The extending archive of the Greenhouse Gases Observing Satellite (GOSAT)
measurements (now covering about 6 years) allows increasingly robust
statistics to be computed, that document the performance of the
corresponding retrievals of the column-average dry air-mole fraction of
CO

CO

The Japanese GOSAT, launched in January 2009, and the USA second Orbiting
Carbon Observatory (OCO-2), launched in July 2014, observe the NIR/SWIR
radiation with unprecedented spectral resolution in order to specifically
address this remote sensing challenge. The GOSAT archive already covers 6 years and can provide good insight into the adequacy of NIR/SWIR retrievals
for CO

This paper aims at contributing to the debate about the relevance of current
GOSAT retrievals for atmospheric inversions. Our starting point is a
critical review of the basic principles behind the current processing chains
that go in successive steps from GOSAT measured radiance spectra to surface
flux estimates (Sect. 3). We then focus on the GOSAT retrievals provided
by NASA's Atmospheric CO

GOSAT is a joint venture by the Japan Aerospace Exploration Agency (JAXA),
the National Institute for Environmental Studies (NIES) and the Ministry of
the Environment (MOE) in Japan. This spacecraft is operated in a
sun-synchronous polar orbit that crosses the Equator at about 13:00 local
time during daytime and that repeats every 3 days. As described by O'Dell et al. (2012) and Osterman et al. (2013), the ACOS algorithm retrieves

Following Boesch et al. (2006) and Connor et al. (2008), the ACOS algorithm
relies on optimal estimation (i.e. Bayesian methods) to retrieve the
vertical profile of the CO

Previous comparisons between

Since year 2011, the MACC pre-operational service (

the NOAA Earth System Research Laboratory archive (NOAA CCGG,

the World Data Centre for Greenhouse Gases archive (WDCGG,

the Réseau Atmosphérique de Mesure des Composés à Effet de Serre database (RAMCES,

The three databases include both in situ measurements made by automated quasi-continuous analysers and irregular air samples collected in flasks and later analyzed in central facilities. The detailed list of sites is provided in Tables S1 and S2 in the Supplement.

The MACC Bayesian inversion method is formulated in a variational way in
order to estimate the CO

The MACC inversion product also contains the 4-D CO

Like the other retrieval and inversion systems (see, e.g., Oshchepkov et
al., 2013; Peylin et al., 2013), ACOS-GOSAT and MACC both follow the
Bayesian paradigm in its Gaussian linear form (e.g., Rodgers, 2000) in order
to estimate the most likely state, in a statistical sense, of the CO

The error covariance matrix of

For simplicity, Eq. (1) does not make other variables that are
simultaneously inferred appear, like clouds, aerosols or surface variables
for the retrievals, or the 3-D state of CO

The current processing chains that go from radiances to surface fluxes are
two-step processes (let aside some attempts to introduce an additional
intermediate step in the form of a short-window analysis of the 3-D
concentrations; Engelen et al., 2009). We now distinguish the retrieval
process and the inversion process by putting breves on all symbols related to
the former and hats on all symbols related to the latter. In a first step,
the CO

For simplicity, and without loss of generality in our linear framework, let
us consider the assimilation of a single sounding

This equation has the desired shape of Eq. (1), i.e. the sum of the prior
value and of a linear function of model-minus-measurement misfits. By
construction, it does not depend on the retrieval prior

In practice, we see that

In the usual case when

Equation (7) simply expresses consistency between the prior error statistics within the information content of the retrievals: the uncertainty of the retrieval prior and of the flux prior should be the same in radiance space. This condition is not achieved by current satellite retrieval algorithms, at least because they artificially maximize the measurement contribution in the retrievals through the use of very large prior error variances (see Sect. 2.1 or Butz et al., 2009; Reuter et al., 2010). However, if enough intermediate variables were saved by the retrieval schemes, it would be possible to reconstruct the retrievals with appropriate prior error variances and correlations.

Equation (8) can be satisfied in general if the retrieval averaging kernel

As a consequence of deviations from Eqs. (7)–(8), the effective gain matrix

Migliorini (2012) proposed a sophisticated alternative to the averaging
kernel assimilation of Connor et al. (1994), where the retrievals are
assimilated after a linear transformation of both the retrievals and the
observation operator. The transformation is heavier to implement than the
above approach because it involves the retrieval signal-to-noise matrix

The situation complicates even further if we account for the facts that
inversion systems assimilate bias-corrected retrievals (thereby implicitly
re-introducing

Given the particular concerns raised about the optimality of

Figure 1 shows the mean bias-corrected retrievals

Same as Fig. 2a (retrievals minus model), but focussing on the months of March and June.

The jump of the long-term mean difference from the African savannahs to Sahel or equatorial Atlantic (while there is no jump between subtropical Atlantic and Western Sahara for instance) mostly corresponds to data from March (Fig. 3a), at the end of the savannah burning season (e.g. van der Werf et al., 2010). The model shows elevated values (Fig. 1b), but much less than the retrievals (Fig. 1a). If the model was underestimating the intensity of the fire, we would expect the mean difference to take the shape of a plume, i.e. to spread downstream the source region, but this is not the case. This suggests that the retrievals are affected by systematic errors over this region.

Mean surface albedo retrieved in the strong CO

The positive differences of Fig. 2a in Eurasia notably follow the boreal
forests, while negative values are found over the neighbouring regions of
sparse tundra vegetation north of Siberia, or those of grassland/cropland
south of them. The same remark applies to North America. The link with
boreal forests is less obvious when looking at one isolated year because of
the relatively small number of retrievals in these regions (not shown). The
misfit pattern in Siberia and in North America contains many values larger
than 1 ppm corresponding to relatively large retrieved

From a radiative transfer point of view, boreal forests are largely covered
with needle-leaved trees with low albedo in the strong CO

Mean and standard deviation of the retrieval-minus-model misfits between June 2009 and May 2013 for the high-gain mode retrievals over land as a function of the retrieval increment size. The statistics are also shown for the prior-minus-model misfit. The model values are raw pressure-weighted columns and do not account for the averaging kernels in order not to correlate the two axes (in practice, using the averaging kernels actually does not significantly affect the standard deviations shown). The grey shade shows the distribution of the retrieval density (axis not shown).

We now look at the

Same as Fig. 5 (high-gain mode over the lands) but we reduce the
retrieval increment size by 50 % without any bias correction (we call

The mean difference significantly varies with the increment size: starting at
0.7 ppm for the smallest increments it reaches about 2 and

The standard deviation for

The fact that the standard deviation smoothly increases with increment size
suggests that the increment size is systematically overestimated. Figure 6
presents a simple test where we halve the retrieval increments, without any
bias correction: we call

Same as Fig. 5 for the medium-gain mode.

Same as Fig. 5 for the glint mode over the ocean.

For the medium-gain retrievals (Fig. 7) and for the ocean glint retrievals
(Fig. 8), the standard deviation of the misfits using

Small uncertainties in aerosols, cirrus cloud or surface albedo are known to
heavily affect the quality of the

From the theory, we have shown that a two-step approach to infer the surface
fluxes from the GOSAT measured radiances, with

We have compared the ACOS-GOSAT retrievals with a transport model simulation
constrained by surface air-sample measurements in order to find some
evidence of retrieval sub-optimality. Flaws in this transport model and in
these inverted surface fluxes necessarily flaw the simulation in many places
over the globe and at various times of the year. We therefore carefully
selected some of the relatively large discontinuities in the

Given the diversity of existing satellite retrieval algorithms, our
conclusions cannot be easily extrapolated to other GOSAT retrieval products
and even less to

Some of this work was performed using HPC resources of DSM-CCRT and of CCRT
under the allocation t2014012201 made by GENCI (Grand Équipement
National de Calcul Intensif). It was co-funded by the European Commission
under the EU H2020 Programme (grant agreement No. 630080, MACC III). The
ACOS GOSAT data can be obtained from