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 C3 plants, the Collatz et al. (1992) model for C4 plants, and the Ball et al. (1987) model for the stomatal conductance. A main novelty is the introduction of a mesophyll conductance linking the CO2 concentration at the carboxylation sites, Cc, to the CO2 intracellular concentration, Ci. For each PFT, the reference value for the maximum photosynthetic capacity at 25 ∘C, Vmax,25, is derived from literature survey and observation databases and possibly later calibrated using FLUXNET observations (e.g. Kuppel et al., 2012). To compute the maximum photosynthetic capacity at leaf level, Vmax, the reference value is multiplied at a daily time step by the relative photosynthetic efficiency of leaves based on the mean leaf age following Ishida et al. (1999) (see Eq. A12 and Fig. A12 in Krinner et al., 2005). Leaves are very efficient when they are young and stay so till they approach their pre-defined leaf lifespan. The temperature dependence of the maximum photosynthetic capacity follows Medlyn et al. (2002) and Kattge and Knorr (2007). A water stress function varying between 0 and 1 depending on soil moisture and root profile (de Rosnay and Polcher, 1998) is applied on maximum photosynthetic capacity and conductances. The canopy is discretised in several layers of growing thickness, the number depending on the actual leaf area index (LAI). All the incoming light is considered to be diffuse, and no distinction is made between sun and shaded leaves. The light is attenuated through the canopy following a simple Beer–Lambert absorption law. The CO2 assimilation, the stomatal conductance, and the intercellular CO2 concentration Ci are computed per LAI layer, provided LAI is higher than 0.01 and the monthly mean air temperature is higher than -4 ∘C. The CO2 assimilation and the stomatal conductance are further summed up over all layers to compute GPP and the total conductance at canopy level. The scaling to the grid cell is made using means weighted by the plant functional type fractions. Phenology is fully prognostic with PFT-specific phenological models as described in Botta et al. (2000) and MacBean et al. (2015). ORCHIDEE can be run from the site scale to the global scale, coupled with an atmospheric general circulation model, or in off-line mode forced by meteorological fields. In this study, we prescribed the vegetation distribution for site simulations and used yearly PFT maps derived from the ESA Climate Change Initiative (CCI) land cover products for global simulations (Poulter et al., 2015). The soil type is derived from the Zobler map (Zobler, 1986). To account for the CO2 fertilisation effect, we considered global means of CO2a with yearly varying values, as provided by the TRENDY model inter-comparison project (Sitch et al., 2015). The impact of not taking into account the spatial and temporal variations in CO2a on GPP has been studied in Lee et al. (2020); while this simplification has indeed no impact at a global yearly scale for GPP, this may be less true at site and seasonal scales. We used the recent ORCHIDEE version fine-tuned for the Climate Model Intercomparison Project (CMIP) 6 exercise (Boucher et al., 2020), forced by micro-meteorology fields at FLUXNET sites or by 2∘ CRUNCEP reanalyses at the global scale (https://rda.ucar.edu/datasets/ds314.3/, last access: 19 April 2021).

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 (gB_COS) to gas transfer between the leaf surface and the atmosphere, (2) the stomatal conductance (gS_COS), and (3) the internal conductance (gI_COS). Internal conductance combines the mesophyll conductance and the CA activity into a single equivalent 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, Vmax (µmol m-2 s-1) (Badger and Price, 1994; Evans et al., 1994). The mesophyll conductance and the first-rate constant are then regrouped into a single equivalent internal conductance, proportional to Vmax: 2gI_COS=α×Vmax.

The parameter α takes two values depending on the plant photosynthetic pathway (C3 or C4). These values were determined experimentally by Berry et al. (2013), who estimated an α=0.0012 for C3 and an α=0.013 for C4 species. We thus have the final equation: 3FCOS=COSa×gT_COS=COSa×1.0gB_COS+1.0gS_COS+1.0gI_COS-1=COSa×1.56gB_W+1.94gS_W+1.0gI_COS-1, where FCOS is the flux of COS uptake (pmol COS m-2 s-1); COSa is the background atmospheric COS mixing ratio considered here to be a constant (500 ppt); gT_COS, gB_COS, gS_COS, and gI_COS are respectively the total, boundary layer, stomatal, and internal conductances to COS (mol COS m-2 s-1); and gB_W and gS_W are respectively the boundary layer and stomatal conductances to water vapour (mol H2O m-2 s-1). Note that in this work COSa is held constant when computing the COS fluxes, contrary to Berry et al. (2013) and Campbell et al. (2017), where COSa is dynamic and taken from the previous time step's PCTM (Parameterized Chemical Transport Model) value. The uncertainty introduced by this simplification is evaluated in the Discussion section. The vegetation COS flux and related conductances are computed for each LAI layer and then summed up to get total values at the canopy level. Unless specified otherwise, fluxes, conductances and LRU are further presented and discussed at the canopy level.

As plant CO2 uptake only occurs under certain conditions such as with sufficient light, temperature, and water, CO2 assimilation is not calculated in ORCHIDEE when these conditions are not fulfilled. Therefore, the stomatal conductance to CO2 that is needed to obtain the stomatal conductance to COS is not always computed in ORCHIDEE. However, some studies have shown incomplete stomatal closure at night (Dawson et al., 2007; Lombardozzi et al., 2017; Kooijmans et al., 2019), leading to nighttime COS plant uptake (Berry et al., 2013; Kooijmans et al., 2017). Therefore, we had to define a minimal stomatal conductance to COS under these particular conditions when there is no CO2 assimilation. The minimal conductance to CO2 used in ORCHIDEE is based on the residual stomatal conductance if the irradiance approaches zero, represented as the g0 offset in the stomatal conductance models (see Eq. 15 for C3 and Eq. 25 for C4 plants in Yin and Struik, 2009). In the absence of water stress, g0 takes a constant value for C3 (0.00625 mol CO2 m-2 s-1) and C4 (0.01875 mol CO2 m-2 s-1) plants. This constant is multiplied by a water stress function to compute the minimal conductance. This minimal conductance to CO2 was then applied under conditions when there is no CO2 assimilation, multiplied by the ratio to convert the conductance to CO2 into a conductance to COS. We thus model COS assimilation even at night, for all PFTs, and in winter for evergreen species, depending on water stress conditions.

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, CO2 atmospheric concentrations) (e.g. Wei et al., 2014). A few decades are enough to equilibrate above-ground biomass and GPP. As we transport not only COS, but also CO2 (see Sect. 2.4 below), we need a longer spin-up where all carbon pools including those in the soil are stable and the net CO2 fluxes oscillate around zero. Equilibrating the ecosystem photosynthesis with its respiration takes a long time as the slowest soil carbon pool has a residence time on the order of 1000 years. The ORCHIDEE model has a built-in spin-up procedure to accelerate the convergence towards this equilibrium state, using a pseudo-analytical iterative estimation of the targeted carbon pools, based on Lardy et al. (2011). For global simulations, we first performed a 340-year spin-up phase with non-varying pre-industrial atmospheric CO2 concentration and vegetation map, cycling over the same 10 years of meteorological forcing files, where the final relative variation in the global slowest soil carbon pool was less than 5 %. Starting from this equilibrium state, a transient state simulation was then run applying climate change, land use change, and increasing CO2 atmospheric concentrations, and COS and GPP fluxes were calculated from 1860 to 2017. We performed site simulations at the Harvard Forest (United States) and Hyytiälä (Finland) FLUXNET sites (see below). For the two sites, we first performed a spin-up simulation cycling over the available years of the FLUXNET forcing files, for around 340 years, using a constant atmospheric CO2 concentration corresponding to the first year of the FLUXNET forcing file. We then performed the transient simulations over the available FLUXNET years, for each site, with a varying CO2 atmospheric concentration.

In order to simulate COS and CO2 concentrations in the atmosphere, we used the version of the atmospheric component LMDz of the Institut Pierre Simon Laplace Coupled Model (IPSL-CM) (Dufresne et al., 2013), which has been contributing to the CMIP6 exercise. To reduce the computation time, we used its off-line mode: precomputed air mass fluxes provided by the full version of LMDz are used to transport the different tracers (Hourdin et al., 2006). This version is further called LMDz6 and is described in Remaud et al. (2018) and references therein for the transport of CO2. The horizontal winds are nudged towards ECMWF meteorological analyses (ERA-5, https://www.ecmwf.int/en/forecasts/datasets/archive-datasets/reanalysis-datasets/era5) to realistically account for large-scale advection. The tropospheric OH oxidation of COS is calculated from OH monthly data that are produced from a first simulation done with the INCA tropospheric photochemistry scheme (Folberth et al., 2006; Hauglustaine et al., 2004, 2014). The photolysis reaction of COS in the stratosphere is not considered: the lifetime of COS in the stratosphere is 64 years (Barkley et al., 2008). The model is set up at a horizontal resolution of 3.8∘×1.9∘ (96 grid cells in longitude and latitude) with 39 hybrid sigma-pressure levels reaching an altitude up to about 75 km, corresponding to a vertical resolution of about 200–300 m in the planetary boundary layer. The model time step is 30 min, and the output concentrations are 3-hourly averaged.

We ran the LMDz6 version of the atmospheric transport model described above for the years 2000 to 2009. The prescribed COS and CO2 fluxes used as model inputs are presented in Tables 2 and 3. The GPP estimated by ORCHIDEE (148.1 Gt C yr-1) is in the high range among the model estimates (Anav et al., 2015), with a corresponding high respiration (145.7 Gt C yr-1) to ensure a realistic net ecosystem exchange (Friedlingstein et al., 2019). However, other high GPP estimates can be found in the literature such as Welp et al. (2011) that suggest a range of 150 to 175 based on δ18O data. Likewise, Joiner et al. (2018) have proposed a new GPP product, based on satellite data and calibrated on FLUXNET sites, with an estimate around 140 Gt C yr-1 for 2007. The fluxes are given as a lower boundary condition of the atmospheric transport model (LMDz), which then simulates the transport of COS and CO2 by the atmospheric flow. The atmospheric COS seasonal variations are likely to be dominated by the seasonal exchange with the terrestrial vegetation, while the mean mole fractions result from all sources and sinks of COS, some of which are still largely unknown (e.g. ocean fluxes, Whelan et al., 2018). In this study, we only focus on the seasonal cycle and do not attempt to simulate the annual mean value; we thus started from a null initial state. The atmospheric transport is almost linear with respect to the fluxes: the linearity is a property of the atmospheric transport, though it is violated in LMDz because of the presence of slope limiters in the advection scheme. Overall, since all the other LMDz components are linear, LMDz transport is generally considered linear with fluxes (Hourdin and Talagrand, 2006). Relying on this relationship, we first transported each flux separately, and then we added all the simulated concentrations in the end, for each species.

For all COS and CO2 observations, the model output was sampled at the nearest grid point and vertical level to each station and was extracted at the exact hour when each flask sample had been taken. For each station, the curve-fitting procedure developed by the NOAA Climate Monitoring and Diagnostic Laboratory (NOAA/CMDL) (Thoning, 1989) was applied to modelled and observed COS and CO2 time series to extract a smooth detrended seasonal cycle. We first fitted a function including a second-order polynomial term and four harmonic terms, and then we applied a low-pass filter with either 80 or 667 d as short-term and long-term cut-off values, respectively, to the residuals. The detrended seasonal cycle is defined as the smooth curve (full function plus short-term residuals) minus the trend curve (polynomial plus long-term residuals).

We used the NOAA/GML measurements of both CO2 and COS at 10 sites located in both hemispheres, listed in Table 4.

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 ftp://ftp.cmdl.noaa.gov/hats/carbonyl_sulfide/ (last access: 19 April 2021). The CO2 atmospheric measurements come from the NOAA’s GlobalView Plus Observation Package (ObsPack; Cooperative Global Atmospheric Data Integration Project, 2018).

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 (R). NSD is calculated as the ratio between the standard deviation of the simulated concentrations and the observed concentrations at the NOAA surface sites. NSD and R values closer to 1 indicate a better accuracy of the model.

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 -8 pmol m-2 s-1 while field observations vary between -5 and 0 pmol m-2 s-1. In the morning, both simulated and observed uptakes increase. However, while the simulation shows a maximum assimilation of -38 pmol m-2 s-1 at noon, the maximum assimilation for observations is reached at 10:00 with a flux of -49 pmol m-2 s-1. Observed fluxes thus have a greater daily amplitude than simulated fluxes and are a little ahead of the simulation, but this shift does not seem significant given the large variability of observations, as represented by the 1 standard deviation in Fig. 1a. RMSD for this mean diel cycle is 8.0 pmol m-2 s-1, and relative RMSD is 35 %. The bias is -1.7 pmol m-2 s-1, the standard deviations are 17.5 pmol m-2 s-1 for the observations and 12.8 pmol m-2 s-1 for the simulated fluxes, and the correlation coefficient is 0.91. A similar study at the Hyytiälä site over July–September in the year 2015 (Fig. B1a) yields a similar underestimation of the amplitude of the mean diel cycle, with an RMSD of 4.0 pmol m-2 s-1 and a relative RMSD of 36 %; the bias is 2.4 pmol m-2 s-1, the standard-deviations are 5.5 pmol m-2 s-1 for the observations and 2.7 pmol m-2 s-1 for the simulated fluxes, and the correlation coefficient is 0.93.

The simulated weekly seasonal vegetation COS uptake roughly follows the same trend as the observed one (r=0.53, Fig. 1b). COS uptake increases in spring when the vegetation growing season starts and decreases in autumn at the end of the forest activity period. Simulated and observed fluxes also take similar values over the 2 years. There are however differences: in 2013 the start of the season is simulated about 2 weeks too late in May instead of late April, and measured fluxes peak in May–June and August–September, while the modelled fluxes peak in July. We notice that the amplitude of observed COS flux variations is larger than the one of modelled fluxes. Kohonen et al. (2020) have quantified the relative uncertainty of weekly-averaged ecosystem COS fluxes at 40 %, which is coherent with the large standard deviation computed for field data (Fig. 1b). RMSD for the seasonal cycle is 7.0 pmol m-2 s-1, and the relative RMSD is 41 %. The bias is low (-0.3 pmol m-2 s-1), and the standard deviations are similar: 6.6 pmol m-2 s-1 for the observations and 7.7 pmol m-2 s-1 for the simulated fluxes. At the Hyytiälä site in the year 2015 (Fig. B1b), the RMSD for the seasonal cycle is 2.4 pmol m-2 s-1, and the relative RMSD is 25 %; the bias is low too (0.2 pmol m-2 s-1) and the standard deviations are also close: 3.6 pmol m-2 s-1 for the observations and 3.5 pmol m-2 s-1 for the simulated fluxes. The correlation coefficient is 0.78.

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 µmol m-2 s-1 to split between daytime and nighttime fluxes. We see that the modelled nighttime flux varies across the growing season, with a maximum uptake of -10 pmol m-2 s-1 reached in July and a lower absorption in the enclosing colder months. This seasonal variation can be explained by the seasonal change in LAI and the conductance dependency on Tair, which increases in summer. The observed nighttime fluxes are of the same magnitude but present an opposite seasonal cycle with lower uptake at the summer peak, albeit variations are within the 1 standard deviation represented in Fig. 1a. The modelled nighttime fluxes account from 22 % of the total COS uptake at the peak of the growing season to 45 % in April at the very beginning. The observed ones exhibit slightly lower values, between 14 % and 37 %. At Hyytiälä, the modelled nighttime ratio is also slightly higher (between 30 % and 34 %) than the observed one (between 20 % and 25 %, Fig. B2). These ratios are in line with other studies: Maseyk et al. (2014) reported a ratio of 29±5 % over a wheat field in Oklahoma, and Sun et al. (2018c) reported one of 23 % for the San Joaquin Freshwater Marsh site in California. The results may vary given the definitions adopted for nighttime and daytime periods.

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 (gS_COS) and internal (gI_COS) conductances, which are the two most limiting factors to plant COS uptake.

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-2 s-1); both scale with LAI to get canopy estimates. Wehr et al. (2017) found similar maximum values around 0.27 mol m-2 s-1 during daytime, from May to October, for the stomatal conductance and for the biochemical conductance (their Fig. 4); adding the slightly larger mesophyll conductance (peaking around 1.0 mol m-2 s-1) to the biochemical conductance would thus also lead to a more limiting role of the internal conductance (peaking around 0.21 mol m-2 s-1) during daytime, albeit not as strong as for the modelled one (peaking around 0.13 mol m-2 s-1); the simulated stomatal conductance exhibits minimum and maximum values similar to the observation-based ones but peaks more sharply in the morning.

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 (Tair), photosynthetically active radiation (PAR), vapour pressure deficit (VPD), and soil moisture (SM), as well as LAI, as leaf-level conductances are summed over LAI layers to provide canopy-level conductances. Partial correlations are computed for all half-hourly values of the variables associated with LRU values between 0 and 8 and are provided in Table A2. We also used half-hourly ORCHIDEE outputs associated with LRU values between 0 and 8 to train random forest models for conductances at the two sites, taking into account the same five predictors. A random predictor was also added to check that the variable importance was correctly estimated. All RF models have an accuracy of at least 96 %. Figures B3 and B4 present the relative ranking of the five predictors for the two conductances and the two sites. The ranking is different between the two methods (partial correlation versus RF), but they agree that at both sites the main driver for the internal conductance is air temperature and the main driver for the stomatal conductance is PAR.

As expected, gI_COS mainly depends on Tair. This is explained by the fact that gI_COS is proportional to Vmax, which represents the Rubisco activity for CO2; Vmax is assumed to be a measure for the mesophyll diffusion and for the CA activity for COS, which are the components of the internal conductance (Berry et al., 2013). Vmax depends on Tair, considered here to be a proxy of the leaf temperature (Yin and Struik, 2009). This strong link explains why gI_COS is more limiting in winter, as Tair is low with thus lower enzyme activities, and, as soon as Tair rises in spring, gI_COS becomes less limiting, especially at night. PAR is the most important variable for the stomatal conductance at the two sites. Due to how gS_COS is simulated according to Yin and Struik (2009), there is a linear relationship with the CO2 assimilation, which depends mainly on PAR.

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 CO2.

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, CO2 fluxes tend to zero when PAR decreases while COS is still taken up in the dark, leading in theory to infinite values of LRU. The drop of LRU when PAR increases is however much sharper in the model than in the observations. It is to be noted that here we compare LRU values estimated from measurements at the branch level to modelled LRU estimated at canopy level. We conducted a similar modelling study considering only the top-of-canopy level and the associated COS and GPP fluxes, yielding similar results (not shown). This can be linked to the fact that the version of ORCHIDEE we use considers all the incoming light to be diffuse and does not distinguish between sun and shaded leaves. We thus have similar LRU values at all canopy levels.

Following the model developed in Seibt et al. (2010, their Eq. 8), the LRU explicitly depends on only two variables: the gS_COS-to-gI_COS ratio and the ratio of the CO2 intracellular concentration, Ci, to CO2a (equally named Ca) ratio. The modelled daily mean values for the Ci/Ca ratio computed at the two sites vary between 0.68 and 1.00 (Fig. B5). These variations are in agreement with Prentice et al. (2014), who state that the Ci/Ca ratio is pretty stable with only ±30 % variations. These values are in the upper part of the range reported in Seibt et al. (2010, their Table 2); following their Fig. 3, for a given Ci/Ca ratio a larger gS_COS-to-gI_COS ratio implies a lower LRU, consistent with our results.

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, Tair, and LAI.

The mechanistic approach simulated in the ORCHIDEE model gives a plant COS uptake of -756 Gg S yr-1 over the 2000–2009 period. COS fluxes are the strongest in South America, Central Africa, and Southeast Asia (Fig. 5), as expected as these regions are also the most productive ones for GPP.

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 -490 Gg S yr-1, using 3D modelling of COS atmospheric concentrations, constrained by surface site observations. We note that our estimate is similar to the -738 Gg S yr-1 found by Berry et al. (2013), which was implemented in the Simple Biosphere (SiB) 3 LSM. The reason for this similarity can be that, on top of using the same mechanistic model for vegetation COS uptake, the leaf photosynthesis and stomatal conductance in both LSMs are derived from the same classical models from Farquhar et al. (1980), Collatz et al. (1992), and Ball et al. (1987).

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 -1343.3 Gg S yr-1. Seibt et al. (2010) report LRU values for different internal conductance limitations. The LRU values that we used here represent a small limitation of internal conductance to the total COS uptake (the ratio of stomatal to internal conductances is 0.1). A smaller global COS uptake can be expected when the LRU values with a more limiting effect of the internal conductance are used. Applying the LRU values derived from Whelan et al. (2018) (Table 1) leads to an intermediate estimate of -808.3 Gg S yr-1, which is closer to the global uptake obtained with the mechanistic model. This analysis shows that the choice for certain LRU values introduces an uncertainty on the global vegetation COS uptake (around 70 % in this case) and highlights the importance of deriving accurate PFT-dependent LRU values.

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).

The distributions are usually not Gaussian; nor are they all unimodal, as is the case for PFT 12 C3 agriculture for C4 PFTs (PFT 11 C4 grass and PFT 13 C4 agriculture) exhibit a large spread. The median values are represented by vertical red bars in Fig. 6 and listed in Table 1. The optimal values (LRU_Opt) obtained by linearly regressing monthly COS fluxes against monthly GPP fluxes multiplied by the ratio of the mean COS to CO2 concentrations (see Fig. C1) are represented by vertical green bars and also listed in Table 1. They are usually higher than the median values, with a mean difference of 12.1 %. Using either monthly means or yearly means of fluxes gives very similar optimal LRU values, the mean difference being only -0.2 %.

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 -0.2 and the correlation is 0.67. This shows that LRU is scale-dependent. The values to be considered should be coherent with their usage. For example, the optimal values we computed are lower than values estimated from measurements, but they are adapted to make the link with atmospheric COS studies.

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 C3 PFTs except the tropical broadleaved evergreen forests and higher for C4 PFTs (Table 1). In the LRU_Opt set, the most productive PFTs (tropical forests and C4 crops) have the highest values around 1.7, while the less productive PFTs (boreal forests and grasses) have the lowest values around 0.9. To the contrary, in the LRU_Seibt set, temperate broadleaved forests have the highest values (3.6) while needleleaf forests have the smallest value around 1.9.

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 CO2 concentrations (Fig. C1). For most PFTs, it is in fact obvious that the relationship shows non-linear features, disagreeing with the classical linear LRU model. Based on these findings, we fitted a simple exponential model as FCOS=aebGPPCOSa[CO2]a-1, with two parameters a and b. However, given the large spread of the data around the model, the Akaike criterion is always favourable to the LRU linear model, so we will not investigate further with this exponential model. More specific research is needed here in order to bridge this data gap. Still, it is important to note that the larger COS fluxes will in general be underestimated using a linear LRU approach. It also appears that in certain PFTs (4, 5, 7) small COS fluxes will be underestimated.

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-2 s-1 in absolute values and are mainly positive, with the main exception over the Amazon region where the mechanistic approach shows a larger uptake than the linear LRU approach. The difference between the global estimates of the two approaches is less than 2 %; we could still improve the linear regression determining the LRU optimal value by weighting grid-cell fluxes with the corresponding surface of the PFT.

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 C4 agriculture, the LRU_Opt-based cycle is slightly in advance compared to the mechanistic cycle.

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 COSa, not accounted for in our model, cannot explain these differences, as they would only affect FCOS but not the conductances. These discrepancies advocate for the assimilation of COS fluxes to optimise the parameters related to the internal and stomatal conductances. In our modelling framework, the internal conductance is assumed to be the product of Vmax by the α parameter. This parameter has been calibrated by Berry et al. (2013) using gas exchange measurements of COS and CO2 uptake (Stimler et al., 2010, 2012). As this α parameter seems much more uncertain compared to the relatively well-known Vmax, we should first try to optimise α keeping Vmax fixed.

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 α parameter when the internal conductance limits COS fluxes, at least as modelled on the C3 species of the two sites, and we could investigate whether the α parameter should be further quantified per PFT rather than simply per photosynthetic pathway. It is to be noted that for C4 species, the internal conductance is larger than for C3 species by a factor of 10, so that stomatal conductance is limiting, and it could be difficult and useless to try optimising internal conductance using the α parameter. We have to acknowledge the large uncertainty regarding the modelling of the internal conductance. In parallel to optimising the parameters of the internal conductance, an improvement could thus also be to replace it by the two factors it represents, i.e. the mesophyll conductance and CA activity. A model for the mesophyll conductance is already implemented in ORCHIDEE, with a simple parameter depending on temperature through a multiplication by a modified Arrhenius function following Medlyn and al. (2002) and Yin and Struik (2009). The impact of mesophyll conductance on photosynthesis and water use efficiency is now more studied (e.g. Buckley and Warren, 2014), even if its modelling remains challenging too: the temperature response has notably been reported as highly variable between plant species (von Caemmerer and Evans, 2015), which would imply having PFT-dependent parameters. Regarding measurements, 13C discrimination of the isotopic composition of CO2 exchanges allows for an estimation of the mesophyll conductance (Stangl et al., 2019). Concerning CA activity, we could test the simple model using a constant value presented in Wehr et al. (2017). Measuring CA activity can be done at a coarse frequency, using different techniques (Henry, 1991).

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 CO2, g0, take two different values: 6.25 mmol m-2 s-1 for C3 species and 18.75 mmol m-2 s-1 for C4 species. However, Lombardozzi et al. (2017), using data from literature, found that observed nighttime conductances to CO2 range from 0 to 450 mmol m-2 s-1 with an overall mean value of 78 mmol m-2 s-1. Moreover, they defined a mean value for each PFT (see Table A3) while the ORCHIDEE model uses one value for all C3 species and another one for all C4 species. Using higher nighttime stomatal conductances in models has the impact of increasing plant transpiration and reducing available soil moisture, which alters water and carbon budgets, especially in semi-arid regions (Lombardozzi et al., 2017). Lower VPD values at night, which could limit the impact of higher nighttime stomatal conductances, follow an increasing trend however (Sadok and Jagadish, 2020). A better representation of these minimal conductances in the model could then improve the constraint of gas exchange between the atmosphere and the terrestrial biosphere. It is to be noted that Barnard and Bauerle (2013) found, based on sensitivity analyses, that g0 was the parameter having the largest influence on their modelled transpiration estimates. They also stress that g0 should maybe be seen as an asymptotic minimal value, rather than an offset. During nighttime, the stomatal conductance limits COS uptake. In the model, the nocturnal stomatal conductance to COS is calculated from the above-mentioned minimum stomatal conductance values. For now, the absolute vegetation COS fluxes at night are slightly overestimated compared to observed fluxes (updated Fig. 1a for Harvard and Fig. B1a for Hyytiälä), thus hinting to overestimated nighttime stomatal conductances. Therefore, nighttime observations of COS fluxes could be used to optimise the minimum stomatal conductance values for each PFT.

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.