OCS is emitted from the oceans to the atmosphere either directly, because surface waters are generally supersaturated in OCS, or indirectly through oxidation of atmospheric dimethylsulfide (DMS) and carbon disulfide (CS2) which are both produced in the surface layer of the ocean. Oceans are a major source of OCS (Kettle et al., 2002). Berry et al. (2013) found that the marine source accounted for 876 Gg S yr-1, about 74 % of total sources, but this estimate was not well constrained since the authors increased the direct marine emissions of Kettle et al. (2002) by 600 Gg S yr-1 to provide a balanced global budget of OCS (Table 2).

Here, the direct emissions are based on parameterizations of ocean production and removal processes of OCS implemented in the NEMO-PISCES oceanic general circulation and biogeochemistry model (Launois et al., 2015). These parameterizations lead to a direct ocean emission of 813 Gg S yr-1. We further accounted for indirect emissions of OCS both from DMS and from CS2. Details of the parameterizations for the direct and indirect ocean emissions are provided in Appendix A1. Note that for the optimizations, we scaled the standard direct and indirect emissions within a range of variation of -30 to 50  %.

OCS and CO2 both diffuse through plant stomata into the leaves. CO2 and OCS are both hydrated in leaves by the carbonic anhydrase enzyme (Protoschill-Krebs and Kesselmeier, 1992; Protoschill-Krebs et al., 1995, 1996; Stimler et al., 2010), following the reactions: H2O+CO2↔H2CO3↔HCO3-+H+,OCS+H2O↔HCOOS-+H+↔H2S+CO2.

Since HCOOS- and H2S are found at very low concentrations in plant cells and soil water (Stimler et al., 2010) and H2S formation is exergonic, thus spontaneous, the hydration of OCS leads irreversibly to the formation of H2S (Schenk et al., 2004). Irreversible hydrolysis of OCS is therefore expected within leaves during photosynthesis (Wöhlfahrt et al., 2012; Simmons et al., 1999; Stimler et al., 2010). OCS and CO2 are both potential substrates for RuBisCO, but CO2 is favored over OCS by a factor 110 for species studied by Lorimer and Pierce (1989). Stimler et al. (2010) noted that no significant cross-inhibition was measured between OCS and CO2 uptakes.

Different approaches can be used to model leaf uptake of OCS, from process-based formulations with an explicit representation of diffusion and hydration of OCS as in Berry et al. (2013) to more simple parameterizations where the uptake of OCS is expressed as a linear function of GPP: FOCS=kplant_uptake×(kLRU×GPP), where kLRU is the leaf relative uptake of OCS compared to CO2 (normalized by their ambient concentrations) and defined for different plant functional type. KLRU is species-specific and several studies have focused on the quantification of this coefficient (Sandoval-Soto et al., 2005, 2012; Stimler et al., 2010; Seibt et al., 2010). We took this latter approach with KLRU values from Seibt et al. (2010). We also added a global scaling parameter, kplant_uptake, to further optimize the relative OCS to CO2 uptake through the inversion scheme. Set to an initial value of 1, kplant_uptake is allowed to vary in the optimization from 0.5 to 1.5, representing a ±50 % uncertainty range on initial estimate of surface fluxes (Table 1). Note that the KLRU values from Seibt et al. are in the upper range of recent estimates. A few more details about the implementation of this parameterization can be found in Appendix A2.

The general picture is that oxic soils are a sink of OCS while anoxic soils are a source (Whelan et al., 2013).

OCS uptake by oxic soils is believed to be essentially a microbial and enzymatically driven process with carbonic anhydrase and OCS hydrolases playing central roles (Chin and Davis, 1993a, b; Seibt et al., 2006; Wingate et al., 2008; Ogawa et al., 2013). There are also clear indications that OCS soil uptake varies according to soil type, temperature and soil water content (Kesselmeier et al., 1999; Van Diest and Kesselmeier, 2008). Previous studies used different approaches based either on temperature and water content (Kettle et al., 2002) or on soil heterotrophic respiration (which tracks microbial activity) and the fraction of water filled pore space (Berry et al., 2013). Here we propose a new approach, based on observed co-variations of OCS and dihydrogen (H2) deposition to soils and the existence of global H2 deposition maps. Consequently, OCS uptake by soil is represented in our model as FOCS=ksoil×νH2×ν_cos_νH2×[OCS]atm, where νH2 is the deposition velocity of H2 into the soil (cm s-1), ν_cos⁡_νH2 the relative ratio of OCS and H2 deposition velocities and [OCS]atm the atmospheric concentration of OCS (in ppt). νcos⁡/νH2 was set to an initial value of 0.75 in the standard run (following Belviso et al., 2013, and H. Chen et al., personal communication, 2014). As for leaf uptake, a scaling parameter, ksoil, is added to optimize the global uptake of OCS by soils. Details about the overall approach and the global H2 deposition fluxes (taken from a model simulation (Morfopoulos et al., 2012) for our standard simulations and from Bousquet et al. (2011) for tests) can be found in Appendix A3. Given the uncertainties associated with the νH2 estimates and the ratio νcos⁡/νH2 the surface fluxes were further optimized with a 30 % range of variation for ksoil coefficient (Table 3).

The role of soils in the OCS budget was recently reviewed by Whelan et al. (2013), with special attention to anoxic soils. The authors underlined the major influence of soil temperature and flooding on OCS emissions from anoxic soils and wetlands. Therefore, we followed their approach but used a model simulation for the spatial and temporal distributions of anoxic soils (from Wania et al., 2010). More details on this OCS source can be found in Appendix A4. For optimization purposes, we defined a scaling parameter, kanoxic_soil (set to a prior value of one), that is optimized with an assigned ±30 % variation range (Table 1).

Other sources are related to biomass burning and anthropogenic emissions. OCS emissions from biomass burning were simulated from the gridded CO2 emission maps of Van der Werf et al. (2010) (GFEDv3 product) rescaled to a source of 70 Gg S yr-1, as estimated by Nguyen et al. (1995). The associated uncertainty (maximum range of variation) was set to ±10 %. For anthropogenic emissions (both direct and indirect), we took the fluxes proposed by Kettle et al. (2002). These fluxes were attributed a ±10 % maximum variation in the optimization scheme. Additional direct and indirect emissions of OCS from volcanoes were neglected because they are highly uncertain (Belviso et al., 1986).

The removal of atmospheric OCS by OH radicals is also a significant sink of OCS. We used monthly maps of OH radicals concentration (integrated vertically up to the tropopause) from Hauglustaine et al. (1998), to distribute both horizontally and temporally a total annual atmospheric sink of 100 Gg S yr-1, as suggested in previous global budgets (Kettle et al., 2002; Berry et al., 2013). This flux was attributed a ±30 % maximum variation in the optimization scheme.

For the purpose of this study, three independent DGVMs have been used: LPJ, ORCHIDEE (referred as ORC) and CLM4CN. We used the simulated GPP from each model that was performed for the TRENDY inter-comparison experiment (http://dgvm.ceh.ac.uk/) designed to evaluate global carbon budgets and regional trends of the land carbon sinks over the 1990–2009 period. We took the simulated values over the period 2006–2009 where the models were run with the same 11 climate forcing, variable atmospheric CO2 concentrations and fixed land cover (as a first-order analysis). Details about the DGVMs and the simulations can be found in Sitch et al. (2015); additional information is available in Appendix A5.

The simulated mixing ratios were obtained using the global atmospheric circulation model (GCM) of the Laboratoire de Météorologie Dynamique (LMDZ, version 3; Hourdin et al., 2006). The OCS surface fluxes described above are transported in offline mode using the LMDZ transport model, nudged with wind from the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis. The transport model uses a 3.75∘ × 2.5∘ (longitude × latitude) horizontal resolution and 19 vertical layers between the surface and the top of the troposphere. LMDZ has been previously used in many tracer transport studies (Chevallier et al., 2010; Carouge et al., 2010a, b). In this study we used pre-calculated transport fields, corresponding to the sensitivity of the monthly concentration at each site with respect to the daily surface fluxes for all pixels of the transport grid (see Peylin et al., 2005). These pre-calculated sensitivities were derived from the adjoint of the transport model and were multiplied by the surface fluxes to get the atmospheric OCS concentration. They will also be directly used in the inversion (see below) as the optimization algorithm requires the sensitivity of the concentrations to the surface fluxes.

An optimization algorithm was used to correct the surface OCS fluxes in order to improve the simulation of atmospheric OCS temporal and spatial gradients. The optimization scheme relies on a Bayesian framework that accounts for prior knowledge of the surface fluxes (Tarantola, 1987). Each flux has been assigned a scalar coefficient x (see Sect. 2.2) to account for uncertainties in the calculation of the OCS fluxes. These coefficients are the optimized variables (global scaling factors) for all OCS surface flux components described above. Their optimization will provide a better agreement between modeled and observed atmospheric OCS concentrations. The allowed range of variation for each coefficient, x, was determined from an analysis of the uncertainties (see Sect. 2.2).

The optimization is based on a 5-year-long simulation covering the 2004–2009 period, long enough to characterize broad atmospheric OCS concentration features (trends and mean seasonal cycles). OCS monthly mean concentrations are used as the observational constraint in the optimization.

Assuming a Gaussian probability density function (PDF) distribution for the measurement errors, model structure errors (including flux and transport models) and model parameter errors (flux scalars), the optimal set of parameters under the Bayesian framework corresponds to the minimum of the following cost function J(x) (Tarantola, 1987): Jx=Y-MxTR-1Y-Mx+x-xpTB-1x-xp, x represents the parameters to be optimized (i.e., the OCS surface flux scalars), xp their a priori values, Y the vector of observations (i.e., the measured OCS mixing ratios at NOAA sites), and M(x) the model outputs (i.e., the OCS mixing ratios simulated with the LMDZ transport model). R and B are error variances/covariances matrices associated to the observations and the parameters, respectively.

Details about the optimization scheme (gradient-based algorithm with imposed range of variation) as well as the setup of the inversions (uncertainties on the observations and parameters) are presented in Appendix A6. We performed standard optimizations with the OCS leaf uptake derived from each DGVMs and a large range of variation for the scaling parameters but also a few additional sensitivity optimizations summarized in Sect. 2.5.

A series of simulations was performed, for which the setups are summarized in Table 1. We carried out three major runs using the three different DGVMs (STD_ORC, STD_LPJ, STD_CLM4CN, see Table 1 for details). We made four sensitivity experiments to the representation of soil OCS uptake (with ORC for plant uptake) varying the H2 flux from Morfopoulos et al. (2012) (MORF) to Bousquet et al. (2011) (BOUSQ) and varying the ratio of OCS to H2 uptake as follows: TEST_SOIL_MORF_1:1, TEST_SOIL_MORF_0.5:1, TEST_SOIL_BOUSQ_1:1, TEST_SOIL_BOUSQ_0.5:1. We also undertook two sensitivity experiments varying the magnitude of the oceanic emissions by ±30 % (TEST_OCE_+30 and TEST_OCE_-30). The other surface fluxes were kept unchanged in all sensitivity tests.

An additional series of simulations was performed to calculate CO2 concentrations at the same stations. The LMDZ transport model was forced with the net ecosystem carbon fluxes from the same three vegetation models (ORC, LPJ, CLM4CN), also using the air–sea exchange from the climatology of Takahashi et al. (2009), biomass burning fluxes from GFEDv3.1 (Van der Werf et al., 2010) and fossil fuel emissions from EDGAR-v4.1 (Marland et al., 1999). Simulations with only the gross ecosystem carbon fluxes (GPP and respiration) were also performed separately, to show the individual impact of the two gross fluxes on the CO2 seasonal cycle at all stations.

Optimization experiments of the surface fluxes (optimization of a scaling coefficient for each OCS flux component; see Sect. 2.4) were conducted, based on the three different vegetation models. For each model, we tested five scenarios (see Table 1):

OPTIM_H-Er: marine, soil and vegetation fluxes are allowed to vary over a large range (up to 50 %)

Observed and simulated monthly OCS and CO2 concentrations were processed to derive mean seasonal cycles and mean annual trends. To accomplish this, raw data were fitted with a function including a polynomial term (first order) and four harmonics. The residuals of the functions were further smoothed in the Fourier space, using a low-pass filter (cutoff frequency of 65 days) to define a so-called smoothed curve (function plus filtered residuals). The mean seasonal cycle is defined from the smoothed curve after subtraction of the polynomial term. The mismatches between simulated and observed concentrations is also analyzed in terms of bias, phase and variance, following the mean square error (MSE) decomposition of Kobayashi and Salam (2000): MSE=Xi-Xi′2+σi-σi′2+2σi×σi′1-r2.

The meaning of the squared data bias is obvious. The second term indicates differences in the fast variability: the lack of correlation (r) between Xi and Xi′ is an estimator for phase errors.

Following the standard run defined by Launois et al. (2015), oceans emit a yearly total of 813 Gg S (Table 2). The spatial distribution indicates a large tropical ocean source (45 % of total OCS emissions). Overall, our simulation provides direct oceanic emissions that are about 20 times larger than those from Kettle et al. (2002) and that are roughly comparable to the estimates from Berry et al. (2013), obtained using an optimization procedure (Table 3). Details about the regional and seasonal distribution of these emissions can be found in Appendix A7.

On a yearly and global basis, the oceans are also a net source of DMS and CS2 to the atmosphere. In NEMO-PISCES, each year 133 Gg S of OCS are indirectly injected into the atmosphere from DMS, assuming that 0.7 % of the total emissions are converted into OCS. This estimate is in good agreement with that of Kettle et al. (2002). Ocean fluxes of CS2 rely on those of Kettle et al. (2002), since they are not parameterized in NEMO-PISCES. Globally, CS2 indirectly brings 81 Gg S yr-1of OCS into the atmosphere, as 87 % of the CS2 is assumed to be oxidized into OCS. For more details, see Appendix A7.

As described in Sect. 2.2, the standard run for oxic soil uptake of OCS is obtained using the H2 monthly soil uptake by Morfopoulos et al. (2012) and 0.75 as the ratio between the deposition velocities of OCS and H2. The resulting OCS fluxes (see Fig. 1 for January and July maps) range between 0 and 15 pmol m2 s-1; they lead to a global annual uptake of 510 Gg S (Table 2), which is 3 times larger than the soil uptake modeled by Kettle et al. (2002) and 40 % larger than the one reported by Berry et al. (2013). Using a different H2 flux map (from Bousquet et al., 2011) and ratio between the deposition velocities of OCS and H2 significantly change the global OCS uptake, its regional distribution and its seasonal variations. More details about the regional distribution of the oxic soil uptake can be found in Appendix A7.

The emissions from anoxic soils, as described in Sect. 2.2, mainly take place in the northernmost regions (above 60∘ N), where fluxes up to 12.5 pmol m2 s-1 were simulated (Fig. 1). Total emissions are estimated to be 101 Gg S on an annual basis (Table 2). OCS emissions by peatlands can turn the extratropical regions of the Northern Hemisphere into a net source of OCS in late autumn and winter.

Overall, at a global scale, soils constitute a net sink of OCS. In the Northern Hemisphere, our estimated sink is lower than that of Kettle et al. (2002) and that of Berry et al. (2013) where the OCS emissions by anoxic soils were not taken into consideration. Details of the regional and spatial variations of the net OCS soil fluxes can be found in Appendix A7.

Global maps of OCS mean uptake by plants for the months of January and July constructed from the GPP of the ORC model are shown in Fig. 1 (bottom). Using ORC, plants take up 1335 Gg S yr-1 (Table 1), which is a considerably larger sink than that modeled by Kettle et al. (2002) or Berry et al. (2013). This yearly global uptake is strongly model dependent as shown in Table 2 and Fig. S3. Given the linear dependence of OCS uptake to GPP (Eq. 2) the spatial gradients and the phase and amplitude of the seasonal cycle of OCS plant uptake follow those of the GPP. In particular the seasonal cycle shows a distinct peak at high latitudes. Differences between the GPP of the three models are large, especially in terms of amplitude (60 % difference between the models) and to a small extent in terms of phase of the seasonal cycle (1-month shift) (see Fig. S3 for integrated values over latitudinal bands of the Northern Hemisphere). The main spatial and temporal pattern differences are discussed in Appendix A7.

An OCS sink of about 100 Gg S yr-1 representing photochemical oxidation by OH radicals was implemented, (see Sect. 2.2). The global annual destruction of OCS is relatively evenly distributed, with seasonal variations higher at high latitudes than in the tropics.

The direct and indirect anthropogenic fluxes were taken from Kettle et al. (2002), who estimated that 180 Gg S are emitted on an annual basis, without strong seasonal variations. Eastern Asia, eastern Europe and the eastern parts of Canada and the United States concentrate most of the emissions.

As described in Sect. 2.2, the OCS emissions from biomass burning are proportional to the emissions of CO2, and therefore 60 % of the global emissions come from tropical regions.

Table 2 provides an overview of the global sources and sinks of OCS. Only Kettle et al. (2002) and Berry et al. (2013) have provided balanced budgets between sources and sinks, but it is worth remembering that Berry et al. (2013) artificially increased the marine emissions of Kettle et al. (2002) by 600 Gg S yr-1 for this purpose. Other global budgets, including ours, are largely unbalanced, with sinks exceeding sources by hundreds of Gg S yr-1. The budget of Montzka et al. (2007) and the one we derived using ORC's GPPs are the most unbalanced (-776 and -566 Gg S yr-1, respectively).

Figure 2 compares the simulated monthly mean atmospheric OCS concentrations with the observations at Mauna Loa (MLO), a mid-latitudinal background station in the middle of the tropical Pacific Ocean (20∘ N, altitude 3500 m). This site therefore represents the integrated contribution of the surface fluxes from the entire Northern Hemisphere (Conway et al., 1994). Since the three global budgets (with the three DGVMs) are not balanced with large sinks (Table 2), the simulations show large negative annual trends of the atmospheric OCS concentrations (23 to 70 ppt yr-1), which are inconsistent with the observations. Kettle et al. (2002) proposed a roughly balanced OCS budget but with too small seasonal variations when compared with the observations. The situation at South Pole (SPO) resembles that at MLO in terms of annual trends (Fig. 3)

Results of sensitivity tests on the ocean OCS source (see Sect. 2.5) are displayed in Fig. 3. Changing the ocean source significantly (by ±30 %) impacts the simulated trend and only marginally the phase and amplitude of the seasonal cycle (except at SPO). In the case of ORC, the test TEST_OCE_+30 provides a global budget close to equilibrium.

Figure 4 (left panel) shows the impact on the annual trend at MLO of four sensitivity tests on the calculation of oxic soils OCS uptake (see Sect. 2.5). The annual trend is more affected by changes in νOCS/νH2 ratios (25 ppt yr-1 between the 1:1 and 0.5:1 ratios) than by changes in the way H2 deposition velocities have been estimated (10 ppt yr-1 difference between the TEST_SOIL_MORF and TEST_SOIL_BOUQ simulations). However, changes in OCS uptake by oxic soils cannot compensate entirely for the strong negative trend imposed by the vegetation sink deduced from ORC GPP.

Figure 5 (right panels) compares the smooth seasonal cycle of OCS concentrations of three different simulations, the concentrations deduced from Kettle inventory and the observations at the South Pole (SPO), Alert (ALT) and MLO stations. The ALT data help in exploring the influence of boreal and temperate ecosystems of the Northern Hemisphere on the biogeochemical cycle of OCS, while SPO station combines the southern ocean and land influences. The simulation based on Kettle et al. (2002) fluxes exhibits amplitudes which are unrealistically low and not in phase with the observations at ALT and MLO. At SPO, on the contrary, Kettle et al. (2002) fluxes produce a good fit to the observations, both in terms of seasonal amplitude and phase. At SPO, our three models simulate slightly larger amplitudes (+ 10–15 ppt relative to observations) and a slight shift in the OCS maximum during austral summer.

The ORC model displays the highest seasonal amplitudes both at ALT and MLO where the northern vegetation influence dominates seasonal variations (around 250 and 80 ppt, respectively). These variations are unrealistically high compared to the observations (100 and 55 ppt, respectively). However, ORC shows seasonal OCS variations more in phase with the observations than when using the two other DGVMs' GPP, especially at ALT. Using CLM4CN leads to the right amplitude of the seasonal variations in OCS concentrations at ALT, but the phase is incorrectly represented (earlier OCS build-up and draw-down). This model provides a better representation of the phase of the OCS cycle at MLO but leads to a 10 % underestimation of the OCS seasonal amplitude at this station. With the data shown in the right panels of Figs. 3 and 4, we aim to characterize the sensitivity of seasonal variations to changes solely in marine emissions and in the soil sink, respectively (following sensitivity experiments described in Sect. 2.5). At MLO, both the phase and the amplitude of the seasonal variations are unaffected by changes in marine emissions (Fig. 3) or oxic soils uptake (Fig. 4). At SPO, a 30 % increase of the ocean flux leads to about 10 % increase in amplitude of the seasonal variations (Fig. 3). Similar experiments were conducted to evaluate the contribution of plant uptake on the overall seasonality of atmospheric OCS (runs where only the plant uptake is transported). Figure 6 shows that the amplitude and the phase of the seasonal variations at ALT and MLO are both primarily determined by the uptake of OCS by vegetation. On the other hand, plant uptake plays a minor role on the seasonality at SPO.

Annual mean mixing ratios for the 10 stations of the NOAA monitoring network, plotted as a function of latitude, are shown in Fig. 7. Note that the simulated global mean OCS concentration (across all sites) has been rescaled to the observed global mean, so that only the gradients between stations should be investigated. The main results from this hypothesis are

Our new OCS surface flux scenarios capture the main differences in annual mean concentration between stations with lower concentrations at continental stations in the Northern Hemisphere (LEF, BRW, ALT) than at background stations as in the Southern Hemisphere (around 50 ppt lower).

The OCS monthly mean concentrations simulated with the optimized surface fluxes of the OPTIM_H-Er scenario (large range of variation for the optimized parameters) are shown in Fig. 8. Allowing a 50 % range of variation on the surface fluxes is sufficient to yield equilibrated global budgets after optimization, in agreement with the observations (see the last line of Table 3). Overall, the total sink is decreased in all optimization results, from an average value (all three DGVMs included) of 1721 Gg S yr-1 in the prior simulation to 1218 Gg S yr-1 after optimization, thus a 29 % reduction. The source flux estimates were also reduced by 13 % on average, from 1379 Gg S yr-1 in the prior simulation to 1204 Gg S yr-1 after the optimization. The new simulated global budgets are almost balanced (-1 to -20 Gg S yr-1) and the annual trend significantly reduced (Fig. 8 versus Fig. 2), especially for ORC (-566 to -10 Gg S yr-1 ).

The soil uptake of OCS is reduced as much as 45 % even if the maximum range of variation allowed is 50 %. The leaf uptake of OCS is also not reduced by the maximum amount when given a variation limit of 50 %. On average, vegetation and soil optimized uptakes are respectively converging around 714 and 396 Gg S yr-1 (Table 3). The atmospheric destruction of OCS by OH radicals and some sources were also optimized at their maximum allowed values (e.g., emissions by anoxic soils, indirect oceanic emissions and indirect anthropogenic emissions).

In the low variation range scenario (OPTIM_L-Er), a negative trend of about 30 ppt yr-1 remains in ORC (Fig. 8). This OPTIM_L-Er configuration could be thought as a theoretical case where the values of kLRU (for OCS leaf uptake) are well constrained and the fluxes are controlled by soil, ocean and anthropogenic processes. In this theoretical case, the mismatch between the simulated and observed annual trend for ORC suggests that

the vegetation plays a determining role in the OCS global atmospheric budget

Figure 9 shows the OCS mean seasonal cycles before and after optimization using the three DGVMs. At most NOAA stations, the optimization of the surface fluxes significantly improves the simulated seasonal amplitude of the atmospheric OCS concentrations, with a global reduction of the MSE (in ppt2) from 162 (83) to 29 (29) ppt for ORC (LPJ) and from 43 to 35 ppt for CLM4CN. Although all optimizations lead to a significant improvement of the amplitude of the OCS cycle, differences between the three models remain:

With the ORC model, the standard OPTIM_H-Er configuration strongly reduces the amplitude of the simulated OCS seasonal cycle, especially at high latitudes (e.g., from 225 to 140 ppt at ALT). The resulting amplitudes are more consistent with the observations but are still too large at high latitudes (140 versus 100 ppt at ALT). At MLO, the amplitude of the OCS levels is reduced from 80 to 45 ppt, a value slightly lower than the observations (50 ppt). Finally, we also note that scaling the surface fluxes through the optimization leads to negligible modifications of the phase of the simulated OCS concentrations.

Figure 10 presents annual mean OCS mixing ratios at all stations as a function of the latitude before and after optimization. The overall improvements from the optimization are summarized with the mean of the MSE for all sites (see the legend). Posterior MSEs are similar between the three scenarios (around 24 ppt2) and the reduction between the prior and the posterior MSEs are equivalent to 74, 31 and 27 % for ORC, CLM4CN and LPJ respectively. Note that such improvement is much smaller than for the seasonal cycle where MSE decreases by 82, 19 and 65 %, respectively (see Fig. 9). The large reduction of the soil and leaf OCS uptakes through the optimization (see Table 3) helps reducing initial differences in the spatial gradients between stations. For example, the simulated difference between SPO and CGO stations in the Southern Hemisphere drops from 10–25 to 2–10 ppt in closer agreement with the observations (around 1 ppt).

As shown in Fig. 11, the optimization successfully corrects the annual trends, for most scenarios. For ORC, the global budget is closed only if the leaf uptake is decreased by 45 %, which is not possible in the low error test. This suggests that LRU values provided by Seibt et al. (2010) are likely too large. Future studies would benefit from using lower LRU values, such as those published in other studies (Sandoval-Soto et al., 2005; Stimler et al., 2012; Berkelhammer et al., 2014). Lower LRU values also correspond to a test in Seibt et al. (2010) where the internal mesophyll conductance is set as the major limitation in the diffusional pathway of OCS (average LRU would be 2.08 with this assumption, instead of 2.8 as used in the present paper). Moreover, several studies have shown that OCS-to-CO2 uptake ratio could be plant-specific (Sandoval-Soto et al., 2005; Campbell et al., 2008; Seibt et al., 2010; Stimler et al., 2012; Berkelhammer et al., 2014) and even that, under certain conditions, some plants can release some of the absorbed OCS (Xu et al., 2001; Geng and Mu, 2006; White et al., 2010). Therefore, recent estimates of the vegetation OCS uptake are still largely uncertain and differ by up to a factor of 6 (Xu et al., 2001; Kettle et al., 2002; Sandoval-Soto et al., 2005; Berry et al., 2013).

Optimizing only one flux component is usually enough to correct the trend, except for ORC, pointing out again the likely too high leaf uptake, which can be due to overestimated LRU or too large GPP

Looking at the phase component of the MSE decomposition, a few general features can be drawn:

On average, only small changes are observed at most sites between prior and posterior estimates (only shown for MLO and ALT, Fig. 11, second and third rows). A 35 % reduction of the phase error is observed at MLO for ORC and also a 25 % improvement for LPJ.

The improvement compared with the prior main results from the optimization of the OCS leaf uptake.

We use the bias estimates from the MSE decomposition, which also accounts for any remaining trend mismatch, to analyze the annual mean gradients. As demonstrated by the results of the optimization of only one component (OPTIM_XXX_ONLY tests), all processes make a similar impact on the annual mean OCS concentrations. However, the optimization scheme leads to a degradation of the bias at MLO for the three models and the bias remains highly variable at other sites. The constraint imposed by the annual mean gradients cannot be significantly improved through optimization. The overall fit at some stations can be decreased (see for instance CLM4CN at MLO, Fig. 11) because of compensation by improvements at other sites. When testing the impact of the observation errors on the optimization, including a test with equal observation errors (18 ppt), the results were not substantially modified.

The analysis of the concentrations at boreal stations provides a first hint on northern high-latitude ecosystems. Both OCS and CO2 simulated seasonal amplitude are too large at ALT (by factors of 2 and 1.5, respectively). While the analysis based soley on CO2 would suggest either too large a GPP during boreal summer or too small an amplitude of the respiration seasonal cycle, the additional OCS diagnosis indicates that the GPP of ORC is indeed too large for high-latitude ecosystems. For OCS, uncertainties in LRU values also contribute to the model data mismatch. As suggested by Berkelhammer et al. (2013) the LRU values from Seibt et al. (2010) are on the upper range of the different estimates published so far (+ 30 % compared to the mean estimates). However, a 45 % reduction of the LRU that corresponds to the optimized fluxes of the INV_H-Er case (see Table 3) still produces an amplitude of the seasonal cycle at ALT larger than the observation by a factor 1.3 (Fig. 12). Such a remaining discrepancy thus confirms that ORC GPP is most likely overestimated at high latitudes. Note that for both tracers the phase of the seasonal cycle is relatively well captured (Fig. 5).

The signal at MLO integrates the contribution from the land (and ocean) fluxes of the whole Northern Hemisphere. In this case, there is relatively good agreement for the phase and amplitude of the CO2 seasonal cycle, while for OCS the amplitude is still too large (by a factor of 1.5). This suggests that the chosen LRU values are indeed too large and that too small GPP values at the mid- and low latitudes may compensate for the too large GPP values for boreal ecosystems, noted above. The result of the standard optimization leads to the right amplitude at MLO, which further indicates that the 50 % global reduction of OCS leaf uptake is sufficient on average to compensate for too high a GPP at northern ecosystems and potentially too large an LRU.

The seasonal cycle at the remote SPO station is more difficult to interpret as (i) the amplitude of the cycle is 8 times smaller than at MLO for CO2 and (ii) all surfaces fluxes (i.e., from leaf, soil, and ocean) have a shared contribution to the overall seasonal cycle. The too large amplitude of ORC for CO2 reflects discrepancies in both GPP and respiration fluxes, but also in air–sea exchanges.

Overall, the joint OCS/CO2 analysis points towards discrepancies in the ORC GPP, with overestimated values at high northern latitudes. Such conclusion directly corroborates the results obtained by Kuppel et al. (2014), using the same ecosystem model, when optimizing its parameters with eddy-covariance flux measurements (CO2 and latent heat flux). They proposed a large reduction of the GPP for boreal broadleaf and boreal needleleaf forests.

The amplitude of the seasonal cycle simulated with CLM4CN is underestimated at nearly all stations for both OCS and CO2, with a modeled-to-observed ratio between 0.6 and 0.9, except at CGO where the amplitude is overestimated (Fig. 12). Moreover, as shown in Fig. 5, the phase shift in the OCS seasonal cycle at boreal stations (i.e., ALT) also occurs for CO2, with an earlier drawdown of the modeled concentrations compared to the observation (around 2 months). Such phase shift is much smaller or close to zero at temperate and low-latitude stations of the Northern Hemisphere.

The combined OCS and CO2 discrepancies point toward biases in the CLM4CN simulated gross carbon fluxes. First, the GPP of northern high-latitude ecosystems is most likely out of phase, with a too strong increase of photosynthesis in spring. Using only the CO2 tracer would suggest that one or both gross carbon fluxes are out of phase (photosynthesis and respiration). The benefit of the OCS tracer is to clearly point toward GPP as the major source of discrepancies, given that for OCS the leaf uptake, which is proportional to GPP, drives the overall seasonal cycle (see Fig. 6). Second, the amplitude of the GPP is also most likely underestimated for most ecosystems. While the CO2 concentrations do not allow one to find cause in GPP rather than respiration, the OCS points again towards too small a GPP during the peak of the growing season.

Increasing CLM4CN GPP by 20 % and shifting its seasonal course by 2 months for high latitudes would create a significant improvement of both OCS and CO2 simulated concentrations. At SPO, the CO2 seasonal cycle is in good agreement with the observations, while the OCS seasonal cycle shows too large an amplitude and an earlier maximum – similarly with the two other DGVMs.

Using the GPP from LPJ leads to intermediary results for the seasonal amplitude, for both tracers, with no systematic biases across stations (Fig. 12). If we consider boreal stations, the modeled seasonal amplitude for CO2 is 20 % lower than the observations, while for OCS it is 50 % higher. As noted above, the temporal variation of the OCS concentrations at these sites is slightly out of phase, with a too early drawdown in spring. This would suggest that the increase of boreal ecosystems GPP in spring is too early and too strong in LPJ (see for instance Fig. S4 in the Supplement). However, matching both OCS and CO2 atmospheric signals would also require a change in the temporal variation of the ecosystem respiration (to fit the CO2 signal).

At MLO, the phase shift becomes much lower for OCS. The too low amplitude for CO2 would suggest that either the GPP is underestimated during the peak of the growing season (it is much smaller than when using ORC, see Fig. S4) or that the respiration is too large during summertime. The OCS diagnostic with slightly too large amplitude at MLO (Fig. 5) suggests that (i) the main bias comes from the respiration, and (ii) the LRU values from Seibt et al. (2010) are likely overestimated (as already pointed out), which would explain the too large amplitude for OCS. As can be seen in Fig. S4, the LPJ model is the only one with respiration fluxes of the same magnitude as GPP fluxes, in temperate northern regions during mid- and late summer. Reducing the intensity of the respiration during this period would allow for larger annual variations of the CO2 concentrations, more consistent with the observations while still keeping the correct GPP-based representation of the OCS leaf uptake.

Overall, the above joint OCS and CO2 analysis points towards deficiencies for each model's gross carbon fluxes. The results obtained for the combined OCS-based and CO2-based analyses are coherent between the three models. For instance, the decrease of ORC GPP for temperate and high-latitude ecosystems or the phase shift of CLM4CN GPP would bring the different GPP estimates close together. However, some caution is still needed before drawing firm conclusions. For instance we should further investigate the following:

the spatial and temporal variations of the OCS-to-CO2 uptake ratio (LRU). More recent estimates based on additional in situ measurements are likely to provide lower LRU values than those of Seibt et al. (2010). LRU values have also been proven to vary depending on available light, and therefore to change according to seasons (Maseyk et al., 2014).