# TROLL 4.0: representing water and carbon fluxes, leaf phenology and intraspecific trait variation in a mixed-species individual-based forest dynamics model – Part 1: Model description

Isabelle Maréchaux, Fabian Jörg Fischer, Sylvain Schmitt, Jérôme Chave

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## To cite this version:

Isabelle Maréchaux, Fabian Jörg Fischer, Sylvain Schmitt, Jérôme Chave. TROLL 4.0: representing water and carbon fluxes, leaf phenology and intraspecific trait variation in a mixed-species individual-based forest dynamics model – Part 1: Model description. 2024. hal-04769295

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https://hal.inrae.fr/hal-04769295v1

Preprint submitted on 6 Nov 2024

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Distributed under a Creative Commons Attribution 4.0 International License
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# TROLL 4.0: representing water and carbon fluxes, leaf phenology and intraspecific trait variation in a mixed-species individual-based forest dynamics model – Part 1: Model description

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Isabelle Maréchaux¹, Fabian Jörg Fischer²,³, Sylvain Schmitt¹,⁴,⁵, Jérôme Chave²

1. AMAP, Univ Montpellier, CIRAD, CNRS, INRAE, IRD, 34000 Montpellier, France

2. CRBE, Université de Toulouse, CNRS, IRD, Toulouse INP, 118 route de Narbonne 31062 Toulouse, France

3. School of Biological Sciences, University of Bristol, Bristol, BS8 1TQ United Kingdom

4. CIRAD, UPR Forêts et Sociétés, F-34398, Montpellier, France

5. Forêts et Sociétés, Univ Montpellier, CIRAD, Montpellier, France

Correspondence to: Isabelle Maréchaux (isabelle.marechaux@inrae.fr)

**Short summary:** We describe TROLL 4.0, a simulator of forest dynamics that represents trees in a virtual space at one-meter resolution. Tree birth, growth, death and the underlying physiological processes such as carbon assimilation, water transpiration and leaf phenology depend on plant traits that are measured in the field for many individuals and species. The model is thus capable of jointly simulating forest structure, diversity and ecosystem functioning, a major challenge in modelling vegetation dynamics.

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**Abstract.** TROLL 4.0 is an individual-based forest dynamics model that is capable of jointly simulating forest structure, diversity and ecosystem functioning, including the ecosystem water balance and productivity, leaf area dynamics and the tree community functional and taxonomic composition. It represents ecosystem flux processes in a manner similar to dynamic global vegetation models, while adopting a representation of plant community structure and diversity at a resolution consistent with that used by field ecologists. Specifically, trees are modeled as three-dimensional individuals with a metric-scale spatial representation, providing a detailed description of ecological processes such as competition for resources and tree demography. Carbon assimilation and plant water loss are explicitly represented at tree level using coupled photosynthesis and stomatal conductance models, depending on the micro-environmental conditions experienced by trees. Soil water uptake by trees is also modelled. Physiological and demographic processes are parameterized using plant functional traits measured in the field. Here we provide a detailed description and discussion of the implementation of TROLL 4.0. An evaluation of the model at two tropical forest sites is provided in a companion paper (Schmitt et al., submitted companion paper). TROLL 4.0's representation of processes reflects the state of the art, and we discuss possible developments to improve its predictive capability and its capacity to address challenges in forest monitoring, forest dynamics and carbon cycle research.

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# 1 Introduction

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Modelling vegetation dynamics remains a major challenge (Prentice et al., 2015; Song et al., 2021; Mahnken et al., 2022), and the wide variety of modelling concepts that coexist depend on models’ initial objectives. Early versions of global vegetation models were developed to provide boundary conditions for energy, carbon and water budgets in global atmospheric models (Sellers et al., 1986, 1997). With the refinement of modeling concepts and computer power, feedback loops between the atmosphere and vegetation have gradually been taken into account (Charney, 1975; Cox et al., 2000; Meir et al., 2006), leading to an improved representation of fluxes of energy, carbon and water across the vegetation layer (Fisher et al., 2015; Moorcroft, 2003; Pitman, 2003). However, dynamic global vegetation models (DGVMs) typically adopt a simplified representation of floristic composition and vegetation structure (Fisher et al., 2014; Prentice et al., 2007). In many of these models, fluxes between vegetation and the atmosphere are still calculated in an average environment per grid cell (e.g. 1°*1°), for an average leaf of an individual drawn from a dozen of plant functional types (PFTs). The diversity of plant strategies is therefore typically represented by a small number of PFTs even in highly diverse tropical forests (Fisher et al., 2014; Poulter et al., 2011).

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In parallel, stand-scale process-based models have been developed to better understand the exchanges between vegetation and the atmosphere through an up-scaling of fine-scale ecophysiological processes, and to account for within-stand micro-environmental heterogeneity (Wang and Jarvis, 1990; Gu et al., 1999; Williams et al., 1996; Ogée et al., 2003; Duursma and Medlyn, 2012; Fyllas et al., 2014). These process-based models are conceptually close to DGVMs, but they implement a more detailed representation of plant structure at the stand scale, and they have nurtured some important advances in DGVM-development over the past decades (e.g., Chen et al., 2016). Typically used to assimilate eddy-flux data, they do not include demographic processes however.

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Forest growth models have a different history as they were initially developed to predict successional dynamics and inform forest management (Watt, 1947; Botkin et al., 1972; Vanclay, 1994; Porté and Bartelink, 2002; Liang and Picard, 2013). A key innovation have been gap models that represent recruitment, growth, mortality and competition between individual trees within forest patches. Forest patches are typically the size of a canopy opening created by the fall of a dominant tree (gap, or chablis, Bugmann 2001) and modelled as horizontally homogeneous, with a spatially implicit representation of tree positions. Through the simulation of a large number of patches, gap models can represent spatial heterogeneity due to gap dynamics within stands. Overall, these models adopt a finer representation of vegetation structure than classic DGVMs, but biogeochemical processes are generally modeled more coarsely, using ideal yield curves for tree growth rates combined with limiting factors imposed by the patch environment. Since these empirical relationships can only be parameterized on the basis of a large amount of data – readily available in plantations, but difficult to obtain elsewhere –, gap models typically also use plant functional types to simulate diverse forest stands. The number and definition of these groups has been much discussed in the literature, with no clear consensus (Botkin, 1975; Swaine and Whitmore, 1988; Vanclay, 1991; Köhler and Huth, 1998;
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Köhler et al., 2000; Gourlet-Fleury et al., 2005; Kazmierczak et al., 2014), and these plant functional types are difficult to transfer from one site to another (Picard and Franc, 2003; Picard et al., 2012).

Modelling vegetation from a completely different perspective and building upon flora distribution maps and biogeographic concepts (Humboldt, 1849; Grisebach, 1872), plant species distribution models have been developed for long (SDMs; Guisan et al., 2017). Generally, SDMs first estimate the envelope of environmental conditions for a species based on species occurrence data (Guisan and Thuiller, 2005; Hutchinson, 1957; Soberón, 2007), which is used to infer a probability distribution in space (Elith and Leathwick, 2009). These models require little knowledge on the processes underlying species distribution, which explains their widespread use. However, because these models are statistical in nature, their ability to project future states is unclear, and a great deal of research has been devoted to implementing process-based versions of these SDMs (Chuine and Beaubien, 2001; Ferrier and Guisan, 2006; Morin and Lechowicz, 2008; Morin and Thuiller, 2009; Kearney and Porter, 2009; Dormann et al., 2012; Journé et al., 2020).

From this brief and non exhaustive overview it emerges that each research community in vegetation modeling emphasizes one representation of vegetation dimension – functioning, structure or diversity -- to the detriment of the others (Maréchaux et al., 2021). Data availability and computing power partly explain such tradeoffs, and increasing model complexity does not necessarily translate into an increase in reliability and robustness (Mahnken et al., 2022; Prentice et al., 2015). However, a consensus has emerged in the literature that a better integration of plant species diversity, structure and functioning should improve the predictive power of vegetation models (Purves and Pacala, 2008; Thuiller et al., 2008; McMahon et al., 2011; Evans, 2012; Dormann et al., 2012; Mokany et al., 2016; Fisher et al., 2018). For example, tree species diversity influences the productivity and resilience of forest ecosystems (Schnabel et al., 2019), and these biodiversity-ecosystem functioning relationships result from local interactions where competition for resources is a key process (Fichtner et al., 2018; Guillemot et al., 2020; Jourdan et al., 2020; Yu et al., 2024; Nemetscheck et al. 2024). Similarly, the fine details of stand structure control the uptake of resources by vegetation (Braghiere et al., 2019, 2021; Brum et al., 2019; Ivanov et al., 2012; De Deurwaerder et al., 2018), and they also determine the response to environmental stresses and disturbances (Blanchard et al., 2023; Jucker et al., 2018; Seidl et al., 2014; De Frenne et al., 2019). More generally, the contribution of vegetation in biogeochemical cycles, albeit typically quantified from stand to global scales (e.g. biomass, productivity), ultimately depends on individual processes (e.g. mortality, Johnson et al., 2016) controlled by fine-scale heterogeneity and the various ecological strategies of species (Poorter et al., 2015).

Therefore, recent developments in DGVMs have sought to better represent plant community structure and diversity. Several cohort-based DGVMs have been developed to refine the representation of vegetation heterogeneity (Moorcroft et al., 2001; Fisher et al., 2015; Longo et al., 2019; Smith et al., 2001). Continuous representations of functional diversity have also been proposed using the distribution and co-variation of traits at the individual level or trait-climate relationships (Sakschewski et al., 2015; Verheijen et al., 2015; Scheiter et al., 2013; Pavlick et al., 2013; Berzaghi et al., 2020; Van Bodegom et al., 2014). These developments represent major advances in vegetation modelling, but scale mismatches between field data and model representations limit the ability to assimilate data of various nature and resolution. While inverse modelling approaches can
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partially alleviate these constraints (Hartig et al., 2012; Dietze et al., 2013; LeBauer et al., 2013; Fer et al., 2018; Lagarrigues et al., 2015), they rely heavily on confidence in the model structure, can therefore raise equifinality issues (Medlyn et al., 2005), and increase rapidly in computational complexity in high-dimensional parameter sets.

Finally, most of these challenges are exacerbated for tropical forests, as they are structurally complex (Doughty et al., 2023), support a large number of tree species per hectare (up to several hundred, Wilson et al., 2012), and are more difficult to access for evaluation in the field (Schimel et al., 2015). Given that they provide a range of ecosystem services and play a major role in regional and global biogeochemical cycles (Beer et al., 2010; Bonan, 2008; Pan et al., 2011; Harper et al., 2013), tropical forests and their responses to changing environmental factors have been identified as one of the greatest sources of uncertainty in Earth system models (Koch et al., 2021; Powell et al., 2013; Restrepo-Coupe et al., 2017; Huntingford et al., 2013). Thus, many advances in vegetation modelling have been, and still are, motivated by the challenge of tropical forests.

Here we describe a major upgrade of the TROLL forest dynamics model (Chave, 1999; Maréchaux and Chave, 2017; Fischer, 2019), referred to here as TROLL 4.0. TROLL 4.0 brings together various modelling traditions, including elements of DGVMs, stand-scale process-based models and forest gap models while adopting a species-level representation of plant diversity, to jointly simulate the functioning, structure and diversity of forest ecosystems, and in particular tropical forests. TROLL is a spatially explicit forest dynamics model, with an individual- and trait-based representation (Fig. 1). Individual trees from 1cm diameter at breast height (*dbh*) are explicitly represented in a three-dimensional space discretized at a resolution of one meter, allowing a fine representation of stand structure and local interactions via explicit competition for resources. Each tree belongs to a species, with a list of mean traits per species provided as input. These traits control the physiological and demographic processes of the tree's functioning and life cycle, from recruitment to growth, to seed dispersal and death. This type of trait-based parameterization is based on recent advances in plant physiology and functional ecology, has been facilitated by the expansion of large databases of functional traits (Díaz et al., 2016, 2022; Kattge et al., 2011, 2020), in particular for tropical trees (Baraloto et al., 2010a; Vleminkx et al., 2021).

In TROLL 4.0, carbon assimilation and water loss by transpiration are represented explicitly using a photosynthesis model coupled with a stomatal conductance model. Both take into account variation in micro-environmental conditions between and within tree crowns, as well as the tree's access to soil water. A water cycle is now simulated, with the state and dynamics of soil water explicitly represented and coupled with the vegetation dynamics. The influence of water availability on leaf-level gas exchanges, leaf phenology, tree recruitment and death is parameterized through the leaf water potential at turgor loss point (Bartlett et al., 2012) and mechanistic-based coordination with other hydraulic traits (Bartlett et al., 2016). Carbon that is not consumed by the respiration of living tissues is then allocated to leaf production, carbon storage and tree growth through allometric relationships. Compared to TROLL version 2.3.2 (Maréchaux and Chave, 2017), TROLL 4.0 includes other improvements: plant functional traits can vary among trees of the same species; tree crown shapes can be more realistic than cylinders; and leaf density can vary within the tree crowns.

In this contribution, we provide a detailed description of the structure and objectives of the TROLL 4.0 model, discussing how new modeling representations are an outcome of the state of knowledge and the availability of data. Finally,
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132 we discuss the limitations of the model and future developments. An evaluation of the model's ability to simulate forest structure, diversity and functioning for two Amazonian forest sites is reported in a companion paper (Schmitt et al., submitted 133 companion paper). The model is written in C++ and wrapped in the R environment through a dedicated package named rcontroll (Schmitt et al. 2023). 134 135

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<figure><img src="image_8.png" /><figcaption>Figure 1: Representation of individual trees in a spatially explicit environment in TROLL 4.0 (right) allowing direct comparison with data of various nature (left). In TROLL 4.0, each tree is composed of a trunk, a crown, whose shape evolves from a cylinder to an umbrella as the tree grows, and root biomass that decreases exponentially with soil depth. Tree dimensions are updated at each timestep, depending on the net assimilated carbon that is allocated to growth, and following allometric relationships depending on tree diameter at breast height (dbh). Each tree has a species label associated with plant functional traits, which, together with an individual effect randomly attributed at tree birth, determines the tree's functional traits. These traits are used to parameterize physiological and demographic processes that govern tree functioning throughout its life cycle. Light diffusion is computed explicitly at each time step and within each voxel from the canopy top to the ground. Water balance is also computed at each timestep, and the resulting water availability across soil voxels influence tree functioning. With this representation of forest structure, composition and functioning, model outputs can be directly compared with a wide range of data, including carbon and water fluxes provided by eddy-flux towers, field inventories, and 3D structure estimates from remote sensing (left). In TROLL 4.0, aboveground voxels typically have a finer horizontal resolution than belowground voxels, but the latter are vertically finer and increasing in thickness with depth (right). This resolution matches the one of fine-scale remote-sensing products or soil water content monitoring (left).</figcaption></figure>

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## 2 Model description

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### 2.1 Environmental conditions

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TROLL 4.0 simulates an idealized forest stand with a typical size of 1 to 100 ha. Parallel computing may be used to simulate several times the same stand, or to simulate several forest stands with different environmental conditions. Climatic drivers are similar to those represented in many DGVMs (air temperature, vapor pressure deficit, wind speed, and light intensity above the canopy, as well as precipitation). The forest ecosystem is divided into an above-ground and below-ground part. Soil is explicitly represented as a water reservoir, but soil nutrients are not modeled. The topography within a stand is assumed to be flat.

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### 2.2 Light availability and aboveground variation in micro-climate

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Above ground, the simulated forest stand is represented as a discrete grid of 1m³ cubic voxels. Light diffuses through the forest's leaf layers from the top of the canopy to the ground, with one recalculation each day. In a given voxel, light availability is the photosynthetic photon flux density in µmol photons m⁻² s⁻¹ and is computed as a function of the incident light intensity at top canopy (PPFDtop, see Table A1 for a list of symbols), the cumulated leaf density of voxels above and the (constant) leaf density within the voxel itself. The Beer-Lambert extinction of light within the canopy allows to calculate the incident PPFD (per unit ground area) above any layer at vertical extent v as:

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$$PPFD(v) = PPFD_{top} \times \exp[-k \times LAI(v)] \quad (1)$$

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where LAI(v) is the cumulated leaf area above height v, and k is the extinction coefficient. We here define k = kgeom × absorptanceleaves, where kgeom reflects the geometric arrangement of leaves in the voxel (a value of 0.5 reflecting spherical leaf distribution; Ross, 1981) and absorptanceleaves, the fraction of absorbed light within a single leaf (Long et al., 1993; Poorter et al., 1995). The absorbed light in a layer a of thickness Δa is then

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$$PPFD_{abs}(a) = PPFD_{top} \times \exp[-k \times LAI(a)] - PPFD_{top} \times \exp[-k \times LAI(a + \Delta a)] \quad (2)$$

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Assuming that leaf area per unit ground area (m² m⁻²), or dens(a), is constant within the layer, this simplifies to:

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$$PPFD_{abs}(a) = PPFD_{top} \times \exp[-k \times LAI(a)] \times (1 - \exp[-k \times dens(a)]) \quad (3)$$

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For photosynthesis calculations, absorbed PPFD per unit ground area is converted into absorbed PPFD per unit leaf area by dividing $PPFD_{abs}(a)$ by $dens(a)$.

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Air microenvironmental variation within the canopy is represented as follows. Nighttime temperature (Tnight) is assumed constant throughout the night and within the canopy, while temperature (T) and vapor pressure deficit (VPD) vary across voxels depending on the variable $λ(v) = LAI(v) / LAI_{sat}$ with LAI_{sat} a threshold LAI and LAI(v) the LAI above voxel v. At height v above ground, we calculate temperature and VPD as follows:
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$$T(v) = T_{top} - \Delta T \times \lambda(v) \qquad (4)$$

$$VPD(v) = VPD_{top} \times [C_{VPD0} + (1 - C_{VPD0}) \sqrt{1 - \lambda(v)}] \qquad (5)$$

where $\Delta T$ and $C_{VPD0}$ are set parameters and $T_{top}$ and $VPD_{top}$ are values at the top of canopy. For any given layer $a$ of depth $\Delta a$, temperatures and VPDs are then calculated by averaging both functions from $a$ to $a + \Delta a$:

$$T_{mean}(a) = \frac{1}{\Delta a} \int_{a}^{a+\Delta a} \left( T_{top} - \frac{\Delta T}{LAI_{sat}} \times LAI(v) \right) dv \qquad (6)$$

$$VPD_{mean}(a) = \frac{1}{\Delta a} \int_{a}^{a+\Delta a} VPD_{top} \times \left[ C_{VPD0} + \frac{(1-C_{VPD0})}{\sqrt{LAI_{sat}}} \sqrt{(LAI_{sat} - LAI(v))} \right] dv \qquad (7)$$

Equations 6 and 7 can then be simplified using the assumption of constant leaf density within a layer and redefining $v$ with respect to the current layer $a$, so that $LAI(v) = LAI(a) + dens(a) \times v$.

This representation of variation of $T$ and $VPD$ within the canopy is in qualitative agreement with empirical observations of microclimate gradients within tropical forest canopies (Camargo and Kapos, 1995; Shuttleworth, 1985; Shuttleworth et al., 1989, Tymen et al. 2017), with a consistent buffering effect of forest canopies on understory micro-environment (De Frenne et al., 2019), and a strong control by forest structure (Gril et al., 2023b, a; Tymen et al., 2017; Zellweger et al., 2019).

Wind speed attenuation inside the canopy is simulated as described in Rau et al. (2022), who explored the effect of wind speed on forest structure in a forest exposed to cyclones using TROLL. Wind speed is usually measured above the canopy and decreases as one approaches the canopy top layer, so wind speed at the top of the canopy is (Monteith & Unsworth 2008):

$$u(z) = \frac{u_*}{\kappa} \ln\left(\frac{z-d}{z_0}\right), \quad \text{if } z \ge H \qquad (8)$$

where $u(z)$ is the horizontal wind speed in m s⁻¹ at a height $z$ (in m) above ground, $H$ the height of the top of the canopy (in m), $u_*$ is the friction velocity, $\kappa$ the von Karman constant ($\kappa=0.40$), $d$ the zero-plane displacement height, here assumed to be equal to 0.8H, and $z_0$ the aerodynamic roughness, here assumed to be equal to 0.06H (Rau et al., 2022). Within the canopy, wind speed decreases as (Inoue 1963):

$$u(z) = u(H) \exp\left(-\alpha\left(1 - \frac{z}{H}\right)\right), \quad \text{if } z < H \qquad (9)$$

with $\alpha \approx 3$ (Raupach et al., 1996). Wind speed was not computed at the voxel scale, but using the coarser horizontal resolution of the belowground field (see section 2.3 below, e.g. 25x25 m), and a mean top canopy height $H$ was computed as input to Eqs (8) and (9).

## 2.3 Soil water availability

In TROLL 4.0, the belowground part of the ecosystem is explicitly represented, and its discretization is specified by the user, including the number and depth of layers, and horizontal dimensions of the cells. Belowground voxels are typically coarser horizontally (e.g. 25m x 25m, as commonly implemented in gap models Bugmann, 2001), but finer vertically, than aboveground 1-m³ voxels. Metric-scale lateral water fluxes are difficult to parameterize and evaluate, and neglecting them
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here limits the computational burden. Soil layers typically increase in thickness with depth, as in most DGVMs or forest physiological models (Prentice et al., 2015) and in standard soil assessments (e.g. Hengl et al., 2017). In this representation, contrasting root depth and access to water can be represented across individual trees together with potential variation in soil properties and hydraulic state. This approach contrasts with some forest dynamics models that use a single-layer belowground representation (e.g. Gutiérrez et al., 2014; Christoffersen et al., 2016; Fyllas et al., 2014).

The water content in each belowground voxel is simulated using a bucket model, which relies on the vertical water balance for each voxel. Neglecting horizontal lateral fluxes, the water balance for a given soil column amounts to:

$$\Delta SWC = P - I - Q - E - T - L \qquad (10)$$

where SWC is the soil water content, P the incident rainfall, I the canopy interception, Q the run-off, E the evaporation from the soil, T the transpiration, i.e. the plant water uptake, and L the leakage. This water balance is established for each soil layer, with inputs from upwards and outputs downwards starting from the top layer ($l=1$): outputs of layer $l$ are inputs for layer $l+1$, with $L$ corresponding to the output of the deepest layer, and $P-I-Q$ to the input of the top layer. Note that this downward iteration neglects: (i) potential hydraulic lift (upward water redistribution, see e.g. Dawson, 1993; Burgess et al., 1998; Oliveira et al., 2005); and (ii) potential interaction with the water table (Costa et al., 2023; Sousa et al., 2022). Further developments could account for these two mechanisms where they are expected to play a significant role. In particular, flooded areas could be easily represented, with a shallower soil depth and a prescribed boundary condition, i.e. a shallower water table. We now describe and discuss each term of the water balance and the corresponding modeling choices.

**Rainfall.** Rainfall ($P$, in 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).

**Interception.** Rainfall interception by the canopy is simulated using a model where interception depends on LAI, as proposed by Liang et al. (1994):

$$I = \min(P, K \times LAI) \qquad (11)$$

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 $625=25^2$ 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).

**Run-off and infiltration.** 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 timestep 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. In the absence of an explicit wetting front,
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runoff 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.

*Soil evaporation.* We assumed that water evaporates from the top soil layer only, a reasonable assumption if the top soil 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):

$$E = \frac{M_w}{RT_s} \times \frac{e_s - e_a}{r_{soil} + r_{aero}} \qquad (12)$$

where E is in kg m⁻² s⁻¹, M_w is the molar mass of water vapor (M_w=18 kg mol⁻¹), R is the ideal gas constant (R=8.31 J mol⁻¹ K⁻¹), T_s is the temperature at soil surface in K, e_s is the vapor pressure of the soil surface in Pa, e_a is the vapor pressure of air above the soil surface in Pa, r_soil is the soil surface resistance in s m⁻¹, and r_aero is the aerodynamic resistance to heat transfer in s m⁻¹. Soil water pressure e_s is a function of the water potential of the top soil belowground voxel (ψ_soil,top, in MPa; Jones, 2013, Eq. (5.14) therein):

$$e_s = e_{sat}(T_s) \times \exp\left(\frac{V_w}{RT_s} \times \psi_{soil,top}\right) = e_{sat}(T_s) \times \exp\left(2.17 \times \frac{\psi_{soil,top}}{T_s}\right) \qquad (13)$$

Where V_w is the partial molal volume of water (V_w = 18 × 10⁻⁶ m³ mol⁻¹), and e sat (T_s) is the saturated vapor pressure at T_s computed following the Buck equation (Jones, 2013, Appendix 4 therein). e_a is by definition equal to e sat (T_s) - VPD ground, where the latter is the VPD at ground level in Pa. r soil is computed following Sellers et al. (1992, Eq. (19) therein, see also Merlin et al., 2016, Eq. (12)):

$$r_{soil} = \exp\left(8.206 - 4.255 \times \frac{\theta_{top}}{\theta_{fc,top}}\right) \qquad (14)$$

where θ_top is the water content of the top soil belowground voxel and θfc,top is its water content at field capacity (in m³). Aerodynamic resistance r_aero is computed as follows (Merlin et al., 2016, Eq. (B10) therein):

$$r_{aero} = \frac{1}{\kappa^2 \times u(Z)} \ln\left(\frac{Z}{z_m}\right)^2 \qquad (15)$$

with κ again the von Karman constant (κ=0.40), u(Z) is the wind seed (in m s⁻¹) at reference height Z, here taken at 1m above ground, and Z_m is the momentum soil roughness in m, set to 0.001m.

*Transpiration.* Trees transpire soil water from the belowground voxel they are rooted in (see section 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 day-time half hours (see section 2.5.2). Soil layers contribute to water uptake as a function of tree-dependent weights, w_t (see Eq. (21), section 2.4.3), which depend on root biomass and on the soil hydraulic state in each layer.

For each belowground voxel in layer 1, the soil water potential (ψ_t) and the soil hydraulic conductivity (K_t) 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 Matthews et al., 2014). Parameters of
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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 is 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).

## 2.4 Representation of trees in the model

### 2.4.1 Species affiliation and intra-specific trait variability

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 (dbhthres, hlim, ah, all in m; see section 2.4.2). The number of species provided in 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 e$^{εi,j}$ where $εi,j \sim N(0, σi)$ where $σi$ 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 $εwsg,j \sim N(0, σwsg)$. 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 structured in space or time nor heritable, and 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 is left for future version.

### 2.4.2 Aboveground structure

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 dbhj, we calculate its height hj, its crown radius crj, and its crown depth cdj as follows:

$$h_j = \frac{h_{lim} \times dbh_j}{(a_h + dbh_j)} \times e^{\epsilon_{h,j}} \qquad (16)$$

$$cr_j = e^{a_{cr}} \times dbh_{j}^{b_{cr}} \times e^{\epsilon_{cr,j}} \qquad (17)$$
<figure><img src="image_15.png" /></figure>

$$cd_j = \min\left(\frac{h_j}{2}, (a_{cd} + b_{cd} \times h_j) \times e^{\varepsilon_{cd,j}}\right) \qquad (18)$$

where $h_{lim}$ and $a_h$ are species-specific coefficients of the Michaelis-Menten function, and $a_{cr}$, $b_{cr}$, $a_{cd}$, and $b_{cd}$ allometric coefficients that are species independent. $\varepsilon_{h,j}$, $\varepsilon_{cr,j}$ and $\varepsilon_{cd,j}$ are variance terms to simulate intraspecific variation with $\varepsilon_{h,j} \sim N(0, \sigma_h)$, $\varepsilon_{cr,j} \sim N(0, \sigma_{cr})$, and $\varepsilon_{cd,j} \sim N(0, \sigma_{cd})$. 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 previous published version (Maréchaux and Chave, 2017), tree crowns were represented as cylinders with homogeneous leaf densities. Since v.3.0, TROLL can also 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 (e.g., 50%, 30%, 20%) to reflect gradients in leaf densities from the upmost to lower crown layers (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. Instead, the treetop grows quicker in height than the outer crown parts. As a result, the three 1-m layers are 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). Different functional forms are available to describe height variation from treetop to crown edge, but here we chose a simple linear decrease between the radius at the top of the crown to the radius at the bottom of the crown. The ratio between both 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.

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 percentage of total crown area that is not filled with leaves, $f_{gap}$. This allows for the modelling of a spatially heterogeneous light environment in the understory (Tymen et al., 2017), with a theoretical range from $f_{gap} = 0\%$ (full crown cover, no openings) to $f_{gap} = 100\%$ (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 $f_{gap} = 15\%$ 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 $e^{2\varepsilon_{cr,j}}$). Within species, variation in crown extent is thus assumed as decoupled from variation in leaf area, i.e., reflecting variation in branch angles and directions, but not branch number or biomass.

### 2.4.3 Belowground structure

TROLL 4.0 makes the common assumption that total fine root biomass is equal to leaf biomass. Future developments should endeavor 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;
<figure><img src="image_16.png" /></figure>

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 predawn leaf water potential, or isotope labeling (Brum et al., 2019; Stahl et al., 2013), but this does not give access to the actual rooting depth. Tree root depth was here assumed to increase with tree size, and was computed as a function of tree dbh as follows (Kenzo et al., 2009, Fig. 4 therein):

with root depth, RD, in m, and diameter at breast height, dbh, in 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=1cm) was adjusted to avoid unrealistic water depletion of the top soil 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 coordination 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 1, at depths ranging from $z_l$ to $z_{l+1}$ ($> z_l$) is computed as:

$$RB_l = RB_t \times \left( \exp\left(-3\frac{z_l}{RD}\right) - \exp\left(-3\frac{z_{l+1}}{RD}\right) \right) \quad (20)$$

where $RB_l$ is the total tree fine root biomass (in g), $RB_t$ the fine root biomass in layer 1 (in g), RD the tree rooting depth (in m). The factor 3 was determined so that about 95% of the tree biomass is contained between soil surface and RD (note that $\log(0.05) \approx 3$) (Arora and Boer, 2003). Tree roots are distributed across vertical layers, but do not spread across belowground voxels horizontally. As a result, trees only deplete the water content of the belowground voxels located below their trunk position (see section 2.3).

The soil water potential in the root zone, $\psi_{root}$ (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:

$$\psi_{root} = \sum_l w_l \times \psi_l \text{ with } w_l = \frac{(\psi_l - \psi_{R,min}) \times G_l}{\sum_{ll} (\psi_{ll} - \psi_{R,min}) \times G_{ll}} \quad (21)$$

where $\psi_l$ is the soil water potential in layer 1, and $\psi_{R,min}$ 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). $G_l$, the soil-to-root water conductance in layer 1, in mmol H$_2$O m$^{-2}$ s$^{-1}$ MPa$^{-1}$, computed as follows (Gardner, 1964):

$$G_l = \frac{2\pi L_{a,l} K_l}{\log\left(\frac{r_s}{r_r}\right)} \quad (22)$$

In Eq (22), $L_{a,l}$ 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 $RB_l \times SRL$ where SRL is the specific root length, here assumed to be constant (10 m g$^{-1}$, Bonan et al., 2014; Metcalfe et al.,
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

2008; Weemstra et al., 2016). K<sub>l</sub> is the soil hydraulic conductivity of layer 1 (in mmol H<sub>2</sub>O m<sup>-1</sup> s<sup>-1</sup> MPa<sup>-1</sup>, see section 2.3), r<sub>r</sub> is the mean fine root radius, here set at 1mm, and r<sub>s</sub> is half the mean distance between roots, calculated with the assumption of uniform root spacing in a given layer (Newman, 1969):

$r_s = \frac{1}{\sqrt{\pi L_{v,l}}}$ (23)
where L<sub>v,l</sub> is the total root length per unit soil volume in the layer (in m m<sup>-3</sup>), computed in the same way as L<sub>a,l</sub>, but also divided by layer depth.

A range of other models have been used to infer $\psi_{root}$ using the relative tree root biomass in each layer directly as weights (De Kauwe et al., 2015; Naudts et al., 2015; Powell et al., 2013; Schaphoff et al., 2018; Sakschewski et al., 2021; Verbeeck et al., 2011). However, trees do not uptake 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 sustain forest productivity during dry seasons.

## 2.5 Leaf physiology

The carbon assimilated and the water transpired by a tree within a day are the sum of the leaf-level carbon and water fluxes across day-time half hours. Leaf-level carbon assimilation is computed per crown layer of each tree, using the Farquhar-von Caemmerer-Berry model of C<sub>3</sub> photosynthesis (Farquhar et al., 1980, see section 2.5.1), coupled to the model of stomatal conductance of Medlyn et al. (2011; see section 2.5.2) as in Maréchaux and Chave (2017). In TROLL 4.0 the dependences on leaf temperature (T<sub>l</sub>), vapor pressure deficit at the leaf surface (VPD<sub>s</sub>), and CO<sub>2</sub> concentration at the leaf surface (c<sub>s</sub>) are now determined iteratively at the leaf surface, starting from air temperature (T), air vapor pressure deficit (VPD<sub>a</sub>) and air CO<sub>2</sub> concentration (c<sub>a</sub>) averaged across the tree crown layer (see sections 2.2 and 2.4.2) and with transpiration computed using the Penman-Monteith equation (see section 2.5.4).

### 2.5.1 Photosynthesis

In Farquhar et al. (1980), leaf-level net carbon assimilation rate (A<sub>n</sub>, µmol CO<sub>2</sub> m<sup>-2</sup> s<sup>-1</sup>) is limited by either Rubisco activity (A<sub>v</sub>, µmol CO<sub>2</sub> m<sup>-2</sup> s<sup>-1</sup>), or RuBP regeneration (A<sub>j</sub>, µmol CO<sub>2</sub> m<sup>-2</sup> s<sup>-1</sup>):

$$A_n = \min\{A_v, A_j\} - R_p(T_l) ; \quad A_v = V_{cmax}(T_l, \psi_{pd}) \times \frac{c_l - \Gamma^*}{c_l + K_m(T_l)} ; \quad A_j = \frac{1}{4} \frac{c_l - \Gamma^*(T_l)}{c_l + 2\Gamma^*(T_l)} \quad (24)$$

where R<sub>p</sub> is the photorespiration rate (µmol C m<sup>-2</sup> s<sup>-1</sup>), V<sub>cmax</sub> is the maximum rate of carboxylation (µmol CO<sub>2</sub> m<sup>-2</sup>s<sup>-1</sup>), c<sub>i</sub> the CO<sub>2</sub> partial pressure at carboxylation sites, Γ* the CO<sub>2</sub> compensation point in the absence of dark respiration, K<sub>m</sub> the apparent
<figure><img src="image_19.png" /></figure>

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:

$$J = \frac{1}{2\theta} \left[ \alpha \times PPFD + J_{max}(T_l, \psi_{pd}) - \sqrt{\left(\alpha \times PPFD + J_{max}(T_l, \psi_{pd})\right)^2 - 4\theta \times \alpha \times PPFD \times J_{max}(T_l, \psi_{pd})} \right] \quad (25)$$

$J_{max}$ 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 $α = (1 - LSQ) \times 0.5$, with LSQ the effective spectral quality of light, fixed at 0.15, and the factor 0.5 accounts for the fact that each photosystem absorbs half of the photons.

The $V_{cmax}$ and $J_{max}$ parameters depend on leaf properties, leaf temperature ($T_l$) and water state (through the leaf predawn water potential, $\psi_{pd}$, 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 $V_{cmax}$ and $J_{max}$ are co-limited by the leaf concentration of nitrogen and phosphorus as follows (see also Walker et al., 2014):

$$V_{cmax-M} (25^{\circ}\text{C}) = \min\{-1.56 + 0.43 \times N - 0.37 \times \text{LMA} ; -0.80 + 0.45 \times P - 0.25 \times \text{LMA} \} \quad (26)$$

$$J_{max-M} (25^{\circ}\text{C}) = \min\{-1.50 + 0.41 \times N - 0.45 \times \text{LMA} ; -0.74 + 0.44 \times P - 0.32 \times \text{LMA} \} \quad (27)$$

with $V_{cmax-M}$ and $J_{max-M}$ 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. $V_{cmax-M}$ and $J_{max-M}$ can be converted into area-based $V_{cmax}$ and $J_{max}$ by multiplying by LMA. We used this leaf trait-based parameterization of $V_{cmax}$ (25°C) and $J_{max}$ (25°C) in the absence of water stress (as in Fyllas et al., 2014; Mercado et al., 2011). The dependence of $V_{cmax}$ and $J_{max}$ with temperature was given by equations in Bernacchi et al. (2003), and the dependence with water availability was modelled by a function of $\psi_{pd}$ ($WSF_{ns}$, see section 2.5.3, Eq. (40)):

$$V_{cmax}(T_l, \psi_{pd}) = V_{cmax}(25^{\circ}\text{C}) \times e^{\left(\frac{26.35 - \frac{65.33}{R \times (T_l + 273.15)}}{298 \times R \times (273 + T_l)}\right)} \times WSF_{ns}(\psi_{pd}) \quad (28)$$

$$J_{max}(T_l, \psi_{pd}) = J_{max}(25^{\circ}\text{C}) \times e^{\left(\frac{17.57 - \frac{43.54}{R \times (T_l + 273.15)}}{298 \times R \times (273 + T_l)}\right)} \times WSF_{ns}(\psi_{pd}) \quad (29)$$

where R is the molar gas constant (0.008314 kJ K⁻¹ mol⁻¹), and $T_l$ is the internal leaf temperature in Celsius degrees. The temperature dependence of $\Gamma^*$ and $K_m$ followed von Caemmerer (2000):

$$\Gamma^*(T_l) = 37 \times e^{23.4 \times \frac{(T_l - 25)}{298 \times R \times (273 + T_l)}} \quad (30)$$

$$K_m(T_l) = 404 \times e^{59.36 \times \frac{(T_l - 25)}{298 \times R \times (273 + T_l)}} \times \left(1 + \frac{210}{35.94 \times \frac{T_l - 25}{298 \times R \times (273 + T_l)}}\right) \quad (31)$$

Temperature dependencies in Eqs (28)-(31) are consistent with Domingues et al. (2010), following recommendations from Rogers et al. (2017).

Leaf photorespiration rate $R_p$ was assumed to be a fixed fraction (40%) of leaf dark respiration rate (Atkin et al., 2000). We used Atkin et al. (2015) ‘broadleaved trees’ empirical model to estimate mature leaf dark respiration rates as a function of plant functional traits:
<figure><img src="image_20.png" /></figure>

$$R_{d-M}(25^{\circ}\text{C}) = 8.5341 - 0.1306 \times N - 0.5670 \times P - 0.0137 \times \text{LMA} + 11.1 \times V_{cmax-M} + 0.1876 \times N \times P \quad (32)$$

with R<sub>d-M</sub> the leaf dark respiration rate on a dry mass basis and at reference temperature of 25°C (in nmol CO<sub>2</sub> g<sup>-1</sup>s<sup>-1</sup>). Multiplying R<sub>d-M</sub> by LMA gives the area-based leaf dark respiration R<sub>d</sub> (in µmol C m<sup>-2</sup>s<sup>-1</sup>). 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):

$$R_d(T_l) = R_d(25^{\circ}\text{C}) \times \left[ 3.09 - 0.043 \times \frac{(T_l+25)}{2} \right]^{\frac{(T_l-25)}{10}} \quad (33)$$

Long-term acclimation to temperature is not considered in TROLL 4.0 (Kattge and Knorr, 2007; Smith and Dukes, 2013).

## 2.5.2 Stomatal conductance

Carbon assimilation by photosynthesis is limited by the CO<sub>2</sub> partial pressure at carboxylation sites, which is controlled by stomatal transport as modeled by the diffusion equation:

$$A_n = g_s(c_s - c_i) \quad (34)$$

with g<sub>s</sub> the stomatal conductance to CO<sub>2</sub> (mol CO<sub>2</sub> m<sup>-2</sup>s<sup>-1</sup>). 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 vapor is simulated as (Medlyn et al., 2011):

$$g_{sw} = g_0 + 1.6 \times \left(1 + \frac{g_1}{\sqrt{VPD_s}}\right) \times \frac{A_n}{c_s} \quad (35)$$

where g<sub>sw</sub> is the stomatal conductance to water vapor in mol H<sub>2</sub>O m<sup>-2</sup>s<sup>-1</sup>, 1.6 is the factor needed to convert one mole of CO<sub>2</sub> into one mole of H<sub>2</sub>O, VPD<sub>s</sub> is the vapor pressure deficit at the leaf surface in kPa, A<sub>n</sub> is the assimilation rate in µmol CO<sub>2</sub> m<sup>-2</sup>s<sup>-1</sup> (Eq. (24) above), c<sub>s</sub> is the CO<sub>2</sub> concentration at the leaf surface in ppm, g<sub>0</sub> is the minimum conductance for water vapor in mol H<sub>2</sub>O m<sup>-2</sup>s<sup>-1</sup> (Duursma et al., 2019), and g<sub>1</sub> is a model parameter in kPa<sup>1/2</sup>. Equations 24, 34 and 35 taken together lead to two quadratic equations for c<sub>i</sub>, one when Rubisco activity is limiting and one when RuBP regeneration is limiting, and the solution is the highest root.

The parameter g<sub>1</sub> 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 g<sub>1</sub> should differ across plant functional types (e.g. Xu et al., 2016). Here we assumed a dependence of g<sub>1</sub> with wood density (wsg, in g cm<sup>-3</sup>) as in Lin et al. (2015). We also assumed a dependence with water availability, modelled by a function of ψ<sub>pd</sub> (WSF<sub>s</sub>; see section 2.5.3):

$$g_1 = (-3.97 \times wsg + 6.53) \times WSF_s(\psi_{pd}) \quad (36)$$

This parameterization of g<sub>1</sub> based on wood density is a matter of debate however, and alternatives have been proposed (Wu et al., 2020; Lamour et al., 2023).

The parameter g<sub>0</sub> 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;
<figure><img src="image_21.png" /></figure>

Martin-StPaul et al., 2017), its values and variation with other functional traits is poorly documented (Duursma et al., 2019; Slot et al., 2021; Nemetschek et al., 2024), and we here assumed a fixed value. Note that some previous studies have defined $g_0$ as cuticular conductance only, ignoring stomatal leak effects, and thus underestimating $g_0$.

Both $g_0$ and $g_1$ 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 measurement and experiment (Cochard, 2021).

### 2.5.3 Effect of water availability on leaf-level gas exchange

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 being 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., 2015; 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 ($\psi_{leaf}$; 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 on leaf CO₂ assimilation under drying conditions, reflecting contrasted 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 on stomatal conductance, or stomatal conductance model parameters (e.g. $g_1$). 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 on $V_{cmax}$ and $J_{max}$ (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 $g_1$ parameter ($WSF_s$; Eq. (36)), and one for non-stomatal limitations, modifying the $V_{cmax}$ and $J_{max}$ parameters of the photosynthesis model ($WSF_{ns}$; Eq. (28) and (29)). Both water stress factors are assumed to depend on the leaf predawn water potential ($\psi_{pd}$; De Kauwe et al., 2015; Verhoef and Egea, 2014), which is a function of the soil water potential in the root zone ($\psi_{root}$, Eq. (21)) (Stahl et al., 2013, but see Bucci et al., 2004; Donovan et al., 2003) as follows (Jones, 2013; Eq. (4.9) therein):
<figure><img src="image_22.png" /></figure>

$$ \psi_{pd} = \psi_{root} - \rho gh \approx \psi_{root} - 0.01 \times h \qquad (37) $$

where $\rho$ is the density of water, $g$ the gravitational force (g=9.81 m s⁻²), and $h$ total tree height in m. Here, $WSF_s$ was computed as (Zhou et al., 2013; De Kauwe et al., 2015):

$$ WSF_s = \exp(b \times \psi_{pd}) \qquad (38) $$

where $b$ is a parameter. To parameterize $b$, we used the relationship between the leaf water potential at turgor loss point ($\pi_{tlp}$ in MPa) and the water potential causing 90% of stomatal closure ($\psi_{gs90}$, in MPa): $\pi_{tlp} = 0.97 \times \psi_{gs90}$ (P<0.01, R²=0.4; Fig. 1 in Martin-StPaul et al. 2017), and assumed that $WSF_s \approx 0.1$ at $\psi_{gs90}$ (an approximation given the shape of Eq. (35)), leading to:

$$ WSF_s = \exp \left( -2.23 \times \frac{\psi_{pd}}{\pi_{tlp}} \right) \qquad (39) $$

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 $WSF_s$ in Eq (39) was preferred over alternatives, such as a linear relationship between $WSF_s$ and $\psi_{pd}$ (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 ($WSF_{ns}$) was computed following Xu et al. (2016):

$$ WSF_{ns} = \left( 1 + \left( \frac{\psi_{pd}}{\pi_{tlp}} \right)^a \right)^{-1} \qquad (40) $$

with $a=6$ estimated from data reported in Brodribb et al. (2003). In this formula, $WSF_{ns} = 1/2$ when $\psi_{pd} = \pi_{tlp}$, in agreement with empirical findings (Brodribb et al., 2002; Manzoni, 2014).

The parameterization of $WSF_s$ and $WSF_{ns}$ based on $\pi_{tlp}$ is supported by the fact that leaf cells need to maintain turgor to sustain functioning (Hsiao, 1973). These functions do not depend on $\pi_{tlp}$ when $\psi_{pd} = \pi_{tlp}$, so there is a simple link between the leaf drought tolerance, as informed by $\pi_{tlp}$, 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 ($WSF_{ns}$) 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).
<figure><img src="image_23.png" /></figure>

523

<figure><img src="image_24.png" /><figcaption>Figure 2: Responses of leaf-level gas exchange to water stress, depending on the leaf drought tolerance. Water stress factors for the stomatal conductance parameter $g_1$ (stomatal limitation, WSF$_s$, Eq. (39); solid lines) and for the photosynthetic capacities $J_{max}$ and $V_{cmax}$ (non-stomatal limitation, WSF$_{ns}$, Eq. (40); dashed lines) as a function of leaf predawn water potential ($\psi_{pd}$, in MPa). WSFs are shown for a drought vulnerable species ($\pi_{tlp}$=-1.41 MPa, the least negative value reported in Maréchaux et al., 2015; blue lines), and for a drought tolerant species ($\pi_{tlp}$=-3.15 MPa, the most negative value reported in Maréchaux et al., 2015). Vertical dotted lines: $\pi_{tlp}$, horizontal dotted black lines: WSF$_s$ and WSF$_{ns}$ at $\pi_{tlp}$.</figcaption></figure>

524

525

526

527

528

529

530

531

### 2.5.4 Leaf energy balance

532

533

534

535

536

537

538

539

540

541

In TROLL 4.0, leaf temperature ($T_l$), vapor pressure deficit (VPD$_s$) and CO$_2$ concentration ($c_s$) 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 on gas exchanges, and especially so 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, $T_l$, VPD$_s$ and $c_s$ are set equal to surrounding air values (T, VPD and $c_a$). Leaf photosynthesis ($A_n$) and stomatal conductance ($g_{sw}$) are computed using Eqs (24), (34) and (35); next, the boundary layer conductance and radiation conductance are computed; and finally leaf-level transpiration rate is deduced from the Penman-Monteith equation (Eq. (41) below). After these steps, new values for $T_l$, VPD$_s$ and $c_s$ are computed, and the above steps are repeated until leaf temperature converges, i.e., when the absolute difference between the $T_l$ of two consecutive iteration is lower than 0.01°C.

542

Leaf-level transpiration rate $E_l$ (in mol H$_2$O m$^{-2}$ s$^{-1}$) is calculated as:
<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /></figure>

$$E_l = \frac{1}{\lambda} \times \frac{sR_{ni} + VPD_a g_H C_p M_a}{s + \gamma \frac{g_H}{g_w}} \quad (41)$$

where $\lambda$ is the latent heat of water vapor (in J mol⁻¹), s is the slope of the (locally linearized) relationship between saturated vapor pressure and temperature (in Pa K⁻¹, see Jones, 2013, Eq. (5.15) therein), $R_{ni}$ is the isothermal net radiation (in J m⁻² s⁻¹), $g_H$ is the total leaf conductance to heat (in mol m⁻² s⁻¹), $C_p$ is the heat capacity of air (1010 J kg⁻¹ K⁻¹), $M_a$ is the molecular mass of air (28.96 × 10⁻³ kg mol⁻¹), $\gamma$ the psychrometric constant (in Pa K⁻¹), and $g_w$ the total conductance to water vapor (mol H₂O m⁻² s⁻¹). The latent heat of water vapor $\lambda$ depends on air temperature as follows:

$$\lambda = (2.501 \times 10^3 - 2.365 \times T) \times 18 \quad (42)$$

The isothermal net radiation $R_{ni}$ has two components, the absorbed solar radiation ($S_{abs}$), including both PAR and NIR wavebands, and the net longwave radiation (Leuning et al., 1995; Appendix D therein):

$$R_{ni} = S_{abs} - B_{n,0} \times k_d \exp(-k_d LAI) \quad (43)$$

where $B_{n,0}$ is the net longwave radiation at the top of the canopy, and $k_d \exp(-k_d LAI)$ accounts for its extinction within the canopy, with $k_d$ set equal to 0.8. To account for the absorbed NIR radiation at a given height within the canopy in $S_{abs}$, 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. $B_{n,0}$ is then computed as the absorbed minus the emitted longwave radiation:

$$B_{n,0} = \varepsilon_l(1 - \varepsilon_a)\sigma T_{top}^4 \quad (44)$$

where $T_{top}$ is the top canopy air temperature in K, $\sigma$ is the Stefan-Boltzmann constant ($\sigma = 5.67 \times 10^{-8} \text{ W m}^{-2} \text{ K}^{-4}$), $\varepsilon_l$ is the emissivity of the canopy leaves, here assumed to be 1, and $\varepsilon_a$ the emissivity of the atmosphere. Several models exist for $\varepsilon_a$, with varying performance depending on the sky conditions (Marthews et al., 2012). We here used Dilley and O'Brien (1998), which compromises between parsimony and performance across sky conditions (Marthews et al., 2012; Tables 2 and 5 therein).

$g_H$, the total leaf conductance to heat, has three components, the boundary layer conductance for free convection $g_{bHf}$, the boundary layer for forced convection $g_{bHu}$, and the radiation conductance $g_r$ (Leuning et al., 1995; Jones, 2013):

$$g_H = 2 \times (g_{bHf} + g_{bHu} + g_r) \quad (45)$$

where the factor 2 accounts for the two sides of the leaves. $g_{bHf}$, the boundary layer conductance for free convection, is given by:

$$g_{bHf} = 0.5 \times D_H \times \left( \frac{1.6 \times 10^8 \times |T_l - T|}{w_l} \right)^{0.25} \times \frac{Press}{RT} \quad (46)$$

where $D_H$ is the molecular diffusivity to heat ($D_H = 21.5 \times 10^{-6} \text{ m}^2 \text{ s}^{-1}$), $Press$ the atmospheric pressure (in Pa), $R$ the universal gas constant ($R=8.314 \text{ J mol}^{-1} \text{ K}^{-1}$) and $T$ the temperature of surrounding air in K. Leaf width $w_l$ (in m) is estimated as the square root of leaf area ($w_l = \sqrt{LA}$). $g_{bHu}$, the boundary layer for forced convection (in mol m⁻² s⁻¹), is given by:

$$g_{bHu} = 0.003 \times \sqrt{\frac{u}{w_l}} \times \frac{Press}{RT} \quad (47)$$
<figure><img src="image_27.png" /></figure>

where u is the wind speed in m s⁻¹ (see Eq. (9)). g_r, the radiation conductance in mol m⁻² s⁻¹ varies with T_a as follows (Jones, 2013, p.101 therein):

$$g_r = \frac{4 \times \varepsilon_l \sigma T^3}{c_p M_a} \qquad (48)$$

g_w the total conductance to water vapor has two components that represent hydraulic resistances in series: the stomatal conductance (g\_sw, in mol H₂O m⁻² s⁻¹, Eq. (35)) and the boundary layer conductance (g\_bw in mol H₂O m⁻² s⁻¹) to water vapor:

$$g_w = \frac{g_{bw} \times g_{sw}}{g_{bw} + g_{sw}} \qquad (49)$$

$$\text{with } g_{bw} = 1.075 \times (g_{bHf} + g_{bHu}) \qquad (50)$$

where 1.075 accounts for the relative diffusivities of heat and water vapor in air. Equations (49) 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).

## 2.6 Carbon allocation

### 2.6.1. Net carbon uptake: whole-tree integration and respiration

At each daily timestep, the individual tree net primary productivity of carbon, NPP\_ind (in gC), is obtained by the following balance equation (Fig. 3):

$$NPP_{ind} = GPP_{ind} - R_{maintenance} - R_{growth} \qquad (51)$$

GPP\_ind (in gC) is computed each half hour as the carbon assimilation rate A_n (Eq. (19)), multiplied by the leaf area in each tree crown layer (LA_l, 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 LA_t= 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, net assimilation rate is a fraction ϱ < 1 of that of mature leaves, so that:

$$GPP_{ind} = C_{GPP} \times \frac{(\rho \times LA_{young} + LA_{mature} + \rho \times LA_{old})}{LA_{t}} \sum_{l} \sum_{t} A_{n}(t, l) \times LA_{l} \qquad (52)$$

where the factor C\_GPP is a conversion factor, 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 (R\_maintenance) 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
<figure><img src="image_28.png" /></figure>

603 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 rate equal to $\rho' = 0.75$ that of mature leaves, leading to lower water use efficiency than mature leaves. Tree-level 604 605 606 nighttime leaf respiration and daytime respiration are computed as follows at each timestep:

$$X_{ind} = C_{X} \times \frac{(\rho' \times LA_{young} + LA_{mature} + \rho' \times LA_{old})}{LA_{t}} \sum_{l}(\sum_{i} X(i, l)) \times LA_{l} \quad (53)$$

608 where $X_{ind}$ is either the carbon respired by leaves during the night or the total water transpired by the tree, in gC or m³ 609 respectively, X being the leaf dark respiration (Eqs. (32) and (33)) or the leaf-level respiration rate (Eq. (41)) respectively, 610 and $C_{X}$ is a conversion factor.

611 Stem maintenance respiration ($R_{stem}$, in µmol C s⁻¹) was modeled assuming a constant respiration rate per volume of 612 sapwood (39.6 µmol m⁻³ s⁻¹, Ryan et al., 1994), so that:

$$R_{stem} = C_{sresp} \times 39.6 \times SA \times (h - cd) \quad (54)$$

614 where SA is the tree sapwood area (in m²) and $C_{sresp}$ is a conversion factor. Stem respiration response to temperature was 615 modeled using a $Q_{10}$ value of 2.0 (Meir and Grace, 2002; Ryan et al., 1994), and using mean daytime and nighttime 616 temperatures. Stahl et al. (2011) reported that $R_{stem}$ varies among individual trees, even when controlling for sapwood volume. 617 However, in absence of a clear understanding of the drivers, Eq. (54) is a parsimonious choice. In TROLL 4.0, sapwood area 618 is computed dynamically. We used an inversion of the pipe model to derive sapwood area from the tree's leaf area ($LA_t$, in 619 m²), height (h, in m) and wood density following Fyllas et al. (2014; Eqs (7) and (8) therein):

$$SA = C_{SA} \frac{2 \times LA_t}{\lambda_1 + \lambda_2 \times h + \delta_1 + \delta_2 \times wsg} \quad (55)$$

621 with $\lambda_1 = 0.066 \text{ m}^2 \text{ cm}^{-2}$, $\lambda_2 = 0.017 \text{ m}^2 \text{ cm}^{-2}$, $\delta_1 = -0.018 \text{ m}^2 \text{ cm}^{-2}$, and $\delta_2 = 1.6 \text{ cm}^3 \text{ g}^{-1}$, and $C_{SA}$ a conversion factor. In addition 622 623 to Eq. (55), there are both lower and upper limits on sapwood extent. Sapwood has a minimum thickness of 0.5 cm and any 624 newly grown wood is always considered sapwood, irrespective of leaf area. TROLL 4.0 also imposes an upper limit on 625 sapwood growth based on stem diameter growth, so that increases in living tissue cannot exceed increases in total tissue. 626

625 Other contributions of maintenance respiration were prescribed as proportions of leaf and stem maintenance 626 respiration. Fine root maintenance respiration was assumed to be half of leaf maintenance respiration (Malhi, 2012), and coarse 627 root and branch maintenance respirations were assumed to account for half of stem respiration (Asao et al., 2015; Cavaleri et 628 al., 2006; Meir and Grace, 2002).

629 Growth respiration ($R_{growth}$) was assumed to account for 30% of the carbon uptake by photosynthesis (gross primary 630 productivity) minus the maintenance respiration (Cannell and Thornley, 2000). These assumptions are commonly made in the 631 literature, but remain a major source of uncertainty in the carbon flux modeling (Atkin et al., 2014; Huntingford et al., 2013).

632 Contrary to the last published version of TROLL, in which the allocation of NPP$_{ind}$ to plant organs was fully prescribed 633 634 by fixed factors ($f_{canopy} = f_{leaves} + f_{fruit} + f_{twigs}$ and $f_{wood}$, Maréchaux and Chave, 2017), the allocation scheme implemented in 635 TROLL 4.0 can now be additionally modulated depending on the current tree state and it includes an explicit carbon storage 636 compartment (sections 2.6.2 and 2.6.3; Fig. 3).
<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /><figcaption>Figure 3: Diagram of structures and processes driving individual and community dynamics, as investigated under the modeling approach adopted in TROLL 4.0. Elements in bold letters refer to novel implementation in comparison to the previous published version, while italic letters refer to elements still not included in this present version. Abiotic environment is modeled at the voxel scale and drive C assimilation in the leaves (gross primary productivity, GPP) and maintenance respiration rates of the different plant organs (R<sub>MAINTENANCE</sub>). The C amount resulting from the balance between GPP and R<sub>MAINTENANCE</sub> can be used for tissue production (NPP<sub>FRUITS</sub>, NPP<sub>LEAVES</sub>, NPP<sub>WOOD</sub> and NPP<sub>ROOTS</sub>) or stored (CARBON RESERVES) in the different tree organs. Both allocations induce metabolic costs (R<sub>GROWTH</sub> and R<sub>STORAGE</sub>; but the latter is not represented nor included). CARBON RESERVES represents non-structural carbohydrates (NSC), mainly stored as sugar or starch, and its maximal storage capacity is given by NSC<sub>r</sub>. Allocation to these different compartments follows a hierarchical scheme initialized by default proportions (f<sub>fruits</sub>, f<sub>leaves</sub>, f<sub>wood</sub>). If the tree leaf area (LA<sub>t</sub>) exceeds the optimal leaf area (LA<sub>opt</sub>, a function of both tree properties and its micro-environment), then the surplus of NPP<sub>LEAVES</sub> is allocated to carbon reserves. If the tree leaf area is lower than optimal, then NPP<sub>WOOD</sub>, and if further needed, carbon reserves, are mobilized for leaf production. If carbon reserves surpass storage capacity (NSC<sub>r</sub>), then stored carbohydrates are used for woody growth. C allocated to tissue production leads to an increment of trunk diameter and height following allometric relationships, and the production of new young leaves and roots. Simultaneously with tissue turnover, this leads to the update of leaf density and root biomass distribution, influencing both abiotic environment (eg. light diffusion and water interception) and light and element acquisition, and thus carbon assimilation and metabolism. C allocated to reproduction leads to the production of seeds, which are dispersed randomly. This generates a spatially-explicit seedling bank, from which winners are locally recruited depending</figcaption></figure>
<figure><img src="image_31.png" /></figure>

on both light and water availability. Tree death may be triggered by environmental or mechanical constraints, or carbon starvation. In a future version, litter decomposition, wood decay and nutrient mineralization, could lead to soil nutrient availability for plant uptake, and take place through the action of soil microorganisms, which activity, and hence respiration ($R_{HETEROTROPHIC}$), depends particularly on temperature and soil moisture.

## 2.6.2 Leaf production and leaf shedding

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 vapor 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 predawn 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 timestep, 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 (section 2.4.2), leaf photosynthetic capacities and respiration rate (section 2.5.1), and local light environment. At each timestep, the amount of carbon allocated to the production of new young leaves, $NPP_{leaves}$, and to woody growth, $NPP_{wood}$, are determined by default as: $NPP_{leaves} = f_{leaves} \times NPP_{ind}$, with $f_{leaves} = 0.68 \times f_{canopy}$ (Chave et al., 2008, 2010; Maréchaux and Chave, 2017), and $NPP_{wood} = 0.6 \times f_{wood} \times NPP_{ind}$, 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 $LA_{opt}$, $NPP_{leaves}$ is reduced so that $LA_t = LA_{opt}$. Second, if the carbon allocated to leaf production is not sufficient to compensate leaf loss, then the carbon attributed by default to tree woody growth is mobilized for leaf production until leaf loss is compensated. If not sufficient, the tree carbon storage (see section 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:

$$ \Delta LA_{young} = \frac{2 \times NPP_{leaves}}{LMA} - \frac{LA_{young}}{\tau_{young}} $$
<figure><img src="image_32.png" /></figure>

$$\Delta LA_{mature} = \frac{LA_{young}}{\tau_{young}} - \frac{LA_{mature}}{\tau_{mature}}$$

$$\Delta LA_{old} = \frac{LA_{mature}}{\tau_{mature}} - \frac{LA_{old}}{\tau_{old}} \qquad (56)$$

where $\tau_{young}$, $\tau_{mature}$, $\tau_{old}$ are the residence times in each class (in yr), so that $LL= \tau_{young}+\tau_{mature}+\tau_{old}$ with LL the maximal tree leaf lifespan (in yr). LL is inferred from the tree LMA, using the following empirical relationships (Schmitt, 2017):

$$LL = \frac{1}{12} \max(3, 12.755 \times \exp(0.007 \times LMA - 0.565 \times N)) \qquad (57)$$

$\tau_{young}$ was fixed to min(LL/3, 1/12) yr (Doughty and Goulden, 2008; Wu et al., 2016), and $\tau_{mature}$ as a third of total leaf lifespan.

The loss term $LA_{old}/\tau_{old}$ corresponds to the rate of leaf litterfall at each timestep. In the previous TROLL version, litterfall resulted from the dynamics of leaf biomass with $\tau_{old}$= LL - $\tau_{young}$- $\tau_{mature}$. 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 vapor 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 predawn 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:

$$\psi_{T,o} = \min(a_{T,o} \times \pi_{tlp}, -0.01 \times h - b_{T,o}) \qquad (58)$$

The first term in $\psi_{T,o}$ with $a_{T,o} < 1$ 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 $b_{T,o} > 0$ in soil water availability for large trees, while preventing them from constantly shedding their old leaves at fast pace (see Eq. (37)). $\tau'_{old}$ is then updated using a multiplying factor $f_o$ ($0.001 \le f_o \le 1$). Initially, $\tau'_{old} = f_o \tau_{old}$ with $f_o = 1$, which is updated daily as follows: $f'_o = f_o - \delta_o$ when $\psi_{pd} < \psi_{T,o}$ and $f'_o = f_o + \delta_o$ when $\psi_{pd} > \psi_{T,o}$, always assuming that $f_o$ has 0.001 as a lower bound, and 1 as an upper bound.

We assumed no variation of $\pi_{tlp}$ with tree height (Maréchaux et al., 2016). The threshold $\psi_{T,o}$ jointly depends on $\pi_{tlp}$ 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 becomes susceptible to a small decrease in soil water availability is $H_{T,o} = -100 \times (a_{T,o}\pi_{tlp} + b_{T,o})$ in m: 28 m at $\pi_{tlp}=-1.5$ MPa and 58m at $\pi_{tlp}=-3$ MPa (when $a_{T,o}= 0.2$ and $b_{T,o} = 0.02$). While this scheme is based on process-based observations, parameters $a_{T,o}$, $b_{T,o}$, and $\delta_o$ are currently calibrated (see Schmitt et al., submitted companion paper).
<figure><img src="image_33.png" /></figure>

## 2.6.3 Carbon storage

In TROLL 4.0, trees can store carbon explicitly in non-structural carbohydrates. The maximal amount of carbon a tree can store and remobilize is determined as follows:

$$NSC_r = 1000 \times 0.5 \times 0.05 \times 1.25 \times AGB \qquad (59)$$

where $NSC_r$ stands for non-structural carbohydrates (in gC), AGB is the tree aboveground biomass (in kg), and $1000 \times 0.5$ converts biomass in kg into C in g (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 $1.25 \times AGB$ is total tree biomass (Ledo et al., 2018). AGB is computed following (Chave et al., 2014; Eq. (5) therein):

$$AGB = 0.0559 \times wsg \times dbh^2 \times h \qquad (60)$$

where dbh is in cm, h in m and wsg in g cm⁻³. The NSC storage compartment is filled by the potential carbon surplus resulting from the allocation to leaf production, i.e. $f_{leaves} \times NPP_{ind} - NPP_{leaves}$, if positive. If the storage compartment has reached its maximal capacity $NSC_r$, then the surplus is allocated to woody growth.

## 2.6.4 Growth

The net primary production allocated to woody growth, $NPP_{wood}$, depends on the outcome of allocation to leaf production and carbon reserves (see sections 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 modeled (Coussement et al., 2018; Peters et al., 2023; Muller et al., 2011; Körner, 2015). $NPP_{wood}$ is converted into an increment of stem volume, $\Delta V$ in m³, as follows:

$$\Delta V = 10^{-6} \times \frac{NPP_{wood}}{0.5 \times wsg} \times Senesc(dbh) \qquad (61)$$

where the factor 0.5 converts dry biomass units into carbon units (Elias and Potvin, 2003). The function $Senesc(dbh)$ 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 $dbh_{max} = \frac{3}{2} dbh_{thresh}$, where $dbh_{thresh}$ depends on species-specific information provided by the user (see section 2.4.1), so that:

$$ \begin{aligned} Senesc(dbh) = 1 & \quad \text{when } dbh \le dbh_{thresh} \\ Senesc(dbh) = \max(0; 3 - 2 \frac{dbh}{dbh_{thresh}}) & \quad \text{when } dbh > dbh_{thresh} \end{aligned} \qquad (62) $$

Trunk diameter growth increment $\Delta dbh$ (in m), is computed from $\Delta V$ as follows. $V = C \pi (\frac{dbh}{2})^2 h$, where C is a form factor (Chave et al. 2014, Eq. (5) therein). The term h (in m) is total tree height inferred from the dbh following Eq. (16), this leads to an expression of V as a function of dbh only. This function can be inverted to estimate $\Delta dbh$ as a function of $\Delta V$, which is known from Eq. (61). Tree height and crown dimensions are then updated using Eqs (16), (17) and (18).
<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>

## 2.7 Tree demography

### 2.7.1 Seed production, dispersal and recruitment

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 1x1 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 of seedling recruitment rather than as true seeds, since not all seed dispersal events are modeled explicitly, and the seed-to-seeding transition is implicit.

In TROLL 4.0 trees are assumed to become fertile above a diameter threshold $dbh_{mature}$ that depends on the tree maximal size (Visser et al., 2016) as follows:

$$dbh_{mature} = 0.5 \times dbh_{thresh} \qquad (63)$$

This relationship is drawn from direct observations of 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, n_s, is assumed 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 a zero-sum game (Coomes and Grubb, 2003; Moles et al., 2004; Moles and Westoby, 2006). Each of the n_s 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 $\sigma_{disp}$ of the distribution is here fixed across species and individuals.

The intensity of the external seed rain is quantified by $N_{tot}$ (in number of incoming seeds per hectare) and its species composition is defined by the relative abundances of species $f_{reg,s}$, both being user-defined. Hence, for each species s, $n_{ext,s}$ events of dispersal due to seeds immigrating from the outside occurred, with:

$$n_{ext,s} = N_{tot} \times f_{reg,s} \times n_{ha} \qquad (64)$$

with $n_{ha}$ 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 section 2.4.1). These traits values are then used to determine the maximum LAI (LAImax) the seedling would support under average environmental conditions, with LAImax defined as the
<figure><img src="image_36.png" /></figure>

781 threshold beyond which the seedling leaf assimilation would be less than respiration (see section 2.6.2). The seedling can be
782 recruited if the site LAI at ground level is lower than LAImax.

783 Water availability is also key to seedling performance (Engelbrecht et al., 2006; Johnson et al., 2017; Kupers et al., 784 2019), hence TROLL 4.0 now implements an additional water-dependent dependence on seedling establishment (Craine et al., 785 2012; Paine et al., 2018). Seedling recruitment is possible only if top-layer soil water potential is less negative than half the 786 turgor loss point ($\pi_{tlp}/2$). Such parameterization is motivated by the fact that, at turgor loss point, the seedlings would not 787 germinate, and a certain level of turgor is needed for germination and growth (Bradford, 1990; Daws et al., 2008; Coussement 788 et al., 2018; Hsiao, 1973; Fatichi et al., 2016).

789 If both conditions on light and water availability are met, the newly recruited tree is initialized with a dbh=0.01m, a 790 total leaf area $LA_t = 0.25 \times LA_{opt}$ distributed across the three leaf age pools in proportion to their relative span ($\tau_{young}/LL$, 791 $\tau_{mature}/LL$, $\tau_{old}/LL$; see section 2.6.2), and a carbon storage compartment filled at half its maximum NSC$_r$ (see section 2.6.3).

792 The assumptions here made on tree reproduction largely reflect limited knowledge on these processes, which remains 793 major sources of uncertainty in current models (König et al., 2022; Hanbury-Brown et al., 2022; Díaz-Yáñez et al., 2024).

794 **2.7.2 Mortality**

795 Mortality processes also play a key role in forest structure and carbon balance (Sevanto et al., 2014; Friend et al., 2014; Johnson 796 et al., 2016; Esquivel-Muelbert et al., 2020; McDowell et al., 2022). TROLL 4.0 explicitly represents several important 797 mechanisms of tree mortality. At each timestep, individual tree death rate (in events yr⁻¹; Sheil et al. 1995) is:

$$798 d = d_b + d_{starv} + d_{treefall} + d_{drought} \qquad (65)$$

799 where $d_b$ is a background death rate, $d_{starv}$ represents death due to carbohydrate shortage (carbon starvation), $d_{treefall}$ 800 represents death due to treefall (including trees indirectly killed by neighboring fallen trees), and $d_{drought}$ the drought-induced 801 tree mortality.

802 Background mortality $d_b$ encapsulates death events that are not attributed to any specific mechanism in the model. 803 Mortality rate is known to vary greatly among species, and we here assume that it is negatively correlated with tree wood 804 density, as observed pan-tropically (King et al., 2006; Kraft et al., 2010; Poorter et al., 2008; Wright et al., 2010). This 805 dependence illustrates a trade-off between investment into construction costs and risk of mortality (Chave et al., 2009). We 806 assumed the following relationship:

$$807 d_b = m \times \left(1 - \frac{wsg}{wsg_{lim}}\right) \qquad (66)$$

808 where m (in events yr⁻¹) is the reference background mortality rate for a species with low wood density and is user-specified. 809 $wsg_{lim}$ is a value large enough so that $d_b$ always remains positive (here set at 1 g cm⁻³).
<figure><img src="image_37.png" /></figure>

A tree can also die because of carbohydrate shortage in case of prolonged stress ($d_{starv}$ in Eq. (65)). In TROLL 4.0 that includes an explicit carbohydrate storage compartment, the tree dies of carbon starvation when this compartment is empty and $NPP_{ind} \le 0$ (Eq. (51)).

Tree death may be caused by treefalls (term $d_{treefall}$ in Eq. (65)). To simulate this process, we first define a stochastic threshold $\Theta$, depending on the tree maximal height, and prescribed at tree birth. Then, the tree can fall with a probability equal to $1 - \frac{\Theta}{h}$ (Chave, 1999) each month. As TROLL 4.0 uses a daily timestep, this probability is uniformly distributed across the days of one month. The parameter $\Theta$ is computed for each tree, as follows:

$$ \Theta = h_{max} \times (1 - v_T \times |\zeta|) \qquad (67) $$

where $h_{max}$ is maximal tree height (i.e. the tree height computed using Eq. (16) at $dbh_{max}$), $v_T$ is a variance term, $|\zeta|$ is the absolute value of a random Gaussian variable with zero mean and unit standard deviation. $v_T$ is modified at tree level so that high risks of treefall (> 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 $\frac{h-CR}{2}$, respectively, if it was lower, where $h$ and $CR$ are the tree height and crown radius of the fallen tree, respectively. The probability to die due to another treefall is then $1 - \frac{h}{2h_{hurt} \times e^{e_{h,j}}}$, where $h$ is the height of the focal tree and $e^{e_{h,j}}$ (see Eq. (16)) accounts for the fact that slender individuals (higher tree height deviation) would be more vulnerable to treefall. Such tree can either fall and itself damage other trees or dies standing, depending on the user choice. The *hurt* variable is reset to zero at each timestep.

Finally, prolonged drought is also a source of mortality. Drought-induced mortality is triggered when the leaf predawn water potential $\psi_{pd}$ is below a lethal level ($\psi_{lethal}$), and $\psi_{lethal}$ is computed from the leaf water potential at turgor loss point, using the relationship provided by the global meta-analysis of Bartlett et al. (2016; P=0.03, R²=0.31, n=15 species from tropical dry and moist biomes), as follows:

$$ \psi_{lethal} = -0.9842 + 3.1795 \times \pi_{tlp} \qquad (68) $$

# 3 Modelling protocol

## 3.1 Model inputs

TROLL 4.0 requires five input files to run a simulation: (i) global parameters, (ii) species parameters, (iii) soil characteristics, and finally, meteorological drivers varying at (iv) half-hour and (v) daily step.
<figure><img src="image_38.png" /></figure>

The global input file contains parameters that define the simulation set-up (e.g. the number of timesteps, size of the simulated plot and of the belowground voxels), and values for biophysical parameters that remain constant throughout the simulation and are not species- or tree-specific. These include the light attenuation coefficient, allocation parameters, minimal death rate, and more (see Table A1). Parameter values can be varied across simulations, to test model sensitivity, transfer across sites, or any other reason. The species input file contains mean functional traits for at least one species and with no upper bound (see Table A1). Functional trait values can be prescribed from local field measurements, or retrieved from global trait databases (e.g. Kattge et al., 2020; Díaz et al., 2022).

The soil input file contains the soil variables needed for the pedotransfer functions, i.e. soil texture (proportion of silt, clay and sand), soil organic matter content, dry bulk density, soil pH, and cation exchange capacity, for each soil layer, with thickness of each layer. The number of soil layers is at least one, and is not theoretically limited. Lacking local soil data, model users may retrieve soil parameters from online databases (e.g. Poggio et al., 2021), bearing in mind the uncertainties of such products, especially in tropical areas (Khan et al., 2024).

Meteorological drivers are provided in two files, depending on their temporal resolution in the model. Daytime temperature, vapor pressure deficit, incident irradiance and wind speed at a reference height above the canopy are provided for every half-hour, while average nighttime temperature and cumulative rainfall are provided at a daily timestep. Such data can typically be retrieved from meteorological stations embedded in eddy-flux towers, or from global products (Muñoz-Sabater et al., 2021), as in Schmitt et al. (2023).

## 3.2 Initial conditions

Two types of initial conditions are useful in most practical settings, and are implemented in TROLL 4.0. First, the user can simulate forest regeneration from bare ground. In this case, forest succession is initiated by the external seed rain, the composition and intensity of which are user-defined (see above). The steady-state forest composition and structure are thus emergent properties of the community assembly mechanisms embedded in the model, and the user-specified seed rain. The second option is to prescribe an initial forest state. This requires that an initial forest state be provided as an additional input file. The code is designed to adapt to the level of information provided by the inventory file, from a minimal requirement of tree *dbh* to the full list of individual variables for each tree. For individual variables missing in the input file, these are either computed from the model relationships or drawn at random. This second initial condition matches a real site forest state given the available data, but will require careful calibration to maintain the forest state over a longer time period (e.g. Fischer et al., 2019). A more common use case is to restart new simulations from an output of a previous simulation, e.g., to perform virtual experiments controlling the initial state.

## 3.3 Standard outputs

TROLL 4.0 provides a range of outputs related to forest structure, forest composition and diversity, and ecosystem functioning (e.g., carbon and water fluxes; Fig. 4). It simulates forest structure and composition and provides outputs comparable to those
<figure><img src="image_39.png" /></figure>

measured in the field: tree size distribution, tree spatial distribution, biomass accumulation curve, functional trait distribution, canopy height and leaf area index maps (Maréchaux and Chave, 2017), and more generally all information that can be retrieved from a detailed field inventory or a meter-scale airborne laser scanning survey (Fischer et al., 2019). In TROLL 4.0, other outputs are also available: litterfall fluxes, carbon and water fluxes comparable to the one provided by eddy-flux towers, soil water state (content and water potential). An evaluation of these outputs for two Amazonian forest sites is provided in a companion paper (Schmitt et al., submitted companion paper).

<figure><img src="image_40.png" /><figcaption>Figure 4: Examples of outputs provided by TROLL 4.0 and related to ecosystem functioning, diversity and structure. (a) Temporal variations of gross primary productivity (red) and evapotranspiration (blue) within and across years. (b) Variation in total leaf area index (red line) and leaf area index per leaf age cohort (young, mature, old; yellow, light green and dark green lines, respectively), together with litterfall (grey bars), within and across years. (c) Mean seasonal variations of water content in soil layers of different depths, with the vertical yellow band in the background depicting the dry season. (d) Distribution of functional traits. (e) Distributions of basal area per diameter class. Panels (a), (b) and (c) show outputs for an Amazonian forest site (Paracou), panels (d) and (e) show outputs for two Amazonian sites (Paracou, red; Tapajos, blue), see Schmitt et al., submitted companion paper. for details on simulation set-ups.</figcaption></figure>

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# 4 Discussion

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TROLL 4.0 is a novel generation of forest growth models designed to bridge the gap between traditional forest growth models and process-based models informed by ecophysiology. It includes an integration of processes underlying ecosystem fluxes closer to a modern DGVM than most other forest growth simulators. It also includes representation of plant community structure and diversity at a resolution similar to that used by ecologists in the field. This enables a direct comparison with a range of field data, including forest inventories, trait distribution, fine- and large-scale remote-sensing products, or eddy-covariance data. Here we discuss the assumptions of the water cycle newly included in the model, as well as transferability and limitations of the current model version.

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## 4.1 Simulating water fluxes and forest responses to water availability

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Previous versions of TROLL assume that water availability does not limit ecosystem fluxes and dynamics, a strong but reasonable assumption in a light-limited forest like in Eastern Amazonia (Guan et al., 2015; Wagner et al., 2016; Maréchaux and Chave, 2017). However, such a simplification does not allow to account for drought-induced inter-annual variability in forest dynamics (Bonal et al., 2008; Aguilos et al., 2018; Leitold et al., 2018) or to transfer the model to sites where water availability is limiting. As droughts will be important drivers for tropical ecosystems in the future (Duffy et al., 2015), such a simplification does not allow to project future states of forest under climate change.

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In TROLL 4.0, we implemented a full water cycle. We introduced a belowground field with a hydraulic state coupled to the vegetation, and a representation of the response of leaf gas exchanges to local atmospheric conditions and their control by the leaf boundary layer. This detailed representation is commonplace DGVMs (Prentice et al., 2007) but to our knowledge, it is new for an individual-based spatially explicit forest dynamic simulator. This paves the way for explorations and projections of the independent effects of soil water availability and atmospheric demand on ecosystem functioning (Novick et al., 2016; Santos et al., 2018), community composition and structure (Esquivel-Muelbert et al., 2019; Fauset et al., 2012; Slik, 2004; Feeley et al., 2011).

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These developments have striven to follow the parsimonious principle: more complex representations do not systematically result in increased model reliability and robustness, especially if the additional parameters are poorly constrained (Mahnken et al., 2022; Prentice et al., 2015). The soil hydraulic state is simulated using a bucket model (Budyko, 1961; Manabe1969; Vargas Godoy et al., 2021). In the future, more complex representations of soil water dynamics could be implemented at finer temporal and spatial resolutions, such as the implementation of Richards' equation (Richards, 1931), and integration of lateral flows, but this would be at a serious computational cost. These could be compared with the current simpler representation to assess the relevance of increasing complexity in various contexts and soil data availability (Van Nes and Scheffer, 2005). However, two aspects were considered to be needed in the current version, based on biological considerations. First, we implemented a multi-layer soil model, a more detailed representation compared with other models using a bucket model approach (e.g. Fischer et al., 2014; Laio et al., 2001). This was motivated by the need to account for contrasting rooting
<figure><img src="image_42.png" /></figure>

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strategies and access to water among coexisting plants, which is an under-explored, but likely key, aspect of community dynamics in forests (Brum et al., 2019; De Deurwaerder et al., 2018; Ivanov et al., 2012). Second, we assumed that the depth of tree water uptake is not only controlled by the distribution of root biomass (as in Naudts et al., 2015; Sakschewski et al., 2021; Paschalis et al., 2024), but also by soil water state and its vertical variation (as in Williams et al., 1996; Duursma and Medlyn, 2012). These improvements are relevant to the temporal variation of water retrieval depth (Bruno et al., 2006) and the sustained dry-season productivity in rainforest ecosystems (Restrepo-Coupe et al., 2017).

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The control of leaf gas exchange by water availability has been implemented by means of multiplicative soil water stress factors. Although the use of such factors has been debated (Powell et al., 2013; Joetzjer et al., 2014), it has been preferred over a more explicit representation of the water flow through the plant column (e.g. Yao et al., 2022; Christoffersen et al., 2016; Cochard et al., 2021; De Cáceres et al., 2023). Although the stem hydraulic traits that would be needed for parameterizing an explicit plant water flow module have been increasingly measured over the past decades, data availability for tropical tree species remains low in regards to the actual number of species coexisting in these communities. Alternatively, correlative relationships have been used to infer these traits from more easily measured traits (Christoffersen et al., 2016; Xu et al., 2016). However, these are context dependent (Brodribb, 2017; Rosas et al., 2019) and have at best low statistical support in rainforest communities that are loosely constrained by water availability (Dwyer and Laughlin, 2017; Delhaye et al., 2020; Maréchaux et al., 2020). Innovative methods alleviate the difficulties of robustly measuring the vulnerability of tropical trees to embolism (Cochard et al., 2016; Sergent et al., 2020; Garcia et al., 2023), and this could provide a key motivation for a more explicit module of plant water flow in TROLL (Kennedy et al., 2019; Paschalis et al., 2024). Such developments could be necessary to correctly represent the legacy of drought in forest ecosystems (Paschalis et al., 2024; Anderegg et al., 2015). However, two important aspects were taken into account in the implementation of the multiplicative water stress factors in TROLL 4.0. These factors were parameterized based on soil water potential as independent variable, and not soil water content, the former directly controlling water availability for plants, while the effect of soil water content is strongly mediated by soil properties (Novick et al., 2022). Also, different water stress factors were used for stomatal and non-stomatal limitations, in order to capture the sequence of effects of decreasing water availability on plant function (Trueba et al., 2019; Fatichi et al., 2016; Hsiao, 1973).

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The effects of water availability on plant function and tree demography were implemented through trait-based parameterization, which allows a range of responses between trees and species. This was made possible through the use of leaf water potential at turgor loss point ($\pi_{tlp}$), a leaf-level trait that is mechanistically linked to plant responses to water availability (Bartlett et al., 2016b) and that is measurable at the community scale in diverse systems through a well-validated method (Maréchaux et al., 2016; Griffin-Nolan et al., 2019; Sun et al., 2020; Bartlett et al., 2012a). Leaf water potential at turgor loss point varies greatly across species within Amazonian forest communities (Maréchaux et al., 2015; Ziegler et al., 2019), and this diversity explains contrasting responses to water availability at the leaf and plant levels (Martin-StPaul et al., 2017; Maréchaux et al., 2018; Powell et al., 2017), and species distribution at local, regional and global scales (Bartlett et al., 2016a; Baltzer et al., 2008; Lenz et al., 2006; Bartlett et al., 2012b). The relationships implemented here involving $\pi_{tlp}$ have a mechanistic basis, as discussed above. However, the relationships controlling the effect of water availability on (1) leaf
<figure><img src="image_43.png" /></figure>

shedding, (2) seed germination and seedling recruitment, and (3) drought-induced mortality would deserve in-depth exploration. More generally, these three processes remain key aspects of community dynamics and ecosystem functioning in high need of sustained empirical investigation (Albert et al., 2019; Díaz-Yáñez et al., 2024; McDowell et al., 2022).

## 4.2 Model-data integration, transferability and limitations

TROLL 4.0 simulates forest structure and diversity, while expanding the types of data with which its results can be compared (Schmitt et al., submitted companion paper). The individual-based species-specific representation of forest yields virtual forest inventories, including the location of each individual, their botanical identity, and their dimensions, and virtual airborne laser scanning point clouds (Fischer et al., 2019; Schmitt et al., 2023). TROLL 4.0 additionally provides water, carbon and litter flux dynamics that are directly comparable to eddy-flux tower data and litter trap monitoring at fine temporal resolutions, and this specificity has numerous advantages.

Data-driven knowledge can be directly assimilated in TROLL 4.0, offering new perspectives for inference or calibration (Dietze et al., 2013; Fer et al., 2018; Hartig et al., 2012; LeBauer et al., 2013; Fischer et al., 2019). TROLL 4.0 can help inform the development of DGVMs, in which the representation of vegetation does not allow this type of assimilation (Fischer et al., 2019). TROLL 4.0 is also easy to use and test by field ecologists as it simulates trees, not cohorts, PFTs, or gap patches: it can reproduce classical experiments in community or ecosystem ecology (e.g. Crawford et al., 2021; Schmitt et al., 2020) while overcoming known empirical challenges such as low repeatability (Schnitzer and Carson, 2016) or limited spatial footprint (Estes et al., 2018). TROLL 4.0 can be compared with data under the control of different biophysical processes supporting a more robust evaluation, and limiting equifinality issues (Franks et al., 1997; Medlyn et al., 2005). Finally, the model is parameterized based on traits directly measured in the field improving model transferability (Rau et al., 2022a).

The individual-scale and spatially-explicit representation of TROLL 4.0 comes with a computational burden. For a reference 4-ha area starting from bare ground, and 600 years of simulation, the computational cost of TROLL 4.0 is about 1820 min, compared with version TROLL2.3 (Maréchaux and Chave 2017) about 12 min. While the shift from a monthly to a daily timestep explains the multiplication by a factor of 30 between the two versions, the addition of a belowground field and of an iterative scheme to simulate leaf gas exchanges explains for a great part the remaining factor of five. Several developments should reduce this computational cost: tree demographic processes do not need to be simulated at the daily timestep and could be represented at a monthly resolution; vegetation models already implement such nested time scales (Moorcroft, 2006). We are also confident that further computer time reduction will be brought about by code optimization. Finally, several strategies can be implemented to up-scale the outputs of individual-based models at reduced computational costs, especially by leveraging large scale remote sensing products (Rödig et al., 2017; Sato et al., 2007; Shugart et al., 2015).

## 4.3 Current and future developments

TROLL 4.0 is a reflection on the state of the art and knowledge gaps in plant physiology and ecology, resulting in an unbalanced representation across processes. TROLL is being continuously developed, as knowledge and data availability
<figure><img src="image_44.png" /></figure>

progress, specific questions to address with the model emerge, or important limitations are identified. In a companion paper (Schmitt et al., submitted companion paper), we use data from forest inventories, litter traps, eddy-flux towers and remote sensing products to evaluate and discuss the performance and limitations of TROLL 4.0 at two forest sites. We here mention several on-going or future developments.

Empirical findings suggest that the contribution of undisturbed tropical forests to the global carbon sink is declining (Hubau et al., 2020; Qie et al., 2017), pointing to the need of integrated modelling to understand and predict such trends (Yao et al., 2023, 2024; Koch et al., 2021). Among the possible steps forward with TROLL 4.0 are an improved representation of stomatal conductance and its coupling with photosynthesis (Lamour et al., 2022, 2023; Dewar et al., 2018), as well as respiration response and acclimation to climatic drivers (Smith and Dukes, 2013; Collalti et al., 2020; Slot et al., 2013; Rowland et al., 2015). Improvements on the carbon budget would also be important, with more explicit carbon allocation to reproductive organs and belowground structures, under the control of environmental drivers (Fig. 3). However, such developments would rely on limited empirical or experimental knowledge belowground (Cusack et al., 2024) and scarce information on tree reproductive strategies (Igarashi et al., 2024; Vacchiano et al., 2018; Norden et al., 2007). An improved representation and evaluation of drought-induced tree mortality would be another important step forward as it might play a key role in the observed changing dynamics and functional and floristic turnover (Esquivel-Muelbert et al., 2019; Feeley et al., 2011; Hubau et al., 2020; Qie et al., 2017). Information provided by long-term through fall exclusion experiments would offer interesting opportunities for model development and evaluation (Powell et al., 2013; Yao et al., 2022).

Tropical forest disturbance by land use change, fire regimes, and other degradations are an important source of C emissions (Lapola et al., 2023), and they must be represented in models. For instance, it is important to understand how edge effects affect the forest microclimate, and consequently forest dynamics, functioning and composition (Camargo and Kapos, 1995; Nunes et al., 2022). To this end, micro-climate models could be coupled to or embedded within TROLL (Gril et al., 2023; Maclean and Klinge, 2021). Fragmentation also impacts seed dispersal, and thus seed rain and seed bank intensity and composition (Warneke et al., 2022; Cubiña and Aide, 2001). Improving TROLL's representation of seed dispersal ability and germination as a function of plant trait and dispersal mode is key to capture the effect of forest loss and fragmentation on forest functioning and biodiversity (Seidler and Plotkin, 2006; Muller-Landau et al., 2008; Tamme et al., 2014; Chase et al., 2020; Riva and Fahrig, 2023). More generally, one overarching objective is to improve model's representation of processes involved in forest regeneration, to simulate secondary forest dynamics and resilience to disturbances (Hanbury-Brown et al., 2022; Díaz-Yáñez et al., 2024; Poorter et al., 2023; Albrich et al., 2020).

Finally, TROLL 4.0 includes major developments that should facilitate its transferability across sites. The explicit integration of the ecosystem water balance and vegetation responses to soil water availability now allows to consider spatio-temporal extrapolation along water stress gradients. The integration of soil topography and heterogeneity would also be an important advance for improved genericity. As nutrient availability is being altered by human activities (Peñuelas et al., 2013), the explicit integration of a nutrient cycle with nitrogen and phosphorous colimitation will be a useful advance in the future
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(Fernández-Martínez et al., 2014; Turner et al., 2018). Similarly, the extension of tree functioning responses to a broader range of temperatures, should support the transferability of TROLL to temperate and boreal forests.

## 5. Conclusion

TROLL 4.0 represents an advance over previous versions as it bridges across forest model types, while maintaining a representation consistent with field ecology and ecosystem science. TROLL 4.0 simulates the responses of tropical forests to water availability through the explicit representation of water dynamics belowground and its coupling with leaf-level gas exchanges and demographic processes. This comes at a computational cost, and a future task is to conduct code optimization and parallelization, and up-scaling in combination with remote-sensing products. The representation of processes in TROLL 4.0 mirrors an unbalanced state of the art, but its ability to dialogue with a range of data of various nature, makes it a valuable tool to take up the fundamental and applied research challenges on tropical forests. TROLL 4.0 has benefited from observations and field experiments that feed the development of models (Medlyn et al., 2015; Paschalis et al., 2020), while modeling exercises inform and guide empirical approaches (Medlyn et al., 2016; Norby et al., 2016; Pacala and Rees, 1998). This is possible because of the fine scale representation of forest structure and diversity and the trait-based parameterization of processes in the model.

**Code and data availability.** The code of TROLL 4.0 is available at https://github.com/TROLL-code/TROLL, a DOI will be linked to this repository upon publication. Additionally, TROLL 4.0 can be set-up and run, and its outputs can be analyzed with an updated version of the R package rcontroll: https://github.com/sylvainschmitt/rcontroll/tree/TROLLV4, also available in R through the command devtools::install_github("sylvainschmitt/rcontroll", ref = "TROLLV4").

**Supplement.** The supplement related to this article will be available online upon publication acceptance.

**Author contributions.** IM led TROLL 4.0, and designed the implementation of the water cycle and its coupling to vegetation. FJF co-led TROLL 4.0 and designed the new implementation of intra-specific variability and crown shapes. SS and JC contributed ideas and discussions. IM wrote the paper with contributions from all authors.

**Competing interests.** The authors declare that they have no conflict of interest.

**Acknowledgements.** We acknowledge Nicolas Martin-StPaul and Rémi Vezy for useful discussions on the representation of gas exchanges and water fluxes in models; Nicolas Barbier, Gregoire Vincent, and James Ball for sharing data and useful
<figure><img src="image_46.png" /></figure>

discussions on leaf phenology; Philippe Verley and Thomas Arsouze for IT support; and Marie Boscher for help in designing figure 1. This work was carried out with the support of MESO@LR-Platform at the University of Montpellier.

*Financial support.* This research has been supported by fundings from ANR (the French National Research Agency) under the "Investissements d'avenir" program with the references ANR-16-IDEX-0006, ANR-10-LABX-25-01, ANR-10-LABX-0041, the Amazonian Landscapes in Transition ANR project (ALT), CNES Biomass-Valo project, and ESA CCI-BIOMASS.

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1643 Jucker, T., Hardwick, S. R., Both, S., Elias, D. M. O., Ewers, R. M., Milodowski, D. T., Swinfield, T., and Coomes, D. A.: Canopy structure and topography jointly constrain the microclimate of human-modified tropical landscapes, *Global Change Biology*, 24, 5243–5258, https://doi.org/10.1111/gcb.14415, 2018.

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1682 Blackman, C., Blanco, C., Blonder, B., Blumenthal, D., Bocanegra-González, K. T., Boeckx, P., Bohlman, S., Böhning-Gaese, K., Boisvert-Marsh, L., Bond, W., Bond-Lamberty, B., Boom, A., Boonman, C. C. F., Bordin, K., Boughton, E. H., Boukili, V., Bowman, D. M. J. S., Bravo, S., Brendel, M. R., Broadley, M. R., Brown, K. A., Bruelheide, H., Brumnich, F., Bruun, H. H., Bruy, D., Buchanan, S. W., Bucher, S. F., Buchmann, N., Buitenwerf, R., Bunker, D. E., et al.: TRY plant trait database – enhanced coverage and open access, Global Change Biology, 26, 119–188, https://doi.org/10.1111/gcb.14904, 2020.

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1692 Keenan, T., Sabate, S., and Gracia, C.: Soil water stress and coupled photosynthesis–conductance models: Bridging the gap between conflicting reports on the relative roles of stomatal, mesophyll conductance and biochemical limitations to photosynthesis, Agricultural and Forest Meteorology, 150, 443–453, https://doi.org/10.1016/j.agrformet.2010.01.008, 2010.

1696 Kennedy, D., Swenson, S., Oleson, K. W., Lawrence, D. M., Fisher, R., Costa, A. C. L. da, and Gentine, P.: Implementing Plant Hydraulics in the Community Land Model, Version 5, Journal of Advances in Modeling Earth Systems, 11, 485–513, https://doi.org/10.1029/2018MS001500, 2019.

1699 Kenzo, T., Ichie, T., Hattori, D., Itioka, T., Handa, C., Ohkubo, T., Kendawang, J. J., Nakamura, M., Sakaguchi, M., Takahashi, N., Okamoto, M., Tanaka-Oda, A., Sakurai, K., and Ninomiya, I.: Development of allometric relationships for accurate estimation of above- and below-ground biomass in tropical secondary forests in Sarawak, Malaysia, Journal of Tropical Ecology, 25, 371–386, https://doi.org/10.1017/S0266467409006129, 2009.

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1729 Krinner, G., Viovy, N., de Noblet-Ducoudré, N., Ogée, J., Polcher, J., Friedlingstein, P., Ciais, P., Sitch, S., and Prentice, I. C.: A dynamic global vegetation model for studies of the coupled atmosphere-biosphere system, Global Biogeochem. Cycles, 19, GB1015, https://doi.org/10.1029/2003GB002199, 2005.

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1735 Kupers, S. J., Engelbrecht, B. M. J., Hernández, A., Wright, S. J., Wirth, C., and Rüger, N.: Growth responses to soil water potential indirectly shape local species distributions of tropical forest seedlings, Journal of Ecology, 107, 860–874, https://doi.org/10.1111/1365-2745.13096, 2019.

1738 Kursar, T. A., Engelbrecht, B. M. J., Burke, A., Tyree, M. T., El Omari, B., and Giraldo, J. P.: Tolerance to low leaf water status of tropical tree seedlings is related to drought performance and distribution, Functional Ecology, 23, 93–102, https://doi.org/10.1111/j.1365-2435.2008.01483.x, 2009.

1741 Lagarrigues, G., Jabot, F., Lafond, V., and Courbaud, B.: Approximate Bayesian computation to recalibrate individual-based models with population data: illustration with a forest simulation model, Ecological Modelling, 306, 278–286, https://doi.org/10.1016/j.ecolmodel.2014.09.023, 2015.

1744 Laio, F., Porporato, A., Ridolfi, L., and Rodriguez-Iturbe, I.: Plants in water-controlled ecosystems: active role in hydrologic processes and response to water stress: II. Probabilistic soil moisture dynamics, Advances in Water Resources, 24, 707–723, https://doi.org/10.1016/S0309-1708(01)00005-7, 2001.

1747 Lamour, J., Davidson, K. J., Ely, K. S., Le Moguédec, G., Leakey, A. D. B., Li, Q., Serbin, S. P., and Rogers, A.: An improved representation of the relationship between photosynthesis and stomatal conductance leads to more stable estimation of