Land surface modellers need measurable proxies to
constrain the quantity of carbon dioxide (CO

Humanity has to face the urgency of climate change if it hopes to limit
adverse future impacts (Allen et al., 2018; IPCC, 2019a, b). In order to
make reliable predictions of future climate, scientists have built powerful
numerical Earth system models (ESMs), where they continuously integrate
gained knowledge on a multitude of climate-related and climate-interacting
processes. The carbon cycle is at the heart of the present global warming,
caused by anthropogenic CO

GPP proxies are also used, such as solar-induced fluorescence (Norton et
al., 2019; Bacour et al., 2019), isotopic composition of atmospheric
CO

The approach generally adopted to constrain GPP with COS relies on the
determination of a leaf relative uptake (LRU), which is the ratio of COS to
CO

LRU can be estimated experimentally and then used as a scaling factor for
estimating GPP, if

However, LRU does not appear constant under some environmental conditions.
For example, the fixation of carbon from CO

Before being able to use COS observations to constrain the simulated GPP,
land surface models (LSMs) first need to have an accurate model to simulate
vegetation COS fluxes. In a former study, Launois et al. (2015b) simply
defined the COS uptake by vegetation as the CO

We used the state-of-the art ORCHIDEE LSM (Krinner et al., 2015), and we implemented in it the vegetation COS uptake model of Berry et al. (2013) to simulate the COS fluxes absorbed at the leaf and canopy levels by the continental vegetation.

We evaluated the simulated COS fluxes against measurements at two forest sites, namely the Harvard Forest, United States (Wehr et al., 2017), and Hyytiälä, Finland (Kooijmans et al., 2019; Kohonen et al., 2020; Sun et al., 2018a). We studied the high-frequency behaviour of the modelled conductances over the season and the dependency of the LRU on the environmental and structural conditions.

We compared the simulated mechanistic COS fluxes at the global scale to former estimates; we studied LRU values estimated from monthly fluxes, which are pertinent for atmospheric studies, and compared them to monthly means of high-frequency LRU values.

The mechanistic and LRU simulated COS fluxes were used with the atmospheric transport model LMDz (Hourdin et al., 2006), to provide atmospheric COS concentrations that were evaluated against measurements at sites of the NOAA network.

ORCHIDEE is an LSM developed mainly at Institut Pierre Simon Laplace (IPSL)
that computes the water, carbon, and energy balances at the interface between
land surfaces and atmosphere (Krinner et al., 2005). Fast processes
including hydrology, photosynthesis, and energy balance are run at a
half-hourly time step, while other slower processes such as carbon allocation
and mortality are simulated at a daily time step. The sub-grid variability
for vegetation is represented using fractions of plant functional types
(PFTs), grouping plants with similar morphologies and behaviours growing
under similar climatic conditions. Photosynthesis follows the Yin and Struik
(2009) approach, bringing improvements to the standard Farquhar et al. (1980) model for C

In the ORCHIDEE LSM we implemented the mechanistic model of plant COS uptake
based on Berry et al. (2013). In this model, COS follows a diffusive law
from the atmosphere to the leaf interior, where it is consumed by CA in the
chloroplasts. The uptake from the atmosphere is assumed to be unidirectional,
reflecting the fact that COS is generally not produced by plants. The model
distinguishes three conductances along the COS path between the atmosphere
and the leaf interior: (1) the boundary layer conductance
(

The stomatal and boundary layer conductances are associated with factors
describing diffusion of COS relative to that of water vapour (1.94 and 1.56,
respectively; Stimler et al., 2010). In the chloroplast, the COS hydrolysis
is catalysed by the enzyme CA, following first-order kinetics. COS uptake
depends on the amount of CA and its relative location to intercellular air
spaces, which brings in the mesophyll conductance. These two factors have
been shown to scale with the maximum reaction rate of the Rubisco enzyme,

The parameter

As plant CO

All simulations were preceded by a “spin-up” phase to get to an
equilibrium state where the considered carbon pools and fluxes are stable
with no residual trends in the absence of any disturbances (climate, land
use change, CO

Vegetation COS fluxes can be measured using branch chambers or estimated
using the difference between measurements of ecosystem and soil fluxes. Such
measurements were available at the Hyytiälä (Finland) and Harvard
Forest (United States) FLUXNET sites. The Hyytiälä site
(61.85

The Harvard Forest site (42.54

The simulated COS fluxes were evaluated against measurements using the root-mean-square deviation:

We also computed the bias, standard deviations, and correlation coefficient.

We used partial correlations to identify the main drivers of the modelled conductances. Given the high non-linearity of the equations linking the conductances to their predictors, we also used random forests (RFs) to simulate ORCHIDEE results, and we applied a permutation technique on these RF models to rank predictors (Breiman, 2001). RFs are well adapted for non-linear problems; they were for example used to rank variables of importance for soil COS fluxes in Spielman et al. (2020).

We compared our estimate for plant COS uptake at global scale to former
studies, with a focus on the LRU approach. We also applied the LRU approach
to derive new estimates of global plant COS uptake for comparison, using a
monthly climatology of our modelled GPP fluxes over the 2000–2009 period, a
constant atmospheric concentration of 500 ppt for COS and global yearly
values for CO

Reciprocally, we derived LRU values using Eq. (1) applied to the monthly climatology of our
modelled COS and GPP fluxes over the 2000–2009 period; these will be further
called LRU_MonthlyFluxes values. LRU_MonthlyFluxes values were computed for all strictly positive GPP values. For
each PFT, we studied the spatio-temporal distribution of LRU_MonthlyFluxes values among grid cells where the PFT was present. We also
compared these LRU_MonthlyFluxes values computed from a
climatology of monthly fluxes to the climatology of monthly mean LRU
values, directly computed from the original half-hourly LRU values and
further called Monthly_LRU. Given the non-linearity of the
problem, we expect LRU_MonthlyFluxes to be different from
Monthly_LRU values. Considering that the objective of the LRU
approach was to estimate COS fluxes from GPP using a constant value per PFT,
the optimal LRU value for each PFT was obtained by linearly regressing
monthly COS fluxes against monthly GPP fluxes multiplied by the ratio of the
mean COS to CO

We compared this new set of optimal PFT-dependent LRU values against LRU_Seibt and LRU_Whelan.

We finally used the LRU_Opt values to re-compute the monthly mean COS fluxes from our modelled monthly mean GPP and compared with the mechanistic COS flux calculation. The differences, due to the non-linearity of the COS flux calculation, provide some information on the use of a simplified approach based on mean LRU values.

Table of LRU per PFT. First column: median and optimal LRU values calculated from the simulated mechanistic COS and GPP fluxes. Middle columns: calculated from Seibt et al. (2010) for the ORCHIDEE PFT classification. Last column: from Whelan et al. (2018).

The vegetation COS fluxes, as well as all other sources and sinks of the global COS budget, based on their latest estimates, are transported with an atmospheric transport model, so that we are able to simulate 3D COS atmospheric concentrations and compare them to the NOAA surface measurements.

In order to simulate COS and CO

We ran the LMDz6 version of the atmospheric transport model described above
for the years 2000 to 2009. The prescribed COS and CO

For all COS and CO

Prescribed COS surface fluxes used as model input. Mean magnitudes of different types of fluxes are given for the period 2000–2009.

Prescribed CO

We used the NOAA/GML measurements of both CO

List of air sampling sites selected for evaluation of COS and
CO

The samples have been collected as pair flasks one to five times a month since
2000 and are then analysed in the NOAA/GML's Boulder laboratories with gas
chromatography and mass spectrometry detection. The measurements are
retained only if the difference between the pair flasks is less than 6.3 ppt
for COS. These COS measurements can be downloaded from the ftp site

To evaluate and compare the performances of the mechanistic and LRU
approaches at different NOAA surface sites, we used the normalised standard
deviation (NSD) and the Pearson correlation coefficient (

COS assimilation is at a minimum at night (between 20:00 and 04:00 local solar time) for observed
and simulated fluxes (Fig. 1a). During night,
uptake of modelled COS flux is around

The simulated weekly seasonal vegetation COS uptake roughly follows the same
trend as the observed one (

Figure 2 compares mean daytime and nighttime
observed and modelled vegetation COS fluxes and the percentage of the
daytime to the total flux, computed for each month over 2012 and 2013 at the
Harvard Forest site. We selected an arbitrary PAR threshold of 50

To investigate the importance of each conductance in vegetation COS uptake,
we compared the three simulated conductances: leaf boundary layer, stomatal,
and internal, studying their variability and their drivers at the diel and
seasonal scales. The boundary layer conductance to COS is higher than the
two other conductances by a median factor larger than 25 (see Table A1 for
more detailed statistics). As a high conductance value is equivalent to a
low resistance to COS transfer, we focused only on the stomatal
(

Mean diel cycles of simulated conductances for each season at
Harvard Forest in 2012

Figure 3 presents the mean diel cycles of the simulated total, stomatal, and internal conductances for each season, computed over 2012 at Harvard Forest and 2017 at Hyytiälä. For practicality, we shifted the month of December before the month of January of the same year to compute the winter mean. The seasonal variations are similar at both sites. The conductances, as well as the amplitude of their diurnal cycle, increase from winter to summer and decline in autumn. Harvard Forest is predominantly a deciduous forest, and winter values of the conductances are zero at this site as there are no leaves in that season. Hyytiälä on the other hand is an evergreen pine forest, such that daytime stomatal conductance in winter does not become zero. The stomatal conductance peaks between 09:00 and 13:00, depending on site and season, while the internal conductance peaks later in the afternoon. The total conductance is in general limited by the internal conductance. The stomatal conductance is limiting roughly between 18:00 and 06:00 from spring to autumn at Harvard and only in June–July–August roughly between 21:00 and 09:00 at Hyytiälä.

These results are consistent with the results obtained at branch level by
Kooijmans et al. (2019), who found that the COS flux was limited by the
internal conductance in the early season and later during daytime, while
the effect of the stomatal conductance was larger at night. For the Harvard
Forest site, Wehr et al. (2017) computed the stomatal conductance using both
a water flux method and a COS flux method and obtained a close agreement
between two different methods; the mesophyll conductance is modelled using
an experimental temperature response, and the biochemical conductance,
representing CA activity, is modelled using a simple parameter (0.055 mol m

To better understand the conductance behaviour, we studied the relative
importance of their drivers. These include environmental variables directly
or indirectly involved in their modelling: air surface temperature
(

As expected,

LRU decreases as a function of PAR, as initially observed by Stimler et al. (2010). Kooijmans et al. (2019) made measurements in two branch chambers
installed at the top of the canopy in two Scots pine trees in
Hyytiälä. They plotted the response of LRU to light, as quantified
by PAR. To compare the ORCHIDEE model behaviour to these field data, we
determined an LRU using our modelled COS and GPP fluxes, considering a
constant atmospheric concentration of 500 ppt for COS and global yearly
values for CO

LRU against PAR (Hyytiälä) for ORCHIDEE outputs and
measurements (hourly data measured between 18 May and 13 July; Kooijmans et
al., 2019). The light green circles represent average LRU values for
chambers 1 and 2, and light orange circles represent modelled LRU values. A
moving average with a window of 50 points leads to the smooth orange curve
for the model. The green line represents the function LRU

LRU increases with low PAR values for both branch chambers and for the
model and converges towards a constant value for high PAR values
(Fig. 4). This demonstrates that assuming a
constant value for LRU, and not considering an increase in LRU under low-light conditions, will result in erroneous estimation of COS fluxes. The
increasing LRU can be explained by the light dependence of the
photosynthesis reaction contrary to the CA activity that is
light-independent. Consequently, CO

Following the model developed in Seibt et al. (2010, their Eq. 8),
the LRU explicitly depends on only two variables: the

We also performed a predictor ranking for LRU, as was done previously with
conductances. The predictors rank similarly for the two sites. As shown in
Fig. B6, the main factors explaining the variability of the simulated LRU
at a half-hourly time step are PAR,

Map of average vegetation COS fluxes over the 2000–2009 period, from the mechanistic model as implemented in ORCHIDEE.

The mechanistic approach simulated in the ORCHIDEE model gives a plant COS
uptake of

Overview of COS plant uptake per year (Gg S yr

The more recent studies (Montzka et al., 2007; Suntharalingam et al., 2008;
Berry et al., 2013; Launois et al., 2015b) show a higher global plant sink
than the one initially found by Kettle et al. (2002)
(Table 5). Kettle et al. (2002) used an LRU-like
approach, based on net primary productivity (NPP) and on the normalised difference vegetation index (NDVI) temporal evolution, and already
acknowledged their estimate was assumed to be a lower-bound one. Estimates
from plant chambers and atmospheric measurements (Sandoval et al., 2005;
Montzka et al., 2007; Campbell et al., 2008) confirmed that the COS plant
sink should be 2-fold to 5-fold larger than estimated in Kettle et al. (2002). Suntharalingam et al. (2008) also found a low estimate of

Launois et al. (2015b) adopted an LRU approach, using constant LRU values for large MODIS vegetation classes, adapted from Seibt et al. (2010). Based on these values and a set of global GPP estimates from three LSMs (ORCHIDEE, LPJ, CLM4), the authors derived the corresponding global vegetation COS uptakes reported in Table 5. The selection of the LSM itself thus introduces an uncertainty on the global vegetation COS uptake of around 40 % in this case.

Applying the LRU values derived from Seibt et al. (2010)
(Table 1) to the global GPP simulated in this study
leads to the highest plant COS uptake with

The PFT distributions of the LRU values, both those computed using Eq. (1) applied to the monthly climatology of mechanistic COS and GPP fluxes over the 2000–2009 period (LRU_MonthlyFluxes) and the climatological monthly means computed directly from the original half-hourly values (Monthly_LRU), do not support the idea of a constant PFT-dependent LRU value (Fig. 6).

Distributions of the LRU values computed from the mechanistic
approach over the 2000–2009 period. Each subplot represents one of the 14
vegetated PFTs used in ORCHIDEE, considering all grid cells where the PFT is
present. The

The distributions are usually not Gaussian; nor are they all unimodal, as is
the case for PFT 12 C

The LRU values from monthly fluxes (LRU_MonthlyFluxes) tend
to be lower than the monthly means of the LRU computed at a half-hourly time
step (Monthly_LRU). This is visible in
Fig. 6 where the blue distributions yield larger
LRU values and in the bi-dimensional histogram of LRU_MonthlyFluxes against Monthly_LRU (Fig. C2). The bias is

LRU_Opt values are much smaller than LRU_Seibt
values for all PFTs, roughly by a factor of 2. They are closer to the
LRU_Whelan values, being smaller for all C

Another way to understand the distribution of LRU values is to look directly
at the scatter plots of monthly COS fluxes against GPP fluxes, multiplied by
the ratio of COS to CO

We computed mean annual vegetation COS fluxes using our modelled GPP and this new LRU_Opt set of values and compared them to the mechanistic COS fluxes (Fig. 7a).

The maps of differences between the mechanistic and LRU_Opt-based COS fluxes (Fig. 7b), and relative
differences (Fig. 7c), provide evidence for the
spatial errors introduced by considering a constant LRU value. The
differences are always lower than 4 pmol m

We also compared the mean seasonal cycles of the COS vegetation flux over
the 2000–2009 period, for the mechanistic approach and the
LRU_Opt-based approach, for each PFT (Fig. C3). The
seasonal cycles are very similar; for PFT 13 C

We transported the global COS and CO

Figure 8 shows the detrended temporal evolution of
CO

For COS, the simulated concentrations match relatively well with the observed
seasonal variations and seem to be more in phase with the observations than
for CO

Detrended temporal evolutions of simulated and observed CO

Normalised standard deviations (NSDs) of the simulated
concentrations by the observed concentrations. Within brackets are the
Pearson correlation coefficients (

Table 6 presents the NSDs and Pearson correlation
coefficients between simulated and observed COS concentrations for the
mechanistic and LRU approaches. We see that the simulation with Seibt et al. (2010) intermediate LRU values overestimates the seasonal standard deviation
and has the lowest accuracy for most stations. It is difficult to tell
whether the mechanistic model is better than the LRU approach based on
Whelan values. While the mechanistic approach captures known features of the
temporal dynamics of the COS-to-CO

The mechanistic model links vegetation COS uptake and GPP fluxes through the
stomatal conductance model, which includes the minimal conductance as an
offset, and the common use of the carboxylation rate of Rubisco,

Without any calibration, the chosen mechanistic model was able to reproduce
observed vegetation COS fluxes at the Harvard Forest and Hyytiälä
sites with relative RMSDs on the order of 40 %. Regarding conductances,
differences are also seen between the diel cycles of simulated and
observation-based conductances from Wehr et al. (2017). Diel variations in
atmospheric

Without being perfect, the mechanistic model could reproduce some expected
behaviours, such as the limiting role of the internal conductance in winter
and then during daytime in the growing season, in relation to the control of
CA activity and mesophyll diffusion by temperature, as also depicted in
Kooijmans et al. (2019). Determining the limiting conductances to COS uptake
depending on the time of day provides useful information, as it can be used
to better target which model parameters to optimise, using data assimilation
approaches. Thus, observations made in the morning and early afternoon could
be used to better constrain the

Recent studies have shown that nighttime field measurements of stomatal
conductances often exhibit larger values than the ones used in models (Caird
et al., 2007; Phillips et al., 2010). In the ORCHIDEE model, minimum
stomatal conductances to CO

We thus see that COS fluxes could be used, through standard data assimilation techniques, to optimise the model parameters related to conductances, thus contributing to the improvement of the GPP. However, many more COS flux measurements are needed over a large variety of biomes, first to assert the validity of the mechanistic COS model at global scale and second to be assimilated in order to improve simulated conductances and GPP estimates.

The mechanistic model is able to reproduce the high-temporal-frequency LRU
variations observed at sites. It is thus legitimate to consider this
approach to be more accurate than the classical linear LRU approach that uses a
time-constant LRU value per PFT to estimate COS fluxes from GPP. Furthermore
we have shown that computing LRU values using Eq. (1) applied to monthly mean fluxes yields
values lower than computing monthly means of high-frequency LRU values
(Fig. 6). This may explain why the LRU values we have thus estimated from
monthly mean fluxes show generally lower values than the ones derived from
measurements, although these cover a large range from 0.7 to 6.2 (Seibt et
al., 2010; Whelan et al., 2018). More recently, Spielman et al. (2019)
estimated LRU values from ecosystem and soil measurements: 0.89 for an
agricultural soybean field, 1.02 for a temperate C

Without any calibration, the mechanistic approach performs similarly to LRU approaches based on monthly mean fluxes, when COS is transported using all known COS fluxes as inputs, and COS concentrations are evaluated at stations of the NOAA network. We now have a much finer representation of the COS fluxes as, at every time step, the model integrates the plant's response to environmental conditions in the calculation of the internal and stomatal conductances, unlike in the LRU approach which uses constant values for each PFT.

In order to quantify the first-order uncertainty on

However, there is currently a larger uncertainty on other COS fluxes in the global COS budget, which have an important impact on simulated COS concentrations (Ma et al., 2020) and their relative seasonal changes. For example, if we use another estimation of the direct oceanic fluxes (Lennartz et al., 2017), which shows a seasonal cycle whose amplitude is comparable to the one from the vegetation in high latitudes, this results in an overestimated seasonal cycle at all sites, with the mechanistic approach having the most realistic seasonal amplitude (see Appendix D1 and Fig. D1). An additional sensitivity test was performed to assess the impact of indirect oceanic emissions via DMS oxidation on simulated seasonal cycles as the importance of these fluxes in the global COS budget is still debated (Whelan et al., 2018). Whereas the impact on northern sites is negligible, the removal of indirect oceanic emissions via the DMS of Kettle et al. (2002) decreases the seasonal amplitude of southern sites (CGO and SPO) in the same proportion in all experiments (see Appendix D2 and Table D2). Transport errors also add uncertainties on the simulated concentrations, especially at elevated continental sites (Remaud et al., 2018). Plus, given the present discrepancies between the GPP estimates of different land surface models, it can be argued that using a mechanistic model instead of an LRU approach when comparing COS concentrations seems to be of a second-order importance (Campbell et al., 2017; Hilton et al., 2017). We nevertheless note in this study that we found an uncertainty on the global vegetation COS uptake of 40 % when considering three different LSMs (Launois et al., 2015b), to be compared to an uncertainty of 70 % when considering three LRU datasets.

Setting aside the uncertainty for the moment, how could we use atmospheric
COS concentrations to constrain GPP? A first optimisation was performed with
the ORCHIDEE model in Launois et al. (2015b), who optimised a single scaling
parameter applied on the vegetation COS fluxes simulated with the LRU
approach, thus equivalent to a scaling factor applied on the GPP or the LRU.
They assimilated the atmospheric COS concentrations measured at the NOAA air
sampling stations, using the LMDz transport model (Hourdin et al., 2006) and
a Bayesian framework as in Kuppel et al. (2012). The optimisation reduced in
absolute value the estimated global vegetation COS uptake from

We have implemented the mechanistic model of Berry et al. (2013) inside the ORCHIDEE land surface model for COS uptake by the continental vegetation. Modelled COS fluxes were compared at site scale against measurements at the Harvard temperate deciduous broadleaf forest (USA) and at the Hyytiälä Scots pine forest (Finland), yielding relative RMSDs of around 40 % at both diel and seasonal scales. We found that the mechanistic model yields a lower and thus more limiting internal conductance compared to former works (Seibt et al., 2010; Wehr et al., 2017). The next step is to perform a sensitivity analysis (Morris, 1991; Sobol, 2001) and to optimise the most sensitive parameters related to the modelled fluxes and conductances, to get a better agreement with observations.

Our global estimate of COS uptake by continental vegetation of

Using appropriate LRU values, we transported the monthly mean COS fluxes from the mechanistic and LRU approaches using the LMDz6 model. The evaluation of the modelled COS atmospheric concentrations against observations at stations of the NOAA network yields comparable results for both approaches.

As a general conclusion and for the moment, we can say that the mechanistic model is particularly valuable when studying small timescales or spatial scales using COS fluxes, while for global analyses using COS concentrations, both the mechanistic and LRU approaches give similar results. The fact that the global COS budget has so many components with a large uncertainty (Whelan et al., 2018) limits the use of COS concentrations as a constraint for GPP in land surface models on the global scale, for the present time.

A further development will be to refine the estimation for COS soil fluxes
and to implement a mechanistic model for soil COS fluxes inside ORCHIDEE
(Ogée et al., 2016; Sun et al., 2015). Having both the vegetation and
soil contributions, we will also be able to assimilate ecosystem COS fluxes
to optimise COS-related parameters such as

Ratios of modelled boundary conductance to stomatal conductance and internal conductance at the two studied sites, computed over the year 2012 at Harvard Forest and 2017 at Hyytiälä.

Partial correlations linking stomatal and internal conductances to
photosynthetically active radiation (PAR), air temperature
(

Minimum stomatal conductance to CO

Variables' importance computed using random forests for the
internal conductance (gi) at the Harvard Forest site in 2012 (left) and at
the Hyytiälä site in 2017 (right). The considered predictors are air
temperature (

Same as B3 for the stomatal conductance (gs).

Seasonal evolution of the simulated

Same as B3 for the leaf relative uptake (LRU).

Scatterplots of COS fluxes against GPP multiplied by the ratio of
COS to CO2 concentrations, using a climatology of monthly fluxes over the
2000–2009 period and yearly global averages for CO

Bi-dimensional histogram of LRU values computed from a
climatology of monthly mean fluxes (LRU_MonthlyFluxes)
against a climatology of monthly means of LRU computed from original
half-hourly values (Monthly_LRU). The colour bar indicates the
number of occurrences per bin of

Mean seasonal cycle (monthly means) of COS for each PFT over the Northern Hemisphere for the 2000–2009 period. The solid line represents the mechanistic model, while the dashed line represents the optimal LRU approach.

We performed the same experiment as in Sect. 3.4, except that the oceanic fluxes (direct and indirect) here are from Lennartz et al. (2017). In our case, the oceanic emissions (in particular direct oceanic emissions) have more impact than the LRU on the seasonality at surface sites from the NOAA network.

Detrended temporal evolutions of simulated and observed CO

Prescribed COS surface fluxes used as model input. Mean magnitudes of different types of fluxes are given for the period 2000–2009.

We further tested the impact of the indirect COS fluxes through DMS on the simulated concentrations at NOAA sites. To do that, we compared the atmospheric concentrations given with and without prescribing indirect oceanic fluxes through DMS using the Launois et al. (2015a) oceanic fluxes. In our case, the removal of the DMS oceanic emissions decreases the seasonal amplitude at SPO and CGO but has very few impacts at other sites. We also performed the same experiment using the Lennartz et al. (2017) fluxes and reported no impact of DMS indirect fluxes on simulated concentrations at NOAA sites.

Normalised standard deviations (NSDs) of the simulated
concentrations by the observed concentrations. Within brackets are the
Pearson correlation coefficients (

The CMIP6 version of the ORCHIDEE model including the COS submodel is available on request to the authors. The LMDz model is available from

For Hyytiälä, we used the 2015 eddy covariance flux data published in Kohonen (2020), the 2015 soil measurements published in Sun et al. (2018b), the 2017 branch chamber and eddy covariance fluxes published in Kooijmans et al. (2018), and local meteorological data available at

FM and PP devised the research. CA and FM coded the ORCHIDEE developments and made the simulations. MR and PP dealt with the transport model. LMJK and KMK provided the Hyytiälä data. RC and RW provided the Harvard Forest data. JEC, SB, SAM, NR, US, YPS, NV, and MEW were consulted on their respective expertise. FM, CA, and MR analysed the results and wrote the first draft. All authors contributed to the manuscript.

The authors declare that they have no conflict of interest.

The authors thank the reviewers for their constructive and useful comments which helped to further improve this study. The LSCE group thanks the administrative and IT teams for managing the recruitment of Camille Abadie and providing the necessary facilities and tools to run the ORCHIDEE model and analyse the outputs.
Operation of the US-Ha1 site is supported by the AmeriFlux Management Project with funding by the U.S. Department of Energy's
Office of Science under contract no. DE-AC02-05CH11231 and additionally is a part of the Harvard Forest LTER site supported
by the National Science Foundation (DEB-1237491).
The authors are very grateful to the ObsPack people who collected and archived the

Camille Abadie, Fabienne Maignan, and Philippe Peylin have been mainly supported by the European Commission, Horizon 2020 Framework Programme, 4C (grant no. 821003) and to a smaller extent VERIFY (grant no. 776810). Marine Remaud was funded by the

This paper was edited by Akihiko Ito and reviewed by Georg Wohlfahrt and one anonymous referee.