intraspecific variation that are randomly drawn at tree birth with εh,j∼N(0,σh), εcr,j∼N0,σcr, and εcd,j∼N(0,σcd). Tree crown architecture is known to depend on species ecological strategies (Bohlman and O'Brien, 2006; Iida et al., 2012; Poorter et al., 2006; Laurans et al., 2024), but given that crown extents are difficult to measure reliably in the dense canopies of tropical forests, we used a single set of parameters for all the species.

In the previously published version (Maréchaux and Chave, 2017), tree crowns were represented as cylinders with homogeneous leaf densities. Since v.3.0, TROLL has also been able to model tree crowns as flexible, umbrella-like shapes with heterogeneous leaf density distributions. Small tree crowns are simulated as cylinders but consist of up to three separate 1 m layers of leaves (top, intermediate, and bottom layer). Each layer can be assigned a percentage of the total leaf area (which results from the processes of carbon allocation to leaf production and leaf shedding, see Sect. 2.6.2) to reflect gradients in leaf densities from the upmost to lower crown layers (e.g. 50 %, 30 %, 20 %; Kitajima et al., 2005), but the default is an equal distribution (33 %, 33 %, 33 %) across all layers. Once a tree surpasses 3 m in crown depth, no new layers are added. In this case, tree height directly above the tree stem (tree top height) and crown extent are derived using the same allometric equations (Eqs. 16–18), but, instead of the flat tops of small trees, it is now possible to prescribe a change in height from the centre of the crown to the crown's edges. Different geometric forms are available to describe this variation, but here we chose a simple linear decrease between the radius at the top of the crown and the radius at the bottom of the crown. The ratio between the two radii is controlled through the global parameter shape_crown, which varies between 0 (conical shape) and 1 (cylinder) and thus allows for various “conifer-like” and “broadleaf-like” shapes in between. Within the first 3 m of the resulting crown shape, leaves are allocated as before and folded around the tree trunk like an umbrella at various stages of opening (see Fig. 1b in Schmitt et al., 2023, and similar tree representations in Strigul et al., 2008). The crown shape only affects the geometry of the crown, not the amount of total leaf area allocated to it (see Sect. 2.6.2).

We also relax the assumption that tree crowns are homogeneously filled across their horizontal extent. In TROLL 4.0, crowns have small 1 m² openings (or gaps) in their crowns, parameterized as a percentage of total crown area that is not filled with leaves, fgap. This allows for the modelling of a spatially heterogeneous light environment in the understorey (Tymen et al., 2017), with a theoretical range from fgap=0 % (full crown cover, no openings) to fgap=100 % (a hypothetical crown with no leaf area). When calibrating TROLL for tropical forests with airborne laser scanning (Fischer et al., 2019), we found a value of fgap=15 % to be a good approximation for this within-crown gap fraction. If intraspecific variation in crown extent is explicitly modelled, the fraction of crown gaps is rescaled so that the absolute crown cover stays constant (i.e. the fraction of crown gaps is divided by e2εcr,j). Within species and for trees with the same stem size (i.e. similar total sapwood area), crown extent is thus assumed to be decoupled from variation in leaf area, i.e. reflecting variation in branch angles and directions, but not branch number or biomass.

As in other models (e.g. Xu et al., 2016), TROLL 4.0 makes the assumption that total fine root biomass is equal to leaf biomass. Future developments should endeavour to represent a more explicit belowground allocation scheme (Merganičová et al., 2019; Huaraca Huasco et al., 2021). Direct estimates of individual tree root depth and root distribution are rare in moist tropical forests (Canadell et al., 1996; Jackson et al., 1996, 1999; Nepstad et al., 1994; Cusack et al., 2024; Guerrero-Ramírez et al., 2021). Some studies have quantified the depth of tree water uptake using indirect methods, such as pre-dawn leaf water potential, or isotope labeling (Brum et al., 2019; Stahl et al., 2013a), but this does not give access to the actual rooting depth. Tree root depth was assumed here to increase with tree size and was computed as a function of tree dbh as follows (Kenzo et al., 2009, Fig. 4 therein): 19RD=0.35×dbh0.54, with root depth (RD, m) and diameter at breast height (dbh, cm). As in Xu et al. (2016), the exponent was based on Kenzo et al. (2009), who reported on data from excavated trees in secondary forests in Malaysia. The first parameter (0.35, root depth at dbh = 1 cm) was adjusted to avoid unrealistic water depletion of the topsoil layer. In the absence of relevant species-specific data, this allometric equation was assumed to hold for all species, even if root depth is known to be highly plastic (e.g. Rowland et al., 2023). Correlations between rooting depth and leaf phenological habit have been reported, but in drier or more seasonal sites than Amazonian rainforests (Brum et al., 2019; Hasselquist et al., 2010; Smith-Martin et al., 2020), and trait coordinations are known to be typically stronger under harsher environmental conditions (Dwyer and Laughlin, 2017; Delhaye et al., 2020).

We assumed that vertical tree root distribution follows an exponential profile, as observed empirically at the stand scale (Fisher et al., 2007; Humbel, 1978; Jackson et al., 1996). The fine root biomass in layer l, at depths ranging from zl to zl+1>zl, is computed as 20RBl=RBt×exp⁡-3zlRD-exp⁡-3zl+1RD, where RB_t is the total tree fine root biomass (g), RB_l the fine root biomass in layer l (g), and RD the tree rooting depth (m). The factor 3 was determined so that about 95 % of the root biomass is contained between the soil surface and RD (note that -log(0.05) ≈ 3) (Arora and Boer, 2003). Tree roots are distributed across vertical layers but do not spread across belowground voxels horizontally. This assumption was considered a first parsimonious representation given the size of belowground voxels and the scarcity of data on root horizontal distribution worldwide, particularly in tropical biomes (see Cusack et al., 2024, where root horizontal distribution is not mentioned, but see Schenk and Jackson, 2002, for data on water-limited systems). As a result, trees only deplete the water content of the belowground voxels located below their trunk position and thus compete for water with trees sharing the same belowground voxels only (see Sect. 2.3), but this could easily be revisited in the future.

The soil water potential in the root zone, ψroot (in MPa), captures how the plant equilibrates with the soil water state across its root profile. It is computed as the weighted mean of the belowground voxel water potentials across layers. We used the weighting scheme proposed by Williams et al. (2001; see also Bonan et al., 2014; Duursma and Medlyn, 2012), which accounts for the variation of soil water availability and conductance across layers as follows: 21ψroot=∑lwl×ψl with wl=ψl-ψR,min×Gl∑llψll-ψR,min×Gll, where ψl is the soil water potential in layer l, and ψR,min is the root water potential below which there is no water uptake within the layer (minimal root water potential, assumed to be -3 MPa as in Duursma and Medlyn, 2012). Gl, the soil-to-root water conductance in layer l, in mmol H₂O m⁻² s⁻¹ MPa⁻¹, is computed as follows (Gardner, 1964). 22Gl=2πLa,lKllog⁡rsrr In Eq. (22), La,l is the total root length per unit area in the layer (in m m⁻²), with the total root length in the layer computed as RBl×SRL where SRL is the specific root length, here assumed to be constant (10 m g⁻¹, Bonan et al., 2014; Metcalfe et al., 2008; Weemstra et al., 2016). Kl is the soil hydraulic conductivity of layer l (in mmol H₂O m⁻¹ s⁻¹ MPa⁻¹, see Sect. 2.3), rr is the mean fine root radius, here set at 1 mm, and rs is half the mean distance between roots, calculated with the assumption of uniform root spacing in a given layer (Newman, 1969): 23rs=1πLv,l, where Lv,l is the total root length per unit soil volume in the layer (in m m⁻³), computed in the same way as La,l, but also divided by layer depth.

A range of other models have been used to infer ψroot using the relative tree root biomass in each layer directly as weights (De Kauwe et al., 2015a; Naudts et al., 2015; Powell et al., 2013; Schaphoff et al., 2018; Sakschewski et al., 2021; Verbeeck et al., 2011). However, trees do not take up water simply as a proportion of root density but can equilibrate with the wettest soil layers (Schmidhalter, 1997; Duursma and Medlyn, 2012): the contrasting temporal variations in water availability across layers result in seasonal changes in the depth of active water withdrawal (Bruno et al., 2006; Joetzjer et al., 2022). For instance, cavitation in the driest part of the soil disconnects roots from the soil (Sperry et al., 2002; see also Fisher et al., 2006). This is likely why deeper roots, although often very rare, disproportionately contribute to sustaining forest productivity during dry seasons.

In Farquhar et al. (1980), the leaf-level net carbon assimilation rate (An, µmol CO₂ m⁻² s⁻¹) is limited by either Rubisco activity (Av, µmol CO₂ m⁻² s⁻¹) or RuBP regeneration (Aj, µmol CO₂ m⁻² s⁻¹): 24An=min⁡Av,Aj-RpTl;Av=VcmaxTl,ψpd×ciΓ∗ci+KmTl;Aj=J4ci-Γ∗Tlci+2Γ∗Tl, where Rp is the photorespiration rate (µmol C m⁻² s⁻¹), Vcmax the maximum rate of carboxylation (µmol CO₂ m⁻² s⁻¹), ci the CO₂ partial pressure at carboxylation sites, Γ∗ the CO₂ compensation point in the absence of dark respiration, Km the apparent kinetic constant of the Rubisco (von Caemmerer, 2000), and J the electron transport rate (µmol e- m⁻² s⁻¹), which depends on PPFD through 25J=12θα×PPFD+Jmax⁡Tl,ψpd-α×PPFD+Jmax⁡Tl,ψpd2-4θ×α×PPFD×Jmax⁡Tl,ψpd. Jmax⁡ is the maximal electron transport capacity (µmol e- m⁻² s⁻¹), θ the curvature factor (unitless), and α the apparent quantum yield to electron transport (mol e- mol photons⁻¹), computed following von Caemmerer (2000) as α=1-LSQ×0.5, with LSQ the effective spectral quality of light, fixed at 0.15, and the factor 0.5 accounting for the fact that each photosystem absorbs half of the photons.

The Vcmax and Jmax parameters depend on leaf properties, leaf temperature (Tl), and water state (through the leaf pre-dawn water potential, ψpd; see Eq. 37) and represent a large source of uncertainty in vegetation models (Zaehle et al., 2005; Mercado et al., 2009; Rogers et al., 2017). In tropical forest environments, Domingues et al. (2010) suggested that Vcmax and Jmax⁡ are co-limited by the leaf concentration of nitrogen and phosphorus as follows (see also Walker et al., 2014): 26Vcmax-M25°C=min⁡-1.56+0.43×N-0.37×LMA;-0.80+0.45×P-0.25×LMA,27Jmax-M25°C=min⁡-1.50+0.41×N-0.45×LMA;-0.74+0.44×P-0.32×LMA, with Vcmax-M and Jmax-M the photosynthetic capacities at 25 °C of unstressed mature leaves on a leaf dry mass basis, in µmol CO₂ g⁻¹ s⁻¹ and µmol e- g⁻¹ s⁻¹, respectively. N and P are leaf nitrogen and phosphorus concentrations in mg g⁻¹, and LMA is the leaf mass per area in g cm⁻². Vcmax-M and Jmax-M can be converted into area-based Vcmax and Jmax⁡ by multiplying by LMA. We used this leaf-trait-based parameterization of Vcmax25°C and Jmax⁡25°C in the absence of water stress (as in Fyllas et al., 2014; Mercado et al., 2011). The dependence of Vcmax and Jmax⁡ on temperature was given by equations in Bernacchi et al. (2003), and the dependence on water availability was modelled by a function of ψpd (WSFns, see Sect. 2.5.3, Eq. 40). 28VcmaxTl,ψpd=Vcmax25°C×e(26.35-65.33R×Tl+273.15)×WSFnsψpd29Jmax⁡Tl,ψpd=Jmax⁡25°C×e(17.57-43.54R×Tl+273.15)×WSFnsψpd R is the molar gas constant (0.008314 kJ K⁻¹ mol⁻¹), and Tl is the leaf temperature in degrees Celsius. The temperature dependence of Γ∗ and Km followed von Caemmerer (2000). 30Γ∗Tl=37×e23.4×Tl-25298×R×273+Tl31KmTl=404×e59.36×Tl-25298×R×273+Tl×1+210248×e35.94×Tl-25298×R×273+Tl Temperature dependencies in Eqs. (28)–(31) are consistent with Domingues et al. (2010), following recommendations from Rogers et al. (2017).

The leaf photorespiration rate Rp (Eq. 24) was assumed to be a fixed fraction (40 %) of the leaf dark respiration rate (Eqs. 32–33; Atkin et al., 2000). We used the Atkin et al. (2015) “broadleaved trees” empirical model to estimate mature leaf dark respiration rates as a function of plant functional traits: 32Rd-M25°C=8.5341-0.1306×N-0.5670×P-0.0137×LMA+11.1×Vcmax-M+0.1876×N×P, with Rd-M the leaf dark respiration rate on a dry mass basis and at a reference temperature of 25 °C (in nmol CO₂ g⁻¹ s⁻¹). Multiplying Rd-M by LMA gives the area-based leaf dark respiration Rd (in µmol C m⁻² s⁻¹). The temperature dependence of mature leaf dark respiration rates was calculated as (Atkin et al., 2015, Eq. 1 therein; see also Heskel et al., 2016) 33Rd(Tl)=Rd25°C×3.09-0.043×(Tl+25)2Tl-2510. Long-term acclimation to temperature is not considered in TROLL 4.0 (Kattge and Knorr, 2007; Smith and Dukes, 2013).

Carbon assimilation by photosynthesis is limited by the CO₂ partial pressure at carboxylation sites, which is controlled by stomatal transport as modelled by the diffusion equation: 34An=gscs-ci, with gs the stomatal conductance to CO₂ (mol CO₂ m⁻² s⁻¹). The representation of stomatal conductance varies greatly across vegetation models (Damour et al., 2010; Bonan et al., 2014; Rogers et al., 2017; see Appendix B, Table B1) and remains an active research topic (Anderegg et al., 2018; Dewar et al., 2018; Lamour et al., 2022; Sperry et al., 2017; Wolf et al., 2016; Sabot et al., 2022). In TROLL 4.0, stomatal conductance to water vapour is simulated as (Medlyn et al., 2011) 35gsw=g0+1.6×1+g1VPDs×Ancs, where gsw is the stomatal conductance to water vapour in mol H₂O m⁻² s⁻¹, 1.6 is the ratio of the diffusivities of H₂O to CO₂ (Massman, 1998), VPDs is the vapour pressure deficit at the leaf surface in kPa, An is the assimilation rate in µmol CO₂ m⁻² s⁻¹ (Eq. 24 above), cs is the CO₂ concentration at the leaf surface in ppm, g0 is the minimum conductance for water vapour in mol H₂O m⁻² s⁻¹ (Duursma et al., 2019), and g1 is a model parameter in kPa^1∕2. Equations (24), (34), and (35) taken together lead to two quadratic equations for ci, one when Rubisco activity is limiting and one when RuBP regeneration is limiting, and the solution is the highest root.

The parameter g1 varies with species ecological strategies and carbon cost of water use (Domingues et al., 2014; Franks et al., 2018; Héroult et al., 2013; Lin et al., 2015; Wolz et al., 2017). Consequently, it is expected that g1 should differ across plant functional types (e.g. Xu et al., 2016). Here we assumed a dependence of g1 on wood density (wsg, in g cm⁻³) as in Lin et al. (2015). We also assumed a dependence on water availability, modelled by a function of ψpd (WSFs; see Sect. 2.5.3). 36g1=-3.97×wsg+6.53×WSFsψpd This parameterization of g1 based on wood density is a matter of debate, however, and alternatives have been proposed (Wu et al., 2020; Lamour et al., 2023a).

The parameter g0 quantifies water fluxes through the leaf cuticle (cuticular conductance) and from stomatal leaks. Although it is increasingly recognized as a key parameter explaining tree water loss in drought conditions (Cochard, 2021; Martin-StPaul et al., 2017), its values and variation with other functional traits are poorly documented (Duursma et al., 2019; Slot et al., 2021; Nemetschek et al., 2024), and here we assumed a fixed value. Note that some previous studies have defined g0 as cuticular conductance only, ignoring stomatal leak effects and thus underestimating g0.

Both g0 and g1 were assumed not to depend on temperature in the absence of clear empirical evidence for tropical forest trees (Duursma et al., 2019; Slot et al., 2021; Rogers et al., 2017), but this may be further explored in the future through measurements and experiments (Cochard, 2021).

Under water stress, leaf-level gas exchanges and photosynthesis are impaired, but how this is represented varies greatly across models (Appendix B, Table B1; Powell et al., 2013; Trugman et al., 2018; Verhoef and Egea, 2014). A common approach is to define a single integrative water stress factor cumulating all effects along the soil–plant–atmosphere pathway, some of which are difficult to evaluate empirically (e.g. Fischer et al., 2014; Gutiérrez et al., 2014; Krinner et al., 2005; Clark et al., 2011). This factor is then used to modify the parameters of the stomatal conductance and/or photosynthesis models (Egea et al., 2011; Verhoef and Egea, 2014). Depending on models, water stress factors have been assumed to depend on soil water content or on soil water potential in the root zone (De Kauwe et al., 2015a; Drake et al., 2017; Joetzjer et al., 2014; Powell et al., 2013; Trugman et al., 2018). Alternatively, some models have implemented a water stress factor as a function of leaf water potential (ψleaf; Anderegg et al., 2017; Christoffersen et al., 2016; Duursma and Medlyn, 2012; Kennedy et al., 2019; Xu et al., 2016; see also the pioneer work of Tuzet et al., 2003) or used optimization approaches (Williams et al., 1996; Anderegg et al., 2018; Sabot et al., 2020; Sperry et al., 2017; Wolf et al., 2016) to account for the cost of water uptake and transportation in the plant water column. The shape of such functions remains contentious, however (Table B1), resulting in substantial differences in model predictions.

Also, there is no consensus on the relative role of stomatal and non-stomatal limitations in leaf CO₂ assimilation under drying conditions, reflecting contrasting experimental results (Drake et al., 2017; Zhou et al., 2014; Keenan et al., 2010; Appendix B, Table B2). Under stomatal limitation, stomatal closure reduces leaf gas exchanges, and the water stress factor is applied to stomatal conductance or stomatal conductance model parameters (e.g. g1). Under non-stomatal limitations, drought (leading to increased leaf temperature and/or decreased leaf water potential) impairs the biochemical photosynthesis apparatus, which results in a reduction of photosynthetic capacities and/or mesophyll conductance (Flexas et al., 2004, 2012). In this latter case, the water stress factor is applied to Vcmax and Jmax⁡ (Drake et al., 2017; Keenan et al., 2010). Some models consider only one limitation and others both (Appendix B, Table B1).

In TROLL 4.0, two water stress factors are used, one for stomatal limitation, modifying the g1 parameter (WSFs; Eq. 36), and one for non-stomatal limitations, modifying the Vcmax and Jmax⁡ parameters of the photosynthesis model (WSFns; Eqs. 28 and 29). Both water stress factors are assumed to depend on the leaf pre-dawn water potential (ψpd; De Kauwe et al., 2015a; Verhoef and Egea, 2014), which is a function of the soil water potential in the root zone (ψroot, Eq. 21) (Stahl et al., 2013a, but see Bucci et al., 2004; Donovan et al., 2003) as follows (Jones, 2013; Eq. 4.9 therein): 37ψpd=ψroot-ρgh≃ψroot-0.01×h, where ρ is the density of water, g the gravitational force (g=9.81 m s⁻²), and h total tree height in metres. Here, WSFs was computed as (Zhou et al., 2013; De Kauwe et al., 2015a) 38WSFs=exp⁡b×ψpd, where b is a parameter. To parameterize b, we used the relationship between the leaf water potential at turgor loss point (πtlp in MPa) and the water potential causing 90 % of stomatal closure (ψgs90, in MPa): πtlp=0.97×ψgs90 (P<0.01, R2=0.4; Fig. 1 in Martin-StPaul et al., 2017) and assumed that WSFs≈0.1 at ψgs90 (an approximation given the shape of Eq. 35), leading to 39WSFs=exp⁡-2.23×ψpdπtlp.

The link between the leaf water potential at stomatal closure and the leaf water potential at turgor loss point is supported by several studies (Bartlett et al., 2016b; Brodribb et al., 2003; Farrell et al., 2017; Martin-StPaul et al., 2017; Meinzer et al., 2016; Rodriguez-Dominguez et al., 2016; Trueba et al., 2019). The formulation of WSFs in Eq. (39) was preferred over alternatives, such as a linear relationship between WSFs and ψpd (Oleson et al., 2008; Powell et al., 2013; Verhoef and Egea, 2014). The latter is less supported by data and leads to threshold responses as soil water content declines and similar responses across species, in contrast with empirical evidence (Kursar et al., 2009; Zhou et al., 2013). The water stress factor for non-stomatal limitation (WSFns) was computed following Xu et al. (2016): 40WSFns=1+ψpdπtlpa-1, with a=6 estimated from data reported in Brodribb et al. (2003). In this formula, WSFns=1/2 when ψpd=πtlp, in agreement with empirical findings (Brodribb et al., 2002; Manzoni, 2014).

The parameterization of WSFs and WSFns based on πtlp is supported by the fact that leaf cells need to maintain turgor to sustain functioning (Hsiao, 1973). These functions do not depend on πtlp when ψpd=πtlp, so there is a simple link between the leaf drought tolerance, as informed by πtlp, and the response of leaf-level gas exchange to water availability. Also, these equations predict that the decline of stomatal conductance as water availability decreases precedes that of photochemistry, consistent with observations (Fig. 2; Fatichi et al., 2016; Trueba et al., 2019).

Note that, since mesophyll conductance is not explicitly represented here, the effect of water stress on photosynthetic capacities (WSFns) includes both direct effects on the photosynthetic machinery and indirect effects from the reduction of mesophyll conductance (Drake et al., 2017; Keenan et al., 2010). Alternative shapes of water stress factors could be explored in the future, and a more explicit representation of the water flow through the plant water column could be implemented (Paschalis et al., 2024). In the absence of a clear consensus on the effect of water stress on respiration, TROLL 4.0 does not assume that respiration depends on water availability (Flexas et al., 2006, 2005; Rowland et al., 2018, 2015; Santos et al., 2018; Stahl et al., 2013b).

In TROLL 4.0, the leaf temperature (Tl), vapour pressure deficit (VPD_s), and CO₂ concentration (cs) at the leaf surface are computed through an iterative scheme that solves the leaf energy balance (Medlyn et al., 2007; Wang and Leuning, 1998; Duursma, 2015; Vezy et al., 2018). This is an important step because the leaf boundary layer plays a key role in gas exchanges, especially in dense tropical moist forests, given the large size of tropical tree leaves and the low wind speeds within canopies (De Kauwe et al., 2017; Jarvis and McNaughton, 1986; Meinzer et al., 1997). The iterative scheme is as follows. Initially, Tl, VPD_s, and cs are set equal to surrounding air values (T, VPD, and ca). Leaf photosynthesis (An) and stomatal conductance gsw are computed using Eqs. (24), (34), and (35). Next, the boundary layer conductance and radiation conductance are computed, and finally the leaf-level transpiration rate is deduced from the Penman–Monteith equation (Eq. 41 below). After these steps, new values for Tl, VPD_s, and cs are computed, and the above steps are repeated until leaf temperature converges, i.e. when the absolute difference between the Tl values of two consecutive iterations is lower than 0.01 °C.

The leaf-level transpiration rate El (in mol H₂O m⁻² s⁻¹) is calculated as 41El=1λ×sRni+VPDagHCpMas+γgHgw, where λ is the latent heat of water vapour (in J mol⁻¹), s is the slope of the (locally linearized) relationship between saturated vapour pressure and temperature (in Pa K⁻¹, see Jones, 2013, Eq. 5.15 therein), Rni is the isothermal net radiation (in J m⁻² s⁻¹), gH is the total leaf conductance to heat (in mol m⁻² s⁻¹), Cp is the heat capacity of air (1010 J kg⁻¹ K⁻¹), Ma is the molecular mass of air (28.96×10-3 kg mol⁻¹), γ the psychrometric constant (in Pa K⁻¹), and gw the total conductance to water vapour (mol H₂O m⁻² s⁻¹). The latent heat of water vapour λ depends on air temperature as follows. 42λ=2.501×103-2.365×T×18 The isothermal net radiation Rni has two components, the absorbed solar radiation (Sabs), including both PAR and NIR wavebands, and the net longwave radiation (Leuning et al., 1995; Appendix D therein): 43Rni=Sabs-Bn,0×kdexp⁡-kdLAI, where Bn,0 is the net longwave radiation at the top of the canopy, and kdexp⁡-kdLAI accounts for its extinction within the canopy, with kd set equal to 0.8. To account for the absorbed NIR radiation at a given height within the canopy in Sabs, we used the relationship reported by Kume et al. (2011; Fig. 4 therein) that links the transmitted NIR to the transmitted and incident PAR and assumed a leaf absorptance in the NIR equal to 0.1. Bn,0 is then computed as the absorbed minus the emitted longwave radiation: 44Bn,0=εl(1-εa)σTtop4, where Ttop is the top canopy air temperature in Kelvin, σ is the Stefan–Boltzmann constant (σ=5.67×10-8 W m⁻² K⁻⁴), εl is the emissivity of the canopy leaves, here assumed to be 1, and εa is the emissivity of the atmosphere. Several models exist for εa, with varying performance depending on the sky conditions (Marthews et al., 2012). We used Dilley and O'Brien (1998) here, which compromises between parsimony and performance across sky conditions (Marthews et al., 2012; Tables 2 and 5 therein).

gH, the total leaf conductance to heat, has three components, the boundary layer conductance for free convection gbHf, the boundary layer for forced convection gbHu, and the radiation conductance gr (Leuning et al., 1995; Jones, 2013): 45gH=2×gbHf+gbHu+gr, where the factor 2 accounts for the two sides of the leaves' gbHf. The boundary layer conductance for free convection is given by 46gbHf=0.5×DH×1.6×108×Tl-Twl0.25×PressRT, where DH is the molecular diffusivity to heat (DH=21.5×10-6 m² s⁻¹), Press the atmospheric pressure (in Pa), R the universal gas constant (R=8.314 J mol⁻¹ K⁻¹), and T the temperature of surrounding air in Kelvin. Leaf width wl (m) is estimated as the square root of leaf area (wl=LA). gbHu, the boundary layer for forced convection (in mol m⁻² s⁻¹), is given by 47gbHu=0.003×uwl×PressRT, where u is the wind speed in m s⁻¹ (see Eq. 9). gr, the radiation conductance in mol m⁻² s⁻¹, varies with Ta as follows (Jones, 2013, p. 101 therein). 48gr=4×εlσT3CpMa gw, the total conductance to water vapour, has two components that represent hydraulic resistances in series: the stomatal conductance (gsw, in mol H₂O m⁻² s⁻¹, Eq. 35) and the boundary layer conductance (gbw in mol H₂O m⁻² s⁻¹) to water vapour: 49gw=gbw×gswgbw+gsw,50 with gbw=1.075×gbHf+gbHu, where 1.075 accounts for the relative diffusivities of heat and water vapour in air. Equations (9) and (50) assume that all leaves are hypostomatous (stomates on the ground-facing side of the leaves only), a reasonable assumption in tropical forests (Drake et al., 2019; Muir, 2015).

At each daily time step, the individual tree net primary productivity of carbon, NPPind (gC), is obtained by the following balance equation (Fig. 3). 51NPPind=GPPind-Rmaintenance-Rgrowth GPPind (gC) is computed each half-hour as the carbon assimilation rate An (Eq. 19), multiplied by the leaf area in each tree crown layer (LAl, in m²), then summed over tree crown layers and cumulated across the day.

Young leaves and old leaves have been reported to have lower photosynthetic capacities and activities than mature leaves (Doughty and Goulden, 2008; Kitajima et al., 2002, 1997b; Wu et al., 2016; Albert et al., 2018; Menezes et al., 2021). For each tree, total leaf area (LA_t) is partitioned into three leaf age pools: young, mature, and old leaves so that LAt= LA_young + LA_mature + LA_old (all in m²). These three leaf age pools are assumed to be uniformly distributed within the tree crown. In young and old leaves, the net assimilation rate is a fraction ϱ<1 of that of mature leaves so that 52GPPind=CGPP×ϱ×LAyoung+LAmature+ϱ×LAoldLAt×∑l∑tAnt,l×LAl, where the factor CGPP is a conversion factor, and t depicts the daytime half-hours and l the tree crown layers. Here we assume that the carbon uptake efficiency ϱ relative to mature leaves is the same in young and old leaves and ϱ=0.5, a value consistent with observations.

TROLL 4.0 partitions autotrophic respiration into maintenance respiration and growth respiration, even if both come from the same biochemical pathways (Amthor, 1984; Thornley and Cannell, 2000). Maintenance respiration (Rmaintenance) has seldom been documented for stem and roots and is inferred empirically (Cavaleri et al., 2008; Meir et al., 2001; Slot et al., 2013; Weerasinghe et al., 2014). Nighttime leaf maintenance respiration is computed using Eqs. (32) and (33), using the mean nighttime temperature. As stomatal conductance and dark respiration vary less with leaf age than carbon assimilation rate (Albert et al., 2018; Kitajima et al., 2002; Villar et al., 1995), we assumed that young and old leaves have respiration and transpiration rates equal to ϱ′=0.75 that of mature leaves, leading to lower water use efficiency than mature leaves. Tree-level nighttime leaf respiration and daytime transpiration are computed as follows at each time step: 53Xind=CX×ϱ′×LAyoung+LAmature+ϱ′×LAoldLAt×∑l∑iXi,l×LAl, where Xind is either the carbon respired by leaves during the night or the total water transpired by the tree (gC or m³, respectively), X is the leaf dark respiration (Eqs. 32 and 33) or the leaf-level transpiration rate (Eq. 41), respectively, and CX is a factor to convert leaf-level rates in µmol C m⁻² s⁻¹ or in mol H₂O m⁻² s⁻¹ to total fluxes per individual per day (gC or m³, respectively).

Stem maintenance respiration (Rstem, in µmol C s⁻¹) was modelled assuming a constant respiration rate per volume of sapwood (39.6 µmol m⁻³ s⁻¹, Ryan et al., 1994) so that 54Rstem=Csresp×39.6×SA×h-cd where SA is the tree sapwood area (in m²) and Csresp is a conversion factor. Stem respiration response to temperature was modelled using a Q10 value of 2.0 (Meir and Grace, 2002; Ryan et al., 1994) and using mean daytime and nighttime temperatures. Stahl et al. (2011) reported that Rstem varies among individual trees, even when controlling for sapwood volume. However, in the absence of a clear understanding of the drivers, Eq. (4) is a parsimonious choice. In TROLL 4.0, sapwood area is computed dynamically. We used an inversion of the pipe model to derive sapwood area from the tree's leaf area (LA_t, in m²), height (h, m), and wood density following Fyllas et al. (2014; Eqs. 7 and 8 therein): 55SA=CSA2×LAtλ1+λ2×h+δ1+δ2×wsg, with λ1= 0.066 m² cm⁻², λ2=0.017 m cm⁻², δ1=-0.018 m² cm⁻², and δ2=1.6 cm³ g⁻¹, and CSA a conversion factor. In addition to Eq. (55), there are both lower and upper limits on sapwood extent. Sapwood has a minimum thickness of 0.5 cm and any newly grown wood is always considered sapwood, irrespective of leaf area. TROLL 4.0 also imposes an upper limit on sapwood growth based on stem diameter growth so that increases in living tissue cannot exceed increases in total tissue.

Other contributions of maintenance respiration were prescribed as proportions of leaf and stem maintenance respiration. Fine root maintenance respiration was assumed to be half of leaf maintenance respiration (Malhi, 2012), and coarse root and branch maintenance respirations were assumed to account for half of stem respiration (Asao et al., 2015; Cavaleri et al., 2006; Meir and Grace, 2002).

Growth respiration (Rgrowth) was assumed to account for 30 % of the carbon uptake by photosynthesis (gross primary productivity) minus the maintenance respiration (Cannell and Thornley, 2000). These assumptions are commonly made in the literature but remain a major source of uncertainty in carbon flux modelling (Atkin et al., 2014; Huntingford et al., 2013).

Contrary to the last published version of TROLL, in which the allocation of NPP_ind to plant organs was fully prescribed by fixed factors (fcanopy=fleaves+ffruit+ftwigs and fwood; Maréchaux and Chave, 2017), the allocation scheme implemented in TROLL 4.0 can now be additionally modulated depending on the current tree state and it includes an explicit carbon storage compartment (Sect. 2.6.2 and 2.6.3; Fig. 3).

Leaf phenology is a key driver of the variation of tropical forest productivity (Manoli et al., 2018; Restrepo-Coupe et al., 2013; Wu et al., 2017). However, its underlying drivers remain poorly understood, and its representation in vegetation models remains challenging (Chen et al., 2020; Restrepo-Coupe et al., 2017). In ORCHIDEE, Chen et al. (2020, 2021) proposed a leaf phenological scheme in which the production of young leaves is partly controlled by incident shortwave radiation, while the shedding of old leaves is controlled by vapour pressure deficit. This scheme reproduces the simultaneous increase in leaf production and litterfall observed in many Amazonian rainforest sites where productivity increases during the dry season (Chave et al., 2010; Wagner et al., 2016; Yang et al., 2021), but not the observed seasonality in productivity at some sites (e.g. GUYAFLUX eddy flux site in French Guiana; Chen et al., 2020). Additionally, this scheme overlooks the contrasted leaf phenological patterns observed across canopy individuals within and across species within communities (Nicolini et al., 2012; Loubry, 1994). In ED2, Xu et al. (2016) implemented a leaf phenological scheme driven by water availability in the root zone in a seasonally dry tropical forest. Since leaf shedding is often triggered by drought-induced loss of leaf turgor in these systems (Sobrado, 1986), leaf shedding and production are assumed to depend on the difference between leaf pre-dawn water potential and leaf water potential at turgor loss point. However, such a scheme cannot simulate the simultaneous leaf production and shedding observed in moist tropical forests.

In TROLL 4.0, we propose an alternative approach. At each time step, the optimal tree total leaf area (LA_opt) is estimated as the leaf area beyond which producing more leaves leads to a net carbon loss due to self-shading and respiration costs. LA_opt depends on tree crown size and leaf area density (Sect. 2.4.2), leaf photosynthetic capacities and respiration rate (Sect. 2.5.1), and local light environment. At each time step, the amount of carbon allocated to the production of new young leaves, NPPleaves, and to woody growth, NPPwood, is determined by default as NPPleaves=fleaves×NPPind, with fleaves=0.68×fcanopy (Chave et al., 2008, 2010; Maréchaux and Chave, 2017) and NPPwood=0.6×fwood×NPPind, where the factor 0.6 accounts for the fact that about 40 % of woody NPP is actually used for branch fall repair (Malhi et al., 2011). When leaf area LA_t exceeds LA_opt, NPPleaves is reduced so that LA_t = LA_opt. Second, if the carbon allocated to leaf production is not sufficient to compensate for leaf loss, then the carbon attributed by default to tree woody growth is mobilized for leaf production until leaf loss is compensated for. If not sufficient, the tree carbon storage (see Sect. 2.6.3) is then also mobilized. Hence this scheme prioritizes the maintenance of the assimilating tissues over woody growth (Schippers et al., 2015). The variation of leaf area for each leaf age pool is then computed as follows: 56ΔLAyoung=2×NPPleavesLMA-LAyoungτyoungΔLAmature=LAyoungτyoung-LAmatureτmatureΔLAold=LAmatureτmature-LAoldτold, where τyoung, τmature, and τold are the residence times in each class (in years) so that LL =τyoung+τmature+τold with LL the maximal tree leaf lifespan (in years). LL is inferred from the tree LMA using the following empirical relationships (Schmitt, 2017): 57LL=112max⁡(3,12.755×exp⁡0.007×LMA-0.565×N) τyoung was fixed to min(LL/3, 1/12) yr (Doughty and Goulden, 2008; Wu et al., 2016) and τmature as a third of total leaf lifespan.

The loss term LAold/τold corresponds to the rate of leaf litterfall at each time step. In the previous TROLL version, litterfall resulted from the dynamics of leaf biomass with τold=LL-τyoung-τmature. This leaf shedding scheme is passive and does not simulate the observed seasonality in leaf litterfall. Here we propose a new approach to simulate leaf shedding. We first observed that within species and sites, canopy trees can shed their leaves at different times, suggesting that causal environmental drivers should display fine-scale heterogeneity in space (unlike atmospheric shortwave radiation and vapour pressure deficit). In addition, old leaves display nutrient resorption before abscission (Albert et al., 2018; Kitajima et al., 1997a; Urbina et al., 2021); similarly, solute translocation from older to younger leaves can lower osmotic potential and leaf water potential at turgor loss point, thus increasing the drought tolerance of younger leaves to the detriment of older leaves (Pantin et al., 2012). We therefore used pre-dawn leaf water potential as a trigger of leaf shedding as in Xu et al. (2016), but with different thresholds for leaves of different ages, older leaves being more susceptible to a small decrease in tree water availability, while younger leaves can maintain turgor and grow at the same time. More specifically, we defined the following threshold. 58ψT,o=min⁡aT,o×πtlp,-0.01×h-bT,o The first term in ψT,o with aT,o<1 represents old leaves' lower ability to maintain turgor as soil dries. The second term modulates this susceptibility to drought depending on tree height (Bennett et al., 2015): it induces a susceptibility to a (small) decrease bT,o>0 in soil water availability for large trees, while preventing them from constantly shedding their old leaves at a fast pace (see Eq. (37) and Fig. 4). τold is then updated using a multiplying factor fo0.001≤fo≤1. Initially, τold′=foτold with fo=1, which is updated daily as follows: fo′=fo-δo when ψpd<ψT,o and fo′=fo+δo when ψpd>ψT,o, always assuming that fo has 0.001 as a lower bound and 1 as an upper bound.

We assumed no variation of πtlp with tree height (Maréchaux et al., 2016). The threshold ψT,o jointly depends on πtlp and tree height h to account for drought tolerance and tree height on leaf-level water stress. Practically, the tree height above which old leaves become susceptible to a small decrease in soil water availability is HT,o=-100×aT,oπtlp+bT,o in metres: 28 m at πtlp=-1.5 MPa and 58 m at πtlp=-3 MPa (when aT,o=0.2 and bT,o=0.02; see Fig. 4). While this scheme is based on process-based observations, parameters aT,o, bT,o, and δo are currently calibrated (see Schmitt et al., 2025).

In TROLL 4.0, trees can store carbon explicitly in non-structural carbohydrates. The maximum amount of carbon a tree can store and remobilize is determined as follows: 59NSCr=1000×0.5×0.05×1.25×AGB, where NSCr stands for non-structural carbohydrates (gC), AGB is the tree aboveground biomass (in kg), and 1000×0.5 converts biomass in kilograms into C in grams (Elias and Potvin, 2003). It is assumed that NSC can account for 10 % of the tree biomass, half of which is mobilizable (Martínez-Vilalta et al., 2016), hence the factor 0.05. The other half of NSC supports critical metabolic functions or is no longer accessible. The factor 1.25 accounts for an additional 25 % biomass storage in coarse roots, so 1.25×AGB is total tree biomass (Ledo et al., 2018). AGB is computed following (Chave et al., 2014; Eq. 5 therein): 60AGB=0.0559×wsg×dbh2×h, where dbh is in centimetres, h in metres, and wsg in g cm⁻³. Note that Eqs. (59) and (60), together with Eq. (61) below, induce a growth–storage trade-off mediated by wood density variation across individual and species, in agreement with observations (Signori-Müller et al., 2022). The NSC storage compartment is filled by the potential carbon surplus resulting from the allocation to leaf production, i.e. fleaves×NPPind-NPPleaves, if positive. If the storage compartment has reached its maximum capacity NSCr, then the surplus is allocated to woody growth.

The net primary production allocated to woody growth, NPPwood, depends on the outcome of allocation to leaf production and carbon reserves (see Sect. 2.6.2 and 2.6.3; Fig. 3). In TROLL 4.0, hydraulic control on carbon assimilation and leaf phenology both influence carbon allocation to trunk growth (e.g. Doughty et al., 2014; Farrior et al., 2013; Friedlingstein et al., 1999), but turgor-mediated processes are not explicitly modelled (Coussement et al., 2018; Peters et al., 2023; Muller et al., 2011; Körner, 2015). NPPwood is converted into an increment of stem volume, ΔV in m³, as follows: 61ΔV=10-6×NPPwood0.5×wsg×Senescdbh, where the factor 0.5 converts dry biomass units into carbon units (Elias and Potvin, 2003). The function Senescdbh is designed so that the largest trees cannot allocate carbon as efficiently into growth, reflecting empirical evidence of a size-related relative growth decline in trees (Yoda et al., 1965; Ryan et al., 1997; Mencuccini et al., 2005; Woodruff and Meinzer, 2011; Stephenson et al., 2014). We assumed that trees cannot exceed a trunk diameter of dbhmax⁡=32dbhthresh, where dbhthresh depends on species-specific information provided by the user (see Sect. 2.4.1), so that 62Senescdbh=1 when dbh≤dbhthreshSenescdbh=max⁡0;3-2dbhdbhthreshwhen dbh>dbhthresh. The trunk diameter growth increment Δdbh (m) is computed from ΔV as follows. V=Cπ(dbh2)2h, where C is a form factor (Chave et al. 2014, Eq. 5 therein). The term h (m) is total tree height inferred from the dbh following Eq. (16), and this leads to an expression of V as a function of dbh only. This function can be inverted to estimate Δdbh as a function of ΔV, which is known from Eq. (61). Tree height and crown dimensions are then updated using Eqs. (16), (17), and (18).

The starting point for a tree life cycle, as represented in TROLL 4.0, is an event of seed dispersal into the seed bank. On each 1×1 m ground site and for each species s, a “seed” bank stores all the seeds dispersed from the mature trees as well as from an external seed rain. The seed bank is updated once a year. Here, our conceptual “seeds” represent opportunities for seedling recruitment at 1 cm dbh (henceforth denoted “reproduction opportunities”) rather than as true seeds, since not all seed dispersal events are modelled explicitly, and the seed-to-seedling transition is implicit.

In TROLL 4.0 trees are assumed to become fertile above a diameter threshold dbh_mature that depends on the tree maximum size (Visser et al., 2016) as follows. 63dbhmature=0.5×dbhthresh This relationship is drawn from direct observations of the reproductive status of tree species in the tropical forest of Barro Colorado Island, Panama, with maximal tree dbh spanning a range of 0.05 to 2 m (see Fig. S9 in Visser et al., 2016; R2=0.81, n=60 species). The number of reproduction opportunities per mature tree, ns, is assumed to be fixed and equal for all individuals, and its value is user-defined. This assumption of a fixed reproductive opportunity per tree is predicated on the fact that there is a trade-off between seed number and seed size, itself related to seed and seedling survival. Thus, the probability of germination does not depend strongly on seed size or on the number of produced seeds and can be assumed to be a zero-sum game (Coomes and Grubb, 2003; Moles et al., 2004; Moles and Westoby, 2006). Each of the ns events is scattered away from the tree in a random direction and at a distance randomly drawn from a Rayleigh distribution, thus allowing for potential long-dispersal events. Although seed dispersal distance is known to vary depending on dispersal syndrome and plant traits (Tamme et al., 2014; Seidler and Plotkin, 2006; Muller-Landau et al., 2008), the scale parameter σdisp of the distribution is fixed here across species and individuals.

The intensity of the external seed rain is quantified by Ntot (number of incoming seeds per hectare) and its species composition is defined by the relative abundances of species freg,s, both being user-defined. Hence, for each species s, next,s events of dispersal due to seeds immigrating from the outside occurred, with 64next,s=Ntot×freg,s×nha, with nha being the number of hectares of the simulated plot. These reproduction opportunities are uniformly distributed within the simulated area.

If several species are competing for recruitment in a local seed bank, one of the species is picked at random as the winner out of all the seeds present, as in a lottery model (Chesson and Warner, 1981). The recruitment event occurs only if ground-level light availability is sufficiently high. To test if this condition is met, the seedling is first attributed individual trait values depending on the species-specific averages (see Sect. 2.4.1). These trait values are then used to determine the maximum LAI (LAI_max⁡) the seedling would support under average environmental conditions, with LAI_max⁡ defined as the threshold beyond which the seedling leaf assimilation would be less than respiration (see Sect. 2.6.2). The seedling can be recruited if the site LAI at ground level is lower than LAI_max⁡.

Water availability is also key to seedling performance (Engelbrecht et al., 2006; Johnson et al., 2017; Kupers et al., 2019); hence, TROLL 4.0 now implements an additional dependence of water availability on seedling establishment (Craine et al., 2012; Paine et al., 2018). Seedling recruitment is possible only if the top-layer soil water potential is less negative than half the turgor loss point (πtlp/2). Such parameterization is motivated by the fact that, at turgor loss point, the seedlings would not germinate, and a certain level of turgor is needed for germination and growth (Bradford, 1990; Daws et al., 2008; Coussement et al., 2018; Hsiao, 1973; Fatichi et al., 2016).

If both conditions on light and water availability are met, the newly recruited tree is initialized with dbh = 0.01 m, a total leaf area of LAt=0.25×LAopt distributed across the three leaf age pools in proportion to their relative span (τyoung/LL, τmature/LL, τold/LL; see Sect. 2.6.2), and a carbon storage compartment filled at half its maximum NSC_r (see Sect. 2.6.3).

The assumptions here made on tree reproduction largely reflect limited knowledge of these processes, which remain major sources of uncertainty in current models (König et al., 2022; Hanbury-Brown et al., 2022; Díaz-Yáñez et al., 2024).

Mortality processes also play a key role in forest structure and carbon balance (Sevanto et al., 2014; Friend et al., 2014; Johnson et al., 2016; Esquivel-Muelbert et al., 2020; McDowell et al., 2022). TROLL 4.0 explicitly represents several important mechanisms of tree mortality. At each time step, the individual tree death rate (in events per year; Sheil et al., 1995) is 65d=db+dstarv+dtreefall+ddrought, where db is a background death rate, dstarv represents death due to carbohydrate shortage (carbon starvation), dtreefall represents death due to tree fall (including trees indirectly killed by neighbouring fallen trees), and ddrought the drought-induced tree mortality.

Background mortality db encapsulates death events that are not attributed to any specific mechanism in the model. The mortality rate is known to vary greatly among species, and here we assume that it is negatively correlated with tree wood density, as observed pan-tropically (King et al., 2006; Kraft et al., 2010; Poorter et al., 2008; Wright et al., 2010). This dependence illustrates a trade-off between investment in construction costs and risk of mortality (Chave et al., 2009). We assumed the following relationship: 66db=m×1-wsgwsglim, where m (in events per year) is the reference background mortality rate for a species with low wood density and is user-specified. wsg_lim is a value large enough so that db always remains positive (here set at 1 g cm⁻³).

A tree can also die because of carbohydrate shortage in the case of prolonged stress (dstarv in Eq. 51). In TROLL 4.0, which includes an explicit carbohydrate storage compartment, the tree dies of carbon starvation when this compartment is empty and NPPind≤0 (Eq. 51).

Tree death may be caused by tree falls (term dtreefall in Eq. 65). To simulate this process, we first define a stochastic threshold Θ, depending on the tree maximal height and prescribed at tree birth. Then, the tree can fall with a probability equal to 1-Θh (Chave, 1999) each month. As TROLL 4.0 uses a daily time step, this probability is uniformly distributed across the days of 1 month. The parameter Θ is computed for each tree, as follows: 67Θ=hmax⁡×(1-vT×ζ), where hmax⁡ is maximal tree height (i.e. the tree height computed using Eq. 16 at dbh_max⁡), and vT is a variance term, ζ is the absolute value of a random Gaussian variable with zero mean and unit standard deviation. vT is modified at tree level so that high risks of tree fall (> 99.5th percentile of the Gaussian variable) occur at the same height for all individuals of the same species. This implicitly introduces a growth–mortality trade-off, as more slender trees (larger ratio of height to trunk diameter) should reach this height threshold quicker. The orientation of tree falls is random. Trees on the trajectory of the falling tree can be damaged, especially if they are smaller than the fallen tree (van der Meer and Bongers, 1996). To model this effect, an individual variable hurt is defined. If a tree is within the trajectory of the fallen stem or of the fallen crown, its variable hurt is updated to h and h-CR2 , respectively, if it was lower, where h and CR are the tree height and crown radius of the fallen tree, respectively. The probability of dying due to another tree fall is then 1-12hhurt×eεh,j, where h is the height of the focal tree and eεh,j (see Eq. 16) accounts for the fact that slender individuals (higher tree height deviation) would be more vulnerable to tree fall. Such a tree can either fall and damage other trees itself or die standing, depending on the user choice. The hurt variable is reset to zero at each time step.

Finally, prolonged drought is also a source of mortality. Drought-induced mortality is triggered when the leaf pre-dawn water potential ψpd is below a lethal level (ψlethal), and ψlethal is computed from the leaf water potential at turgor loss point, using the relationship provided by the global meta-analysis of Bartlett et al. (2016b; P=0.03, R2=0.31, n=15 species from tropical dry and moist biomes), as follows. 68ψlethal=-0.9842+3.1795×πtlp