Carbonyl sulfide (COS), a trace gas showing striking similarity to CO

Globally, the amount of carbon assimilated by plant photosynthesis, known as gross primary productivity (GPP), exceeds plant respiration by a few GtC yr

The two most common methods for estimating ecosystem-wide GPP and respiration are based on eddy covariance measurements and land surface models (LSMs). While eddy covariance measurements, on one hand, can be used to routinely estimate GPP and respiration at the local scale, their extrapolation to a whole biome is not straightforward due to their small footprint

Carbonyl sulfide (COS) is recognized as a promising tracer of GPP at the leaf scale

The terrestrial sink induced by both plants and soils has been estimated between 500–1200 GgS yr

As an alternative to modelling direct emissions, attempts
have been made to constrain the COS budget through inverse or “top-down” approaches. With the help of a transport model and a priori information, these approaches adjust the surface fluxes to better match simulated atmospheric concentrations with observations. Previous top-down assessments of the COS budget identified the missing source as likely being from the ocean, with a total oceanic release between 500 and 1000 GgS yr

Here, we present an update of the

We assume a linear relationship between GPP and biospheric COS uptake under a leaf relative uptake (LRU) approach. We also take advantage of the additional sophistication of the inversion system to assimilate COS measurements together with CO

The objectives of our study are threefold:

evaluate the analytical inverse system applied for the first time to the joint assimilation of COS and CO

provide an improved COS budget estimate, and

provide improved estimates of GPP and respiration based on the joint assimilation of COS and CO

We simulate the global atmospheric transport at a spatial resolution of

For the sake of simplicity, we refer to LMDz as the offline model in the following.
LMDz is weakly non-linear with respect to the surface fluxes,
following the use of slope limiters in the

In our study, we assimilate LMDz to one of its Jacobian matrices: we linearized LMDz beforehand around a top-down estimation of the CO

In practice, we considered 8 d average synthetic observations at each selected measurement site (see Sect. 2.2.1) between 2008 and 2019. The implication is that the atmospheric transport model can not represent the temporal variability within a week. For sites below 1000 m a.s.l., only afternoon observations were used as the models do not simulate the accumulation of the tracers in the nocturnal boundary layer well

In total, we have computed 15 stations

As explained below in Sect. 2.4.2, LMDz is complemented here for the modelling of COS in the atmosphere by a chemical sink, represented by a surface flux.

We used the NOAA/ESRL measurements of both CO

The Jacobian matrix

Annual climatology of Jacobians computed by the adjoint of the LMDz model: map of the partial derivatives, in ppm kg

Note that, if computed with respect to the COS fluxes, the annual climatology of the Jacobian shown in Fig.

An ensemble of independent observations – i.e., data that are not assimilated in LMDz – is used to evaluate the fluxes retrieved by our inverse system. We focus here on the observations used to evaluate the COS and the GPP fluxes.

The first observation programme is the HIAPER Pole-to-Pole Observations (HIPPO;

In order to assess the north–south latitudinal COS gradient over Japan, surface measurements for winter and summer 2019 at three sampling sites in Japan from

The French sampling site, GIF (48

The fourth observation programme is made of the satellite COS retrievals from MIPAS. The MIPAS spectrometer measured limb-emission spectra for several trace gases in the mid-infrared

Last, the SIF satellite retrievals from the Global Ozone Monitoring Experiment-2 (GOME-2) make it possible to evaluate the seasonality of GPP inferred by inverse modelling for each PFT. SIF represents the amount of light reemitted by chlorophyll molecules as a byproduct of photosynthesis. Satellite-based SIF data are considered a proxy for the GPP of terrestrial ecosystems at large spatial–temporal scales

Location of the HIPPO airborne measurements, NOAA airborne platforms and surface sites in Japan and France that are used as independent observations for evaluating the inverse results. The HIPPO measurements have been averaged into bins of 10

For each species and each measurement, the simulated concentration fields were sampled at the LMDz 3D grid box closest to the observation location. As mentioned above, the observations at selected local times are assimilated as 8 d averages. For the independent observations, LMDz is sampled at the closest time from the observations. All observations are dry-air mole fractions calibrated relative to the compound World Meteorological Organization (WMO) mole fraction scale. Satellite retrievals are dry-mole fractions tuned by the data providers to the compound World Meteorological Organization (WMO) mole fraction scale. For comparison, the corresponding dry-air variables in the model simulations are used.

When comparing MIPAS data with LMDz simulations, the a priori and vertical sensitivity of the retrievals must be taken into account. For each MIPAS retrieval, the modelled COS profiles have been interpolated linearly to the MIPAS vertical resolution (60 layers) while ensuring the conservation of the column-average mixing ratio

The a priori profile for the COS retrievals is a zero profile

Our inverse system seeks to estimate the amplitude of

In order to regularize the inverse problem corresponding to Eq. (1), we use a Bayesian framework involving an a priori control vector,

In the following, we call “reference fluxes” the maps of CO

Our reference fluxes combine several information sources. Fossil fuel emissions are from the gridded fossil emission dataset GCP-GridFED (version 2019.1)

The components of the COS budgets that are considered are biomass burning, soil emissions and uptake, anthropogenic emissions, plant uptake, oceanic emissions, and the atmospheric oxidation by the

Overview of the global budget of COS. Units are GgS yr

Reference air–surface exchanges from oxic soils have been simulated by the steady-state analytical model of

We chose the empirical formulation of the COS uptake by leaves from

In this equation,

We have only made a distinction between C

For anthropogenic fluxes, we use the inventory of

COS is directly emitted by the ocean in places where the sea water is saturated in COS. Emissions typically happen in summer in high latitudes. COS is also indirectly emitted through the oxidation of DMS and

Zonal mean distribution of the prior oceanic fluxes as a function of latitude averaged over the year 2010. The direct COS emissions are shown in blue whereas the indirect COS emissions through DMS (

We have not considered DMS and

We use the inventory emissions from

Since the highest reaction rate is close to the surface

Our inversion window covers 12 years. The spatiotemporal resolution of the control vector

We control COS oceanic fluxes in three latitudinal bands: the tropics, the northern latitudes and the southern latitudes. This separation allows the inverse system to modify the latitudinal distribution of the reference emissions, which remains subject to large uncertainties, while preserving the prior longitudinal patterns. This amounts to saying that the coastal sites located in the Northern Hemisphere constrain the total oceanic emissions over the whole Northern Hemisphere above 30

For the CO

Controlled variables for 1 year. The size of the control vector is equal to 149 630 for the inversion period 2008–2019.

Assigned error standard deviations for each station and for

Observation errors are defined with respect to the observation operator

Description of the prior error covariance matrix. Since the control vector is made of low-resolution multipliers to reference maps, the standard deviations are fractions of the reference values. The lag-1 autocorrelation coefficients are the correlations assigned between two consecutive time steps for each controlled variable, the time step being defined in Table

Our prior error covariance matrix

The seasonal cycle is derived from the surface data using the CCGVU curve-fitting procedure developed by

The simulated atmospheric concentrations (for CO

The global

The

Column “RE” presents the fractional reduction of the model vs. assimilated measurement RMSE

Table

The consistency of the estimate with the measurement errors and the a priori flux errors assumed is analysed first with the global normalized chi-squared statistic (see Eq.

In addition to the global consistency between data errors and a priori flux errors, the validity of the relative weights (inverse of the squared data error) assumed for the individual measurement residuals (i.e., at each station) is assessed (see Eq.

In order to better visualize the improvement on the seasonal cycle, we compare in Fig. 5 the simulated a priori and a posteriori concentrations against observations at three sites: BRW, NWR and LEF. These time series have been detrended beforehand to retain the seasonal cycle. At BRW, the inversion has corrected the too low seasonal amplitude and the phase lag in the a priori concentrations within the range of observation uncertainties. At LEF, the a priori concentrations were already in good agreement with the observations, and the inversion has not improved the simulated concentrations much. However, at NWR, the inversion struggles to correct the advanced phase, especially in the CO

Detrended temporal evolutions of simulated and observed CO

Table

The total oceanic COS emission remains lower than previous top-down studies using different configurations and observations, which instead estimated an oceanic source between 700 and 1000 GgS yr

Prior and posterior total fluxes and their associated 1

Figure

Latitudinal distribution of the prior (dashed line) and posterior fluxes (full line) for the continental (brown) and oceanic components (blue) of the COS budget. The fluxes have been averaged over the years 2009–2019.

Regarding the impact on the CO

Latitudinal distribution of the prior (dashed line) and posterior net CO

In order to assess the realism of the a posteriori GPP, its seasonal cycle is compared with the seasonal cycle of the GOME-2 SIF product. Although the ecosystem-dependent bias in the SIF products makes a direct comparison with GPP impossible, SIF has been recognized as a good indicator of the temporal dynamics in GPP. At the ecosystem scale, SIF is anti-correlated with the GPP: a maximum in SIF corresponds with a minimum in GPP. Figure

Mean seasonal cycle of the total prior (black) and posterior (orange) GPP

As a second step, we assess the a posteriori concentrations using several datasets: the MIPAS satellite retrievals, the HIPPO airborne measurements, and the surface measurements over Japan and France (see Sect. 2.2). In particular, the MIPAS retrievals of COS atmospheric concentrations at 250 hPa in the tropics give insight into the magnitude of the main biospheric sink located over Brazil during the wet season, when convective air masses reach the upper troposphere

Climatological seasonal COS distributions at 250 hPa measured by

We further assess the latitudinal distribution of the COS sources and sinks given by the inversion with the help of the HIPPO airborne measurements. For this purpose, Fig.

Comparison of the latitudinal variations in the a priori and a posteriori LMDz COS abundance with the HIPPO observations. Because of the unbalanced prior, the LMDz COS abundances have been vertically shifted such that the means of the a priori are the same as the mean of the HIPPO data (521 ppt). The error bar is calculated as the standard variation in the COS concentration averaged over longitudes and heights.

The optimized COS fluxes are now assessed at three surface sites in Japan: Miyakojima (MIY; 24

In summer, sites YOK and OTA sample air masses coming both from continental Japan and from the Pacific Ocean to the east of Japan. The southernmost site MIY seems to be mostly affected by oceanic sources originating from the east (see the LMDz footprints in Fig. S12). The sites OTA and YOK overestimate the COS concentrations by 60 and 150 ppt and reflect the influence of the misplaced anthropogenic source in central Japan (Fig. S13). At MIY, the comparison with observations suggests that the oceanic source is too strong because the atmospheric concentrations are overestimated by 40 ppt in southern Asia and in northern Japan. However, the oceanic source may not be overestimated in southern Asia because we have assumed that

The spatial pattern of the

Finally, we perform a similar assessment of the optimized COS fluxes in winter at the station GIF in France. Measurements at the site GIF represent background values of COS in western Europe, and no COS anthropogenic sources have been detected near by

Mean COS concentration sampled at the first level of the LMDz model in

To conclude, there is a need for continuous in situ carbonyl sulfide observations. The lack of continuous in situ observations, especially over the tropics, limits our capacity to infer the COS surface fluxes by inverse modelling and therefore to optimize GPP. There is some hope that new satellite products could address this issue, but at this stage, current COS retrievals also have their limitations such as, for instance, cloud interference or the lack of sensitivity to the surface fluxes

We have developed an analytical system that optimizes GPP, plant respiration CO

Several aspects of the inferred COS fluxes, such as the inter-hemispheric gradient, the tropical spatial distribution, and the anthropogenic emissions over Japan, China and France, were evaluated with independent atmospheric measurements over different parts of the globe. In the tropics, independent observations of the upper-troposphere COS partial column and the SIF weaken our confidence in the change in tropical GPP; the inverse system actually lacks measurements in this area to ensure a robust partitioning between the oceanic and the continental components of the COS budget. Indeed, the footprint map of the assimilated measurements indicates that the tropical areas, in particular the continents, are poorly constrained by the inverse system. The inverse system partly relies on the terrestrial reference fluxes and adjusts the tropical source to match the surface measurements over the tropics. If the tropical oceanic release is indeed underestimated in the reference fluxes, its magnitude remains highly uncertain. In contrast, in the high latitudes, independent measurements suggest that the inversion has rightly corrected an underestimation of the GPP in the ORCHIDEE land surface model. Concerning the COS anthropogenic sources, Japanese measurements suggest that these are underestimated in eastern China, highlighting the need for an improved anthropogenic inventory.

The COS MIPAS retrievals are available from

The supplement related to this article is available online at:

MR, FC and PP conceived the research with contributions from SB. MR built the analytical inverse system and conducted the analysis. AP helped in the analysis of the simulation outputs. CA and FM conducted the ORCHIDEE simulations. SL provided the oceanic fluxes of COS and

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This study was funded by the

This research has been supported by the H2020 Innovation In SMEs (grant no. 776186).

This paper was edited by Anita Ganesan and reviewed by J. Elliott Campbell and one anonymous referee.