# Plant Hydraulic Architecture for a Mechanistic Representation of Soil-Plant-Atmosphere Water Transfer in the Land Surface Model ORCHIDEE (r9107)

Julien Alléon, Nicolas Vuichard, Catherine Ottlé, Andrée Tuzet, Sebastiaan Luyssaert, Matthias Cuntz, Jean-marc Limousin, Jean Kempf, Philippe Peylin

► To cite this version:

Julien Alléon, Nicolas Vuichard, Catherine Ottlé, Andrée Tuzet, Sebastiaan Luyssaert, et al. Plant Hydraulic Architecture for a Mechanistic Representation of Soil-Plant-Atmosphere Water Transfer in the Land Surface Model ORCHIDEE (r9107). Journal of Advances in Modeling Earth Systems, 2025, 17 (11), pp.e2024MS004869. 10.1029/2024MS004869. hal-05468856

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
RESEARCH ARTICLE

10.1029/2024MS004869

**Key Points:**

* A new plant hydraulic architecture representation with an adaptive numerical resolution scheme is proposed

* A detailed multi-scale evaluation showed similar performances between the hydraulic architecture and the standard configurations

* Global scale evaluation highlighted the impacts of the site-calibrated hydraulic architecture on the global ORCHIDEE land surface model performance

**Correspondence to:**

J. Alléon,
julien.alleon@lsce.ipsl.fr

**Citation:**

Alléon, J., Vuichard, N., Ottlé, C., Tuzet, A., Luysaert, S., Cuntz, M., et al. (2025). Plant hydraulic architecture for a mechanistic representation of soil-plant-atmosphere water transfer in the land surface model ORCHIDEE (r9107). *Journal of Advances in Modeling Earth Systems*, 17, e2024MS004869. https://doi.org/10.1029/2024MS004869

Received 9 DEC 2024
Accepted 21 OCT 2025

**Author Contributions:**

**Conceptualization:** Nicolas Vuichard, Andrée Tuzet

**Data curation:** Julien Alléon

**Formal analysis:** Julien Alléon

**Funding acquisition:** Nicolas Vuichard, Philippe Peylin

**Investigation:** Julien Alléon

**Methodology:** Julien Alléon, Nicolas Vuichard, Catherine Ottlé, Andrée Tuzet, Philippe Peylin

**Project administration:** Philippe Peylin

**Resources:** Julien Alléon, Andrée Tuzet, Matthias Cuntz, Jean-Marc Limousin, Jean Kempf

**Software:** Julien Alléon

**Supervision:** Nicolas Vuichard, Catherine Ottlé, Philippe Peylin

© 2025 The Author(s). Journal of Advances in Modeling Earth Systems published by Wiley Periodicals LLC on behalf of American Geophysical Union. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

<figure><img src="image_2.png" /></figure>

# Plant Hydraulic Architecture for a Mechanistic Representation of Soil-Plant-Atmosphere Water Transfer in the Land Surface Model ORCHIDEE (r9107)

Julien Alléon¹ ID, Nicolas Vuichard¹ ID, Catherine Ottlé¹, Andrée Tuzet², Sebastiaan Luyssaert³ ID, Matthias Cuntz⁴ ID, Jean-Marc Limousin⁵, Jean Kempf⁶, and Philippe Peylin¹ ID

¹LSCE, CEA-CNRS-UVSQ, Gif-sur-Yvette, France, ²EcoSys, Université Paris-Saclay, INRAE, AgroParisTech, Palaiseau, France, ³A-Life, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands, ⁴Silva, Université de Lorraine, AgroParisTech, INRAE, Nancy, France, ⁵CEFE, Université de Montpellier, CNRS, EPHE, IRD, Montpellier, France

**Abstract** Land surface models (LSMs) typically represent soil moisture control on stomatal conductance through an empirical sensitivity function, without considering plant hydrology. This study proposes integrating water transfer representation within the soil-plant-atmosphere continuum in the ORCHIDEE land surface model. This new configuration includes vegetation hydraulic architecture and a stomatal control based on leaf water potential ($\psi_{leaf}$), along with a mechanistic representation of water absorption by roots via radial diffusion around the roots. An adaptive numerical scheme is implemented to prevent numerical instabilities during hydric stress, reducing hourly instabilities by a factor of 2. The implementation and the standard configuration of ORCHIDEE are calibrated and evaluated at FLUXNET sites with eddy-covariance flux measurements. A detailed assessment is carried out at two well-documented forest sites (FR-Hes and FR-Pue), where both configurations perform similarly regarding the seasonal dynamics of latent heat flux (RMSEs of 16.0 W/m² for the potential-based configuration and 15.8 W/m² for the standard configuration at FR-Hes). An evaluation of leaf water potential at FR-Pue shows correlations of 0.87 and 0.72 for predawn and midday $\psi_{leaf}$ respectively. A second evaluation across 135 sites from the FLUXNET2015 database highlights similar performances for both configurations. Finally, a global assessment of the differences between the two schemes emphasizes the good performance of the hydraulic architecture model. Overall, the new hydraulic architecture provides a more mechanistic description of stomatal conductance response to soil water stress and paves the way for incorporating physiological processes controlling tree mortality and using in situ observations to calibrate plant responses to water stress.

**Plain Language Summary** Land surfaces models (LSMs), which aim at representing the exchanges between the land surfaces and the atmosphere, usually represent the rate of water exchanges between the vegetation and the atmosphere according to soil water stress defined as an empirical function and without considering the plant water status. Here, we propose to represent the water transfers from the soil-root interface toward the leaves via a hydraulic architecture model, accounting for potential water storage in the plant. This model provides a more mechanistic description of the response of stomatal conductance to soil water stress and opens for the representation of important physiological processes such as cavitation. In order to evaluate the model, a detailed analysis has been performed at two forest sites. It enabled to understand the behavior of the new configuration and to verify its capacity to reproduce observations of water exchanges with the atmosphere. An extended analysis over 135 FLUXNET sites illustrated the overall good performances of the model. Finally, a study at global scale highlighted significant differences between the new hydraulic architecture and the standard model with respect to energy, water and carbon fluxes.

## 1. Introduction

The description of water transport in the soil-plant-atmosphere continuum in global land surface models (LSM) is critical to simulate the dynamics of plant transpiration and CO₂ uptake and in particular their response to drought (Lemordant et al., 2018; Trugman et al., 2018). In this context, the regulation of stomatal aperture by the plant, in order to maximize CO₂ uptake from the atmosphere and minimize water loss by transpiration, is a key process that bridges energy, water and carbon transfers (Liu et al., 2020). The regulation of stomatal conductance is driven by several physiological and physical processes that control the turgor pressure difference between the leaf epidermis and the guard cells surrounding the pores (Buckley, 2005; Franks et al., 1998). Among these processes, the
**Validation:** Julien Alléon

**Visualization:** Julien Alléon

**Writing – original draft:** Julien Alléon

**Writing – review & editing:**
Julien Alléon, Nicolas Vuichard,
Catherine Ottlé, Sebastiaan Luyssaert,
Matthias Cuntz, Jean-Marc Limousin,
Philippe Peylin

extraction of water from the soil matrix and its transfer to the leaf, the sensitivity to atmospheric vapor pressure, and the response to leaf sugar concentration are considered essential (Damour et al., 2010). This study focuses on modeling the water transfers from the soil to the leaf, which is called plant hydraulic architecture.

Different formalisms have been used to model stomatal conductance. One of the earliest and most used is the model of Ball et al. (1987) which is common to most LSMs, with several updates as described for instance in Medlyn et al. (2001), Verhoef and Egea (2014), and Damour et al. (2010). As the Ball and Berry model does not account for a control of the soil drying on stomatal closure, up to recently, most LSMs added and employed a simple empirical function to describe the decrease of stomatal conductance due to soil moisture limitation (Fatichi et al., 2016; Mencuccini et al., 2019). Various functions have been used from a linear dependence on soil moisture content (i.e., usually defined between the two key thresholds: wilting point and field capacity) up to more complex functions (i.e., exponential function as in Meridja (2011) or more complex as in Trugman et al. (2018)).

More recently, ecophysiological modeling intended to account for physically-based water plant transport in LSMs, with an explicit simulation of water transport across the soil, root, stem, leaves and the atmosphere continuum, following a gradient of water potentials and organ-specific conductivity parameters (Bonan et al., 2014; Dewar, 2002; Hickler et al., 2006; Sperry et al., 1998). These process-based hydraulic architectures offer numerous advantages compared to the standard empirical function. First, the computation of water potentials at different levels along this continuum can be evaluated against potential measurements of water potentials (expressed in potential energy per unit of volume) in the soil or in the plant organs (see for instance, Scholander et al. (1965) and Novick et al. (2022)). Such formalism thus offers the possibility to evaluate more directly the implementation of key processes driving the water transfers from the roots to the leaves, especially during drought events. The hydraulic architecture representation also facilitates the comparison to sapflow measurements (Poyatos et al., 2016). Second, it allows the inclusion of water reservoirs in the plant (root, trunk, stem) in a straightforward way using the concept of capacitance (i.e., an analog to electric circuits). Dynamic plant water storage is key to simulate diurnal effects linked to the rehydration of plants at night (Tuzet et al., 2003) or seasonal effects (Tian et al., 2018; Wright et al., 2017). Third, it is well suited to account for the impact of plant growth on plant hydraulics, especially trees, where organ conductivities vary with plant height and the overall plant physiology (Phillips et al., 2003) and to study the opposite, the impact of plant hydraulics on plant growth. Finally, such formalism opens the door for a more process-based description of specific tree mortality causes, such as those related to cavitation following severe drought, also known as embolism (Cochard et al., 2013; de Kauwe et al., 2022; Yao et al., 2022), or other related disciplines such as fire ecology, plant pathologies or crop sciences as detailed in Torres-Ruiz et al. (2024).

Given the additional complexities linked to this formalism, only a few global LSMs explicitly use a process-based description of the plant hydraulic architecture, among others CLM v5 (Kennedy et al., 2019), following developments from Bonan et al. (2014) in CLM4.5, ORCHIDEE-CAN (Naudts et al., 2015), CABLE (de Kauwe et al., 2020, 2022) and NOAH-MP (Li et al., 2021). These models implemented different numerical approaches. In a first simple approach, stomatal conductance can be decoupled from plant hydraulics which only act as a correction term when plant water supply cannot match the atmospheric demand during periods of drought. This leads to an iteration of the energy budget in those periods (Bonan et al., 2014; Naudts et al., 2015). With a more complex coupled approach, stomatal conductance is directly linked to plant water status and the potential oscillations introduced by the coupling can be circumvented using an iterative scheme (Tuzet et al., 2003), shorter time steps such as in the explicit configuration of the model SurEau described in Cochard et al. (2021), Ruffault et al. (2022) or more complex analytical solutions as in the implicit and semi-implicit configurations of SurEau-Ecos v2.0 (Ruffault et al., 2022). However, these solutions potentially lead to an increase in computational cost that may decrease their suitability for a global LSM.

In this context, this study proposes a new implementation of a hydraulic architecture in the ORCHIDEE LSM. The proposed scheme follows previous work that included a plant hydraulic architecture in the specific model branch ORCHIDEE-CAN (Naudts et al., 2015), almost 10 years ago. In this initial scheme, stomatal conductance was decoupled from the hydraulic architecture. The scheme was further updated in Joetzjer et al. (2022) and Yao et al. (2022) for a specific application for tropical forest, but was still not addressing all the challenges mentioned above. For details on these previous ORCHIDEE versions see Section 2.3.

The presented study thus expands on these initiatives with the aim to develop a more dynamic hydraulic architecture in a recent version (r9107) of the main version of the ORCHIDEE code. This study aims to (a) fully
couple the computation of plant water potential to stomatal conductance and transpiration, accounting also for plant water storage, (b) implement a new numerical scheme that avoids, as much as possible, iterations to save computing time, (c) include a mechanistic description of the soil-to-root water absorption, and (d) implement and calibrate the proposed hydraulic architecture for all plant functional types (PFTs), following a statistical calibration of key model parameters using local flux measurements such as those provided in the FLUXNET database (Pastorello et al., 2020), and (e) assess the potential of the new hydraulic architecture to simulate the impact of soil water stress especially during drought periods on transpiration by comparing it against the current standard in ORCHIDEE, that is, an empirical representation of the impact of soil water stress on stomatal conductance.

The paper first describes the two stomatal conductance models implemented in ORCHIDEE, the standard approach with the empirical dependency of stomatal conductance to soil water content and the new approach with an interactive hydraulic architecture representation (Section 2). The results of the two modeling approaches are compared to in situ observations at two well-documented forest sites (Section 4.2) and a larger ensemble of sites representative of a wider set of PFTs (Section 4.3). Last, global simulations with the two stomatal conductance models are compared regarding their skill at simulating water, energy and carbon fluxes (Section 4.4).

## 2. ORCHIDEE and Model Developments

### 2.1. ORCHIDEE General Description

#### 2.1.1. Model Overview and Forcing Data

ORCHIDEE is a LSM developed for studying energy, water, carbon, and nitrogen fluxes in the soil-plant-atmosphere continuum and their interactions (Krinner et al., 2005; Vuichard et al., 2019). It is used for impact studies from the site level to the global scale in a stand-alone mode, driven by meteorological forcings. ORCHIDEE can also be coupled to the atmospheric general circulation model (LMDZ) (which, further coupled with an ocean and an ice-sheet models, makes up the Institut Pierre Simon Laplace (IPSL) Earth System Model (Boucher et al., 2020; Cheruy et al., 2020) dedicated to climate studies). In both configurations, the meteorological fields that drive ORCHIDEE consist of the incoming short-wave and long-wave radiations, precipitation, near-surface air humidity and temperature, and wind speed. At local scales, the meteorological forcing is usually based on in situ measurements (see Section 3.1). At the global scale, atmospheric reanalyzes are generally used. In this study, the CRU-JRA 2.4 meteorological forcing (Sitch et al., 2024) was used. ORCHIDEE also uses information on atmospheric CO₂ concentration (Dlugokencky & Tans, 2020) and atmospheric nitrogen deposition (Hegglin et al., 2016).

#### 2.1.2. Vegetation and Soil Representations

Vegetation diversity is accounted for through 13 PFTs, including bare soil, that can coexist within a grid cell. When running globally, the information on the PFT distributions within each grid cell is prescribed by a global land cover map such as the ESA-CCI-LC vegetation map (Lurton et al., 2020). For site level simulations, vegetation distribution can also be derived from global land cover maps or prescribed. The leaf area index (LAI) is either a prognostic variable computed by the model following carbon allocation for each PFT or prescribed from field observations or remote sensing. For the site analysis in this study, the soil type and vegetation type were prescribed according to the site characteristics and the LAI followed a satellite-derived LAI product provided by the Copernicus Global Land Service (Baret et al., 2013). LAI observations are available at a 1-km resolution with one measurement every 10 days. From this product, maximum and minimum LAI values are extracted along with the key phenological dates (i.e., start and end of growing, maturity and senescence periods) to derive daily time series at each site.

Prescribing LAI requires bypassing some carbon allocation processes simulated by ORCHIDEE in order to derive coherent vegetation height and above-ground biomass. First, the leaf biomass is derived from LAI using PFT-specific leaf surface-to-mass ratio formulations. The vegetation height is then imposed to site-specific values and fixed in time, permitting the allocation scheme of ORCHIDEE that relates sapwood biomass to leaf biomass and height.

For the global simulations, the ESA-CCI-LC map is used and LAI and biomass were calculated by the model. Soil texture was prescribed according to the global soil map provided by Reynolds et al. (2000) based on the USDA classification that distinguishes 12 different soil texture classes.
### 2.1.3. Energy and Water Budgets

The water budget is computed in each grid cell over three hydrological tiles which represent different PFTs: one hydrological unit contains the bare soil, one the forest PFTs, and one contains both the grasslands and croplands. The soil water dynamics are solved using a semi-implicit resolution of Richard's equation on an 11-layer soil hydrology scheme (de Rosnay et al., 2002; d'Orgeval et al., 2008). Soil depth is fixed to 2 m, bare soil evaporation at the top of the column and free drainage at the bottom are calculated by accounting for the soil hydrological state and the water uptake by roots to sustain the transpiration which are computed for each soil layer.

This study focuses on the transpiration term and its sensitivity to soil water content. In ORCHIDEE r9107 the standard stomatal control on transpiration (detailed in Section 2.2) was maintained so that the model can still be configured to run the standard approach. In the same version the water-potential-based approach in which soil water controls transpiration through plant hydraulics (detailed in Section 2.3) was added and can be run as an alternative configuration. Such a modeling framework enables a simulation experiment in which two model runs, only differing by their control on transpiration, can be compared and differences between the runs can be assigned to the approach used to calculate the stomatal control on transpiration.

### 2.2. Empirical Soil Moisture Control on Stomatal Conductance

In the standard configuration of ORCHIDEE, the resistance to transpiration is defined as the inverse of the stomatal conductance for water vapor ($g_{H2O}$). The computation of $g_{H2O}$ is based on the original model of Leuning (1995) and Y. P. Wang and Leuning (1998), with further small modification described in Yin and Struik (2009):

$$g_{H2O} = f_D \cdot (g_0 + \frac{A + R_d}{c_i - c_{i*}} \cdot \frac{1}{\frac{1}{a_1 - b_1 \cdot VPD} - 1}) \cdot U_s \quad (1)$$

where, $f_D$ is the ratio of molecular diffusivities for water and CO₂ (equals to 1.6), $g_0$ is the residual stomatal conductance (µmol(CO₂) m⁻² s⁻¹), A is the CO₂ assimilation rate (µmol(CO₂) m⁻² s⁻¹), $R_d$ is the daytime respiration (µmol(CO₂) m⁻² s⁻¹), $c_i$ is the inter-cellular CO₂ partial pressure (µmol mol⁻¹) and $c_{i*}$ is the Cᵢ-based CO₂ compensation point in the absence of daytime respiration (µmol mol⁻¹). VPD is the vapor pressure deficit of the atmosphere which is an input of the model, and $a_1$ and $b_1$ are empirical parameters that control the sensitivity of $g_{H2O}$ to VPD and the assimilation rate. $U_s$ (unitless) is a soil water stress function that modulates $g_{H2O}$ by the soil water status. It is defined as

$$U_s = \sum_{i \ge 1} n_{root,i} \cdot \min \left( 1, \frac{\theta_i - \theta_w}{p_\% \cdot (\theta_{fc} - \theta_w)} \right) \quad (2)$$

where $n_{root,i}$ is the fraction of the total root mass located in layer i, $\theta_i$ the water content (m³/m³) in layer i, $\theta_w$, the water content at wilting point, $\theta_{fc}$, the water content at field capacity, and $p_\%$ (unitless, default value of 0.8), a parameter reflecting the sensitivity of the stress function to $\theta_i$. The impact of $p_\%$ on the stress function is illustrated in Figure 1.

### 2.3. Water Potential-Based Soil Moisture Control on Stomatal Conductance

The hydraulic architecture implemented in a previous branch of ORCHIDEE (r2290) (Naudts et al., 2015) relied on developments introduced in the LPJ-DGVM following Hickler et al. (2006). In this previous ORCHIDEE version, two estimations of the transpiration flux were calculated: a first one following the standard configuration of ORCHIDEE as presented above which did not account for plant hydraulics, and a second one corresponding to the maximum transpiration supply derived from soil and plant hydraulics. The supply was based on the potential difference between a prescribed minimum leaf water potential and the soil water potential and the hydraulic resistances of the roots, stem, and leaves. When the supply was lower than the demand, a correction was made on the prior demand-based transpiration estimate requiring recalculating the energy budget. This approach was not
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Impact of the $p_{\%}$ parameter on the stress function $U_x$ that controls stomatal conductance in the standard approach to simulate the stomatal control on transpiration.</figcaption></figure>

fully process-based as there was no direct control of plant hydraulics on stomatal conductance. In addition, the representation of the plant water status was strongly simplified by fixing the leaf water potential, and a scaling factor was applied to mimic the effect of the soil-to-root hydraulic resistance on the soil water potential.

A first improvement of this initial scheme was implemented by Joetzjer et al. (2022) to include a dynamic root scheme to calculate, rather than prescribe, the soil-to-root resistance at each soil layer with a maximum limit to the amount of water that can be taken from each layer. This development was implemented and improved in another branch of ORCHIDEE (r7236) (Yao et al., 2022). In r7236, the supply calculation accounts for (a) water storage in the leaves, stem, and roots, (b) a dependency of stomatal conductance to leaf water potential, and (c) a dependency of plant hydraulic resistances to the water potential for the calculation of xylem cavitation. However, the scheme still followed the same corrective approach as r2290. Moreover, it uses a computationally demanding iterative numerical scheme to calculate plant water potentials, given the dependency of plant hydraulic conductivity on water potential for each organ. Finally, this scheme was developed for tropical forests and evaluated on this type of forests only (Yao et al., 2022).

This study presents a new hydraulic scheme that was developed in ORCHIDEE to overcome the shortcomings of the previous implementations in r2290 and r7236 by (a) accounting for the coupling between stomatal conductance and plant water potentials, (b) enhancing computating performances and avoiding numerical oscillations, and (c) revising soil-to-root water absorption with a more mechanistic description.

### 2.3.1. Stomatal Conductance as a Function of Leaf Water Potential

The main feature of the new water potential-based approach, also referred to as “Hydraulic Architecture” in the following, is the coupling of the stomatal conductance, $g_{H_2O}$, with the water potential of the leaf stomatal cavities, $\psi_{leaf}$ (MPa). Following Tuzet et al. (2003), stomatal conductance can be expressed as a function of $\psi_{leaf}$ ($f_{\psi_{leaf}}$), [0–1]) and can be written as:

$$g_{H_2O} = f_D \cdot \left( g_0 + a \cdot \frac{A + R_d}{c_i - c_{i*}} \right) \cdot f_{\psi_{leaf}} \quad (3)$$

and

$$f_{\psi_{leaf}} = \frac{1 + \exp(s_f \cdot \psi_{ref})}{1 + \exp(s_f \cdot (\psi_{ref} - \psi_{leaf}))} \quad (4)$$

where, $s_f$ (MPa⁻¹) is a parameter reflecting the sensitivity of the stomatal conductance to $\psi_{leaf}$, $\psi_{ref}$ (MPa) is the reference water potential for stomatal conductance and a (unitless) is a parameter reflecting the sensitivity of stomatal conductance to CO₂. The impact of $\psi_{ref}$ and $s_f$ on $f_{\psi_{leaf}}$ is shown on Figure 2.

Based on the review made by Flexas et al. (2006), the same stress function is applied to the mesophyll conductance ($g_m$), the maximum velocity of carboxylation ($V_{c,max}$) and the respiration ($R_d$).

### 2.3.2. Hydraulic Architecture

The computation of $\psi_{leaf}$ relies on an explicit description of the water transport from the soil-root interface to the stomata as defined by a set of resistances and capacitances (Figure 3). The different pools for which the water potential is calculated are: (a) a lower soil layer (soil, low), (b) an upper soil layer (soil, up) (corresponding to averages of the 11 layer scheme of ORCHIDEE as explained further in Section 2.3.4), (c) the soil-root interface in the upper layer (rootsurf, up), (d) the soil-root interface in the lower layer (rootsurf, low), (e) the node between roots and trunk (root), (f) the node between trunk and the trunk storage pool (trunk), (g) the trunk storage pool
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Sensitivity of the stress function $f_{\psi/leaf}$ controlling the stomatal conductance to values of $s_f$ (a) and $\psi_{ref}$ (b) parameters. On panel (a), $\psi_{ref} = -1.6$ MPa, and on panel (b), $s_f = 4$ MPa$^{-1}$.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Hydraulic Architecture resistance and capacitance network. For the resistances: (1) Mesophyll resistance ($R_{meso}$); (2) Trunk to leaf xylem resistance ($R_{trunk-leaf}$); (3) Root to trunk resistance ($R_{root-trunk}$); (4) Leaf storage resistance ($R_{leaf,store}$); (5) Trunk storage resistance ($R_{trunk,store}$); (6) Upper root system resistance ($R_{root,up}$); (7) Lower root system resistance ($R_{root,low}$).</figcaption></figure>
(trunk, store), (h) the node between leaf xylem and leaves storage pool (leaf, xylem), (a) the leaves storage pool (leaf, store) and (j) the leaf stomatal cavity (leaf). As an option, the user can run a simplified scheme that omits the storage pools in the trunk and leaves from the calculations.

During unstressed periods, at the beginning of the time step, $g_{H_2O}$ is the first calculated variable, using Equation 3 and the leaf water potential from the previous time step. Then, the transpiration flux, $F_{transp}$ (mm.s⁻¹) is computed using $g_{H_2O}$. The different water fluxes within the hydraulic system are computed from the top to the bottom imposing $F_{transp}$ flux as a boundary condition at the leaf level. The flux between each storage pool and the nearest node ($F_{trunk,store}$ or $F_{leaf,store}$) is assessed following a predictor-corrector scheme described in the next section. Using Kirchhoff's current law and the storage water fluxes ($F_{trunk,store}$ and $F_{leaf,store}$), all water fluxes can be determined down to $F_{root-trunk}$, above the two root horizons. At this interface, the two fluxes of water uptake by roots, $F_{root,up}$ and $F_{root,low}$, are assessed from $F_{root-trunk}$ and the root water potentials of the previous time step with Equation 5.

$$F_{\text{root,low}}^{t+1} = \frac{F_{\text{root-trunk}}^{t+1} + \frac{\psi'_{\text{rootsurf,low}} - \psi'_{\text{rootsurf,up}}}{R_{\text{root,up}}} + \frac{F_{\text{leaf,store}}^{t+1}}{1 + \frac{R_{\text{leaf,low}}}{R_{\text{root,up}}}}}{1 + \frac{R_{\text{leaf,low}}}{R_{\text{root,up}}}} \quad (5)$$

Based on the two root water fluxes, water absorption by roots (presented in Section 2.3.4) is solved. The water contents in the two soil layers are updated as well as the resulting root water potentials $\psi_{rootsurf,up}$ and $\psi_{rootsurf,low}$ (see Section 2.3.4). The other water potentials of the hydraulic system are then updated, from the bottom to the top, using the previously calculated fluxes and the water potential of the compartment down the flux. Thus, the updated water potential at a given level ($\psi_{upper,level}$) is expressed as:

$$\psi_{\text{upper,level}} = \psi_{\text{lower,level}} - F_{\text{level}} \cdot R_{\text{level}} \quad (6)$$

Where $\psi_{lower,level}$ is the water potential at the level down the flux; and $F_{level}$ and $R_{level}$ are the flux and the resistance between the two levels, respectively.

With this explicit resolution, the non-linearity brought by Equation 3 during transient and drought periods induces numerical instabilities. This problem, due to non-compliance with the Courant-Friedrich-Lewy (CFL) condition, can be overcome in several ways. The first solution is to keep with an explicit resolution scheme and reduce the time-step length ((Cochard et al., 2021; Ruffault et al., 2022) estimated the time-step length limit for the SurEau model between $10^{-1}$ s and 1 s according to the value of their parameters). This solution with time steps lower than 1s cannot be envisaged for a global LSM as ORCHIDEE. Another way to bypass the problem is to implement a fully implicit or semi-implicit solution. However, those solutions either necessitate the implementation of an iterative scheme as in (Tuzet et al., 2017), but such scheme would increase drastically the time calculation, or to find an analytical solution as performed in (Ruffault et al., 2022), but such solution would need a complete restructuring of the ORCHIDEE code. (Ruffault et al., 2022) proposed an exhaustive comparison of the impacts of those resolution schemes on the accuracy, the time calculation and stability of the SurEau-Ecos v2.0 model. As the previous solutions can hardly be implemented in ORCHIDEE, an adapted solution based on a prediction/ correction method is proposed in this paper to prevent instabilities during drought periods only. A detailed description of the computation method is provided in Appendix A.

### 2.3.3. Water Storage

The presence of capacitances in the storage branches makes their resolution more complicated than the flux division at the trunk-root interface. Water potentials in the leaf and trunk storage compartments are calculated outside from the bottom-up calculation presented above. The storage compartments water potentials are determined by solving the following differential equation (Tuzet et al., 2017, Equation 5):

$$\frac{d\psi_{X,store}}{dt} = \frac{1}{C_{X,store} \cdot (R_{X,store} + R_{low})} \cdot (\psi_{low} - F_{up} \cdot R_{low}) - \frac{1}{C_{X,store} \cdot (R_{X,store} + R_{low})} \cdot \psi_{X,store} \quad (7)$$
where, $\psi_{X,store}$ is the water potential of the storage pool, $C_{X,store}$ is the capacitance of the pool, derived from the sapwood and leaf biomass described in Section 2.1, $R_{X,store}$ is the hydraulic resistance between the pool and the xylem, $R_{low}$ is the hydraulic resistance of the lower stage, $\psi_{low}$ is the water potential of the lower stage and $F_{up}$ is the water flux in the upper stage. Capacitances are not constant but following water volume to water potential relationships after Tuzet et al. (2017, Equations 7 and 8). They are calculated with the storage pool water potential of the previous time-step. Moreover, in those equations, the maximum amount of water ($V_{max}$) stored in the leaves and trunk corresponds to leaf and sapwood volumes, respectively. The residual amount of water ($V_r$) is defined as 40% of $V_{max}$.

The differential equation is solved by using a predictor-corrector scheme (a two step resolution where the state variable at time-step $t + 1$ is first predicted with a classical explicit resolution and then corrected by a second calculation involving the prediction). This resolution permits to avoid instabilities when calculating the new value of the storage water potential. In this resolution, the predictor term $\{\psi_{X,store}\}_{predict}^t$ is calculated and used as follows:

$$ \{\psi_{X,store}\}_{predict}^t = \psi_{X,store}^t + \Delta t \cdot f(t, \psi_{X,store}^t) \quad (8) $$

$$ \psi_{X,store}^{t+1} = \psi_{X,store}^t + \frac{\Delta t}{2} \cdot \left( f(t, \psi_{X,store}^t) + f(t, \{\psi_{X,store}\}_{predict}^t) \right) \quad (9) $$

Where, $f(t, \psi_{X,store}^t)$ corresponds to the right-hand side of Equation 7.

Once the water potential of the storage pool is known, the amount of water extracted from or stored in the storage pool is calculated. This corresponds to the calculation of the water fluxes $F_{leaf,store}$ and $F_{wood,store}$ that are needed in the bottom-up calculations of the fluxes presented in the previous section.

### 2.3.4. Water Absorption by Roots

At the level of the root-soil interface, the water absorption by the roots is computed for two soil layers, an upper layer between 0 and 50 cm and a lower layer between 50 and 200 cm where the boundaries of these layers are user-defined parameters. Those two layers result from an averaging of the moisture contents of the 11-layer soil hydrology model used in ORCHIDEE (Section 2.1). Averaging is only used in the calculation of the hydraulic architecture, whenever appropriate the other hydrological calculations make use of the 11 layers. Modeling directly the water absorption for the 11 layers of the soil model was not considered as it would largely increase the complexity of the scheme with potential numerical instabilities given that the first 7 layers of the soil only represent 9 cm. It has thus been chosen to keep the initial approach of Tuzet et al. (2017) with two layers but further work will be conducted to test the impact of adding more layers. The root absorption in the upper and lower soil layers (respectively $F_{root,up}$ and $F_{root,low}$) are calculated based on the flux above the collar $F_{root-trunk}$ following Equation 5. After the calculation of hydraulic architecture, these two fluxes are distributed in the 11-layer soil hydrology scheme according to the root biomass in each layer and correspond to the soil water uptake through the roots in each soil layer.

The hydraulic scheme provides two options regarding the soil resistance to water uptake by roots:

* In the first and more mechanistic approach, the water potential at the soil-root interface is explicitly computed following Tuzet et al. (2003). This approach is an alternative to the inclusion of a soil-root resistance for water uptake by the roots as was the case in r2290 and r7236. At the soil-root interface, the water flux through soil water uptake by the roots ($F_{root,up}$ or $F_{root,low}$) creates a gradient of moisture content in the soil around the root. It is assumed that the roots can be represented by a cylinder with a fixed radius and their length ($l_{root}$) calculated as a function of the root biomass. As the roots are assumed to be uniformly distributed throughout the soil layer, the soil volume in each soil horizon is uniformly distributed as a cylinder of length $l_{root}$ around the fixed root radius. The water movement in the soil is assumed to occur radially toward the roots. As a consequence, the moisture content profile is computed only along the radial axis of the root system by solving Richard's equation radially:
$$ \frac{\partial \theta}{\partial t} = \frac{1}{r} \cdot \frac{\partial}{\partial r} \left( r \cdot D(\theta) \cdot \frac{\partial \theta}{\partial r} \right) \qquad (10) $$

where D(θ) is the soil diffusivity and r, the distance from the root axis. Richard's equation is solved at a half hourly time step for n_muff nodes along the radial axis. At the soil-root interface (i = 0), the absorbed water flux (F_root,up or F_root,low) is applied as a boundary condition.

* A second and simpler approach works with the mean soil moisture of the layer and the corresponding water potential and assumes that the resistance to water absorption by the roots is, among other variables, a function of the soil hydraulic conductivity which in turn is based on the layer-mean water potential. The lower the water potential, the lower the hydraulic conductivity and the higher the soil resistance. This approach is based on the work of Bonan et al. (2014, Section A4.2, Equations A23 and A25). The results of this approach are, however, not discussed in this paper.

In ORCHIDEE r9107, the conversion between moisture content and soil water potential and the relationship between soil water potential and hydraulic conductivity follows van Genuchten (1980). We found that numerical instabilities of the scheme during drought periods were reduced by following Campbell's (1986) representation and retained this parametrization following Tuzet et al. (2003, Equations 4a and 4b) for the radial resolution of Richard's equation.

# 3. Methods

## 3.1. Data Sets

The standard and potential-based configurations were evaluated against two data sets. The first data set gathers in situ measurements from two well-documented forest sites in France often labeled as FR-Hes and FR-Pue. The second data set is the FLUXNET2015 database (Pastorello et al., 2020).

The in situ data collected at FR-Hes and FR-Pue gathers all meteorological data needed to force the ORCHIDEE model (see Section 2.1), as well as carbon, water and energy fluxes, and specific hydrological observations. Both sites are equipped with eddy-covariance towers, which provide carbon dioxide fluxes as well as latent and sensible heat every half-hour. For FR-Hes, the observations used range from 2014 to 2020 and were taken from the “WarmWinter database” (Warm Winter 2020 Team and ICOS Ecosystem Thematic Centre, 2022), while for FR-Pue, the observations cover the period 2000–2014 and were taken from FLUXNET2015 (Pastorello et al., 2020).

FR-Hes site is located in the temperate broadleaf forest of Hesse near Nancy in the northeastern France. This beech forest lays on a 5 m deep soil composed by two main horizons: a horizon with a low clay content in the first 80 cm and a higher clay accumulation starting at 80 cm depth separating from the rest of the soil (Granier et al., 2000, 2007; Zapater et al., 2013). The site experiences a semi-continental climate with a mean annual precipitation of around 820 mm. The root system is mainly allocated in the upper soil layer but some fine roots can reach 1.5 m depth (Betsch et al., 2011). The droughts that occurred during the summers of 2018 and 2019 make this site well-suited for a model evaluation study. Specific data gathered at FR-Hes was soil water content down to a depth of 80 cm measured with a TDR sensors several times (the total soil water content on site is supposed to correspond to the water content on the 0–80 cm soil horizon because of the relative impermeability of the clay accumulation at 80 cm).

FR-Pue is located in Puéchabon near Montpellier in southeastern France, in the Mediterranean climate zone. The experimental station is situated in an evergreen holm oak forest. The forest grows in a hard rocky soil composed of Jurassic limestone; the average volumetric fractional content of stones and rocks is about 0.75 for the top 0–50 cm and 0.90 below. The stone-free fraction of the soil is a homogeneous silty clay loam (USDA texture triangle; 38.8 % clay, 35.2 % silt, and 26 % sand). The soil water reserve is therefore limited and less than 150 mm of water can accumulate in the 4.5 m deep rooting zone of the trees (Rambal et al., 2003; Ruffault et al., 2023). Most of the roots (90 %) can be found in the first 50 cm but some roots can grow up to 4.5 m deep (Allard et al., 2008). Along with this particular soil properties, the mean annual precipitation is 916 mm with a range of 550–1,549 mm over the past 30 years. It occurs mainly (75%) from September to April, making the forest evolve into a dry environment with
extended drought periods occurring almost every summer. Measurements of leaf water potential at pre-dawn and mid-day are available at FR-Pue, which were valuable to evaluate the hydraulic architecture.

The second data source used in the evaluation was the FLUXNET2015 data set which contains in situ data for 212 sites over the globe for a total of 1,500 site-years from 1995 to 2014. In this study, the sites for which less than 1 year of data was available and the sites with vegetation i.e. currently not represented by ORCHIDEE r9107 (e.g., irrigated croplands or wetlands), have been removed. At the end, 135 sites with a total of 1,096 site-years were available for model evaluation.

Missing half-hourly climate in situ data were gap-filled following Vuichard and Papale (2015), a prerequisite to be used by LSM such as ORCHIDEE. The energy budget derived from eddy-covariance measurements is rarely closed (Foken, 2008), which could be accounted for through correction terms. However, as the correction may sometimes result in substantial overestimation of the amplitude of the annual cycle of sensible and latent heat fluxes, it was, contrary to Jung et al. (2011), decided to use the data without any correction.

## 3.2. Model Calibration

In recent years, the ORCHIDEE Data Assimilation System (ORCHIDAS) has been used to calibrate various model configurations at the local scale (Bastrikov et al., 2018; Kuppel et al., 2014; MacBean et al., 2018; Peylin et al., 2016; Raoult et al., 2021). ORCHIDAS relies on a Bayesian framework and assumes that the model and the observation errors, as well as the parameter errors, follow Gaussian distributions. A cost function $J(x)$ (Equation 11) is minimized, based on a least square metric (Tarantola, 2005).

$$J(x) = \frac{1}{2} \cdot \left[ (M(x) - y)^T \cdot R^{-1} \cdot (M(x) - y) + (x + x^b)^T \cdot B^{-1} \cdot (x + x^b) \right] \quad (11)$$

where, $x$ is the vector of parameters to calibrate and $y$ the observations. The first part of Equation 11 represents the mismatch between the predicted variables and the observations while the second part is a regularization term, measuring the mismatch between the prior parameter values and the considered set of parameters. The two terms of the cost function are weighted by the prior covariance matrices: $R^{-1}$ for the observation errors (including model structural error, measurement errors and meteorological forcing errors) and $B^{-1}$ for the parameter errors. Given the difficulty to define error covariances, the two matrices R and B are considered diagonal (only the variance terms are prescribed and the covariance terms are neglected). For the R matrix, the variances are calculated as the mean squared difference between the prior model results and the observations (giving a focus on the model structural error). For the B matrix, they are defined as 40% of the physical range of variation of each parameter. Finally, the minimization of this cost function is performed with a genetic algorithm that is more efficient for in situ flux data assimilation than a gradient-based approach as discussed in Bastrikov et al. (2018).

Large parameter errors (and ranges) were imposed to give more weight to the information coming from the observations in the calibration process. This choice was made to reflect the lack of information for the parameter values used in a first potential-based approach of the hydraulic architecture. The cost function was defined by default with daily latent and sensible heat fluxes. A few additional tests listed in Table 2, were also performed.

A restrictive set of influential parameters was selected based on previous parameter screening studies (Bastrikov et al., 2018; Raoult et al., 2021) for surface fluxes using the Morris' approach (Morris, 1991). The calibrated parameters of the potential-based configuration include the reference water potential which controls the stomatal conductance response to leaf water potential ($\psi_{ref}$, MPa), the sensitivity of the stomatal conductance to leaf water potential ($s_f$, MP$^{-1}$), the xylem hydraulic resistance ($R_{xylem}$, MPa.s.m$^{-3}$) and the slope of stomatal conductance formulation ($a$, unitless, see Equation 3). Moreover, because of the relatively rough estimation of the sapwood and leaf water storage compartments (see Section 2.3.3), two scaling factors (leaf_sto_fac and wood_sto_fac, unitless) are applied to the volumes of the leaf and wood water storage pools used to calculate the capacitances in Equation 7. For the standard configuration, the soil water stress function, the slope of the stomatal conductance and its VPD dependency (Equations 1 and 2) are included in the list of calibrated parameters, i.e., $p_\%$, $a_1$ and $b_1$.

Because ORCHIDEE's soil depth representation is fixed to 2 m and does not account for coarse materials (i.e., stones) and because roots explore the whole soil volume, it is complicated to adjust directly, through an optimization procedure, the water holding capacity of the soil in ORCHIDEE. Given the importance of such holding
<table><caption>**Table 1**

Configurations Used to Compare the Potential-Based and the Standard Scheme of ORCHIDEE</caption><thead><tr><th>Short name</th><th>Description</th></tr></thead><tbody><tr><td>Standard</td><td>Standard configuration of ORCHIDEE with stomatal conductance directly driven by the soil moisture stress function as described in Section 2.2</td></tr><tr><td>Potential-based</td><td></td></tr><tr><td>-</td><td>Hydraulic architecture configuration including: (1) water absorption by roots modeled with the radial resolution of Richard's equation around the roots; (2) leaves and wood water storage compartments represented as described in Section 2.3.3; (3) iterative scheme to avoid numerical instabilities</td></tr><tr><td>Without water storage</td><td>Potential-based configuration with storage compartments disabled</td></tr><tr><td>Without numerical iterations</td><td>Potential-based configuration with no iteration in the numerical scheme (see Appendix A)</td></tr></tbody></table>

capacity to properly evaluate plant hydraulics, especially during periods of drought and for sites such as FR-Pue, it has been decided to include the residual ($\theta_{res}$) and saturated ($\theta_{sat}$) soil water content in the list of calibrated parameters for the standard configuration (MCR\_imp and MCS\_imp) and potential-based configurations (MCR\_sup, MCS\_sup, MCR\_inf and MCS\_inf). Changing artificially these parameters (i.e., independently of the soil texture) allows to directly increase or decrease the soil water holding capacity (defined as $(\theta_{sat} - \theta_{res}) * h$ where $h$ is the total soil depth). In addition, in order to get a full control of soil water dynamics, the hydraulic conductivity and soil water retention curves were also calibrated, that is, nvan, avan and kimp for van Genuchten (1980) parametrization and kimp, b\_muff and psi\_air\_entry for Campbell (1986) parametrization. A complete list of the parameters calibrated for both model configurations (standard and potential-based), as well as their range of variations, is given in Tables B2 and B3.

### 3.3. Experimental Set-Up

The experimental set-up (Table 1) includes different calibration and simulation runs (Table 2) in order to:

1. Quantify the performance of the new potential-based configuration with respect to the old standard scheme for water and energy fluxes;

2. Estimate the impact of water storage and a mechanistic description of water absorption by roots in the potential-based scheme;

3. Evaluate the impact of the proposed numerical scheme based on iterations during drought periods to avoid numerical oscillations (Appendix A);

4. Evaluate the potential-based configuration on a wide range of sites equipped with eddy-covariance flux measurements as well as at the global scale.

To meet these goals, we evaluated our developments in three different steps described in the next section. This evaluation process justified several calibration strategies described right after.

#### 3.3.1. Evaluation Strategy

The new potential-based model was evaluated and compared to the standard version at three different levels:

1. A first evaluation of both configurations was performed at the two intensively monitored sites, FR-Hes and FR-Pue (goal 1), against observations of LE, H, soil water content (at FR-Hes only), and leaf water potential (at FR-Pue only) for a 2-year calibration period and a longer evaluation period (see Table 2). In addition, the diurnal cycles of the turbulent fluxes were evaluated at FR-Pue during drought periods for the potential-based configuration with plant water storage enabled and disabled (goal 2). Drought periods were defined according to simulated soil moisture dynamics simulated, using different thresholds for the two sites. In FR-Hes, drought periods were defined as periods during which the soil water content is lower than 5% of the soil water reserve during more than 5 consecutive days. At FR-Pue, the soil water content had to be lower than 2.5% of the soil water reserve for more than 10 consecutive days. Finally, to evaluate the new potential-based numerical scheme (goal 3), an additional simulation was performed at FR-Hes without iterations during drought periods (see Appendix A);
<caption>**Table 2**</caption>

Description of the Different Tests Used in the Paper, Including the Calibration Method, the Assimilated Data, the Periods and the Objective of the Test

<table><thead><tr><th>Site</th><th>Config. name</th><th>Calibration/data</th><th>Calibration period</th><th>Evaluation period</th><th>Objective</th></tr></thead><tbody><tr><td rowspan="3">Hesse</td><td>Potential-based</td><td>Single site/LE and H daily</td><td rowspan="3">2018–2019</td><td rowspan="3">2014–2020</td><td>Default calibration of potential-based config.</td></tr><tr><td>Potential-based config. without iterations</td><td>Same as initial potential-based</td><td>Highlight the impacts of the iteration in the numerical resolution scheme</td></tr><tr><td>Standard</td><td>Single site/LE and H daily (different params)</td><td>Default calibration of standard config.</td></tr><tr><td rowspan="5">Puéchabon</td><td>Potential-based</td><td>Single site/LE &amp; H daily</td><td rowspan="5">2005–2006</td><td rowspan="5">2000–2014</td><td>Default calibration of potential-based config.</td></tr><tr><td>Potential-based with ψ<sub>leaf</sub></td><td>Single site/LE, H &amp; ψ<sub>leaf</sub></td><td>Highlight the impact of including ψ<sub>leaf</sub> in the calibration</td></tr><tr><td>Hourly calibrated potential-based config.</td><td>Single site/LE and H hourly</td><td>Test the benefits of using hourly data instead of daily for the calibration</td></tr><tr><td>Potential-based without water storage</td><td>Same as initial potential-based config. (no water storage)</td><td>Highlight the impacts of the water storage pools in the potential-based config.</td></tr><tr><td>Standard</td><td>Single site/LE &amp; H daily</td><td>Default calibration of standard config.</td></tr><tr><td rowspan="5">FLUXNET 2015</td><td>Single-site calibrated potential-based config.</td><td>Single site/LE &amp; H daily</td><td rowspan="5">Site specific</td><td rowspan="5"></td><td>Highlight the best results with potential-based config. at each individual site</td></tr><tr><td>Multi-site calibrated potential-based config.</td><td>Multi site/LE &amp; H daily</td><td>Highlight the impact of calibrating a unique set of plant-specific parameters per PFT</td></tr><tr><td>Single-site calibrated standard config.</td><td>Single site/LE &amp; H daily</td><td>Highlight the best results with standard config. at each site</td></tr><tr><td>Multi-site calibrated standard config.</td><td>Multi site/LE &amp; H daily</td><td>Highlight the impact of calibrating a unique set of plant-specific parameters per PFT</td></tr><tr><td>Standard without calibration</td><td>None</td><td>Reference without calibration</td></tr><tr><td rowspan="2">Global</td><td>Potential-based</td><td>PFT-parameters from FLUXNET2015 multi-site calibration</td><td>Simulation period: 2000-2010</td><td rowspan="2"></td><td rowspan="2">Assess the robustness and genericity of the multi-site calibration performed on FLUXNET2015 database; Highlight the global behavior of the potential-based configuration</td></tr><tr><td>Standard</td><td></td><td>Evaluation period: 2008-2010</td></tr></tbody></table>

2. At the FLUXNET2015 sites, both configurations were evaluated over the whole time series for each site, focusing on daily *LE* and *H* (goal 4). Model performances were also evaluated specifically over dry periods, defined uniformly for all sites, as days where the simulated daily mean soil water content was lower than 25% of the total soil water reserve;

3. Finally, the standard and potential-based configurations were compared at the global scale (goal 4). This analysis focused on a few energy-related (*LE*, *H*, surface temperature) and carbon-related (water use efficiency, LAI) variables.

### 3.3.2. Calibration Strategy

The multi-scale evaluation protocol defined above, required a specific strategy for the models calibration of each evaluation level.

At FR-Hes and FR-Pue, for each model configuration (see first 8 rows in Table 2), ten single-site calibrations have been realized, ending in different estimations of the posterior parameters due to the random nature of the genetic algorithm calibration method. This approach accounts for the risk that the cost function may converge to a local minimum which in turn could indicate parameter equifinality. From the 10 calibrations, both the one for which the cost function is the lowest and the range obtained from the ensemble are presented in the result section. Calibrations were performed over two specific years: 2018–2019 for FR-Hes in order to catch the drought events that occurred in those years, and 2005–2006 for FR-Pue in order to capture the summer drought of 2005 and the particularly dry year 2006 as shown in Allard et al. (2008).
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Amplitude of the spectrum of the Fourier transform of the latent heat flux at FR-Hes for two different numerical implementations: potential-based configuration with iterations during periods of hydric stress (referred as HA) and potential-based configuration without these iterations (referred as HA-NoIter).</figcaption></figure>

At the FLUXNET2015 sites, two types of calibration experiments have been performed at the local scale. In the single-site calibrations, the parameter calibration is done independently at each site, enabling to highlight the best performances of the model. In the multi-site calibrations, a unique parameter calibration is done simultaneously for a set of sites, leading to one model parametrization for all sites. Usually, a multi-site calibration is performed for an ensemble of sites with similar plant characteristics, under the assumption that they share the same common parameters. In this study, multi-site calibrations are performed at the PFT level for the sites of the FLUXNET2015 database.

The calibrated parameters that are considered fixed per PFT in the multi-site calibration are provided in Tables B2 and B3; they consist of plant-related parameters. However, for the soil-related parameters, even in these multi-site calibrations, a different parameter is kept for each site (like in the single-site case). This approach was chosen to account for very different soil characteristics and soil water holding capacities between sites of a given PFT.

Both multi-site and single-site calibrations were performed for the same selection of FLUXNET2015 sites for the standard and potential-based model configurations (see Table 2). The calibration was done for each site over one or two specific years selected to meet the two following criteria: years with more than 80% available data for latent and sensible heat fluxes and, if possible, years with a drought period (i.e., 2003 in Europe or 2010 to 2013 in the Southern United States).

One multi-site calibration has been performed for 11 PFTs: Tropical Evergreen Broadleaf Forest (tropical evergreen forests (TrEF), 2 sites), Tropical Raingreen Broadleaf Forest (TrRF, 5 sites), Temperate Evergreen Needleleaf Forest (TeENF, 19 sites), Temperate Evergreen Broadleaf Forest (TeEBF, 9 sites), Temperate Deciduous Broadleaf Forest (TeDBF, 18 sites), Boreal Evergreen Needleleaf Forest (BoENF, 26 sites), Boreal Deciduous Needleleaf Forest (BoDNF, 7 sites), C3 Grassland (C3G, 17 sites), C4 Grassland (C4G, 18 sites), C3 Cropland (C3C, 12 sites), and C4 Cropland (C4C, 2 sites).

Finally, at global scale, to assess the robustness of the multi-site parameter calibration for the global analysis, two simulations were performed, one for each configuration (standard and potential-based), over the historical period (2000–2010), using the CRU-JRA reanalysis providing the meteorological forcing at 0.5° and a 6-hourly time step (Section 2.1). Only plant-specific parameters per PFT were taken from the FLUXNET2015 multi-site calibration, while the soil-specific parameters were kept at their default values following the USDA soil texture map (see Section 2.1). The comparison was performed over the last 3 years of the 10-year simulation.

# 4. Results

## 4.1. Impacts of the Numerical Resolution Scheme

The impact of the numerical scheme on the stability of the different simulated fluxes is assessed through a Fourier analysis on the 30 min model output. Figure 4 presents the amplitude spectrum of the latent heat flux at FR-Hes
for the potential-based configuration with the standard numerical resolution scheme presented in Appendix A and for the potential-based configuration using the same scheme but without iterations during drought periods. Each spike in the spectrum represents a periodic signal of the latent heat flux. These can be natural reoccurring phenomena or oscillations introduced by the numerical scheme. The first two peaks are observed at frequency $f_1 = 0.0315$ µHz corresponding to a period of $T_1 \approx 365$ days and at $f_2 = 11.6$ µHz, that is $T_2 \approx 24$ h, corresponding to the annual and diurnal cycles, respectively. The Fourier spectrum increases again at the higher end of the spectrum, that is around $270$ µHz or $T \approx 1$ h. The spectrum of configuration without iterations presents a strong signal there of the order of 1% of the diurnal cycle when averaged over the whole simulation period. Its intensity can reach 50–70% of the diurnal cycle amplitude during periods of soil moisture stress. The intensity of the signal at around $270$ µHz decreases strongly by approximately a factor of two if iterations are used to find a numerical solution. Iterations avoid large unrealistic oscillations but without completely removing them. A very similar amplitude spectrum was obtained for the simulated leaf water potential (results not shown).

## 4.2. Calibration and Evaluation at Two Forest Sites

### 4.2.1. Temperate Broad-Leaf Deciduous Forest (FR-Hes Site)

The two model configurations captured the main variations of the observed mean seasonal cycle of latent and sensible heat fluxes (LE and H) with some systematic biases (Figure 5). For LE, both configurations simulated a too-early increase in spring and a subsequent underestimation in early summer. Over the evaluation period (2014–2020), the potential-based configuration provided similar results to the standard configuration for LE for both the Root Mean Square Error (RMSE) and the correlation (based on daily mean values; Table 3). Note that RMSEs for the calibration period (2018–2019), which included a strong drought in 2018, are relatively similar to those for the whole evaluation period (2014–2020) (i.e., 14.2 vs. 16.0 W/m² for LE for the potential-based configuration).

Model-data discrepancies were larger for sensible heat $H$ than $LE$. The negative $H$ fluxes measured in winter are not reproduced by the model, which only simulates small and mainly positive fluxes during winter. During summertime, the observations showed fluctuations of up to 20 W/m² that are not reproduced by the model, although the mean simulated and observed fluxes were similar and close to 30–40 W/m². The new potential-based configuration performed similarly as the standard version for $H$ with no substantial difference in RMSE and correlation of the daily mean values over the calibration and evaluation periods. The ensemble of 10 calibrations provided very similar simulations of LE and $H$ for both model versions (standard and potential-based) with a resulting model spread far smaller than the model-observation differences.

Compared to the standard configuration, the potential-based configuration better matched the observed seasonal variations of soil water content (Figure 5). Daily mean RMSE are 0.035 m³/m³ against 0.040 m³/m³ for the potential-based and standard configurations, respectively (Table 3). In particular, the potential-based configuration presents a higher winter soil water content than the standard configuration, explained by a higher soil water holding capacity (418 kg/m² for the potential-based and 360 kg/m² for standard configurations, respectively). However, simulated seasonal amplitudes of both configurations are lower than the observed amplitudes. On both configurations, the spread was larger for soil water content compared to LE and $H$, with a spread (around 0.15 m³/m³) reaching 50% of mean soil water content for both configurations.

The RMSEs of the mean diurnal cycle of LE over the summer months (June, July and August) were 7.4 and 6.2 W/m² for the potential-based and standard model configurations, respectively (Figure 5). The observed peak of the diurnal cycle around noon is included in the spread of both configurations, although the spread in the middle of the day for the potential-based configuration was 3 times larger than for the standard configuration. The potential-based configuration also sustains more LE than the standard configuration in the afternoon.

### 4.2.2. Temperate Broadleaf Evergreen Forest (FR-Pue)

The RMSEs of the daily mean $LE$ simulated for the FR-Pue field site differed by less than 0.2 W/m² between the standard and potential-based configurations (see Table 4 and panels A and B on Figure 6) over the evaluation period (2000–2014). The spread of the 10-member ensemble obtained with the potential-based configuration for $LE$ at FR-Pue was similar to the one at FR-Hes, while it is larger for the standard configuration in particular over the period from May to June 2006. An overestimation of $LE$ of nearly 15 W/m² for both configurations in early summer from May to July is noticeable compared to the observations. However, the seasonal dynamics, in
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Comparison at Hesse (FR-Hes) between potential-based (referred as HA, red line: best calibration, red spread: range of results obtained for the 10 calibrations), standard (referred as STD, blue line: best calibration, blue spread: range of results obtained for the 10 calibrations) and the observations (black line) for daily mean latent heat (a), daily mean sensible heat (b), daily mean total soil water content (over the 0–80 cm horizon for the observation; over the total 2 m soil depth for the model) (c) and mean diurnal latent heat over summer (June, July, and August) (d). The seasonal cycles were smoothed by rolling means with a 1 month window and the diurnal cycles were smoothed with a rolling mean window of 2 time steps, that is, 1 hr, see Section 4.1.</figcaption></figure>

particular the large reduction of *LE* due to soil water stress during the drying period and the increase of *LE* in November, are captured by both configurations, albeit the increase during the 2005 fall is too large. For *H*, both configurations performed similarly, with, in particular, an overestimation of the flux in 2005. The RMSE for *H* (daily mean values) differed by only 0.3 W/m² between the standard and potential-based configurations (Table 4). As for the FR-Hes forest, the winter *H* fluxes at FR-Pue are not well reproduced as shown by both configurations failing to reach the observed negative sensible heat flux values. Overall, the simulated *LE* and *H* fluxes are both larger than the observations (over most of the year in 2005), which suggests issues with energy balance closure in the observations (Foken, 2008).

Leaf water potential $\psi_{leaf}$ at pre-dawn and mid-day are available at FR-Pue several times during the growing season. Following calibration of the potential-based configuration against $LE$ and $H$, the RMSEs for $\psi_{leaf}$ was 0.96 MPa for the pre-dawn and 1.51 MPa at mid-day (Table 4 and panel D on Figure 6). To reduce the RMSEs, a second calibration of the same set of parameters against $LE$, $H$ but also $\psi_{leaf}$ was run over the calibration period.
<caption>**Table 3**</caption>

Root Mean Square Error (RMSE) and Pearson Correlation Coefficient (r) Between the Simulated LE, H, SWC (Soil Water Content) and the Observations at FR-Hes for Both Standard and Potential-Based Configurations and Both, Calibration (2 Years) and Evaluation Periods

<table><thead><tr><th rowspan="2"></th><th colspan="2">Potential-based</th><th colspan="2">Standard</th></tr><tr><th>2018-2019</th><th>2014-2020</th><th>2018-2019</th><th>2014-2020</th></tr></thead><tbody><tr><td>LE seas: RMSE (W/m²)/r</td><td>14.2/0.94</td><td>16.0/0.92</td><td>14.2/0.94</td><td>15.8/0.92</td></tr><tr><td>LE diur: RMSE (W/m²)/r</td><td>-</td><td><strong>7.4</strong>/0.997</td><td>-</td><td><strong>6.2</strong>/0.998</td></tr><tr><td>H seas: RMSE (W/m²)/r</td><td>27.1/0.78</td><td>25.8/0.74</td><td>26.7/0.79</td><td>25.6/0.75</td></tr><tr><td>SWC seas: RMSE (m³/m³)/r</td><td><strong>0.032</strong>/0.98</td><td><strong>0.038</strong>/0.98</td><td><strong>0.035</strong>/0.94</td><td><strong>0.040</strong>/0.94</td></tr><tr><td>Soil water holding capacity (kg/m²)</td><td colspan="2"><strong>417.5</strong></td><td colspan="2"><strong>360</strong></td></tr></tbody></table>

*Note.* Seasonal cycle analysis is based on daily means while diurnal cycle analysis is based on hourly means. The last line provides the calibrated soil water holding capacity (defined as the difference between saturated and residual soil water content integrated over the 2 m soil depth). Bold numbers indicate differences between hydraulic architecture and standard model above 2%.

Using this alternative calibration, whose results are detailed in Figure B4, decreased RMSEs to 0.61 MPa at pre-dawn and 0.95 MPa at mid-day. However, this calibration approach negatively impacted the model performance, with LE RMSE values increasing from 14.9 W/m² to 16.1 W/m² after the account of $\psi_{leaf}$ in the calibration, while H RMSE remains around 20.7 W/m² for both calibrations (Table 4).

Analyzing the model at simulating the mean diurnal cycle of the LE flux during the summer growing season period (JJA) shows that for both configurations the maximum peak was shifted compared to the observations (15hr for the potential-based configuration, 13h30 for the standard configuration, 12h30 for the observations) with larger LE flux compared to the observations (Panel C on Figure 6). Both configurations being calibrated on daily mean fluxes, an additional test was performed with a calibration of the potential-based configuration on hourly averaged fluxes. This calibration, whose results are detailed on Figure B5, led to a shift of the LE peak from 15hr (for the potential-based configuration calibrated on daily energy fluxes) to 14h30 (for the potential-based configuration calibrated over hourly fluxes). However, using the hourly fluxes in the calibration slightly increased the RMSE of LE from 14.9 to 15.1 W/m² (Test not reported in Table 4). A third test, whose results are described in Figure B6, was performed with a prescribed decreased soil hydraulic conductivity at saturation (kimp). It was arbitrarily decreased after the potential-based configuration calibration from 3,802 mm/d to a value of 20 mm/d which is more realistic given the silty-clay soil type of FR-Pue. This drastic decrease allowed for a shift of the daily maximum LE to 12hr, as in the observations. This sequence of three tests highlights the importance of soil hydraulic conductivity in matching the peak of the diurnal cycle. However, the improvement in

<caption>**Table 4**</caption>

Root Mean Square Error (RMSE) and Pearson Correlation Coefficient (r) Between the Simulated LE, H, $\psi_{leaf}$ (Both Pre-Dawn and Mid-Day) and the Observations for FR-Pue Site, for Three Model Configurations (Potential-Based Configuration, Potential-Based Configuration With $\psi_{leaf}$ Included in the Calibration Procedure, and Standard Configuration) and Both, Calibration (2 Years) and Evaluation Periods

<table><thead><tr><th rowspan="2"></th><th colspan="2">Potential-based</th><th colspan="2">Potential-based with $\psi_{leaf}$ in the calibration</th><th colspan="2">Standard</th></tr><tr><th>2005-2006</th><th>2000-2014</th><th>2005-2006</th><th>2000-2014</th><th>2005-2006</th><th>2000-2014</th></tr></thead><tbody><tr><td>LE seas: RMSE (W/m²)/r</td><td><strong>9.8</strong>/0.87</td><td><strong>14.9</strong>/0.80</td><td><strong>12.1</strong>/0.86</td><td><strong>16.1</strong>/0.81</td><td><strong>10.5</strong>/0.86</td><td><strong>15.1</strong>/0.81</td></tr><tr><td>LE diur: RMSE (W/m²)/r</td><td>-</td><td><strong>18.3</strong>/0.95</td><td>-</td><td><strong>19.2</strong>/0.96</td><td>-</td><td><strong>13.5</strong>/0.98</td></tr><tr><td>H seas: RMSE (W/m²)/r</td><td>17.8/0.94</td><td>20.7/0.89</td><td>17.8/0.93</td><td>20.6/0.89</td><td>18.3/0.93</td><td>21.0/0.88</td></tr><tr><td>$\psi_{leaf}$ pre-dawn: RMSE (MPa)/r</td><td>-</td><td><strong>0.96</strong>/0.88</td><td>-</td><td><strong>0.61</strong>/0.87</td><td>-</td><td>-</td></tr><tr><td>$\psi_{leaf}$ mid-day: RMSE (MPa)/r</td><td>-</td><td><strong>1.51</strong>/0.47</td><td>-</td><td><strong>0.95</strong>/0.72</td><td>-</td><td>-</td></tr></tbody></table>

*Note.* Seasonal cycle analysis is based on daily means while diurnal cycle analysis is based on hourly means. Bold numbers indicate differences between hydraulic architecture and standard model above 2%.
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Comparison at Puechabon (FR-Pue) between potential-based configuration (referred as HA, red line: best calibration, red spread: range of results obtained for the 10 calibrations), standard configuration (referred as STD, blue line: best calibration, blue spread: range of results obtained for the 10 calibrations) and the observations (black line) of daily mean latent heat (a), daily mean sensible heat (b), mean diurnal latent heat over summer (June, July and August) (c) and leaf water potential at predawn and midday (d). The seasonal cycles are obtained with rolling averages over 1 month, the diurnal one is obtained by rolling averaging over 2 time steps (see Section 4.1).</figcaption></figure>

simulating the diurnal cycle came with an increase of the seasonal RMSEs from 14.9 W/m² with the default potential-based configuration calibration to 20.4 W/m² when considering the decrease of *kimp*. These tests highlight the difficulty of calibrating at the same phase of the diurnal cycle and the amplitude of the daily mean seasonal cycle.

Finally, Figure B7 presents the results of the potential-based configuration with and without the storage compartments enabled (see Table 1) during dry events. The configuration which does not account for water storage showed an asymmetry in its diurnal cycle during drying events. Such asymmetry was not apparent in simulations with the account of the water storage. This effect was, however, only noticeable during strong dry events but was absent from the mean diurnal cycles over the summer period (Panel B on Figure 6).

### 4.3. Calibration and Evaluation Over FLUXNET2015 Sites

The multi-site calibration of the two model configurations (Table 2) slightly reduced the RMSE for LE for most PFTs compared to the default parametrization without calibration (Figure 7). RMSE reduction was of the order of
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Root Mean Square Errors (RMSEs) of the standard configuration without calibration (STD\_prior, black), the standard configuration with the multi-site calibration (STD\_MS in blue), the multi-site calibration of the potential-based configuration (HA\_MS in red) for latent heat (top panel) and sensible heat (bottom panel) for all sites over the whole evaluation period. Parameter calibration is performed at multi-site scale and sites are regrouped by Plant Functional Type (see Table B1 for acronyms). Boxplots are over the RMSE at each sites. The boxes represent the inter-quartile range and the median, whiskers represent the minimum and maximum values, outliers are represented with thick open circles.</figcaption></figure>

10% on average for the different PFTs with the highest error reduction for TrEF and temperate evergreen broadleaf forest (TrEBF, -15%). The reductions ranged between 1 and 5 W/m² depending on PFT. The performances of the standard and potential-based configurations at simulating *LE* are of the same order of magnitude for most PFTs, in terms of PFT-average RMSE, but also inter-site RMSE distribution within each PFT (Figure 7). In particular, the RMSE at sites where the model performed best (resp. the worst) were similar for the two configurations for each PFT (Figure 7). The only exception is for temperate evergreen broafleaf forest (TeEBF) where the standard configuration performed better than the potential-based configuration, with site-average RMSE of 24.9 and 28.7 W/m² for the standard and potential-based configurations, respectively. This difference is mostly explained by lower RMSE for the standard configuration for the temperate evergreen broafleaf forest (TeEBF) sites for which the model performed the least.

For C4 crops (C4C) sites, the calibration of both configurations increased the RMSE. Note that RMSE shown in Figure 7 corresponds to values over the entire evaluation period, that is not the calibration period (see discussion, Section 5). When computed over the calibration period, the RMSE of calibrated standard and potential-based configurations are always, by construction, lower than the default parametrization for any PFTs. Thus, the RMSE increase after model calibration at C4 crops (C4C) sites is the result of an overfitting issue during the calibration step.

Results of the model calibration for *H* over the evaluation period are similar to those obtained for *LE* (Figure 7), although RMSE reduction due to calibration was lower for *H*, with a PFT-average RMSE reduction of 7%–8% (compared to 10% for *LE*). At temperate evergreen needleleaf forest (TeENF) the potential-based configuration (mean RMSE of 32.0 W/m², error reduction of 10%) performs better than the standard one (mean RMSE of 34.3 W/m², error reduction of 4%). This higher performance of the potential-based configuration at the level of the temperate evergreen needleleaf forest (TeENF) PFT is mainly due to improvement at sites with the highest RMSE for the standard configuration.
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Maps of the differences obtained between the two ORCHIDEE simulations (standard – potential-based) for: (a) Latent heat Flux (in W/m²), (b) Evaporative fraction (EF = LE/(LE + H)), (c) GPP (g[C]/m²/day), (d) Water Use Efficiency (WUE = GPP/ET) (g[C]/kg[H₂O]), Surface temperature Tsurf (°C) and Leaf Area Index LAI (m²/m²). Differences are averaged over the northern hemispheric summer season (JJA) for 2008–2010.</figcaption></figure>

The results showed that the use of the potential-based configuration (following the multi-site calibration) led to an increase of the latent heat flux of a few tens of W/m² in many regions of the world, especially over Europe, North East America, Amazonia and South East Asia (while, in the standard configuration, the latent heat flux ranges from, on average on the same period, 60 W/m² in temperate regions to 130 W/m² in the Amazon forest). The analysis of the differences in the partition of transpiration and soil evaporation (not shown) according to dominant PFTs, showed that these differences correspond to an increase of transpiration for boreal deciduous forest, C3 crops, and C4 crops and to a decrease in transpiration for Tropical raingreen forest and C4 grasslands. These differences are the result of differences in the stomatal conductance of the two configurations, with (a) larger slopes of the Ball and Berry function after calibration for the potential-based configuration compared to the standard model for most of the PFTs (Tables B2 and B3), leading to a lower plant water use efficiency and higher transpiration, and (b) a shift of the threshold under which the vegetation starts to be stressed and to reduce water losses to a higher soil moisture content for TrRF, BoENF and C3 grasslands. These differences in stomatal conductance parametrization also explain the larger discrepancies in leaf area cover in tropical regions where the LAI difference between configurations was up to 1 m²/m². The differences between the standard and potential-based configurations for the evaporative fraction which reflects the partitioning of net radiation at the surface, showed consistent patterns with LE differences with larger evaporative fraction values in regions where the LE fluxes were larger. Simulated differences in LE were up to +20% higher with the potential-based configuration compared to the standard configuration in regions dominated by croplands such as southwestern Siberia, US Central Great Plains, Mato Grosso state in Brazil and Central Africa. Between configurations, large decreases in LE, i.e., -20% were seen in the north of Canada, mainly covered by boreal grasses for which the soil water stress threshold increased in the potential-based configuration.
As a result of the changes in the turbulent fluxes, the surface temperature differed between configurations with up to 3°C during summer in the tropical zone (e.g., Sahel region), which is large enough to potentially lead to substantial impacts on the air temperature and regional climate when the model is run coupled to an atmospheric general circulation model. Finally, concerning the carbon cycle, GPP differences were mostly in line with the differences in stomatal conductance, with lower values where stomatal conductances decreased which led to differences of up to 5 g[C]/m²/day in the north of Canada or the south of Sahel (representing a decrease of neatly 50%). Such large differences were enabled by an increase in LAI of up to 2 m²/m². However, a very slight increase of GPP is observed in regions where stomatal conductance increased (e.g., in the eastern US and over the Eurasian continent), suggesting that water is not the main limiting factor in these areas. The consequence of these changes was an overall decrease of the water use efficiency up to 3 g[C]/kg[H₂O] over semi-arid regions such as the southern Sahel or north Chili and south Argentina.

# 5. Discussion and Conclusion

## 5.1. Hydraulic Architecture

This study explores the benefits of a fully coupled hydraulic architecture scheme into the ORCHIDEE LSM. The scheme enables a complete representation of the water transport from the soil-root interface to the stomatal cavities which directly constrains the stomatal conductance. This new configuration has been evaluated against the standard configuration at different scales: (a) a detailed (although less detailed than Kennedy et al. (2019)) evaluation at two intensively monitored forest sites, that is FR-Hes and FR-Pue, (b) an overall calibration and evaluation over 135 eddy-covariance sites included in the FLUXNET2015 data set, and (c) global comparison of the two model configurations. Across scales and PFTs, the calibrated standard configuration of ORCHIDEE, in which water control on stomatal conductance is represented with a simple soil moisture stress function, performs similarly to the calibrated potential-based configuration. The potential-based configuration makes ORCHIDEE r9107 more process-based and thus more realistic than previous revisions with a similar level of accuracy (Prentice et al., 2015).

The hydraulic architecture implementation enabled, at the temperate broadleaf forest of Hesse (FR-Hes), a simulation of the seasonal latent and sensible heat flux variations as good as the standard model over dry and normal years (r of 0.92 for LE for both configurations, and r of 0.74 and 0.75 for H for the potential-based and the standard configurations respectively in Table 3). Furthermore, the hydraulic architecture captured the dynamics of the soil water content (Table 3). The radial diffusion of water through Richards' equation around the roots in the potential-based configuration, allows a higher soil water holding capacity than in the standard configuration (Table 3). The higher soil water holding capacity of the potential-based configuration is close to the observations (Figure 5).

At the Mediterranean forest site of Puéchabon (FR-Pue), both model configurations performed similarly in terms of seasonal dynamics of LE and H and the simulations are in good agreement with the observations, with, however, an overestimation of the LE flux in early summer (Figure 6). The overestimation in early summer may be partly due to an overestimation of the LAI (which was prescribed in these simulations) which in turn resulted in higher transpiration. This hypothesis likely played a role in 2005, when a caterpillar attack defoliated the trees in spring (Allard et al., 2008), possibly increasing the difference between the model and the observations during this year (Figure 6). The discrepancy between the modeled and observed LE in early summer may also be due to a bias in the observations. Indeed, the energy flux observations used in this study were not corrected which resulted in a non-closure of the energy budget (Ingwersen et al., 2015; Maayar et al., 2008). The overestimation of LE and H fluxes with both configurations in 2005 could be in part assigned to the observed energy budget that was not closed at FR-Pue for this year (confirmed but not shown here).

Further analysis of the simulated leaf water potential dynamics showed that the potential-based configuration, calibrated only with daily-averaged latent and sensible heat fluxes, resulted in a poor representation of $\psi_{leaf}$. The strong overestimation of $\psi_{leaf}$ with the potential-based configuration was attributed to the poor calibration of the $\psi_{ref}$ parameter. Indeed, including $\psi_{leaf}$ in the calibration resulted in a lower reference water potential which, in turn, led to a better model-data fit for the leaf water potential (Figure B4). However, the reference water potential resulting from the introduction of leaf water potential in the calibration was still insufficient to completely capture the strong decrease in leaf water potential measured at FR-Pue. This behavior is coherent with the results of (Tuzet
et al., 2003, Figure 6) which highlight the impact of each parameter of Equation 3 on the resulting leaf water potential, and especially that decreasing the reference water potential enables a decrease of the minimum modeled leaf water potential.

On average over both sites, the anisohydric behavior (Moreno et al., 2024; Tuzet et al., 2017) of the dominant tree species at the sites, that is, *Fagus sylvatica* for FR-Hes and *Quercus ilex* for FR-Pue, is not well captured by the model. The impact of soil parametrization on the simulation of plant transpiration has been highlighted (Verhoef & Egea, 2014). The relatively simple description of the soil in ORCHIDEE may prevent it from simulating site-specific soil water dynamics. For example, the shallow rocky soil at FR-Pue, is represented by a 2 m deep soil in ORCHIDEE which results in a higher water availability for the plants (given that roots cover the 2 m soil depth).

The analysis of the diurnal cycle (Figures B5 and B6) highlights a drawback of the calibration. The rocky soil at Puechabon is very specific and, therefore, difficult to represent in a global LSM like ORCHIDEE. The calibration compensated the too-deep soil in ORCHIDEE compared to the observations, by calibrating soil hydraulic conductivity to values that are unrealistic given the soil texture at the site (without considering stones). The calibration suggested a soil hydraulic conductivity of 3,000 mm/d, which is far from the 126 mm/d measured at the FR-Pue site (Schaap et al., 1998). This problem has also been documented by other modeling experiments (Ruffault et al. (2023), de Marty, JMSC 2022 presentation).

The comparison between potential-based configurations with and without water storage highlights the impact of water storage on the diurnal cycle. As mentioned in Tuzet et al. (2017), the radial resolution of Richards' equation around the roots leads to an early decrease of the *LE* flux in the morning due to the drying of the soil near the root. This drying effect, is at the origin of a possible asymmetry in the diurnal cycle, but it is dampened by the tree water storage pools. Diurnal asymmetry can be observed from Figure B7. Compared to other models (Li et al., 2021; Paschalis et al., 2024), the diurnal asymmetry in ORCHIDEE was largely dampened because of the high hydraulic conductivity compared to the other models. As this dampening effect increases with plant water storage and is not apparent in the observations, it confirms the need to include dynamic plant water storage pools in hydraulic architecture schemes, as already mentioned in Salomón et al. (2017) or Huang et al. (2017).

The results obtained at the 135 FLUXNET2015 sites showed that the new potential-based configuration can be used for all PFTs, including non-forested sites such as grasslands or croplands. Note that Xie et al. (2023) performed a similar study with a different LSM also including a hydraulic architecture based on Tuzet et al. (2017). Their single-site calibration at 30 sites covering different PFTs, provided better results than their standard model version without hydraulic architecture representation. This different behavior between the calibration of ORCHIDEE and the one of Xie et al. (2023) highlights the importance of the overall model structure, especially the soil water dynamic description, to assess the potential benefit of including a hydraulic architecture.

At the global scale, the differences in latent heat between standard and potential-based configurations, with primarily an increase of *LE* in the potential-based configuration, are mainly explained by changes in stomatal conductance and the applied soil water stress functions. This behavior is, however, not visible at the evaluation step at site level. Indeed, site-specific soil water content parameters are calibrated at site level and the LAI is prescribed, whereas at the global scale a dynamic LAI and a fixed soil depth with generic parameters (from the multi-site calibration) are used. These differences highlight the difficulty of calibrating a global LSM with site-specific observations when both PFTs and soil types are mixed.

## 5.2. Impact of the Choice of the Calibration Strategy

This study questions how global LSM should be calibrated. The simulations performed at FR-Pue highlighted that a calibration based on daily fluxes improved the seasonal cycle of *LE* fluxes but not the diurnal cycle. The test case where calibration was performed with half-hourly fluxes led to a lower soil hydraulic conductivity and a higher model performance at the diurnal scale with a slight improvement of the early maximum and the asymmetry of the cycle during the day but degraded the performances at the seasonal scale. Further work is needed to jointly minimize errors in both, the diurnal and the seasonal cycle.

Moreover, the standard configuration of ORCHIDEE, which has been calibrated for a few model parameters in this study, has already been calibrated during previous model developments for a much broader set of parameters (Bacour et al., 2019; MacBean et al., 2018; Peylin et al., 2016). As a consequence, the ORCHIDEE standard version was already well-calibrated to maximize the performance of the soil water stress function. The additional
standard calibration performed in this study for a restricted parameter set, can be viewed as an incremental step, aiming at improving a small part of the already calibrated model. The calibration of a limited set of parameters of the new hydraulic architecture configuration, gives, however, only a first approximation of the potential of the new scheme. The larger model spread for total soil water content than for *LE* and *H* fluxes at FR-Hes reveals that parameters controlling the soil water content are not strongly constrained through the assimilation of *LE* and *H* fluxes or that equifinality is occurring between several parameters. Implementing the new hydraulic architecture justifies a more complete re-calibration of ORCHIDEE. This was, however, out of the scope of this study.

Plant traits related to plant hydrology can vary widely among plant species (Anderegg et al., 2018; Guillemot et al., 2022; Martin-StPaul et al., 2017) and PFTs. Trait variation is in part coherent with the large range of values obtained for some parameters after the single-site calibrations in this study and in Xie et al. (2023). This observed parameter range calls for alternative descriptions of plant trait variability in global LSMs with, for instance, the use of spatially varying parameters.

### 5.3. Potential Hydraulic Architecture Model Improvements

The potential-based configuration includes a resolution scheme that prevents two common pitfalls associated to the numerical implementation of a hydraulic architecture: (a) an iterative scheme over a large number of equations including soil water and energy budgets, and (b) an incompletely coupled hydraulic architecture, with plant hydraulics that acts only as a correction term when soil-plant water supply is lower than atmospheric demand (Section 2.3). The iterative scheme implemented in this study is only acting on a reduced number of equations and during periods of high instabilities. It relies on an estimation of the transpiration at the next time step, which enables a strong reduction of the oscillations occurring from one time step to the next, that is, at half-hourly time scale in ORCHIDEE. However, such a numerical scheme could be further improved through a better estimate of the predicted transpiration flux. As an example, a machine learning algorithm that could estimate the next time step transpiration flux based on the state of the model at the current time step would likely decrease the oscillations and the number of iterations needed to converge.

Other improvements could target the coupling between plant physiological state and plant hydraulics. In the present study, the hydraulic resistances are considered fixed and only aim at representing the transport inside the plant. However, this transport depends directly on gravity and on the physiological state of the vessels in the xylem, which in turn depends on the water potential. Including a dependency of each resistance on the water potential of the stage where they act as it is done in CABLE (de Kauwe et al., 2022) and introducing gravity in the equations as it is done in CLM5 (Kennedy et al., 2019) would lead to a more physiological and physical representation of the water transport. Including dynamic resistances would also open new research fields, such as the representation of mortality through embolism (de Kauwe et al., 2020, 2022; Yao et al., 2022). In addition, the loss of conductivity during severe drought would also impact the dynamics of the LAI, which, in turn, feedbacks on the water demand and soil water potential. All those additional developments were beyond the scope of the present study which aimed at paving the way to a more process-based representation of the drought effects in ORCHIDEE. However, taking into account embolism and other physiological aspects in the newly proposed hydraulic architecture scheme would lead to a more accurate representation of plant water flow dynamics, capturing the direct influence of plant physiology and not only of plant biomass and soil water dynamics as it is currently done. This would enable us to significantly improve the results, especially under drought conditions, as proven by Ruffault et al. (2023) and their results at FR-Pue site.

The model being highly dependent on the soil depth, soil properties and root representations, the introduction of this hydraulic architecture in ORCHIDEE also highlights some shortcomings of the LSM on those processes. Indeed, the fixed 2 m-depth of the soil columns with homogeneous parametrization in ORCHIDEE does not enable a proper representation of the soil water content and dynamics globally (countered here by calibrating the soil properties on-site). The introduction of a spatially variable soil depth could, therefore, help to prevent this inconvenience (see Brunke et al. (2016) for such a study with CLM4.5). The fixed soil root profile (exponential decay in the entire soil depth) is also a strong approximation that should be reviewed (Y. Wang et al., 2018). A dynamic rooting system depending on plant species and soil physical characteristics, would also provide a better representation of the plant water uptake.

Finally, the stomatal conductance's semi-empirical formulation (following Tuzet et al. (2003)) used in the potential-based implementation is crucial and can be further improved. Sabot, et al. (2022) presents a comparison
of several stomatal conductance formulations. It highlights that semi-empirical formulations like the one used here can lead to different responses between the stomatal closure and leaf water potential under different environmental conditions. Yang et al. (2019) supports this analysis by showing that the Tuzet et al. (2003) formulation can result in an erroneous representation of the stomatal conductance in periods of high VPD. Various feedbacks between all variables can further introduce numerical instabilities in the numerical scheme as mentioned in this study. Stomatal conductance formulations based on optimality principles, aiming at maximizing carbon uptake and minimizing water losses, could potentially bring some improvements and add value to the plant hydraulics representation but they remain complicated to constrain.

## 5.4. Future Evaluations

This study presents an evaluation of two model configurations at site level and global scale, focusing on latent and sensible heat fluxes. Observations used for model evaluation result from indirect measurements (like eddy covariance) and are subject to biases and uncertainties. By representing water potentials, hydraulic architecture-based models can also be compared directly to measurements of water potential (Novick et al., 2022; Restrepo-Acevedo et al., 2024). One interesting perspective of using the hydraulic architecture-based models is the direct link between the modeled flow of water inside the vegetation and some measurements from new data sets that are currently being assembled (Poyatos et al., 2016). Representing plant hydraulic conductivity as a function of plant water potentials also enables the comparison to current measurements of water potentials inducing a 12%, 50%, and 88% loss in hydraulic conductivity; these measurements have been made for a lot of species (de Kauwe et al., 2022; Xie et al., 2023). Overall, compared to the standard statistical soil water stress representation, the hydraulic architecture thus opens for the use of a larger set of observations to calibrate the physiological response of plants to soil water stress (at least at site level). This should further help reduce the uncertainty associated with LSM water and carbon budgets.

## Appendix A: Resolution Scheme

The hydraulic architecture model presented here relies on three main variables: the stomatal conductance, $g_{H_2O}$, the transpiration flux, $E_{transp}$, and the leaf water potential, $\psi_{leaf}$. Each variable depends on the other variables within the presented scheme. Leaf water potential impacts stomatal conductance, which drives transpiration, which in turn impacts leaf water potential. ORCHIDEE being solved implicitly, the whole scheme has to be solved in this way in order to avoid instabilities during drought periods when the relationship between stomatal conductance and leaf water potential is highly non-linear due to the sigmoidal function. Solving this scheme in an implicit way would mean introducing an iterative process in the code such as a Newton method. However, because the three variables above are calculated in three different modules of ORCHIDEE (the first module, *difluco*, aims at solving the different resistances applied to water exchanges with the atmosphere, among them, the photosynthesis model is solved, resulting in the calculation of the stomatal conductance; the second module, *enerbil*, solves the big-leaf energy balance model and the partitioning of the evapotranspiration flux into its components (such as transpiration); the third module, *hydrol*, solves the soil water budget and the hydraulic architecture presented in this article), implementing such a scheme on several modules would lead to an exploding calculation time.

To bypass this problem, a revisited numerical scheme that mimics an implicit scheme over several equations only and during drought periods only has been implemented. The scheme is presented in Figure A1.

During non-drought periods, when the leaf water potential is not lower than the reference water potential ($\psi_{ref}$) plus a threshold, the model behaves like a purely explicit scheme. The stomatal conductance relies on the leaf water potential at the previous time step. It permits the calculation of the transpiration which leads to the calculation of the new leaf water potential. During drought periods, the resolution of the two first modules stays the same: the stomatal conductance permits the calculation of the transpiration flux which is given to the third module to calculate the leaf water potential of the time step. However, once this calculation is finished, the value of $\psi_{leaf}$ is not directly sent to the first module to calculate the stomatal conductance at the next time step. In this case, a second calculation is started, still in the third module. The objective is to estimate the transpiration of the next time step in order to calculate a leaf water potential for the next time step which would be closer to the real one.

The transpiration equation can be summarized as:
<figure><img src="image_11.png" /><figcaption>**Figure A1.** Resolution scheme implemented for the hydraulic architecture. The colors represent the different ORCHIDEE modules (green: *difluco*, orange: *enerbil* and blue: *hydrol*); the temporary variables are either mentioned as “(temporary)” or “_temp.”</figcaption></figure>
$$F_{transp} = \frac{\rho \cdot \Delta t \cdot \Delta q}{R_a + R_g} \qquad (A1)$$

where $\rho$ is the air density, $\Delta t$ is the time step length, $\Delta q$ is the difference of humidity between the surface and the atmosphere, $R_a = \frac{1}{|\tilde{V}|C_d}$ is the aerodynamic resistance and $R_g = 1/g_{H_2O}$ is the stomatal resistance. This equation can be simplified to:

$$F_{transp} = \frac{A}{B + \frac{1}{C \cdot f_{\psi}}} \qquad (A2)$$

The transpiration at time step $t$ and at time step $t + 1$ can be expressed as:

$$F_{transp}^{t} = \frac{A^{t}}{B^{t} + \frac{1}{C \cdot f(\psi_{leaf}^{t})}} = \frac{A^{t}}{B^{t} + \frac{1}{C \cdot f_{\psi}^{t}}} \qquad (A3)$$

$$F_{transp}^{t+1} = \frac{A^{t+1}}{B^{t+1} + \frac{1}{C^{t+1} \cdot f(\psi_{leaf}^{t+1})}} = \frac{A^{t+1}}{B^{t+1} + \frac{1}{C^{t+1} \cdot f_{\psi}^{t+1}}} \qquad (A4)$$

We try to estimate $F_{transp}^{t+1}$ from $F_{transp}^t$. Looking at the components of the transpiration:

* $A^t$ and $A^{t+1}$ represent the evolution of $\Delta q$ over the day;

* $B^t$ and $B^{t+1}$ represent the evolution of the aerodynamic resistance;

* $C^t$ and $C^{t+1}$ represent the evolution of the components of $g_{H_2O}$ that are not directly linked to $f_{\psi}$.

The following assumptions are made:

* $A^{t+1} = A^t \cdot \delta$;

* $C^{t+1} = C^t \cdot \delta$;

* $B^{t+1} = B^t$;

* $\delta$ can be estimated by a sinusoidal function centered on solar noon.

The assumption is hence that in the absence of water stress, transpiration and stomatal conductance will follow a sinusoidal function centered on the solar noon, starting at sunrise and ending at sunset. Following this assumption, $\delta$ can be expressed as the ratio between the values of the sinusoidal function at time step $t$ and $t + 1$. The amplitude of the sine function cancels out in the ratio.

Consequently, the ratio between $F_{transp}^{t+1}$ and $F_{transp}^t$ can be estimated as:

$$\frac{F_{transp}^{t+1}}{F_{transp}^{t}} = \frac{\frac{A^{t+1}}{B^{t+1} + \frac{1}{C^{t+1} \cdot f_{\psi}^{t+1}}}}{\frac{A^t}{B^t + \frac{1}{C^t \cdot f_{\psi}^t}}} = \delta \cdot \frac{1 + \frac{|\tilde{V}| \cdot C_d}{\delta g_{H_2O}}}{1 + \frac{|\tilde{V}| \cdot C_d \cdot f_{\psi}^t}{\delta g_{H_2O} \cdot f_{\psi}^t}} \qquad (A5)$$

This ratio, multiplied by $F_{transp}^t$, permits to have a prediction of $F_{transp}^{t+1}$ only with variables from the previous time step. This approximation enables the solving of the iterative process.

Coming back to the iterative process, the value of the leaf water potential at the previous time step enables an estimation of the transpiration at the next time step. This approximation is used to calculate the value of the leaf water potential at the next time step and iterate until the solution converges toward a single solution. This scheme enables a good approximation of the leaf water potential at the next time step, which is then sent to the first module which calculates the value of the new stomatal conductance. One can note that the scheme can be improved by improving the transpiration flux estimation.
## Appendix B: Supplementary Tables and Figures

See Tables B1–B6 and Figures B1–B9.

<caption>**Table B1**</caption>

Plant Functional Types Acronyms

<table><caption>**Table B2**</caption><thead><tr><th>Acronym</th><th>Long name</th><th>Number</th></tr></thead><tbody><tr><td>BS</td><td>Bare soil</td><td>1</td></tr><tr><td>TrEF</td><td>Tropical Broadleaf Evergreen Forest</td><td>2</td></tr><tr><td>TrRF</td><td>Tropical Broadleaf Raingreen Forest</td><td>3</td></tr><tr><td>TeENF</td><td>Temperate Evergreen Needleleaf Forest</td><td>4</td></tr><tr><td>TeEBF</td><td>Temperate Evergreen Broadleaf Forest</td><td>5</td></tr><tr><td>TeDBF</td><td>Temperate Deciduous Broadleaf Forest</td><td>6</td></tr><tr><td>BoENF</td><td>Boreal Evergreen Needleleaf Forest</td><td>7</td></tr><tr><td>BoDBF</td><td>Boreal Deciduous Broadleaf Forest</td><td>8</td></tr><tr><td>BoDNF</td><td>Boreal Deciduous Needleleaf Forest</td><td>9</td></tr><tr><td>C3G</td><td>C3 Grassland</td><td>10</td></tr><tr><td>C4G</td><td>C4 Grassland</td><td>11</td></tr><tr><td>C3C</td><td>C3 Crop</td><td>12</td></tr><tr><td>C4C</td><td>C4 Crop</td><td>13</td></tr></tbody></table>

Result of the Parameters Calibration for the Potential-Based Configuration

<table><thead><tr><th>Potential-based</th><th>Description</th><th>Def</th><th>Min</th><th>Max</th><th>FR-Hes (BEST)</th><th>FR-Pue (BEST NOPSI)</th><th>FR-Pue (BEST PSI)</th><th>Multisite F2015</th><th>Single site F2015</th></tr></thead><tbody><tr><td rowspan="10">ψ<sub>ref</sub> (Equation 4)</td><td rowspan="10">Reference water potential at which g<sub>H2O</sub> is decreased by 50%</td><td rowspan="10">-1.6</td><td rowspan="10">-0.8</td><td rowspan="10">-2.0</td><td rowspan="10">-0.81</td><td rowspan="10">-0.86</td><td rowspan="10">-1.4</td><td>TrEF</td><td>-1.97</td><td>-1.72 ± 0.12</td></tr><tr><td>TrRF</td><td>-1.05</td><td>-1.09 ± 0.28</td></tr><tr><td>TeENF</td><td>-1.17</td><td>-1.16 ± 0.3</td></tr><tr><td>TeEBF</td><td>-0.81</td><td>-1.34 ± 0.4</td></tr><tr><td>TeDBF</td><td>-1.67</td><td>-1.21 ± 0.36</td></tr><tr><td>BoENF</td><td>-1.15</td><td>-1.13 ± 0.3</td></tr><tr><td>BoDBF</td><td>-1.46</td><td>-1.3 ± 0.33</td></tr><tr><td>C3G</td><td>-1.31</td><td>-1.3 ± 0.4</td></tr><tr><td>C4G</td><td>-1.60</td><td>-1.29 ± 0.33</td></tr><tr><td>C3C</td><td>-1.45</td><td>-1.52 ± 0.33</td></tr><tr><td>C4C</td><td>-1.53</td><td>-1.13 ± 0.15</td></tr><tr><td rowspan="7">R<sub>root-trunk</sub> and R<sub>trunk-leaf,xylem</sub> (*10<sup>6</sup>)<br>(Hydraulic architecture resolution)</td><td rowspan="7">Xylem water resistance</td><td rowspan="7">4</td><td rowspan="7">0.5</td><td rowspan="7">10</td><td rowspan="7">2.92</td><td rowspan="7">9.25</td><td rowspan="7">9.03</td><td>TrEF</td><td>6.49</td><td>5.67 ± 1.67</td></tr><tr><td>TrRF</td><td>9.04</td><td>7.55 ± 2.51</td></tr><tr><td>TeENF</td><td>2.87</td><td>6.74 ± 2.08</td></tr><tr><td>TeEBF</td><td>6.07</td><td>7.10 ± 1.73</td></tr><tr><td>TeDBF</td><td>8.80</td><td>5.90 ± 2.32</td></tr><tr><td>BoENF</td><td>7.51</td><td>6.72 ± 2.18</td></tr></tbody></table>
<caption>Table B2</caption>

Continued

<table><thead><tr><th>Potential-based</th><th>Description</th><th>Def</th><th>Min</th><th>Max</th><th>FR-Hes (BEST)</th><th>FR-Pue (BEST NOPSI)</th><th>FR-Pue (BEST PSI)</th><th>Multisite F2015</th><th>Single site F2015</th></tr></thead><tbody><tr><td rowspan="10">s<sub>f</sub> (Equation 4)</td><td rowspan="10">Sensitivity of g<sub>H2O</sub> to leaf water potential</td><td rowspan="10">4.3</td><td rowspan="10">2.5</td><td rowspan="10">4.5</td><td rowspan="10">2.92</td><td rowspan="10">2.98</td><td rowspan="10">2.02</td><td>BoDBF</td><td>8.50</td><td>6.46 ± 1.64</td></tr><tr><td>C3G</td><td>5.71</td><td>5.22 ± 2.16</td></tr><tr><td>C4G</td><td>4.00</td><td>4.92 ± 2.79</td></tr><tr><td>C3C</td><td>6.72</td><td>5.36 ± 3.31</td></tr><tr><td>C4C</td><td>1.94</td><td>5.06 ± 1.68</td></tr><tr><td>TrEF</td><td>2.50</td><td>3.56 ± 0.55</td></tr><tr><td>TrRF</td><td>2.82</td><td>3.22 ± 0.6</td></tr><tr><td>TeENF</td><td>2.89</td><td>3.37 ± 0.65</td></tr><tr><td>TeEBF</td><td>2.74</td><td>3.46 ± 0.55</td></tr><tr><td>TeDBF</td><td>3.76</td><td>3.06 ± 0.44</td></tr><tr><td>BoENF</td><td>2.72</td><td>3.23 ± 0.52</td></tr><tr><td>BoDBF</td><td>3.18</td><td>3.19 ± 0.49</td></tr><tr><td rowspan="10">a<sub>fpsi</sub> (Equation 3)</td><td rowspan="10">Ball and Berry slope</td><td rowspan="10">5.66</td><td rowspan="10">2</td><td rowspan="10">10</td><td rowspan="10">2.48</td><td rowspan="10">7.85</td><td rowspan="10">7.02</td><td>C3G</td><td>3.08</td><td>3.25 ± 0.55</td></tr><tr><td>C4G</td><td>2.64</td><td>3.3 ± 0.59</td></tr><tr><td>C3C</td><td>3.63</td><td>3.85 ± 0.43</td></tr><tr><td>C4C</td><td>3.32</td><td>3.56 ± 0.85</td></tr><tr><td>TrEF</td><td>9.10</td><td>9.44 ± 0.28</td></tr><tr><td>TrRF</td><td>3.67</td><td>4.8 ± 1.87</td></tr><tr><td>TeENF</td><td>3.14</td><td>6.24 ± 2.57</td></tr><tr><td>TeEBF</td><td>6.81</td><td>7.28 ± 2.73</td></tr><tr><td>TeDBF</td><td>2.27</td><td>4.12 ± 2.22</td></tr><tr><td>BoENF</td><td>3.02</td><td>5.02 ± 2.55</td></tr><tr><td>BoDBF</td><td>6.85</td><td>5.14 ± 2.71</td></tr><tr><td rowspan="10">Wood_sto fac (impact V<sub>max</sub> and, thus, C<sub>X,store</sub> in Equation 7)</td><td rowspan="10">Scaling factor to correct wood water storage</td><td rowspan="10">5</td><td rowspan="10">0.5</td><td rowspan="10">10</td><td rowspan="10">9.38</td><td rowspan="10">4.10</td><td rowspan="10">4.88</td><td>C3G</td><td>6.96</td><td>6.42 ± 3.06</td></tr><tr><td>C4G</td><td>3.09</td><td>5.11 ± 2.4</td></tr><tr><td>C3C</td><td>6.74</td><td>7.13 ± 2.55</td></tr><tr><td>C4C</td><td>7.04</td><td>8.79 ± 0.69</td></tr><tr><td>TrEF</td><td>5.84</td><td>5.69 ± 1.78</td></tr><tr><td>TrRF</td><td>6.89</td><td>6.33 ± 1.12</td></tr><tr><td>TeENF</td><td>3.9</td><td>5.72 ± 2.59</td></tr><tr><td>TeEBF</td><td>7.6</td><td>4.71 ± 3.3</td></tr><tr><td>TeDBF</td><td>1.82</td><td>4.6 ± 2.67</td></tr><tr><td>BoENF</td><td>6.87</td><td>5.29 ± 3.05</td></tr><tr><td>BoDBF</td><td>8.24</td><td>6.31 ± 1.16</td></tr><tr><td rowspan="10">Leaf_sto fac (impact V<sub>max</sub> and, thus, C<sub>X,store</sub> in Equation 7)</td><td rowspan="10">Scaling factor to correct leaf water storage</td><td rowspan="10">6</td><td rowspan="10">0.5</td><td rowspan="10">10</td><td rowspan="10">2.70</td><td rowspan="10">1.53</td><td rowspan="10">1.65</td><td>C3G</td><td>4.07</td><td>4.93 ± 2.85</td></tr><tr><td>C4G</td><td>6.00</td><td>3.73 ± 2.56</td></tr><tr><td>C3C</td><td>2.94</td><td>6.11 ± 2.44</td></tr><tr><td>C4C</td><td>6.15</td><td>4.5 ± 3.8</td></tr><tr><td>TrEF</td><td>2.18</td><td>4.44 ± 1.56</td></tr><tr><td>TrRF</td><td>7.35</td><td>5.04 ± 3.51</td></tr><tr><td>TeENF</td><td>6.79</td><td>2.66 ± 2.43</td></tr><tr><td>TeEBF</td><td>2.25</td><td>3.0 ± 2.3</td></tr><tr><td>TeDBF</td><td>8.5</td><td>5.57 ± 2.79</td></tr><tr><td>BoENF</td><td>8.34</td><td>3.7 ± 2.73</td></tr></tbody></table>
<caption>**Table B2**</caption>

*Continued*

<table><caption>**Table B3**</caption><thead><tr><th>Potential-based</th><th>Description</th><th>Def</th><th>Min</th><th>Max</th><th>FR-Hes (BEST)</th><th>FR-Pue (BEST NOPSI)</th><th>FR-Pue (BEST PSI)</th><th>Multisite F2015</th><th>Single site F2015</th></tr></thead><tbody><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>BoDBF</td><td>2.38</td><td>5.63 ± 2.02</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>C3G</td><td>9.07</td><td>4.82 ± 3.0</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>C4G</td><td>9.35</td><td>4.4 ± 2.82</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>C3C</td><td>0.80</td><td>5.61 ± 3.08</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>C4C</td><td>0.90</td><td>6.83 ± 0.22</td></tr><tr><td>MCR_sup (Root water absorption resolution in Equation 10)</td><td>Residual moisture content in the superficial soil layer</td><td>0.08</td><td>0.05</td><td>0.25</td><td>0.057</td><td>0.091</td><td>0.13</td><td>Calibrated site by site</td><td>Calibrated site by site</td></tr><tr><td>MCS_sup (Root water absorption resolution in Equation 10)</td><td>Saturated moisture content in the inferior soil layer</td><td>0.43</td><td>0.3</td><td>0.65</td><td>0.525</td><td>0.362</td><td>0.438</td><td>Calibrated site by site</td><td>Calibrated site by site</td></tr><tr><td>MCR_inf (Root water absorption resolution in Equation 10)</td><td>Residual moisture content in the superficial soil layer</td><td>0.08</td><td>0.05</td><td>0.25</td><td>0.180</td><td>0.0715</td><td>0.0876</td><td>Calibrated site by site</td><td>Calibrated site by site</td></tr><tr><td>MCS_inf (Root water absorption resolution in Equation 10)</td><td>Saturated moisture content in the inferior soil layer</td><td>0.43</td><td>0.3</td><td>0.65</td><td>0.460</td><td>0.388</td><td>0.469</td><td>Calibrated site by site</td><td>Calibrated site by site</td></tr><tr><td>kimp (Root water absorption resolution in Equation 10)</td><td>Soil hydraulic conductivity at saturation in Campbell (1986)</td><td>249.6</td><td>150</td><td>7,000</td><td>1,682</td><td>3,802</td><td>6,353</td><td>Calibrated site by site</td><td>Calibrated site by site</td></tr><tr><td>b_muff (Root water absorption resolution in Equation 10)</td><td>Empirical parameter in Campbell (1986)</td><td>2.708</td><td>2.5</td><td>3.5</td><td>2.99</td><td>3.17</td><td>3.14</td><td>Calibrated site by site</td><td>Calibrated site by site</td></tr><tr><td>ψ<sub>air_entry</sub> (Root water absorption resolution in Equation 10)</td><td>Air entry water potential of the soil in Campbell (1986)</td><td>-0.015</td><td>-0.07</td><td>-0.001</td><td>-0.0043</td><td>-0.0209</td><td>-0.030</td><td>Calibrated site by site</td><td>Calibrated site by site</td></tr></tbody></table>

*Result of the Parameters Calibration for the Standard Configuration*

<table><thead><tr><th>Standard configuration</th><th>Description</th><th>Def</th><th>Min</th><th>Max</th><th>FR-Hes (BEST)</th><th>FR-Pue (BEST)</th><th>Multisite F2015</th><th>Single site F2015</th></tr></thead><tbody><tr><td rowspan="10">a<sub>1</sub> (Equation 1)</td><td rowspan="10">Empirical parameter in Yin and Struik (2009) (1/(1/a<sub>1</sub> - 1) being the Ball and Berry slope)</td><td rowspan="10">0.85</td><td rowspan="10">0.66</td><td rowspan="10">0.91</td><td rowspan="10">0.712</td><td rowspan="10">0.888</td><td>TrEF</td><td>0.88</td><td>0.9 ± 0.0</td></tr><tr><td>TrRF</td><td>0.75</td><td>0.72 ± 0.09</td></tr><tr><td>TeENF</td><td>0.78</td><td>0.77 ± 0.1</td></tr><tr><td>TeEBF</td><td>0.76</td><td>0.77 ± 0.09</td></tr><tr><td>TeDBF</td><td>0.68</td><td>0.73 ± 0.08</td></tr><tr><td>BoENF</td><td>0.71</td><td>0.78 ± 0.08</td></tr><tr><td>BoDBF</td><td>0.73</td><td>0.71 ± 0.07</td></tr><tr><td>C3G</td><td>0.87</td><td>0.8 ± 0.1</td></tr><tr><td>C4G</td><td>0.90</td><td>0.8 ± 0.08</td></tr><tr><td>C3C</td><td>0.83</td><td>0.81 ± 0.08</td></tr><tr><td>C4C</td><td>0.80</td><td>0.84 ± 0.01</td></tr><tr><td rowspan="3">b<sub>1</sub> (Equation 1)</td><td rowspan="3">Empirical parameter in Yin and Struik (2009)</td><td rowspan="3">0.14</td><td rowspan="3">0.06</td><td rowspan="3">0.22</td><td rowspan="3">0.173</td><td rowspan="3">0.207</td><td>TrEF</td><td>0.10</td><td>0.14 ± 0.06</td></tr><tr><td>TrRF</td><td>0.21</td><td>0.2 ± 0.01</td></tr><tr><td>TeENF</td><td>0.19</td><td>0.19 ± 0.03</td></tr></tbody></table>
<caption>Table B3</caption>

Continued

<table><thead><tr><th>Standard configuration</th><th>Description</th><th>Def</th><th>Min</th><th>Max</th><th>FR-Hes (BEST)</th><th>FR-Pue (BEST)</th><th>Multisite F2015</th><th>Single site F2015</th></tr></thead><tbody><tr><td rowspan="10">p% (Equation 2)</td><td rowspan="10">Percentage of soil water reserve at which stomatal conductance starts to decrease</td><td rowspan="10">0.8</td><td rowspan="10">0.55</td><td rowspan="10">0.95</td><td rowspan="10">0.909</td><td rowspan="10">0.870</td><td>TeEBF</td><td>0.21</td><td>0.2 ± 0.04</td></tr><tr><td>TeDBF</td><td>0.19</td><td>0.18 ± 0.03</td></tr><tr><td>BoENF</td><td>0.20</td><td>0.19 ± 0.03</td></tr><tr><td>BoDBF</td><td>0.21</td><td>0.19 ± 0.04</td></tr><tr><td>C3G</td><td>0.19</td><td>0.14 ± 0.05</td></tr><tr><td>C4G</td><td>0.20</td><td>0.16 ± 0.04</td></tr><tr><td>C3C</td><td>0.19</td><td>0.18 ± 0.05</td></tr><tr><td>C4C</td><td>0.09</td><td>0.21 ± 0.0</td></tr><tr><td>TrEF</td><td>0.93</td><td>0.82 ± 0.01</td></tr><tr><td>TrRF</td><td>0.64</td><td>0.74 ± 0.09</td></tr><tr><td>TeENF</td><td>0.76</td><td>0.75 ± 0.14</td></tr><tr><td>TeEBF</td><td>0.80</td><td>0.8 ± 0.13</td></tr><tr><td>TeDBF</td><td>0.80</td><td>0.73 ± 0.11</td></tr><tr><td>BoENF</td><td>0.67</td><td>0.77 ± 0.12</td></tr><tr><td>BoDBF</td><td>0.68</td><td>0.79 ± 0.12</td></tr><tr><td rowspan="4">MCR_imp (Soil water transport resolution)</td><td rowspan="4">Residual moisture content</td><td rowspan="4">0.08</td><td rowspan="4">0.05</td><td rowspan="4">0.25</td><td rowspan="4">0.173</td><td rowspan="4">0.171</td><td>Calibrated site by site</td><td>Calibrated site by site</td></tr><tr><td>Calibrated site by site</td><td>Calibrated site by site</td></tr><tr><td>Calibrated site by site</td><td>Calibrated site by site</td></tr><tr><td>Calibrated site by site</td><td>Calibrated site by site</td></tr><tr><td>MCS_imp (Soil water transport resolution)</td><td>Saturated moisture content</td><td>0.43</td><td>0.3</td><td>0.65</td><td>0.353</td><td>0.433</td><td></td><td></td></tr><tr><td>kimp (Soil water transport resolution)</td><td>Soil hydraulic conductivity at saturation in van Genuchten (1980)</td><td>249.6</td><td>150</td><td>7,000</td><td>1,154</td><td>2,882</td><td></td><td></td></tr><tr><td>avan (Soil water transport resolution)</td><td>Empirical parameter in van Genuchten (1980)</td><td>0.078</td><td>0.0005</td><td>0.1</td><td>0.0139</td><td>0.000784</td><td></td><td></td></tr><tr><td>bvan (Soil water transport resolution)</td><td>Empirical parameter in van Genuchten (1980)</td><td>1.56</td><td>1.3</td><td>2.3</td><td>1.32</td><td>2.13</td><td></td><td></td></tr></tbody></table>
<caption>**Table B4**</caption>

Root Mean Square Error for Each Calibrations of the 10 Members Ensemble for **FR-Hes** (HA Refers at the Potential-Based Configuration; STD Refers at the Standard Configuration)

<table><caption>**Table B5**</caption><thead><tr><th></th><th>Variable</th><th>Member 1</th><th>Member 2</th><th>Member 3</th><th>Member 4</th><th>Member 5</th><th>Member 6</th><th>Member 7</th><th>Member 8</th><th>Member 9</th><th>Member 10</th><th>Mean ± standard deviation</th></tr></thead><tbody><tr><td rowspan="3">HA</td><td>LE</td><td>15.4</td><td>17.3</td><td>17.4</td><td>17.1</td><td>16.7</td><td>16.0</td><td>16.3</td><td>15.4</td><td>16.0</td><td>16.5</td><td>16.41 ± 0.69</td></tr><tr><td>H</td><td>26.3</td><td>25.3</td><td>26.2</td><td>25.7</td><td>25.9</td><td>25.8</td><td>25.9</td><td>26.0</td><td>26.1</td><td>25.5</td><td>25.87 ± 0.29</td></tr><tr><td>H + LE</td><td>41.7</td><td>42.6</td><td>43.6</td><td>42.8</td><td>42.6</td><td>41.8</td><td>42.2</td><td>41.4</td><td>42.1</td><td>42.0</td><td>42.28 ± 0.61</td></tr><tr><td rowspan="3">STD</td><td>LE</td><td>15.8</td><td>15.8</td><td>15.8</td><td>16.3</td><td>15.8</td><td>16.3</td><td>16.1</td><td>15.4</td><td>15.7</td><td>15.7</td><td>15.87 ± 0.27</td></tr><tr><td>H</td><td>25.8</td><td>26.2</td><td>25.6</td><td>25.5</td><td>25.9</td><td>25.5</td><td>25.4</td><td>26.3</td><td>25.7</td><td>26.0</td><td>25.79 ± 0.29</td></tr><tr><td>H + LE</td><td>41.6</td><td>42.0</td><td>41.4</td><td>41.8</td><td>41.8</td><td>41.9</td><td>41.5</td><td>41.7</td><td>41.4</td><td>41.7</td><td>41.68 ± 0.19</td></tr></tbody></table>

Root Mean Square Error for Each Calibrations of the 10 Members Ensemble for **FR-Pue Without ψ<sub>leaf</sub> in the Calibration (HA) STD Refers at the Standard Configuration**

<table><caption>**Table B6**</caption><thead><tr><th></th><th>Variable</th><th>Member 1</th><th>Member 2</th><th>Member 3</th><th>Member 4</th><th>Member 5</th><th>Member 6</th><th>Member 7</th><th>Member 8</th><th>Member 9</th><th>Member 10</th><th>Mean ± standard deviation</th></tr></thead><tbody><tr><td rowspan="3">HA</td><td>LE</td><td>14.4</td><td>14.1</td><td>14.2</td><td>14.9</td><td>14.3</td><td>14.9</td><td>14.3</td><td>16.7</td><td>14.1</td><td>14.4</td><td>14.63 ± 0.74</td></tr><tr><td>H</td><td>21.1</td><td>21.2</td><td>21.3</td><td>21.2</td><td>21.7</td><td>20.7</td><td>21.5</td><td>21.9</td><td>21.3</td><td>21.3</td><td>21.32 ± 0.31</td></tr><tr><td>H + LE</td><td>35.5</td><td>35.3</td><td>35.5</td><td>36.1</td><td>36.0</td><td>35.6</td><td>35.8</td><td>35.6</td><td>35.4</td><td>36.0</td><td>35.68 ± 0.26</td></tr><tr><td rowspan="3">STD</td><td>LE</td><td>14.9</td><td>15.1</td><td>14.5</td><td>15.2</td><td>15.7</td><td>14.9</td><td>17.5</td><td>14.8</td><td>15.1</td><td>14.8</td><td>15.25 ± 0.81</td></tr><tr><td>H</td><td>21.4</td><td>21.4</td><td>22.0</td><td>21.3</td><td>20.8</td><td>21.4</td><td>22.7</td><td>21.4</td><td>21.0</td><td>21.2</td><td>21.46 ± 0.51</td></tr><tr><td>H + LE</td><td>36.3</td><td>36.5</td><td>36.5</td><td>36.5</td><td>36.5</td><td>36.3</td><td>40.2</td><td>36.2</td><td>36.1</td><td>36.0</td><td>36.71 ± 1.18</td></tr></tbody></table>

Root Mean Square Error for Each Calibrations of the 10 Members Ensemble for **FR-Pue With ψ<sub>leaf</sub> in the Calibration (HA-Psi) (STD Refers at the Standard Configuration)**

<table><thead><tr><th></th><th>Variable</th><th>Member 1</th><th>Member 2</th><th>Member 3</th><th>Member 4</th><th>Member 5</th><th>Member 6</th><th>Member 7</th><th>Member 8</th><th>Member 9</th><th>Member 10</th><th>Mean ± standard deviation</th></tr></thead><tbody><tr><td rowspan="3">HA-psi</td><td>LE</td><td>14.6</td><td>15.2</td><td>14.1</td><td>14.8</td><td>14.8</td><td>16.1</td><td>15.0</td><td>15.8</td><td>14.8</td><td>15.7</td><td>15.09 ± 0.58</td></tr><tr><td>H</td><td>22.2</td><td>21.9</td><td>21.0</td><td>21.8</td><td>21.2</td><td>20.6</td><td>21.6</td><td>21.9</td><td>21.0</td><td>22.2</td><td>21.54 ± 0.53</td></tr><tr><td>H + LE</td><td>36.8</td><td>37.1</td><td>35.1</td><td>36.6</td><td>36.0</td><td>36.7</td><td>36.6</td><td>37.7</td><td>35.8</td><td>37.9</td><td>36.63 ± 0.8</td></tr><tr><td rowspan="3">STD</td><td>LE</td><td>14.9</td><td>15.1</td><td>14.5</td><td>15.2</td><td>15.7</td><td>14.9</td><td>17.5</td><td>14.8</td><td>15.1</td><td>14.8</td><td>15.25 ± 0.81</td></tr><tr><td>H</td><td>21.4</td><td>21.4</td><td>22.0</td><td>21.3</td><td>20.8</td><td>21.4</td><td>22.7</td><td>21.4</td><td>21.0</td><td>21.2</td><td>21.46 ± 0.51</td></tr><tr><td>H + LE</td><td>36.3</td><td>36.5</td><td>36.5</td><td>36.5</td><td>36.5</td><td>36.3</td><td>40.2</td><td>36.2</td><td>36.1</td><td>36.0</td><td>36.71 ± 1.18</td></tr></tbody></table>
<figure><img src="image_12.png" /><figcaption>**Figure B1.** Parameter error correlation matrices for FR-Hes (upper panel) and FR-Pue (lower panel).</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Figure B2.** Comparison between the parameter values of the potential-based configuration obtained for each plant functional type (PFT) via the multi-site calibration (red dots—referred as) and the single-site calibration (boxplots—referred as). For the boxplots the orange lines correspond to the median of the parameter over the different sites in each PFT, while the spreads correspond to the 25%–75% interval around the median.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Figure B3.** Comparison between the parameter values of the standard configuration obtained for each plant functional type (PFT) via the multi-site calibration (red dots—referred as) and the single-site calibration (boxplots—referred as). For the boxplots the orange lines correspond to the median of the parameter over the different sites in each PFT, while the spreads correspond to the 25%–75% interval around the median.</figcaption></figure>
<figure><img src="image_15.png" /></figure>

**Figure B4.** Comparison between the potential-based configuration (red line (HA)): best calibration, red spread: range of results obtained for the 10 calibrations), the standard configuration (blue line (STD)): best calibration, blue spread: range of results obtained for the 10 calibrations) and the Observations (black line) for seasonal latent heat flux (panel A), seasonal sensible heat flux (panel B), mean daily latent heat flux over the summer (June, July, and August) (panel C) and leaf water potential representation at mid-day and pre-dawn (panel D) at Puéchabon forest (FR-Pue) when leaf water potential measurements are used in the parameter calibration. The seasonal cycles are obtained with rolling averages over 1 month, the diurnal one is obtained by rolling averaging over 2 time steps (see Section 4.1).
<figure><img src="image_16.png" /></figure>

**Figure B5.** Comparison between the classical calibration of the potential-based calibration over daily fluxes (red line), a calibration of the potential-based calibration over hourly fluxes (blue line) and the Observations (black line) for seasonal latent heat flux (panel A) and mean normalized daily latent heat flux over the summer (June, July, and August) (panel B) at Puechabon forest (FR-Pue). The seasonal cycles are obtained with rolling averages over 1 month, the diurnal one is obtained by rolling averaging over 2 time steps (see Section 4.1). The diurnal cycles have been normalized by their maximum value in the left panel to facilitate the comparison.

<figure><img src="image_17.png" /></figure>

**Figure B6.** Comparison between HA (red line), HA with the same parameter set as Best opti HA except a decreased hydraulic conductivity at saturation (blue line) and the Observations (black line) for seasonal latent heat flux (panel A) and mean daily latent heat flux over the summer (June, July, and August) (panel B) at Puechabon forest (FR-Pue). The seasonal cycles are obtained with rolling averages over 1 month, the diurnal one is obtained by rolling averaging over 2 time steps (see Section 4.1). The diurnal cycles have been normalized by their maximum value in the left panel to facilitate the comparison.
<figure><img src="image_18.png" /><figcaption>**Figure B7.** Comparison between mean diurnal cycles over strongly drought periods (left panel) and summer periods (right panel) at FR-Pue between the complete potential-based scheme (HA in red) and the same scheme without water storage compartments (HA-NoStor in orange). For the left panel, the thick lines correspond to the mean of the latent heat over the periods while the spreads correspond to the 25%-75% interval around the mean. Both configurations have been normalized by their maximum value in the left panel to facilitate the comparison.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Figure B8.** Root Mean Square Errors (RMSEs) of the standard configuration without calibration (STD\_prior in black), the standard configuration with multi-site calibration (STD\_MS in blue), the multi-site calibration of the potential-based configuration (HA\_MS in red) for latent heat flux (top panel) and sensible heat flux (bottom panel) for all the sites of the database for the drought periods. For this figure, parameter calibration is performed at multi-site scale. All the sites are regrouped by Plant Functional Type (See Table B1 for the acronyms). The points correspond to the RMSE of the considered variable for each sites. The boxes represent the interquartile range and the median, whiskers represent the minimum and maximum values, outliers are represented with thick open circles.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Figure B9.** Root Mean Square Errors (RMSEs) of the standard configuration without calibration (STD\_prior in black), the standard configuration with single-site calibration (STD\_SS in blue), the single-site calibration of the potential-based configuration (HA\_SS in red) for latent heat flux (top panel) and sensible heat flux (bottom panel) for all the sites of the database for the whole period of simulation and drought period. For this figure, parameter calibration is performed at single-site scale. All the sites are regrouped by Plant Functional Type (See Table B1 for the acronyms). The points correspond to the RMSE of the considered variable for each site. The boxes represent the inter-quartile range and the median, whiskers represent the minimum and maximum values, outliers are represented with thick open circles.</figcaption></figure>
## Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

## Data Availability Statement

The vegetation (PFT) maps were based on the ESA-CCI land cover product (ESA, 2017—http://maps.elie.ucl.ac.be/CCI/viewer/download/ESACCI-LC-Ph2-PUGv2_2.0.pdf—last access: 23 September 2025) following a procedure detailed in 2.1 (or detailed in Lurton et al. (2020)). The atmospheric reanalyzes used in this study are provided by the CRU-JRA 2.4 meteorological forcing (Sitch et al., 2024; University of East Anglia Climatic Research Unit; Harris, I.C., 2023). Atmospheric CO₂ concentration data are retrieved from Dlugokencky and Tans (2020). Atmospheric nitrogen deposition are retrieved from Hegglin et al. (2016). The forcings (see Section 2.1 for a description of the forcing variable) and evaluation data (sensible and latent heat flux along with soil water contents) at FR-Hes were extracted from Warm Winter 2020 Team and ICOS Ecosystem Thematic Centre (2022) (https://www.icos-cp.eu/data-products/2G60-ZHAK—last access: 23 September 2025). For FR-Pue, the forcings and the data of latent and sensible heat fluxes were extracted from the FLUXNET2015 database (Pastorello et al. (2020)—https://fluxnet.org/data/fluxnet2015-dataset/—last access: 23 September 2025). The water potential measurements at FR-Pue have been provided personally by the site PIs and can only be accessed upon specific request (jean.kempf@cefe.cnrs.fr and jean-marc.limousin@cefe.cnrs.fr). A table of all the parameters used in this study along with an archive folder of the main simulations can be found at Alléon (2025), or at this link, https://zenodo.org/records/17190689.

**Code availability:** The source code for the ORCHIDEE version (ORCHIDEE r9107) used in this study can be retrieved from Alléon (2024). The ORCHIDEE model code is written in Fortran 90 and is maintained and developed under a subversion (SVN) control system at the Institut Pierre Simon Laplace (IPSL) in France. The source code of ORCHIDEE (https://doi.org/10.14768/ce78ca4a-1462-4137-a54d-c6f308376bc5) is available online via https://forge.ipsl.fr/orchidee browser/branches/publications/ORCHIDEE_HA_JAMES (last access: 23 September 2025). Readers interested in running the model should follow the guidelines at http://orchidee.ipsl.fr/index.php/you-orchidee (last access: 23 September 2025).

## Acknowledgments

This work was partially supported by the French Commissariat à l'énergie atomique et aux énergies alternatives (CEA), especially for the computing resources. The authors also acknowledge the ORCHIDEE core team for fruitful discussions and the anonymous reviewers for their helpful comments which improved the manuscript.

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