The ORCHIDEE Land Surface Model is developed at the Institut Pierre-Simon Laplace (IPSL). The model version used here is the one involved in the Coupled Model Intercomparison Project Phase 6 (CMIP6) (Boucher et al., 2020; Cheruy et al., 2020). ORCHIDEE computes the carbon, water, and energy balances over land surfaces. It can be run at the site level or at the global scale. Fast processes such as soil hydrology, photosynthesis, and respiration are computed at a half-hourly time step. Other processes such as carbon allocation, leaf phenology, and soil carbon turnover are evaluated at a daily time step. Plant species are classified into 14 plant functional types (PFTs), according to their structure (trees, grasslands, or croplands), bioclimatic range (boreal, temperate, or tropical), leaf phenology (broadleaf or evergreen), and photosynthetic pathway (C3 or C4). The vegetation distribution in each grid cell is prescribed using yearly varying PFT maps, derived from the ESA Climate Change Initiative (CCI) land cover products (Poulter et al., 2015).

Soil parameters such as soil porosity, wilting point, and field capacity are derived from a global map of soil textures based on the FAO–USDA (Food and Agriculture Organization of the United Nations–United States Department of Agriculture) texture classification with 12 texture classes (Reynolds et al., 2000). The different textures for the USDA classification are presented in Table S1 in the Supplement. To better represent the observed soil conditions at the different sites that will be used for evaluation in this study, we substituted the soil textures initially assigned in ORCHIDEE from the USDA texture global map with the field soil textures translated into USDA texture classes (Table S2). In a previous study of vegetation COS fluxes in ORCHIDEE, Maignan et al. (2021) used the global soil map based on the Zobler texture classification (Zobler, 1986), which is reduced to three different textures in ORCHIDEE. However, the USDA soil classification gives a finer description of the different soil textures than the Zobler soil classification, considering 12 soil textures instead of 3. The move from the coarse Zobler classes to the finer USDA classes is found to be more important to the mechanistic model than to the empirical model. Since the USDA texture classes are more accurate with its finer discretization of soil textures, in the rest of this study, we only illustrate the results based on the USDA texture classification.

For site level simulations, the ORCHIDEE LSM was forced by local micro-meteorological measurements obtained from the FLUXNET network at the FLUXNET sites following the Creative Commons (CC-BY 4.0) license (Pastorello et al., 2020) and at the remaining sites by other local meteorological measurements performed together with the COS fluxes measurements when available, eventually gap-filled using the 0.25∘ × 0.25∘ hourly reanalysis from the fifth generation of meteorological analyses of the European Centre for Medium-Range Weather Forecasts (ECMWF) (ERA5) (Hersbach et al., 2020). Global simulations were forced by the 0.5∘ and 6-hourly CRU JRA reanalysis (University of East Anglia Climatic Research Unit–Japanese Reanalysis; Friedlingstein et al., 2020). Near-surface COS concentrations (denoted Ca below) were prescribed using monthly mean atmospheric COS concentrations at the first vertical level of the LMDZ (Laboratoire de Météorologie Dynamique) atmospheric transport model (GCM, general circulation model; see description below in Sect. 2.1.3), forced with optimized COS surfaces fluxes. The latter have been inferred by atmospheric inverse modelling from the COS surface measurements of the NOAA network (Remaud et al., 2022). Simulations with constant atmospheric COS concentrations at a mean global value of 500 ppt were also run to evaluate the impact of spatiotemporal variations in near-surface COS concentrations versus a constant value. Near-surface CO2 concentrations were estimated using global yearly mean values provided by the TRENDY (Trends in the land carbon cycle) project (Sitch et al., 2015).

We implemented in the ORCHIDEE LSM the soil COS flux model from Berry et al. (2013), which assumes that COS uptake is proportional to CO2 production by soil respiration, following Yi et al. (2007). Although Yi et al. (2007) reported a relationship between soil COS uptake and total soil respiration, including root respiration, Berry et al. (2013) assumed that COS flux was proportional to soil heterotrophic respiration only. The rationale behind this assumption is that soil CA concentration is related to soil organic matter content and thus ecosystem productivity (Berry et al., 2013). As heterotrophic respiration is also linked to productivity, Berry et al. (2013) considered soil COS uptake to be proportional to soil heterotrophic respiration. However, soil respiration alone did not correlate well in incubation studies (Whelan et al., 2016). As the proportionality between COS fluxes and soil respiration has only been demonstrated for the total (heterotrophic and autotrophic) soil respiration (Yi et al., 2007), we used in this study total soil respiration as a scaling factor for soil COS uptake. This model will be referred to as the empirical model.

The influence of soil temperature and moisture are included in the calculation of soil respiration. Thus, we computed soil COS flux Fsoil,empirical (pmol COS m-2 s-1) as follows: 1Fsoil,empirical=-ksoil⋅Resptot, where Resptot is total soil respiration (µmol CO2 m-2 s-1) and ksoil is a constant equal to 1.2 pmol COS per µmol CO2 that converts CO2 production from respiration to COS uptake. The value of 1.2 pmol COS per µmol CO2 was estimated from field chamber measurements in a pine and broadleaf mixed forest (Dinghushan Biosphere Reserve, southern China) from Yi et al. (2007). In ORCHIDEE, we calculated the total soil respiration as the sum of soil heterotrophic respiration within the soil column, including that of the litter, and root autotrophic respiration.

The mechanistic COS soil model of Ogée et al. (2016) describes both soil COS uptake and production. This model includes COS diffusion in the soil matrix, COS dissolution, and hydrolysis in the water-filled pore space and COS production under low redox conditions. The soil is assumed to be horizontally homogeneous so that the soil COS concentration C (mol m-3) is only a function of time t (s) and soil depth z (m). The mass balance equation for COS can then be written as (Ogée et al., 2016) 2∂εtotC∂t=-∂Fdiff∂z+P-S, where εtot is the soil total porosity (m3 air per cubic metre soil), Fdiff is the diffusional flux of COS (mol m-2 s-1), S is the COS consumption rate (mol m-3 s-1), and P the COS production rate under low redox conditions (mol m-3 s-1).

Under steady-state conditions and uniform soil temperature, moisture, and porosity profiles, an analytical solution of Eq. (2) can be found (Ogée et al., 2016). We assume that the environmental conditions, such as soil temperature and moisture, are constant in ORCHIDEE over the 30 min model time step. We also assume chemical equilibrium between the gaseous and the dissolved COS, neglecting advection as suggested by Ogée et al. (2016). In these conditions, the typical timescale for COS diffusion in the upper active soil layer is much shorter than the 30 min model time step. Although Eq. (2) could also be solved numerically using the soil discretization in ORCHIDEE, we preferred to use the analytical solution, using the mean soil moisture and temperature averaged over the first few soil layers (down to about 9 cm deep), weighted by the thickness of each soil layer. Assuming fully mixed atmospheric conditions within and below the vegetated canopy, we also assumed that the COS concentration at the soil surface C(z=0) is equal to the near-surface COS concentration Ca. With these boundaries' conditions, the steady-state COS flux at the soil surface Fsoil,mechanistic (mol m-2 s-1) is (Ogée et al., 2016) 3Fsoil,mechanistic=kBθDCa-z12PD(1-exp⁡(-zmax⁡/z1)), where k is the first-order COS consumption rate constant within the soil (s-1), B is the solubility of COS in water (m3 water per cubic metre air), θ is the soil volumetric water content (m3 water per cubic metre soil), D is the total effective COS diffusivity (m2 s-1), z1=D/kBθ (m), and zmax⁡ is the soil depth below which the COS production rate and the soil COS gradient are assumed negligible (Ogée et al., 2016). In the following, zmax⁡ is set at 0.09 m.COS diffusion The total effective COS diffusivity in soil D includes the effective diffusivity of gaseous COS Deff,a (m3 air per metre soil per second) and dissolved COS Deff,l (m3 water per metre soil per second) through the soil matrix: 4D=Deff,a+Deff,lB.

The solubility of COS in water B is calculated using Henry's law constant KH (mol m-3 Pa-1): 5B=KHRT, where R=8314 J mol-1 K-1 is the ideal gas constant, T is the soil temperature (K), and (Wilhelm et al., 1977) 6KH=0.00021exp⁡[24900/R(1/T-1/298.15)].

The effective diffusivity of gaseous COS Deff,a is expressed as (Ogée et al., 2016) 7Deff,a=D0,aτaεa, where D0,a is the binary diffusivity of COS in the air (m2 air s-1), τa is the air tortuosity factor representing the tortuosity of the air-filled pores, and εa is the air-filled porosity (m3 air per cubic metre soil). The binary diffusivity of COS in the air D0,a is expressed following the Chapman–Enskog theory for ideal gases (Bird et al., 2002) and depends on temperature and pressure: 8D0,a(T,p)=D0,a(T0p0)TT01.5pp0, where D0,a(T0,p0)=D0,a(25∘C,1atm)=1.27×10-5 m2 s-1 (Massman, 1998).

The expression of the air tortuosity factor τa depends on whether the soil is repacked or undisturbed. In ORCHIDEE, repacked soils correspond to the agricultural soils represented by the C3 and C4 crops. Soils not covered by crops are considered undisturbed soils. The expression of τa for repacked soils τa,r is given by Moldrup et al. (2003): 9τa,r=εa3/2/φ, where φ is the soil porosity (m3 m-3) that includes the air-filled and water-filled pores. Soil porosity is assumed constant through the soil column in ORCHIDEE and is determined by the USDA texture global map. The air-filled porosity εa is calculated as εa=φ-θ.

The expression of τa for undisturbed soils τa,u is given in Deepagoda et al. (2011). We chose this expression rather than the expression proposed by Moldrup et al. (2003) for undisturbed soils because it appears to be more accurate and does not require information on the pore-size distribution (Ogée et al., 2016): 10τa,u=[0.2(εa/φ)2+0.004]/φ.

In a similar way to COS diffusion in the gas phase, the effective diffusivity of dissolved COS Deff,l is described by Ogée et al. (2016): 11Deff,l=D0,lτlθ, where D0,l is the binary diffusivity of COS in the free water (m2 water s-1) and τl is the tortuosity factor for solute diffusion. The binary diffusivity of COS in the free water D0,l is described using an empirical formulation proposed by Zeebe (2011) for CO2, which only depends on temperature: 12D0,l(T)=D0,l(T0)TT0-12, where T0=216 K (Ogée et al., 2016) and D0,l(25∘C)=1.94×10-9 m2 s-1 (Ulshöfer et al., 1996).

The expression of τl is the same for repacked and undisturbed soils. We used the expression given by Millington and Quirk (1961) as a good compromise between simplicity and accuracy (Moldrup et al., 2003): 13τl=θ7/3/φ2. COS consumption COS can be destroyed by biotic and abiotic processes. The abiotic process corresponds to COS hydrolysis in soil water at an uncatalysed rate kuncat (s-1), which depends on soil temperature T (K) and pH (Elliott et al., 1989): 14kuncat=2.15×10-5exp⁡-104501T-1298.15+12.7×10-pKw+pHexp⁡-60401T-1298.15, where pKw is the dissociation constant of water.

This uncatalysed hydrolysis is quite low compared to the COS hydrolysis catalysed by soil microorganisms, which is the main contribution of COS uptake by soils (Kesselmeier et al., 1999; Sauze et al., 2017; Meredith et al., 2018). The enzymatic reaction catalysed by CA follows Michaelis–Menten kinetics. The turnover rate kcat (s-1) and the Michaelis–Menten constant Km (mol m-3) of this reaction depend on temperature. The temperature dependence of the ratio kcatKm is expressed as (Ogée et al., 2016) 15xCA(T)=exp⁡-ΔHaRT1+exp⁡-ΔHdRT+ΔSdR, where ΔHa, ΔHd, and ΔSd are thermodynamic parameters, such as ΔHa=40 kJ mol-1, ΔHd=200 kJ mol-1, and ΔSd=660 J mol-1 K-1.

The total COS consumption rate by soil k (s-1) is described with respect to the uncatalysed rate at T=298.15 K and pH=4.5 (Ogée et al., 2016): 16k=fCAkuncat298.15,4.5xCATxCA298.15, where fCA is the CA enhancement factor, which characterizes the soil microbial community that can consume COS. The CA enhancement factor depends on soil CA concentration, temperature, and pH. Ogée et al. (2016) reported that its values range between 21 600 and 336 000, with a median value at 66 000. We adapted the values of fCA found in Meredith et al. (2019) to have a CA enhancement factor that depends on ORCHIDEE biomes (Table A1 in Appendix A). Oxic soil COS production Abiotic oxic soil COS production has been observed at high soil temperature (Maseyk et al., 2014; Whelan and Rhew, 2015; Kitz et al., 2017, 2020; Spielmann et al., 2019a, 2020). However, photodegradation has also been proposed as an abiotic production mechanism in oxic soils (Whelan and Rhew, 2015; Kitz et al., 2017, 2020). Abiotic COS production is still not well understood but was assumed to originate from biotic precursors (Meredith et al., 2018).

In Ogée et al. (2016), the production rate P is described as independent of soil pH but depends on soil temperature and redox potential. This dependence on soil redox potential enables us to consider the transition between oxic and anoxic soils. However, because little information is available on soil redox potential at the global scale, its influence cannot yet be represented in a spatially and temporally dynamic way in a land surface model such as ORCHIDEE. Thus, we decided to use the production rate described in Whelan et al. (2016) that only depends on soil temperature and land use type: 17Poxic=eα+βT, where Poxic is expressed in pmol g-1 min-1, T is soil temperature (∘C), and α and β are parameters determined by Whelan et al. (2016) for each land use type using the least-squares fitting approach. We adapted the values of α and β given for four land use types to ORCHIDEE biomes (Table A2 in Appendix A). Values of α and β for deserts could not be estimated by Whelan et al. (2016) because COS emission for this biome was not found to increase with temperature. Figure 11 in Whelan et al. (2016) shows that COS emission from a desert soil is always near zero for temperatures ranging from 10 to 40 ∘C. Moreover, COS emission from a desert soil is also found to be near zero in Fig. 1 of Meredith et al. (2018). This could be explained by a lack of organic precursors to produce COS (Whelan et al., 2016). Therefore, we considered that desert soils, which correspond to a specific non-vegetated PFT in ORCHIDEE, do not emit COS. For other ORCHIDEE biomes, COS production was estimated using α and β for each PFT and the mean soil temperature over the top 9 cm. The unit of Poxic was converted from pmol g-1 min-1 to mol m-3 s-1 (in Eq. 3) using soil bulk density information from the Harmonized World Soil Database (HWSD; FAO/IIASA/ISRIC/ISSCAS/JRC, 2012). Anoxic soil COS emission Several studies have shown direct COS emissions by anoxic soils (Devai and DeLaune, 1997; de Mello and Hines, 1994; Whelan et al., 2013; Yi et al., 2007). This has been linked to a strong activity of sulfate reduction metabolisms in highly reduced environments such as wetlands (Aneja et al., 1981; Kanda et al., 1992; Whelan et al., 2013; Yi et al., 2007). A previous approach developed by Launois et al. (2015) was based on the representation of seasonal methane emissions by Wania et al. (2010) in the LPJ–WHyME (Lund–Potsdam–Jena–Wetland Hydrology and Methane) model to represent anoxic soils in ORCHIDEE. The mean values of soil COS emissions from Whelan et al. (2013) were used to attribute to each grid point a value of soil COS emission. In this approach by Launois et al. (2015), salt marshes were not represented despite their strong COS emissions found in Whelan et al. (2013). Emissions from rice paddies were also neglected. Thus, COS emissions from anoxic soils peaked in summer over the high latitudes, following methane production.

Because of the scarce knowledge on anoxic soil COS exchange, here we propose another approach to represent the contribution of anoxic soils, which could be compared to the previous approach developed by Launois et al. (2015). To represent the distribution of anoxic soils, we selected the regularly flooded wetlands from the map developed by Tootchi et al. (2019), as represented in Fig. 1. The regularly flooded wetlands cover 9.7 % of the global land area, which is among the average values found in the literature ranging from 3 % to 21 % (Tootchi et al., 2019). Then, in ORCHIDEE each pixel is considered either anoxic following the wetland map distribution from Tootchi et al. (2019) or oxic for the rest of the land surfaces. The pixels defined as anoxic soils are considered flooded through the entire year: the seasonal variations of the flooding, as happen during the monsoon seasons, are consequently neglected.

On anoxic pixels, we represent anoxic soil COS flux with a production rate based on the expression developed by Ogée et al. (2016): 18Panoxic=Prefzmax⁡Q10T-Tref10, where Pref (mol m-2 s-2) is the reference production term, Tref is a reference soil temperature (K), and Q10 is the multiplicative factor of the production rate for a 10 ∘C increase in soil temperature (unitless). As anoxic soil production ranges from 10 to 300 pmol m2 s-1 for salt marshes and is usually below 10 pmol m-2 s-1 for freshwater wetlands (Whelan et al., 2018), the reference production term was set to 10 pmol m-2 s-1.

All the variables and constants of the empirical and mechanistic models are presented in Tables A3 and A4 in Appendix A.

To simulate the COS atmospheric distribution, we use an “offline” version of the Laboratoire de Météorologie Dynamique general circulation model (GCM), LMDZ 6 (Hourdin et al., 2020), which has been used as the atmospheric component in the IPSL coupled model for CMIP6. The LMDZ GCM has a spatial resolution of 3.75∘ long. × 1.9∘ lat. with 39 sigma-pressure layers extending from the surface to about 75 km, corresponding to a vertical resolution of about 200–300 m in the planetary boundary layer, and a first level at 33 m above sea or ground level. The model u and v wind components were nudged towards winds from the ERA5 reanalysis with a relaxation time of 2.5 h to ensure realistic wind advection (Hourdin and Issartel, 2000; Hauglustaine et al., 2004). The ECMWF fields are provided every 6 h and interpolated onto the LMDZ grid. This version has been shown to reasonably represent the transport of passive tracers (Remaud et al., 2018). The offline model uses pre-computed mass fluxes provided by this full LMDZ GCM version and only solves the continuity equation for the tracers, which significantly reduces the computation time. In the following, we refer to this offline version as LMDZ. The model time step is 30 min, and the output concentrations are 3-hourly averages.

The atmospheric COS oxidation is computed from pre-calculated OH monthly concentration fields produced from a simulation of the INCA (Interaction with Chemistry and Aerosols) model (Folberth et al., 2006; Hauglustaine et al., 2004, 2014) coupled to LMDZ. The atmospheric OH oxidation of COS amounts to 100 GgS yr-1 in the model. Similarly, the COS photolysis rates are also pre-calculated with the INCA model, which uses the Troposphere Ultraviolet and Visible (TUV) radiation model adapted for the stratosphere (Terrenoire et al., 2022). The temperature-dependent carbonyl sulfide absorption cross-sections from 186.1 to 296.3 nm are taken from Burkholder et al. (2019). The calculated photolysis rates are averaged over the period 2008–2018 and prescribed to LMDZ. Implemented in LMDZ, the COS photolysis in the stratosphere amounts to about 30 GgS yr-1, which is of the same order of magnitude as previous estimates: 21 GgS yr-1 (71 % of 30 GgS yr-1) by Chin and Davis (1995), between 11 and 21 GgS yr-1 by Kettle et al. (2002), and between 16 and 40 GgS yr-1 by Ma et al. (2021).

The description of the studied sites is given in Table 1.

Soil COS flux chamber measurements were conducted in 2015 at AT-NEU; in 2016 at DK-SOR, ES-LMA, and ET-JA; and in 2017 at IT-CRO (abbreviations as in Table 1). The aboveground vegetation was removed 1 d before the measurements if needed, and the fluxes were derived from concentration measurements using a quantum cascade laser (see Kitz et al., 2020, and Spielmann et al., 2020, 2019a). At AT-NEU, DK-SOR, ES-LMA, and IT-CRO, a random forest model was calibrated against the manual chamber measurements and then used to simulate half-hourly soil COS fluxes in Spielmann et al. (2019a). We compared the ORCHIDEE half-hourly simulated fluxes to half-hourly outputs of the random forest model. This enabled studying the diel cycle and computing daily observations with no sampling bias for the study of the seasonal cycle. Soil COS fluxes for ET-JA were derived by using the same training method as the one used in Spielmann et al. (2019a).

At FI-HYY, soil COS fluxes were measured using two automated soil chambers in 2015. These chambers were connected to a quantum cascade laser spectrometer to calculate soil COS fluxes from concentration measurements (see Sun et al., 2018, for more information on the experimental setup). Any vegetation was removed from the chambers before the measurements.

At US-HA, soil COS fluxes in 2012 and 2013 were not directly measured but derived from flux-profile measurements, connected to CO2 soil chamber measurements and profiles. A sub-canopy flux gradient approach was used to partition canopy uptake from soil COS fluxes. For more information on this approach and its limitations, see Wehr et al. (2017).

In the study of soil COS fluxes, the difficulty of performing soil COS flux measurements must be acknowledged, as well as the differences between experimental setups and methods to retrieve soil COS fluxes. These limitations are illustrated in the set of observations selected here. Aboveground vegetation had to be removed at some sites to not measure the plant contribution in addition to soil COS fluxes (Sun et al., 2018; Spielmann et al., 2019a; Kitz et al., 2020). Vegetation removal prior to the measurements might lead to artefacts in the observations. Some components of the measuring system can also emit COS. In this case, a blank system is needed to apply a post-correction to the measured fluxes (Sun et al., 2018; Kitz et al., 2020). Litter was left in place at the measurement sites.

The NOAA surface flask network provides long-term measurements of the COS mole fraction at 14 locations at weekly to monthly frequencies from the year 2000 onwards. We use an extension of the data initially published in Montzka et al. (2007). The data were collected as paired flasks analysed using gas chromatography and mass spectrometry. The stations located in the Northern Hemisphere had sample air masses coming from the entire Northern Hemisphere domain above 30∘. Among them, the sites LEF, NWR, HFM, and WIS have mostly continental footprints (Remaud et al., 2022), while the sites SPO, CGO, and PSA sample mainly oceanic air masses of the Southern Hemisphere (Montzka et al., 2007). The locations of these sites are depicted in Fig. B1 in Appendix B.

A “spin-up” phase was performed before each simulation, which enabled all carbon pools to stabilize and the net biome production to oscillate around zero. Reaching the equilibrium state is accelerated in the ORCHIDEE LSM thanks to a pseudo-analytical iterative estimation of the carbon pools, as described in Lardy et al. (2011). For site simulations, the spin-up was performed by cycling the years available in the forcing files of each site, for a total of about 340 years. For global simulations, the spin-up phase of 340 years was performed by cycling over 10 years of meteorological forcing files in the absence of any disturbances.

Following the spin-up phase we ran a transient simulation of about 40 years that introduced disturbances such as climate change, land use change, and increasing CO2 atmospheric concentrations.

This transient phase was performed by cycling over the available years for site simulations. For global simulations, the transient phase was run where we introduced disturbances from 1860 to 1900. After this transient phase, COS fluxes were simulated from 1901 to 2019.

We ran the LMDZ6 version of the atmospheric transport model described above for the years 2009 to 2016. We started from a uniform initial condition, and we removed the first year, as it is considered to be part of the spin-up period. The COS fluxes used as model inputs are presented in Table 2. The fluxes are given as a lower boundary condition, called the surface, of the atmospheric transport model (LMDZ), which then simulates the transport of COS by large-scale advection and sub-grid scale processes such as convection and boundary layer turbulence. In this study, we only evaluate the sensitivity of the latitudinal gradient and seasonal cycle of COS concentrations to the soil COS fluxes. The horizontal gradient aims at validating the latitudinal repartition of the surface fluxes, while the seasonal cycle partly reflects the seasonal exchange with the terrestrial sink, which peaks in spring/summer. This study does not aim at reproducing the mean value, as the top-down COS budget is currently unbalanced, with a source component missing (Whelan et al., 2018; Remaud et al., 2022; see Table 3).

For each COS observation, the 3D simulated concentration fields were sampled at the nearest grid point to the station and at the closest hour of the measurements. For each station, the curve fitting procedure developed by the NOAA Climate Monitoring and Diagnostic Laboratory (NOAA CMDL) (Thoning et al., 1989) was applied to modelled and observed COS time series to extract a smooth detrended seasonal cycle. We first fitted a function including a first-order polynomial term for the growth rate and two harmonic terms for seasonal variations. The residuals (raw time series minus the smooth curve) were fitted using a low-pass filter with either 80 or 667 d as short-term and long-term cut-off values. 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). Regarding vegetation COS fluxes (Maignan et al., 2021), we added the possibility of using spatially and temporally varying atmospheric COS concentrations, as for soil.

We evaluated modelled soil COS fluxes against field measurements using the root mean square deviation (RMSD) as 19RMSD=∑n=1NFCOSObsn-FCOSModn2N, where N is the number of considered observations, FCOSObsn is the nth observed COS flux, and FCOSModn is the nth modelled COS flux, and the relative RMSD (rRMSD) as 20rRMSD=RMSD∑n=1NFCOSObsnN, which is the RMSD divided by the mean value of observations.

Simulated atmospheric COS concentrations were evaluated by computing the normalized standard deviation (NSD), which is the standard deviation of the simulated concentrations divided by the mean of the observed concentrations, and the Pearson correlation coefficients (r) between simulated and observed COS concentrations. The closer NSD and r values are to 1, the better the model accuracy is.

One of the main difficulties with the implementation of a model is to define the parameter values that lead to the most accurate representation of the processes in ORCHIDEE. Calibrating the model parameters is of interest as Ogée et al. (2016) indicate that some of the model parameters such as fCA and the production term parameters have to be constrained by observations. Moreover, the default values for the soil COS model parameters used in this study (Tables A1 and A2 in Appendix A) are determined by laboratory experiments (Ogée et al., 2016; Whelan et al., 2016), which is why it is interesting to study how the values obtained by calibration against field observations differ from these default values. Data assimilation (DA) aims at producing an optimal estimate by combining observations and model outputs. In this study, we used DA to find the model parameter values that improve the fit between simulated and observed soil COS fluxes from the empirical and the mechanistic models. We used the ORCHIDEE Data Assimilation System (ORCHIDAS), which is based on a Bayesian framework. ORCHIDAS has been described in detail in previous studies (Bastrikov et al., 2018; Kuppel et al., 2014; MacBean et al., 2018; Peylin et al., 2016; Raoult et al., 2021), so below we only briefly present the method. Assuming that the observations and model outputs follow a Gaussian distribution, we aim at minimizing the following cost function Jx by optimizing the model parameters (Tarantola, 2005): 21Jx=12[Mx-yT⋅E-1⋅Mx-y+(x+xb)T⋅B-1⋅(x+xb)], where x is the vector of parameters to optimize and y is the observations. The first part of the cost function measures the mismatch between the observations and the model, and the second part represents the mismatch between the prior parameter values xb and the considered set of parameters x. Both terms of the cost function are weighted by the prior covariance matrices for the observation errors E-1 and parameter errors B-1. The minimization of the cost function follows the genetic algorithm (GA) method, which is derived from the principles of genetics and natural selection (Goldberg, 1989; Haupt and Haupt, 2004) and is described for ORCHIDAS in Bastrikov et al. (2018).

For each soil COS model, we selected the eight most important parameters to which soil COS fluxes are sensitive following sensitivity analyses (Sect. 2.4.3). The observation sites selected for sensitivity analyses and DA are the ones with the largest number of observations for model parameter calibration, which are FI-HYY and US-HA.

We conducted sensitivity analyses at two contrasting sites (FI-HYY and US-HA) to determine which model parameters have the most influence on the simulated soil COS fluxes from the empirical and the mechanistic models. Sensitivity analyses can help to identify the key parameters before aiming at calibrating these parameters. Indeed, focusing on the key model parameters for calibration limits both the computational cost of optimization that increases with the number of parameters and the risk of overfitting.

The Morris method (Morris, 1991; Campolongo et al., 2007) was used for the sensitivity analysis, as it is relatively time efficient and enables ranking the parameters by importance. This qualitative method requires only a small number of simulations, (p+1)n, where p is the number of parameters and n is the number of random trajectories generated (here, n=10).

We selected a set of parameters for the Morris sensitivity analyses based on previous sensitivity analyses conducted on soil parameters in ORCHIDEE (Dantec-Nédélec et al., 2017; Raoult et al., 2021; Mahmud et al., 2021). A distinction is made between the soil COS model parameters called first-order parameters (fCA, α, and β for the mechanistic model and ksoil for the empirical model) and parameters called second-order parameters related to soil hydrology, carbon uptake and allocation, phenology, conductance, or photosynthesis (18 parameters; see Tables S3 and S4). The range of variation in the second-order parameters is described in previous studies using ORCHIDEE (Dantec-Nédélec et al., 2017; Raoult et al., 2021; Mahmud et al., 2021). For the first-order parameters, the range of variation is described in Yi et al. (2007) for ksoil (±1.08 pmol COS per µmol CO2) and in Table 1 in Meredith et al. (2019) for fCA. The ranges of variation for α and β parameters are not directly given in the literature and were calculated based on information from the production parameters defined in Meredith et al. (2018) (Text S1 and Table S5).

Figure 2 shows the seasonal cycles of soil COS fluxes at the different sites where measurements were conducted. The empirical model mainly differs from the mechanistic model with a stronger seasonal amplitude of soil COS fluxes (34 % higher), except at the sites where a net COS production is found with the mechanistic model in summer (ES-LMA and IT-CRO). At all sites, the empirical model shows that the simulated uptake increases in spring, reaching a maximum in summer, and decreases in autumn with a minimal uptake during winter. The strong COS uptake in summer from the empirical model can be explained by the proportionality of soil COS uptake to simulated soil respiration, which increases with the high temperatures in summer. In contrast, the mechanistic model depicts almost no seasonality at all the sites where no net COS production is found over the year. As the mechanistic model represents both soil COS uptake and production, the increase in COS production due to higher temperature in summer compensates part of the COS uptake (Fig. C1 in Appendix C). While the uptake from the empirical model is often higher than the one computed with the mechanistic model in summer, soil COS uptake in winter is stronger with the mechanistic representation.

The scarcity of field measurements at AT-NEU, ES-LMA, IT-CRO, DK-SOR, and ET-JA does not allow for an evaluation of the simulated seasonality of COS fluxes. However, at US-HA, the absence of seasonality from May to October in the observations is also found in the mechanistic model, while a maximum net soil COS uptake is reached with the empirical model.

We found that the mechanistic model is in better agreement with the observations for four (IT-CRO, ET-JA, FI-HYY, and US-HA) out of the seven sites, with a mean of 1.58 pmol m-2 s-1 and 2.03 m-2 s-1 for the mechanistic and empirical model, respectively. However, the mechanistic model struggles to reproduce soil COS fluxes at AT-NEU and ES-LMA, with an overestimation of soil COS uptake or an underestimation of soil COS production at AT-NEU and a delay in the simulated net COS production at ES-LMA. We might suspect that the removal of vegetation at these sites prior to the measurements could have artificially enhanced COS production in the observations. Indeed, the removal of vegetation could change soil structure and increase the availability of soil organic matter to degradation (Whelan et al., 2016). AT-NEU and ES-LMA are grassland sites for which soils are expected to receive higher light intensity than forest soils. These sites also show a high mean soil temperature of about 20 ∘C during the measurement periods. Therefore, high soil temperature and light intensity on soil surface could have enhanced soil COS production, as it was related to thermal or photo degradation of soil organic matter (Kitz et al., 2017, 2020; Whelan and Rhew, 2015; Whelan et al., 2016, 2018). This is not the case at FI-HYY, ET-JA, or DK-SOR, where soil temperature is much lower (mean value about 10 ∘C at FI-HYY and 15 ∘C at ET-JA and DK-SOR during the measurement periods) and the forested cover decreases the radiation level reaching the soil. Note that herbaceous biomass is also likely to be higher in grasslands than in forests. Besides, AT-NEU and ES-LMA are managed grassland sites with nitrogen inputs. Then, soil COS production could also be enhanced by a high nitrogen content as suggested by several studies (Kaisermann et al., 2018; Kitz et al., 2020; Spielmann et al., 2020), which is not represented in our models. The mechanistic model is able to represent a net COS production at IT-CRO but overestimates it. This might highlight the importance of adapting the production parameters (α and β) in this model to adequately represent net COS production. In this model, the net soil COS production is related to an increase in soil temperature. However, it is to be noted that IT-CRO is an agricultural site with nitrogen fertilization. Therefore, soil COS production in the observations could also be enhanced by nitrogen inputs. As expected, the empirical model is unable to correctly simulate the direction of the observed positive soil COS exchange rates at ES-LMA and IT-CRO.

Figure 3 shows the comparison between the simulated and observed mean diel cycles over a month. The observations show a minimum net soil COS uptake or a maximum net soil COS production reached between 11:00 and 13:00 at AT-NEU (UTC+2), ES-LMA (UTC+2), IT-CRO (UTC+1), and DK-SOR (UTC+2). At AT-NEU and ES-LMA, neither model is able to represent the observed diel cycle. At these grassland sites, Spielmann et al. (2020) and Kitz et al. (2020) found that the daytime net COS emissions were mainly related to high radiations reaching the soil surface, the impact of which is not represented in the soil COS models. At IT-CRO and DK-SOR, the diel cycles simulated by the mechanistic model show patterns similar to the observations with a peak in the middle of the day but with an overestimation of the net soil COS production and a delay in the peak at IT-CRO and an overestimation of the net soil COS uptake at DK-SOR. The mechanistic model reproduces the absence of a diel cycle observed at FI-HYY and ET-JA but with an underestimation of the net soil COS uptake at ET-JA. AT US-HA, the observed soil COS flux does not exhibit diel variations, while the mechanistic model shows a peak with a decrease in the net soil COS uptake around 15:00. Wehr et al. (2017) explain this absence of the diel cycle in the observations by a range of variations for soil temperature and soil water content that is too low to influence soil COS flux. In ORCHIDEE, the simulated range of temperature at US-HA is larger than the one measured on site, and temperature is the main driver of the decrease in net soil COS uptake at this site (not shown). Therefore, the enhancement of soil COS production by soil temperature could be only found in the simulated flux. Another possibility is that it could be totally compensated by soil COS uptake in the observations. The mismatch between the model and the observations could be due to several factors including (i) an insufficient representation of the vegetation complexity by the division in PFTs; (ii) a poor calibration of the PFT-specific parameters (fCA, α, and β); or (iii) missing processes in the model, such as considering the effect of nitrogen content on soil COS fluxes.

The empirical model shows a maximum soil COS uptake around 15:00 at ET-JA, FI-HYY, US-HA, and IT-CRO, which is not found in the observations at FI-HYY and is in contradiction with the observed diel variations at IT-CRO and ES-LMA. Considering all sites, the mechanistic model leads to a smaller error between the simulations and the observations, with a mean RMSD of 1.38 pmol m2 s-1 against 1.87 pmol m2 s-1 for the empirical model.

Figure 4 represents simulated net soil COS fluxes versus soil temperature and soil water content at the different sites. At the sites where only a net soil COS uptake is simulated by the mechanistic model (all sites except IT-CRO and ES-LMA), soil COS uptake generally decreases with increasing soil water content, which appears to be the main driver of soil COS fluxes. This behaviour can be explained by a decrease in COS diffusivity through the soil matrix with increasing soil moisture, reducing soil COS availability for microorganism consumption. Furthermore, an optimum soil water content for net soil COS uptake is found between 10 % and 15 %, which was also observed in Ogée et al. (2016) and in several field studies to be around 12 % (Kesselmeier et al., 1999; Liu et al., 2010; van Diest and Kesselmeier, 2008). This optimum soil water content for soil COS uptake is related to a site-specific temperature optimum, which is found between 13 and 15 ∘C at US-HA for example. Indeed, Ogée et al. (2016) also describe a temperature optimum with a value that depends on the studied site (Kesselmeier et al., 1999; Liu et al., 2010; van Diest and Kesselmeier, 2008). At IT-CRO and ES-LMA, where a strong net soil COS production is simulated by the mechanistic model, the main driver of soil COS fluxes becomes soil temperature. At these sites, the net soil COS production increases with soil temperature, due to the exponential response of soil COS production term to soil temperature. The increase in soil COS production with soil temperature at IT-CRO and ES-LMA is supported by the observations (Fig. S1 in the Supplement).

Contrary to the mechanistic model, soil COS uptake computed with the empirical model is mainly driven by soil temperature, with a soil COS uptake that increases with increasing soil temperature. This response of the empirical model to soil temperature is due to its relation to soil respiration, which is enhanced by strong soil temperature. However, this net increase in soil COS uptake with soil temperature at all sites is not found in the observations (Fig. S1). It can be noted that low soil moisture values were found to limit soil COS uptake for the empirical model, as seen at ES-LMA for a soil water content below 8 %.

Sensitivity analyses including a set of parameters (19 for the empirical model and 21 for the mechanistic model) were performed to evaluate the sensitivity of soil COS fluxes to each of the selected parameter. The Morris scores were normalized by the highest values to help rank the parameters by their relative influence on soil COS fluxes, where a score of 1 represents the most important parameter and that of 0 represents the parameters that have no influence on soil COS fluxes. For reasons of clarity, in the following we present the results only for the parameters that were found to have an impact on soil COS fluxes (Morris scores not equal to 0).

Figure 5 shows the results of the Morris sensitivity experiments highlighting the key parameters influencing soil COS fluxes from the empirical and the mechanistic models at FI-HYY and US-HA. For the empirical model at both sites, the first-order parameter (ksoil) is the most important parameter in the computation of soil COS fluxes, as it directly scales soil respiration to soil COS fluxes. The following parameters to which soil COS fluxes are the most sensitive are the scalar on the active soil C pool content (soilC) and the temperature-dependency factor for heterotrophic respiration (soil_Q10). Indeed, the soilC parameter determines the soil carbon active pool content, which can be consumed by soil microorganisms during respiration, therefore impacting soil COS fluxes from the empirical model. The soil_Q10 parameter impacts soil COS fluxes at both sites, as it determines the response of soil heterotrophic respiration to temperature, which is included in the proportionality of soil COS fluxes to the total soil respiration in the empirical model. Similarly, one of the second-order parameters, the minimum soil wetness to limit the heterotrophic respiration (min_SWC_resp), has an impact on soil COS fluxes from the empirical model only. The importance of min_SWC_resp for soil COS fluxes is found at US-HA but not at FI-HYY. This can be explained by the difference in soil moisture between the two sites, with an annual mean of 16.2 % at US-HA and reaching a minimum of only 8.8 % against an annual mean of 17.5 % with a minimum of 12.4 % at FI-HYY.

Contrary to the empirical model, soil COS fluxes computed with the mechanistic model are more sensitive to two second-order parameters, the van Genuchten water retention curve coefficient n and the saturated volumetric water content (θSAT). These two second-order parameters are strongly linked to soil hydrology and determine the soil water content, which affects COS diffusion through the soil matrix and its uptake. The van Genuchten coefficients occur in the relationships linking hydraulic conductivity and diffusivity to soil water content (van Genuchten, 1980). At both sites, the strong impact of the van Genuchten water retention curve coefficient n on soil COS fluxes simulated with the mechanistic model highlights the critical importance of soil architecture. Thus, soil COS fluxes computed with the mechanistic model are expected to strongly vary according to the different soil types. Then, the first-order parameters (fCA, α, and β) also influence soil COS fluxes from the mechanistic model. However, the uptake parameter (fCA of PFT 15, boreal C3 grass) has the most influence on soil COS fluxes at FI-HYY, while it is the production-related parameter (α of PFT 6, temperate broadleaved summergreen forest) that has the largest impact at US-HA. The stronger influence of the production parameter involved in the temperature response at US-HA might be explained by the difference in temperature between the two sites, which ranges from -10 to 25 ∘C at US-HA with an annual mean of 7.5 ∘C in 2013, while only ranging from -5 to 15 ∘C with an annual mean of 4.3 ∘C at FI-HYY in 2015. Similar to the difference in the main driver of soil COS fluxes found in Fig. 4, the most important first-order parameters to which soil COS fluxes are sensitive seem to differ between uptake and production parameters depending on the site conditions. It is to be noted that at US-HA, the most important production parameters are the ones of the dominant PFT at this site (PFT 6), which also correspond to a stronger response of the production term to temperature than for PFT 10 (temperate C3 grass). However, at FI-HYY the most influential uptake parameter is for PFT 15 (boreal C3 grass) that only represents 20 % of the PFTs at this site, while PFT 7 (boreal needleleaf evergreen forest) is the dominant PFT. This can be explained by the range of variation that is assigned to fCA of PFT 7 by Meredith et al. (2019), which is larger than the one of fCA for PFT 15 (9000 against 3100).

Finally, a set of parameters related to photosynthesis, conductance, phenology, hydrology, and carbon uptake has an impact on soil COS fluxes computed with both the empirical and the mechanistic models at the two sites. The specific leaf area (SLA), maximum rate of Rubisco activity-limited carboxylation at 25 ∘C (Vcmax25), residual stomatal conductance (g0), and minimum photosynthesis temperature (Tmin⁡) have an impact on soil COS fluxes, as they also indirectly affect soil moisture through their influence on transpiration and stomatal opening. The second-order parameters related to soil hydrology (a, Ks, Zroot, θWP, θFC, θR, and θTransp_max) impact the soil water availability, which affects soil respiration for the empirical model and soil COS diffusion and uptake in the mechanistic model. For example, the parameter for the root profile (Zroot) determines the density and depth of the roots and therefore how much water can be taken up by roots.

Figure 6 presents soil COS fluxes before and after optimization of the model parameters to better fit the observations at FI-HYY and US-HA. For the mechanistic model, the optimization at the two sites mainly changes the mean value of soil COS fluxes, by reducing the net uptake at US-HA and increasing it at FI-HYY. Similar to the mechanistic model optimization, the posterior soil COS uptake computed with the empirical model is enhanced at FI-HYY and reduced at US-HA. However, at US-HA, the increase in soil COS uptake is only found between April and October, while the winter soil COS fluxes are not impacted by the optimization. Using the optimized parameterization improves the RMSD by 7 % and 5 % at US-HA and by 23 % and 25 % at FI-HYY for the mechanistic and the empirical model, respectively. While it leads to similar posterior RMSD values between the two models at US-HA, the optimization of the mechanistic model gives a lower RMSD than the empirical model at FI-HYY, with 0.54 pmol m-2 s-1 against 0.95 pmol m-2 s-1.

At FI-HYY, the difference between prior and posterior soil COS fluxes from the empirical model seems to mainly come from the change in the soil_Q10 value (Fig. E1 in Appendix E). The soil_Q10 value drops from 0.83 to 0.53, which corresponds to a prior Q10 value of 2.29 versus a posterior value of 1.70, decreasing the heterotrophic respiration response to soil temperature. Soil COS fluxes computed with the empirical model were found to be strongly sensitive to soil_Q10 (Fig. 5). The posterior value of this parameter has nearly attained the lower bound of its variation range. Since the range of variation represents the realistic values this parameter can take, we need to be careful about the fact that this parameter is trying to take values close to, or potentially beyond, these meaningful values. Furthermore, the optimization deviates the Q10 value at FI-HYY from the ones calculated in the observations over the measurement period (3.0 for soil chamber 1 and 2.5 for soil chamber 2). We could assume that ksoil should be defined as temperature dependent for linking soil COS flux to soil respiration (Berkelhammer et al., 2014; Sun et al., 2018), instead of being considered a constant. Thus, the optimization of the empirical model could in fact be aliasing the error of ksoil onto soil_Q10 because of the impossibility to account for the temperature dependence of soil COS to the CO2 uptake ratio (Sun et al., 2018). At US-HA, the optimization also leads to a decrease in soil_Q10 but to a lesser extent, with the parameter remaining comfortably within its range of variation.

For the mechanistic model, the optimization reduces the enhancement factor value (fCA) for PFT 10 at US-HA and increases the value of the production parameter α for the dominant PFT (PFT 6). This enhances the reduction in net soil COS uptake, which was slightly overestimated with the prior model parametrization. At FI-HYY, the optimized parameters show higher values of fCA and of α for PFT 15 and of both production parameters (α and β) for the dominant PFT (PFT 7). This increase in both soil COS uptake and production after optimization could correspond to an attempt to better simulate the larger range of variation found in the observations compared to the modelled fluxes.

Finally, the optimization also affects hydrology-related parameters for both models. However, while it improves the simulated water content compared to the observations for the mechanistic model at the two sites (RMSD decreases by 28 % at FI-HYY and 22 % at US-HA), it leads to a degradation at FI-HYY for the empirical model (RMSD increases by more than 3 times). Since the empirical model is quite a simplistic model with few parameters, it relies on parameters from different processes to help better fit the observations – sometimes degrading the fit to the other processes. The mechanistic model is able to both improve the fit to the COS observations and soil moisture values, implying its parameterization is more consistent.

This optimization experiment has been promising, highlighting how observations can be used to improve the models. However, since we only optimized over two sites due to the scarcity of soil COS flux observations, for the global-scale simulations in the rest of this study, we will rely on the default parameter values of each parameterization.

The spatial distribution of oxic soil COS fluxes shows a net soil COS uptake everywhere except in India, in the Sahel region, and in some areas in the tropical zone, where net soil COS production is simulated (Fig. 7a). The strongest uptake rates are found in western North America and South America, as well as in China, with a mean maximum uptake of -4.4 pmol COS m-2 s-1 over 2010–2019. The difference in magnitude between the maximum uptake value and the maximum of production can be noticed, with a net production reaching 67.2 pmol COS m-2 s-1 in the Sahel region. India and the Sahel region, where oxic soil COS production is concentrated, are represented in ORCHIDEE by a high fraction of C3 and C4 crops (Fig. S4). In the mechanistic model, crops are associated with the lowest fCA value due to overall lower fungal diversity and abundance in agricultural fields (Meredith et al., 2019) and the strongest response of oxic soil COS production to temperature as observed by Whelan et al. (2016). Thus, these PFT-specific parameters combined with high temperature in the tropical region can explain the net oxic soil COS production found in these regions. C3 crops are also dominant in China near the Yellow Sea (Fig. S4). However, the mean soil temperature in this region is about 15 ∘C lower than the mean soil temperature in India, leading to a lower enhancement of soil COS production. The highest atmospheric COS concentration is also found in this region with about 800 ppt (Fig. S3). Indeed, recent inventories have shown that China was related to strong anthropogenic COS emissions due to industry, biomass burning, coal combustion, agriculture, or vehicle exhaust (Yan et al., 2019; Zumkehr et al., 2018). High atmospheric COS concentrations increase soil COS diffusion and uptake that can compensate part of soil COS production. The highest values of soil COS fluxes for anoxic soils are located in northern India, with a mean maximum value reaching 36.8 pmol COS m-2 s-1 (Fig. 7b). This region is characterized by rice paddies, which were also associated with strong COS production in previous studies (Zhang et al., 2004).

The total soil COS fluxes (oxic and anoxic) computed with the mechanistic model (Fig. 7c) show a very different spatial distribution than the one obtained with the empirical model (Fig. 7d). Soil COS fluxes from the empirical model are on the same order of magnitude for net COS uptake than the mechanistic model, with a mean maximum uptake of -6.41 pmol COS m-2 s-1. However, most soil COS uptakes simulated by the empirical model is located in the tropical region, where soil respiration is strong due to high temperature. The distribution and magnitude of soil COS flux from the empirical approach is similar to the one presented in Kooijmans et al. (2021) (see Fig. S15 in the Supplement of Kooijmans et al., 2021), when implemented in SiB4. For the mechanistic model, the comparison of oxic soil COS flux distribution with the one in SiB4 shows a net soil COS emission in India in both SiB4 and ORCHIDEE. However, the maximum oxic soil COS flux is about 60 pmol m-2 s-1 higher in ORCHIDEE than in SiB4. The regions with the strongest net oxic soil COS uptake also differ between SiB4 and ORCHIDEE, as it is concentrated in the tropics in SiB4, as well as in western North America and South America, and in China for ORCHIDEE.

The difference in soil COS fluxes between the mechanistic model and the empirical model ranges from -4.1 pmol COS m-2 s-1 to +68.0 pmol COS m-2 s-1 (Fig. D1 in Appendix D). Over western North America and South America; northern and southern Africa; western Asia; and eastern, northern, and central Asia, the net COS uptake from the mechanistic model exceeds the uptake from the empirical model. On the contrary, soil COS uptake from the empirical approach is higher than the net COS uptake simulated with the mechanistic model over eastern North America and South America; western, central, and eastern Africa; and Indonesia. The absence of soil COS production representation in the empirical approach leads to the strongest differences in India and in the Sahel region, reaching +68.0 pmol COS m-2 s-1.

We computed the mean annual soil COS budget over the period 2010–2019 using the monthly variable atmospheric COS concentration, and we compared its evolution to the variations in the mean annual atmospheric COS concentration.

The evolution of the mean annual soil COS budget (Fig. 8) shows small variations in the budget for oxic soils computed with the mechanistic model between 2010 and 2015, with a net sink ranging from -133 to -124 GgS yr-1. Then, from 2016 we see a sharp decrease in this budget, which reaches -98 GgS yr-1 in 2019. This decrease also corresponds to the decrease in atmospheric COS concentration observed between 2016 and 2019 with a loss of 25 ppt in 3 years. Several monitoring stations recorded a drop in atmospheric COS concentration over Europe, as for the Gif-sur-Yvette station with -42 ppt between 2015 and 2021 (updated after Belviso et al., 2020). Note that the decrease in the oxic soil COS budget computed with the mechanistic model is sharper than the drop in atmospheric COS concentration because changes in oxic soil COS budget result from the combined effect of decreasing atmospheric COS concentration and changes in the drivers of soil COS fluxes (i.e. changes in soil temperature and water content during the 10-year period which are not homogenously distributed around the globe; not shown). On the contrary, the soil COS net uptake computed with the empirical model slightly increases from -212 GgS yr-1 in 2010 to -219 GgS yr-1 in 2019. As the empirical model defines soil COS flux as proportional to the total soil respiration independently of atmospheric COS concentration, the budget obtained with this model is not impacted by the variations observed in atmospheric COS concentration. The anoxic soil COS budget follows soil temperature variations (not shown), with an increasing trend of about 0.17 GgS yr-1 over the studied period.

We transported total COS fluxes for the different configurations (i.e. including not only the soil fluxes but also other components of the COS atmospheric budget, listed in Table 2) with the LMDZ6 atmospheric transport model as described in Sect. 2.1.3. We analysed COS concentrations derived from simulated COS fluxes obtained with the mechanistic and two empirical approaches with regards to the COS concentrations observed at 14 NOAA sites depicted in Fig. B1 in Appendix B. Note that atmospheric mixing ratios of COS result from the transport of all COS sources and sinks and that, due to other sources of errors (transport and errors in the other COS fluxes), the comparison presented in the following should be taken as a sensitivity study of COS seasonal cycle and interhemispheric gradient to the soil exchange fluxes rather than a complete validation of one approach or the other. Figure 9 shows the COS atmospheric concentrations at NOAA sites as a function of latitude for each simulated soil flux and for the observations. Here as we want to focus on the latitudinal variations in atmospheric COS mixing ratios; the atmospheric COS concentrations have been vertically shifted to have the same mean as the observations. This means that the concentrations values cannot be compared at each site; we can only compare the interhemispheric gradients of simulated and observed concentrations. The RMSD for the mechanistic model with oxic soils only, the mechanistic model with oxic and anoxic soils, the empirical Berry model (with oxic soils only), and the empirical Launois model (with oxic and anoxic soils) are 36.5, 39.4, 43.0, and 51.0 ppt, respectively. While the different approaches show similar gradient patterns in the southern latitudes, they lead to strong differences in the simulated concentrations in the Northern Hemisphere. Compared to empirical approaches, the mechanistic approach marginally improves the latitudinal distribution of the atmospheric mixing ratios by decreasing the concentrations in the high latitudes. The lower atmospheric mixing ratios above 60∘ N reflect the stronger soil absorption in the mechanistic model (see Fig. 9), where soil COS uptake is dominant and the compensation by COS production is small (Fig. D2 in Appendix D). Despite this slight improvement, there are persistent biases as overestimated concentrations at the high-latitude sites ALT, BRW, and SUM and underestimated concentrations at most tropical sites, i.e. WIS, MLO, and SMO. These model–observation mismatches have led top-down studies to identify vegetation as an underestimated sink in the high latitudes (Ma et al., 2021; Remaud et al., 2022) and the tropical oceanic emissions as the missing source (Berry et al., 2013; Launois et al., 2015; Kuai et al., 2015; Ma et al., 2021; Remaud et al., 2022; Davidson et al., 2021). The present anoxic soil fluxes have little impact on the surface latitudinal distributions and therefore are unlikely to shed new light on the tropical missing source. An explanation for the small impact is that they are located outside areas experiencing deep convection events (e.g. the Indian monsoon domain), and thus the surface concentrations are less sensitive to these fluxes.

Figure 10 shows the detrended temporal evolution of COS concentrations for the mechanistic and empirical approaches at Alert (ALT, Canada) and Harvard Forest (HFM, USA). Because of the mean westerly flow, the HFM site is influenced by continental regions to the west (Sweeney et al., 2015) and is more sensitive to the soil fluxes than other mid-latitude sites located to the west of the ocean as MHD; see Fig. 1 in Remaud et al. (2022). The ALT site samples air masses come not only from high-latitude ecosystems (Peylin et al., 1999) but also from regions further south due to atmospheric transport (Parazoo et al., 2011). The reader is referred to Table B2 in Appendix B for the other sites. At both sites, the mechanistic approach tends to weaken the total seasonal amplitude and increase the model–data mismatch. At HFM, since the mechanistic soil model shows overall good agreement with the observed soil fluxes (e.g. Fig. 2), the model–observation mismatch likely arises from errors in other components of the COS budget (in particular oceanic and vegetation fluxes). Therefore, empirical approaches give a more realistic seasonality of atmospheric concentrations for the wrong reasons, which likely hides an underestimated vegetation uptake. Indeed, as Maignan et al. (2021) showed that the vegetation uptake magnitude in ORCHIDEE was consistent with measurements, the introduction of variable atmospheric COS concentrations decreased the vegetation uptake, which, as a result, is very likely underestimated now. Moreover, the comparison between simulated and observed concentrations shows a degradation of the simulated concentrations in this study compared to Maignan et al. (2021). It is to be noted that in addition to using a variable atmospheric COS concentration in this study, the transported ocean COS fluxes from Masotti et al. (2016) and Lennartz et al. (2017, 2021) differ from the ones used in Maignan et al. (2021), Kettle et al. (2002), and Launois et al. (2015). These results illustrate the necessity of well constraining both the soil and vegetation fluxes in order to optimize the GPP with the help of atmospheric inverse modelling.