Observed atmospheric variations of carbon dioxide (CO2) are due to atmospheric transport and surface flux processes. Using prior knowledge of the spatial and temporal distribution of these fluxes and atmospheric transport it is possible to infer (or invert for) the a posteriori estimate of surface fluxes from atmospheric concentration data. The geographical scarcity of such observations precludes robust flux estimates for some regions due to large uncertainties associated with meteorology and a priori fluxes. Arguably, our knowledge of top-down estimates of regional CO2 fluxes, particularly at tropical and high northern latitudes, has not significantly improved for over a decade (Gurney et al., 2002; Peylin et al., 2013), reflecting the difficulty of maintaining a surface measurement programme over vulnerable and inhospitable ecosystems. Atmospheric transport model errors compound errors introduced by poor observation coverage, resulting in significant differences between flux estimates on spatial scales < O (10 000 km) (e.g. Law et al., 2003; Yuen et al., 2005; Stephens et al., 2007).

The Greenhouse gases Observing SATellite (GOSAT), a space-borne mission launched in a sun-synchronous orbit in early 2009, was purposefully designed to measure CO2 columns using short-wave IR wavelengths. Validation of current XCO2 column retrievals using co-located upward-looking FTS measurements of the Total Carbon Column Observing Network (TCCON) (Wunch et al., 2011) shows a standard deviation of 1.6–2.0 ppm (e.g., Parker et al., 2013). Their global biases are typically smaller than 0.5 ppm (Oshchepkov et al., 2013). The disadvantage of using the TCCON is that sites are mainly at northern extra-tropical latitudes with little or no coverage where our knowledge of the carbon cycle is weakest. Many surface flux estimation algorithms are particularly sensitive to systematic errors so that sub-ppm biases can still significantly change the patterns of regional flux estimates (Chevallier et al., 2010). This is further complicated by the seasonal coverage of GOSAT data at high latitudes during winter months when solar zenith angles are too large to retrieve reliable values for XCO2 (Liu et al., 2014).

Several independent studies have shown that regional flux distributions inferred from GOSAT XCO2 retrievals are significantly different from those inferred from in situ data (Basu et al., 2013; Deng et al., 2014; Chevallier et al., 2014). In particular, these studies report a larger-than-expected annual net emission over tropical continents and a larger-than-expected net annual uptake over Europe. While the GOSAT inversions suffer from larger observation errors, atmospheric transport errors and issues from the seasonal coverage of higher latitudes, the in situ inversions are also unreliable over many regions due to poor coverage and atmospheric transport errors. Inter-comparisons revealed significant inconsistency in regional flux estimates inferred from in situ observations by using different inversion systems, over many regions important for global carbon cycle, including Europe (Peylin et al., 2013). Consequently, there is an ongoing debate about whether a recent study that shows a large European uptake of CO2 (Reuter et al., 2014) reflects a real phenomenon or is an artefact due to deficiencies both in the observations and in the inverse modelling.

We report the results from a small set of experiments that show systematic bias can introduce a large difference between European fluxes inferred from GOSAT and those inferred from in situ data by using a global flux inversion approach. In the next section we provide an overview of the inverse model framework used to interpret data from the in situ observation network (including both the conventional surface observation network and the relatively new TCCON network), and from the space-based GOSAT XCO2 data. In Sect. 3, we present results from two groups of global inversion experiments that characterize the role of systematic bias in regional flux estimates. Further experiments for quasi-regional flux inversions are presented in Appendix A. In Sect. 4, we use a modified version of the inverse model framework to estimate monthly biases by jointly assimilating all data. We conclude the paper in Sect. 5.

We use the GEOS-Chem global chemistry transport model to relate surface fluxes to the observed variations of atmospheric CO2 concentrations (Feng et al., 2009) at a horizontal resolution of 4∘ × 5∘, driven by GEOS-5 meteorological analyses from the Global Modeling and Assimilation Office Global Circulation Model based at NASA Goddard Space Flight Centre. We use an Ensemble Kalman Filter (EnKF) (Feng et al., 2009, 2011) to estimate regional fluxes from in situ or GOSAT observations for 3 years from 2009–2011, but we focus on 2010 to minimize error due to spin-up and edge effects. We estimate monthly fluxes on a spatial distribution that is based on TransCom-3 (Gurney et al., 2002) with each continental region further divided equally into 12 sub-regions and each ocean region further divided equally into six sub-regions. As a result, we estimate fluxes for 199 regions, compared to 144 regions we have used in previous studies (Feng et al., 2009; Chevallier et al., 2014).

In all global inversion experiments we assume the same set of a priori flux inventories, including the following: (1) monthly fossil fuel emissions (Oda and Maksyutov, 2011); (2) weekly biomass burning emissions (GFED v3.0) (van der Werf et al., 2010); (3) monthly oceanic surface CO2 fluxes (Takahashi et al., 2009); and (4) 3-hourly terrestrial biosphere-atmosphere CO2 exchange (Olsen and Randerson, 2004). We assume that the a priori uncertainty for each land sub-region is proportional to a combination of the net biospheric emission (70 %) at the current month, and its annual variation (30 %). We also assume that the a priori errors are correlated with each other with a spatial correlation length of 800 km, and a temporal correlation of 1 month (Chevallier et al., 2014). We then determine the coefficient for the assumed a priori uncertainty by scaling the aggregated annual uncertainty over all 133 land sub-regions to 1.9 GtC a-1. In particular, the resulting annual a priori uncertainty for the European region is about 0.52 GtC a-1, with the monthly uncertainty varying from 2.0 GtC a-1 for the summer months to about 0.8 GtC a-1 for winter months, which is generally larger than the a priori monthly uncertainty used by Deng et al. (2014). Prior uncertainties over oceans are determined under similar assumption but with a longer spatial correlation (1500 km), and a smaller aggregated annual error (0.6 Gt a-1). Our experiments show that doubling the a priori uncertainty increases the European uptake inferred from GOSAT data by about 0.21 GtC a-1 (from 1.40 to 1.61 GtC a-1), compared to a smaller increase of 0.09 GtC a-1 for the in situ inversion (from 0.58 to 0.67 GtC a-1).

Our control inversion experiment (INV_TCCON, Table 1 and Fig. 1) assimilates in situ observations, including the conventional surface observations at 76 sites (Feng et al., 2011) and, in particular, the total column XCO2 retrievals from all the TCCON sites of the GGG2014 data set (see Wennberg et al., 2014, and https://tccon-wiki.caltech.edu for more details) to improve observation constraints. In some studies, TCCON data were used to evaluate posterior fluxes. However TCCON data have been used to derive bias corrections for GOSAT XCO2 retrievals (Cogan et al., 2012), and also the nature of total column measurements means that they are sensitive to air mass transported from other regions, which complicate the assessment of European flux estimates.

We use daytime (09:00 to 15:00 local time) mean TCCON retrievals, with the observation errors determined by the standard deviation about their daytime mean. To account for the inter-site biases as well as the model representation errors, we enlarge the TCCON observation errors by 0.5 ppm. Including TCCON observations increases the annual net uptake over Europe in 2010 from 0.49 GtC a-1, as inferred from surface observations only, to 0.58 GtC a-1. The increase is mainly due to a larger summer uptake. TCCON data also reduce the a posteriori uncertainty by about 15 % from 0.16 to 0.14 Gt a-1. However considering the limited spatial resolution (only 12 sub regions for the whole TransCom European region), and unquantified model transport and representation errors, we anticipate that the complete a posteriori uncertainty is larger than the value estimated by the inversion system itself, as suggested by large inter-model variations found for in situ inversions (e.g., Peylin et al., 2013).

For the two control GOSAT inversions (Fig. 1), we use two independent data sets: (1) XCO2 retrievals from JPL ACOS team (v3.3) (Osterman et al., 2013) (INV_ACOS); and (2) the full-physics XCO2 retrievals (v4.0) from the University of Leicester (Cogan et al., 2012) (INV_UOL). For both data sets, we assimilate only the H-gain data over land regions, and apply the bias corrections recommended by the data providers. We double the reported observation errors, as suggested by the retrieval groups.

As a performance indicator for our ability to fit fluxes to observed XCO2 concentrations, we compare a posteriori model concentrations with GOSAT XCO2 retrievals and show that INV_ACOS and INV_UOL agree much better than INV_TCCON. For example, the bias against ACOS XCO2 retrievals is -0.45 ppm for INV_TCCON and 0.02 ppm for INV_ACOS with a corresponding reduction in the global standard deviation from 1.69 to 1.57 ppm. However comparison of GOSAT a posteriori concentrations against independent HIPPO-3 measurements is worse than INV_TCCON with a positive bias of 0.47 and 0.66 ppm for INV_ACOS and INV_UOL, respectively, which are mainly caused by the overestimation of CO2 concentrations (∼ 1.5–2.0 ppm) at low latitudes (Fig. 2).

Figure 1 and Table 1 shows the three inversion experiments, INV_TCCON, INV_ACOS, and INV_UOL, have similar European uptake values in June 2010 (0.69 GtC for INV_TCCON and ∼ 0.72 GtC for GOSAT inversions), and are generally consistent with other GOSAT inversion experiments (e.g., Deng et al., 2014; Chevallier et al., 2014). But the GOSAT inversions have an annual net uptake of about 1.40 ± 0.19 GtC a-1 compared to the in situ inversion of 0.58 ± 0.14 GtC a-1. Figure 1 also shows significant differences between their monthly flux estimates in early spring and winter when there is only sparse GOSAT observation coverage, particularly over northern Europe. Both INV_UOL and INV_ACOS have a cumulative total of about 0.51 GtC more uptake than INV_TCCON during February–April of 2010, with a further 0.37 GtC uptake accumulated over the following summer and autumn. This larger uptake is partially cancelled out by larger emissions (0.17–0.08 GtC) at the end of 2010.

Figure 2 shows that INV_TCCON a posteriori CO2 mole fractions agree well with the independent HIAPER Pole-to-Pole Observations (HIPPO-3) aircraft measurements below 5 km over the Pacific Ocean in 2010 (Wofsy et al., 2011), with a small bias of 0.05 ppm, and a sub-ppm standard deviation of 0.87 ppm. Figure 3 shows further evaluation of a posteriori CO2 mole fractions using descending and ascending profile observations over two European airports from the CONTRAIL experiment (Machida et al., 2008). We calculate monthly mean CONTRAIL measurements during 2010 using data below 3 km, where there is greater sensitivity to local surface fluxes. Our current model resolution precludes small-scale sources (or sinks) so we expect model bias. We find that INV_TCCON agrees best with CONTRAIL observations, in particular at the beginning of 2010, partially reflecting the poor GOSAT XCO2 coverage over Europe during the winter and early spring. However, we cannot conclude from the slightly degraded agreement with CONTRAIL (as well as with HIPPO-3) that the European uptake inferred from GOSAT data is incorrect, because unaccounted small local emissions and/or sinks, and model transport errors can affect the comparison against aircraft observations.

Figure 3 also presents an additional model simulation forced by a hybrid flux (denoted by the magenta broken line) where the INV_TCCON a posteriori fluxes outside Europe are replaced by the results from INV_ACOS. The resulting CO2 concentrations from these hybrid fluxes are, as expected, higher than the a posteriori model concentrations for INV_ACOS because of the larger European emissions (i.e., less uptake) inferred by INV_TCCON. But they are also systematically higher than the INV_TCCON simulation, in particular during spring months, despite the same European fluxes being used to force these two simulations. This suggests an overestimate of CO2 transported into the European region by the GOSAT inversions. Further comparison of the INV_TCCON simulation and the hybrid run reveals that systematic differences in the inflow into the European domain can affect the atmospheric XCO2 gradient across this region. In the INV_TCCON simulation, the mean XCO2 difference between east (east of 20∘ E) and west (west of 20∘ E) Europe is ∼ 0.04 ppm for May 2010, which is increased to 0.16 ppm in the hybrid run (cf. E–W XCO2 gradient of -0.20 ppm for GOSAT ACOS data).

To understand the differences between the INV_TCCON and GOSAT inversions, we conducted two groups of sensitivity tests (Table 1 and Fig. 4). First, we replaced all or part of the GOSAT XCO2 retrievals assimilated in INV_ACOS with those from a model simulation forced by the a posteriori fluxes from INV_TCCON. In experiment INV_ACOS_MOD_ALL (Fig. 4), where we replace all GOSAT data with CO2 concentrations inferred from INV_TCCON, we reproduce INV_TCCON with small exceptions at the beginning of 2010, reflecting the seasonal variation in GOSAT coverage. In a related experiment INV_ACOS_MOD_NOEU for which we only replace XCO2 retrievals outside Europe with the model simulation, the differences between the GOSAT and in situ inversions are significantly reduced, particularly over the period with limited observation coverage, although the actual XCO2 retrievals are still assimilated over Europe. The simulated GOSAT data outside Europe reduces the estimate of European uptake from 1.40 to 0.88 GtC a-1. In other words, the GOSAT observations outside the European region are responsible for about 60 % (0.52 GtC a-1) of the total enhanced European sink (0.82 GtC a-1) with the remainder (0.30 GtC a-1) due to observations taken directly over Europe. The large contribution from GOSAT retrievals outside Europe has also been confirmed by the high uptake (1.17 Gt a-1) in a counterpart experiment (INV_ACOS_MOD_ONLYEU) where only GOSAT retrievals within Europe are replaced by the model simulations. We show in Appendix B that theoretically the difference between INV_ACOS and INV_ACOS_MOD_ALL is equal to the sum of the individual uptake increases in the paired synthetic inversions of INV_ACOS_MOD_NOEU and INV_ACOS_MOD_ONLYEU.

For INV_UOL, when we replace the XCO2 data outside Europe by the a posteriori INV_TCCON model simulations, European uptake is reduced to 0.67 GtC a-1 (INV_UOL_MOD_NOEU, Table 1), indicating an external contribution of nearly 90 % to the enhanced uptake of 0.82 GtC a-1. Together with Fig. 3, these results suggest that GOSAT inversions result in an overestimated CO2 inflow. This will subsequently lead to the fitted European flux having to compensate, via mass balance, by being erroneously low even when un-biased GOSAT XCO2 data are assimilated over the immediate European region. We find similar effects in the quasi-regional inversions (Fig. A1 in Appendix A), where only observations within the European region are assimilated, with flux estimates from INV_TCCON or from INV_ACOS being used to provide lateral boundary conditions around Europe.

Second, we crudely demonstrate how regional bias could explain the remaining discrepancy of up to 0.30 GtC a-1 between GOSAT and in situ inversions over Europe. In our experiment INV_ACOS_SPR_0.5ppm, we add a bias of +0.5 ppm to the GOSAT ACOS retrievals within Europe taken in February-April, inclusively, which effectively reduces the uptake by 0.1 GtC a-1 from 1.40 to 1.30 GtC a-1. Similarly, when the bias of +0.5 ppm is added to the GOSAT data taken in June–August we find a larger reduction of 0.15 GtC a-1 (INV_ACOS_SUM_0.5ppm), partially due to a larger a priori uncertainty and denser GOSAT coverage during the summer. These results emphasize the importance of characterizing sub-ppm regional bias to avoid erroneous flux estimates.

Here we demonstrate a simple approach to quantify systematic bias in XCO2 retrievals based on a simple on-line bias correction scheme. We assimilate the GOSAT XCO2 retrievals together with the surface and TCCON observations in two experiments: INV_ACOS_INS and INV_UOL_INS (Table 1). We also include monthly GOSAT XCO2 regional biases over 11 TransCom land regions (Gurney et al., 2002) as parameters to be inferred together with surface fluxes from the joint assimilation of in situ and satellite observations. To investigate the spatial pattern of the XCO2 biases within Europe, we split Europe into West Europe (west of 20∘ E) and East Europe (east of 20∘ E). We assume that a priori for monthly biases is 0.0 ± 0.5 ppm. For simplicity, we have assumed that the a priori errors for regional XCO2 biases are not correlated. Compared to the off-line comparisons between GOSAT XCO2 retrieval and model concentrations, the main advantage of the on-line bias estimation is that the uncertainties associated with error in flux estimates can be partially taken into account. However, biases derived by this approach reflect the systematic difference between the model simulation and GOSAT data over large (continental) regions, which also contain systematic model errors (such as the atmospheric transport and representation errors). In addition, the inversion results are affected by the relative weights assigned to different data sets, as well as by the relative prior uncertainty assumed for surface fluxes and for the observation bias. The seasonal variation of the mean CO2 concentration is an important sign of the underlined biosphere seasonal cycle. We show in Appendix A that when we inflate the a priori uncertainty for the assumed observation bias, the observation constraints on flux estimate will become weaker. Also, the on-line bias correction is only effective for detecting and correcting bias at specified patterns, which may increase the sensitivity to other uncharacterized systematic errors. Despite these weaknesses, a joint data assimilation approach can exploit complementary constraints from in situ and satellite XCO2 data: for example there are few GOSAT observations over northern Europe during autumn and winter months, while Eastern Europe has few in situ observations. We have also limited the a priori uncertainty for the monthly observation biases to 0.5 ppm. Figure C1 (Appendix C) shows, for example, the inferred monthly mean bias for March 2010.

In the joint inversions INV_ACOS_INS and INV_UOL_INS, the annual European uptake is estimated to be 0.62 and 0.67 GtC a-1, respectively (Table 1), which is close to the reference value of 0.58 GtC a-1 inferred from the in situ observations. To test the impact of the on-line bias correction, we set the a priori uncertainty of regional XCO2 bias to be 0.01 ppm so that on-line bias correction is effectively turned off. As a result, the annual European uptake for INV_ACOS_INS is increased by 0.15 GtC to 0.77 GtC a-1, which is close to INV_ACOS_MOD_NOEU, but about 55 % of the GOSAT only inversions (1.40 GtC a-1).

Figure 5 shows the estimated monthly biases in ACOS and UOL XCO2 retrievals over East and West Europe during 2010. Monthly biases are typically smaller than 0.5 ppm over the two regions, but have different seasonal cycles. Additional experiment shows that after ACOS XCO2 data over Europe have been corrected for the inferred biases, the European annual uptake by INV_ACOS is reduced by 0.20 GtC a-1, representing more than half of the contribution from GOSAT observations within Europe. This result is consistent with our sensitivity tests. The effect of bias correction is much smaller for INV_UOL (about 0.07 GtC a-1), because of the different bias patterns. Differences in GOSAT XCO2 retrievals and their effects on regional flux estimates have also been investigated in previous studies (e.g., Takagi et al., 2014).

We used an ensemble Kalman Filter to infer regional CO2 fluxes from three different CO2 data sets: (1) surface in situ mole fraction observations and TCCON XCO2 retrievals; (2) GOSAT XCO2 retrievals from the JPL ACOS team; and (3) GOSAT XCO2 retrievals from the University of Leicester. Our results, consistent with previous studies, show that these GOSAT data in a global flux inversion context result in a significantly larger European uptake than inferred from in situ data during 2010.

We showed using sensitivity experiments that a large portion (60–90 %) of the elevated European uptake of CO2 is related to the systematically higher model CO2 mass being transported into Europe, due to the assimilation of GOSAT XCO2 data outside the European region. We find some evidence using aircraft observations over the Pacific that GOSAT a posteriori fluxes result in higher CO2 concentration over lower latitudes. But limited observation coverage and unaccounted model errors prevent us from confidently concluding that GOSAT XCO2 data are biased high or low. Our global and quasi-regional (Appendix A) flux inversion experiments show that the main consequence of the elevated CO2 inflow to the European domain is that the European uptake must increase because of mass balance, even when GOSAT XCO2 retrievals within the European domain are not biased. A crude sensitivity test (INV_ACOS_OUT_0.5ppm) shows that reducing ACOS XCO2 data outside the European region by 0.5 ppm will reduce European annual uptake from 1.40 to 0.98 GtC a-1. Erroneous interpretation of XCO2 data can result from analyses if biased boundary conditions are not addressed. However, as shown in Appendix A, a gross mis-characterization and correction of bias may weaken observation constraints, which can also lead to erroneous flux estimates.

We also showed using sensitivity tests that sub-ppm bias can explain the remaining 0.30 GtC a-1 flux difference between the in situ inversion and INV_ACOS after accounting for biased boundary conditions. By simultaneously assimilating the in situ and GOSAT observations to estimate surface fluxes and monthly XCO2 biases, we infer a monthly observation bias that is typically less than 0.5 ppm over East and West Europe, but is able to cause an elevated sink of up to 0.20 GtC a-1. The inferred monthly biases for UOL XCO2 are also not the same as the ACOS XCO2 data, particularly over West Europe during the summer months. This level of sensitivity of regional flux estimate to time-varying sub-ppm observation bias highlights the challenges we face as a community when evaluating XCO2 retrievals using current observation networks.

Flux estimates are sensitive to a priori assumptions, idiosyncrasies of applied inversion algorithms, and the underlying model atmospheric transport (Chevallier et al., 2014; Peylin et al., 2013; Reuter et al., 2014). The possible presence of regional observation biases further complicates the inter-comparisons of flux estimates based on different inversion approaches, as they may have different sensitivities to certain observation biases. In our assimilation of ACOS XCO2 retrievals, we find that doubling the a priori flux error (INV_ACOS_DBL_ERR) increases the estimated European uptake from 1.40 to 1.61 GtC a-1, consistent with the hypothesis on the increased vulnerability to the observation biases both within and outside Europe when using weak a priori constraints. In contrast, doubling the a priori flux errors only increases the uptake by 0.05 to 0.67 GtC a-1 for the joint data assimilation (INV_ACOS_INS_DBL_ERR), with very little changes in the estimated biases (not shown). Examples in Appendix A also demonstrate different responses to regional and sub-regional biases before and after an on-line scheme is used to correct the systematic error across Europe. These differences emphasize the need for a closer examination of the responses of the inversion systems to the assimilated observations, as well as to their possible biases, to help understand the inter-model variations in estimated regional fluxes.

Complicated interactions between observations and the assimilation system also mean that our present study does not exclude other possible causes for the elevated European uptake reported by previous research from assimilation of GOSAT data. Instead, it highlights the adverse effects of possibly uncharacterized regional biases in current GOSAT XCO2 retrievals that can attract erroneous interpretation of resulting regional flux estimates. A more thorough evaluation of the XCO2 retrievals using independent and sufficiently accurate and/or precise observations is urgently required to increase the confidence of regional CO2 flux estimates inferred from space-based observations. Without additional observations, we cannot rule out either the lower European uptake estimate of around 0.6 GtC a-1 (inferred from the in situ inversion INV_TCCON and the joint inversion INV_ACOS_INS and INV_UOL_INS) or the higher European uptake estimate of around 1.40 GtC a-1 (inferred from GOSAT data). There is also no sufficient reason to believe that the mean value among these diverse estimates is more reliable, because our study suggests that small systematic errors can result in significant differences in the estimated fluxes, and the influences of random errors have also not been fully quantified. The observational density required to infer flux estimates over a limited spatial domain such as Europe is crucial. For the time frame of this analysis, the TCCON network provided good coverage for Europe, North America, Southeast Asia and Australia and New Zealand. Great efforts were also taken to reduce inter-station biases. In future the TCCON measurement network may be supported by smaller, more mobile FTIR instruments, which can be established, at least on a campaign basis, in tropical and high latitude locations where observational gaps are greatest.

Our joint data assimilation approach assimilates in situ and space-borne observations. It also provides estimates of systematic differences between XCO2 retrievals and the inversion system at regional/sub-regional scales. However the resulting differences will include the observation biases and deficiencies in the underlying inversion approach. To achieve consistent flux estimates inferred from assimilating multiple data sets using different inversion approaches, we need to better quantify observation and model errors, and need to better understand the sensitivity of each inversion system to the assimilated observations as well as to their possible biases. It is difficult to develop a robust bias correction scheme before properly characterizing observation biases and the responses by the inversion system.