Edinburgh Research Explorer Consistent regional fluxes of CH4 and CO2 inferred from GOSAT proxy XCH4:XCO2 retrievals, 2010–2014

. We use the GEOS-Chem global 3-D model of atmospheric chemistry and transport and an ensemble Kalman ﬁlter to simultaneously infer regional ﬂuxes of methane (CH 4 ) and carbon dioxide (CO 2 ) directly from GOSAT retrievals of XCH 4 : XCO 2 , using sparse ground-based CH 4 and CO 2 mole fraction data to anchor the ratio. This work builds on the previously reported theory that takes into account that (1) these ratios are less prone to systematic error than either the full-physics data products or the proxy CH 4 data products; and (2) the resulting CH 4 and CO 2 ﬂuxes are self-consistent. We show that a posteriori ﬂuxes inferred from the GOSAT data generally outperform the ﬂuxes inferred only from in situ data, as expected. GOSAT CH 4 and CO 2 ﬂuxes are consistent with global growth rates for CO 2 and CH 4 reported by NOAA and have a range of independent data including new proﬁle measurements (0–7 km) over the Amazon Basin that were collected speciﬁcally to help validate GOSAT over this geographical region. We ﬁnd that large-scale multi-year annual a posteriori CO 2 ﬂuxes inferred from GOSAT data are similar to those inferred from the in situ surface data but with smaller uncertainties, particularly over the tropics. GOSAT data are consistent with smaller peak-to-peak seasonal amplitudes of CO 2 than either the a priori or in situ inversion, particularly over the tropics and the southern extratropics. Over the northern extratrop-ics, GOSAT data show larger uptake than the a priori but less than the in situ inversion, resulting in small net emissions over the year. We also ﬁnd evidence that the carbon balance of tropical South America was perturbed following the droughts of 2010 and 2012 with net annual ﬂuxes not returning to an approximate annual balance until 2013. In contrast, GOSAT data signiﬁcantly changed the a priori spatial distribution of CH 4 emission with a 40 % increase over tropical South America and tropical Asia and a smaller decrease over Eurasia and temperate South America. We ﬁnd no evidence from GOSAT that tropical South American CH 4 ﬂuxes were dramatically affected by the two large-scale Amazon droughts. However, we ﬁnd that GOSAT data are consistent with double seasonal peaks in Amazonian ﬂuxes that are reproduced over the 5 years we studied: a small peak from January to April and a larger peak from June to October, which are likely due to superimposed emissions from different geographical regions.


Introduction
Atmospheric growth of the two most abundant noncondensable greenhouse gases (GHGs), carbon dioxide (CO 2 ) and methane (CH 4 ), increases the absorption of Earth's outgoing infrared radiation (IR) with implications for the radiation budget of Earth's atmosphere and subsequent manifold changes in climate, including an increase in global mean temperatures. The most recent international climate agreement aims to limit the rise in global mean temperature to 2 • C, which will be attempted by reducing the emissions of human-driven (anthropogenic) GHGs. This approach necessarily assumes that we have good knowledge of emissions from all anthropogenic sectors so that targeted reductions are effective. It also implicitly assumes that the Earth's biosphere will continue to be a net annual sink for up to 40-60 % of anthropogenic CO 2 (e.g. Barlow et al., 2015) and the continued stability of natural reservoirs of CH 4 . Current scientific knowledge, informed by mostly ground-based data and models, does not confidently support either assumption even on a continental scale. Here, we present the first multi-year record of self-consistent regional net fluxes (sources minus sinks) of CO 2 and CH 4 inferred from the Japanese Greenhouse gases Observing SATellite (GOSAT). We show these fluxes are significantly different from those inferred from ground-based data, particularly over tropical ecosystems, but are generally consistent with independent data throughout the troposphere.
Inferring CO 2 and CH 4 fluxes directly from atmospheric observations is an ill-posed inverse problem, with a wide range of scenarios that fit these data. Prior information is used to regularize the problem, with care taken to describe data and prior uncertainties to avoid over-or under-fitting the data. There is a growing and progressive literature on estimating GHG fluxes in which an atmospheric chemistry transport model is used to relate observed atmospheric GHG mole fractions to atmospheric surface exchange fluxes. A number of approaches are used to minimize the modelobservation residual to infer spatial and temporal variations in flux. Errors introduced by the incomplete and uneven coverage of current ground-based observation networks are compounded by atmospheric model errors (e.g. transport and chemistry) resulting in significant discrepancies between flux estimates inferred from different models on spatial scales < O(10 000 km) (e.g. Law et al., 2003;Yuen et al., 2005;Stephens et al., 2007;Peylin et al., 2013).
Space-borne observations of short-wave IR (SWIR) that are sufficiently precise to detect small changes in lower tropospheric CO 2 and CH 4 necessary for flux inference are beginning to improve the current understanding of these GHGs. GOSAT (Kuze et al., 2016), launched in 2009, was the first satellite designed purposefully to measure CO 2 and CH 4 columns using SWIR wavelengths. There is a growing body of literature that has inferred regional CO 2 and CH 4 fluxes from GOSAT dry-air CO 2 (XCO 2 ) and CH 4 (XCH 4 ) column mole fractions using the proxy and full-physics data products (Basu et al., 2013;Deng et al., 2014;Houweling et al., 2015;Bergamaschi et al., 2013;Takagi et al., 2014;Fraser et al., 2014). The resulting flux estimates (particularly for CO 2 ) are often found to be inconsistent with the results based on the surface network and with each other using different atmospheric transport models or using different versions of retrievals (Chevallier et al., 2014;Houweling et al., 2015). The reliability of the fluxes inferred from GOSAT XCO 2 retrievals (Reuter et al., 2014;Feng et al., 2016), considering bias in current retrievals  as well as the variations in temporal and spatial coverage (Liu et al., 2014), is still a subject of ongoing discussions.
We build on previous work that developed a novel approach to estimate simultaneously regional CO 2 and CH 4 flux estimates from the GOSAT XCH 4 : XCO 2 ratio measurements, which had been until then used exclusively to develop "proxy" XCH 4 retrievals (Fraser et al., 2014). Previous work has shown that these ratios are less prone to the systematic bias that represents a substantial challenge to the full-physics data products. The underlying assumption of the proxy approach is that, by taking the ratio of the two retrieved values that have been fitted simultaneously in nearby spectral windows (1.65 and 1.61 µm), any interference due to cloud and aerosol scattering will be similar for both retrieved values and will be removed (Frankenberg et al., 2005(Frankenberg et al., , 2006. The ratio is then scaled by a model XCO 2 value, under the assumption that atmospheric gradients of XCO 2 are much smaller than XCH 4 , to generate XCH 4 proxy retrievals. Data products generated by the proxy approach are more robust against scattering than the full-physics approach so that there are more usable retrievals over geographical re-gions that are compromised by seasonal aerosol and cloud distributions, e.g. tropical South America. Fraser et al. (2014) used a series of numerical experiments and the maximum a posteriori (MAP) approach to show that these XCH 4 : XCO 2 ratios could be used, in conjunction with in situ observations of CH 4 and CO 2 mole fractions, to simultaneously estimate regional CO 2 and CH 4 fluxes. Pandey et al. (2016) used a similar approach but using a 4-D variational assimilation approach to infer XCO 2 and XCH 4 fluxes for 20 months from April 2009. They found that after correcting biases in the XCH 4 : XCO 2 retrievals, the ratio inversion results in similar agreement with independent CO 2 and CH 4 observations, as other inversions based on the in situ data only or based on individual GOSAT XCH 4 and XCO 2 products. Here, we use an ensemble Kalman filter (EnKF) to assimilate the XCH 4 : XCO 2 ratio data (UoLv6; Parker et al., 2015) from January 2009 to December 2014, inclusive. A comparison between the UoLv6 data set and the ground-based XCH 4 and XCO 2 data from the Total Carbon Column Observing Network (TCCON) shows a bias of about 0.3 %. We use individual in situ and GOSAT observations (instead of monthly means; Fraser et al., 2014) to estimate monthly fluxes at a higher spatial resolution than Fraser et al. (2014).
In the next section, we describe the ensemble Kalman filter approach, the observations we use to infer the CO 2 and CH 4 fluxes and those we use to evaluate the resulting posteriori flux estimates, and a description of the numerical experiments. In Sect. 3, we describe our results, with a particular focus on tropical South America where we compare our a posteriori model with new aircraft measurements. We conclude the paper in Sect. 4.

Ensemble Kalman filter
We develop an existing EnKF framework that has been used to estimate CO 2 (Feng et al., 2009 and CH 4 fluxes from the in situ or space-based measurements of their atmospheric observations (Fraser et al., 2013). In this study, the state vectors are regional fluxes of CO 2 and CH 4 at location x and time t as where g denotes CO 2 or CH 4 tracer gas and f g 0 (x, t) describes the a priori estimates of CO 2 or CH 4 fluxes. Following Fraser et al. (2014), our basis function set BF g i (xt) is defined as the pulse-like (monthly) CO 2 or CH 4 fluxes from different sectors over predefined geographic regions. The coefficients c g i for both the CO 2 and CH 4 fluxes form a joint state vector c to be estimated by optimally fitting the model to the data.
In the ensemble Kalman filter framework, the prior flux error covariance P is represented by an ensemble of pertur-bations of the coefficients C: P = C C T , where T represents the matrix transpose. The a posteriori coefficient estimates are given by where c a , c f are the prior and posterior estimates, respectively; y obs are the observations; and H is the observation operator that relates surface fluxes (i.e. the coefficients) to the observation data (described below) and includes the atmospheric transport model (Fraser et al., 2014). The Kalman gain matrix K in Eq.
(2) is approximated by Feng et al. (2009): where R is the observation error covariance, and Y T = H ( C) projects the flux perturbation (coefficients) ensemble C to observation space. We use the GEOS-Chem global 3-D chemistry transport model (v9.02) to relate the fluxes to the observation space. For the experiments reported here, we run the chemistry transport model (CTM) at a horizontal resolution of 4 • (latitude) × 5 • (longitude), driven by the GEOS-5 (GEOS-FP for 2013 and 2014) meteorological analyses from the Global Modeling and Assimilation Office Global Circulation Model based at NASA Goddard Space Flight Center. We use monthly 3-D fields of the hydroxyl radical from the GEOS-Chem HO x -NO x -O x chemistry simulation to describe the main oxidation sink of CH 4 (Fraser et al., 2014). We use a 4-month moving lag window to reduce the computational costs related to the projection of the perturbation ensemble into the observation space for longer time periods (Feng et al., 2013 Where possible, we use consistent emission inventories for CO 2 and CH 4 : monthly biomass burning emission (GFEDv4.0; van der Werf et al., 2010) and monthly fossil fuel emissions (ODIAC; Oda and Maksyutov, 2011). To describe atmospheric CO 2 variations, we also use monthlyresolved climatological ocean fluxes (Takahashi et al., 2009) and 3-hourly terrestrial biosphere fluxes (CASA; Olsen and Randerson, 2004). To describe atmospheric CH 4 variations, following Fraser et al. (2014), we use prescribed annual inventories for emissions from oil and gas production, coal mining, ruminant animals (Olivier et al., 2005), termites, and hydrates (Fung et al., 1991). We use monthly-resolved emissions for rice paddies and wetlands for (Bloom et al., 2012. From January 2012, we fix the rice paddy and wetland emissions to their monthly means between 2009 and 2011. We also include a simple soil sink of CH 4 (Fraser et al., 2014).
We define the pulse-like basis functions (Eq. 1) guided by the TransCom-3 regions (Gurney et al., 2002), with each continental region further divided equally into four subregions. Figure 1 shows the 44 land regions and 11 ocean regions that we use in this study; in comparison, Fraser et al. (2014) used 11 land regions and 1 ocean region. We describe the inversion on these smaller geographic regions to help reduce aggregation errors associated with fluxes being estimated on a coarse spatial resolution (Patra et al., 2005).
We assume an a priori uncertainty of 60 % for the coefficients corresponding to the natural CO 2 and CH 4 fluxes, and for CH 4 emissions from coal mines. We assume an a priori uncertainty of 40 % for CO 2 anthropogenic emissions, CO 2 and CH 4 ocean fluxes, and anthropogenic emission of CH 4 from the oil and gas industry. We also assume that a priori errors for the same categories are correlated with a spatial correlation length of 800 km and with a temporal correlation of 1 month . We assume that fire emissions of CO 2 and CH 4 are correlated with a correlation coefficient of 0.5, accounting for the variation and uncertainty of the fire emission factors .

Observations
We assimilated GOSAT XCH 4 : XCO 2 retrievals and in situ surface observations of CO 2 and CH 4 mole fraction. We use version 6 of the proxy GOSAT XCH 4 : XCO 2 retrievals from the University of Leicester, UK, including both the nadir observations over land and glint observations over ocean. Previous analyses have shown that these retrievals have a bias of 0.3 %, with a single sounding precision of about 0.72 % . In our experiments, we globally remove this 0.3 % bias from the GOSAT proxy data. We assume that each single GOSAT proxy XCH 4 : XCO 2 ratio retrieval has an uncertainty of 1.2 % to account for possible model errors, including the errors in atmospheric chemistry and transport.
We also assimilate CO 2 and CH 4 mole fraction observations at surface-based sites, which help anchor the GOSAT ratio observations (Fraser et al., 2014). Figure 1 shows the sites we use from the NOAA observation network . We assume uncertainties of 0.5 ppm and 8 ppb for the in situ observations of CO 2 and CH 4 , respectively. We also assume a model error of 1.5 ppm and 15 ppb for CO 2 and CH 4 , respectively. We adopt a larger percentage for the CH 4 model error to account for difficulties in modelling chemical sinks of CH 4 in atmosphere (Patra et al., 2011;Fraser et al., 2013). A robust description of model error remains a major challenge for this and similar studies. We have assumed a simple formulation to describe model error, which will not fully account for impacts of errors from, for example, model atmospheric transport on resulting CO 2 and CH 4 flux estimates.
To determine the importance of the ratio data, we run twin sets of experiments: (1) "ratio" experiments that include the GOSAT data and the in situ data sets, and (2) "in situ" experiments that use only the in situ surface data.

Independent data to evaluate a posteriori estimates
We use independent observations of atmospheric CO 2 and CH 4 mole fraction to evaluate the atmosphere mole fractions that correspond to the a posteriori fluxes from our inversions. These observations include data collected by TCCON and by four aircraft campaigns. To improve the readability of the main text, we have placed much of the text and many of the figures associated with the evaluation of the a posteriori fluxes in Appendix A.
TCCON is a global network of ground-based Fourier transform spectrometer (FTS) instruments that measure, among other compounds, the total atmospheric columns of CO 2 and CH 4 . We use the bias-corrected TCCON XCO 2 and XCH 4 data at all available sites from the recent GGG2014 release of the TCCON data set . For a comprehensive description of the network and the available data from each TCCON site, we refer the reader to the TCCON project page (e.g. De Maziere et al., 2014;Deutscher et al., 2015;Dubey et al., 2014;Feist et al., 2014;Griffith et al., 2014a, b;Hase et al., 2015;Iraci et al., 2014Kivi et al., 2014;Morino et al., 2014a, b;Sherlock et al., 2014aStrong et al., 2014;Sussmann and Rettinger, 2014;Te et al., 2014;Warneke et al., 2014;Wennberg et al., 2014aWennberg et al., , b, c, 2015. We also use aircraft measurements from four projects to evaluate our a posteriori model concentrations: (1) data collected during experiments 1-5 from the HIAPER poleto-pole observations (HIPPO) that provide latitude-altitude cross sections of tropospheric mole fractions of CO 2 and CH 4 (and other tracers) covering dates from 2009 to 2011  (2) data collected by commercial airliners as part of the Civil Aircraft for the Regular Investigation of the atmosphere Based on an Instrument Container (CARIBIC) experiment, which are mainly at cruise altitudes, but also in ascent/descent over airports (Brenninkmeijer et al., 2007;Schuck et al., 2009) Webb et al., 2016) close to two of the AMAZON-ICA sites from 2012 to 2014: Salinópolis (SAH) and Rio Branco (RBH). These two sites were chosen to best represent air before and after travelling across the Amazon Basin. The purpose of these flights was to improve validation of GOSAT XCH 4 and XCO 2 data over the Amazon Basin so we flew from the surface to 7 km to capture more of the atmospheric column that GOSAT observes. A detailed description of ACO can be found in Webb et al. (2016), and comparison of these data against GOSAT XCH 4 : XCO 2 data are shown below. Figure 2 shows that the in situ only and the ratio inversions result in similar annual net CO 2 flux estimates (averaged for 2010 to 2014) over temperate land regions. But compared to the in situ only inversion, the ratio inversion shows a larger net emission over tropical South America, and a smaller net emission from tropical Asia, although the differences are usually within the 1σ uncertainties. We also find that the a posteriori fluxes for the ratio inversion generally have smaller uncertainties, in particular, over tropical land regions. Figure 3 and Table 1 compare the time series of the prior and posterior global net CO 2 flux estimates. They show that global annual a posteriori net flux estimates are 40-60 % smaller the a priori estimates (Table 1) due to a smaller net emission during boreal winter and a larger net uptake during the boreal summer (Fig. 3). The corresponding global annual CO 2 growth rate agrees with NOAA estimates, inferred from in situ observations, typically within 0.15 ppm a −1 , except for 2013 when the inversions are 0.3 ppm a −1 lower than the NOAA-reported value. Figure 3 also shows that the monthly a posteriori flux estimates by the in situ and ratio inversions are similar over the northern landmasses ( Fig. 1), with the exception of the summer in 2014 when the ratio inversion shows significantly smaller uptake. Over the tropical landmasses, a posteriori fluxes from the ratio inversion show a much smaller seasonal cycle, with exception of boreal summer months in 2014 when these fluxes have larger uptake. In general, uncertainties for the monthly fluxes inferred by the ratio inversion (GOSAT plus in situ data) are smaller (up to 30 %) than using only the in situ data. This reflects the poor spatial coverage of  the current in situ observing network particularly over tropical ecosystems (Fig. 1). Over the southern landmasses, the a posteriori fluxes for the two inversions are similar and typically within their uncertainties. We find that both inversions show a gradual reduction in the peak-to-trough amplitude, which appears to support a similar downward trend in the a priori estimates from about 9.0 GtC a −1 between 2010 and 2011 to about 7.5 GtC a −1 between 2013 and 2014. A posteriori fluxes also consistently show lower net emissions than a priori values during austral winter months. Figure 2 shows that a priori and the a posteriori global annual net CH 4 flux estimates are similar (520 Mt a −1 for the a priori versus 518 Mt a −1 for the ratio inversion), but their geographical distributions are significantly different. The ratio and in situ only inversions show much larger emissions than the a priori estimates over tropical lands, by up to 50 % larger for tropical South America and for tropical Asia (Fig. 2). This increase is partially offset by reduced emissions at midlatitudes (e.g. temperate South America). Over Eurasian temperate areas, we find that the ratio inversion has 15 % smaller emissions than the a priori estimates, but the fluxes inferred from the in situ surface data for the same region are 25 % higher than the a priori (Fig. 2), which is due to the in situ network having little sensitivity to emissions over a large part of Eurasian temperate areas, in particular over southeast China where there are large CH 4 sources from wetlands and rice paddies. Figure 2 also shows that the ratio inversion has much smaller (up to 60 %) uncertainties than the in situ inversions over almost all TransCom land regions, which is due to better spatial observation coverage of GOSAT proxy data. Figure 4 shows that, at the global scale, the monthly a posteriori fluxes inferred from the ratio and in situ inversions have larger seasonal variations than the a priori: a typical seasonal minimum of about 450 Mt a −1 and a typical maximum of 680 Mt a −1 , compared to the a priori that have a minimum of 480 Mt a −1 and a maximum of 620 Mt a −1 . The larger a posteriori seasonal variation is largely due to the seasonal cycle over northern landmasses that is driven by varying wetland and fire CH 4 emissions. The ratio inversions also show a muted peak emission of typically 30 Mt a −1 during January to February, partially due to peak emissions over southern landmasses during the austral summers. Over Northern Hemisphere landmasses, the in situ inversion is systematically 5-10 % higher than the ratio inversion from 2010 to 2014. Over the tropics, we find that a posteriori tropical fluxes from the ratio and in situ inversions are generally larger than a priori estimates. Also, the ratio a posteriori fluxes are systematically higher than those inferred from the in situ surface data, and show a small upward annual trend (Table 2). Over this region, we also find that the ratio inversion consistently shows a double-peak structure with a small peak between January and April and a larger peak between June and October (Fig. 4). This is not shown by the in situ inversion or by the a priori inventory. A posteriori fluxes for the southern landmasses are generally lower by 30-50 Mt a −1 than the a priori values, which, together with northern landmasses, partially offset the increase in tropical CH 4 emissions (Fig. 4). Over Southern Hemisphere landmasses, the seasonal cycles of the ratio and in situ inversions are similar, although the ratio inversion generally has lower seasonal minima, with the exception of 2014 when the phase of the ratio inversion was the opposite of the in situ inversion.

Model evaluation
In general, the ratio inversion shows the best agreement with independent CH 4 observations, particularly over lower latitudes. A posteriori improvements to the CO 2 simulation are relatively small. We find that both the model CO 2 and CH 4 concentrations reproduce the large-scale spatial (e.g. the north-south gradient) and temporal (seasonal cycle) variations in the HIPPO and CARIBIC data (Sect. 2.3). The a posteriori simulations reproduce the observed TCCON XCH 4 and XCO 2 variations. Over most TCCON sites, the a posteriori XCO 2 model biases are within 0.8 ppm (< 0.2 %), and the standard deviations are smaller than 1.6 ppm. The typical model biases for model XCH 4 data are smaller than 10 ppb (i.e. < 0.6 %), with a standard deviation smaller than 15 ppb. For more details, we refer the reader to Appendix A, where we show pictorially the comparisons between observations and the ratio, and in situ a posteriori CO 2 and CH 4 mole fractions.
Here, we focus on tropical South America (Fig. 1) for three reasons. First, in situ surface data are particularly sparse over this geographical region, including two sites (Fig. 5) over which we use the observed CO 2 and CH 4 mole fractions to constrain flux estimates: Arembepe, Bahia, Brazil (ABP; −12.770 • latitude, −38.170 • longitude) and Ragged Point, Barbados (RPB; 13.165 • latitude, −59.432 • longitude). Second, they include vulnerable ecosystems that have recently experienced several widespread drought conditions in 2010 and 2012 (see, for example, Lewis et al., 2011;Rodrigues and McPhaden, 2014), which have affected their ability of absorbing carbon (Doughty et al., 2015) and increased fire emissions Alden et al., 2016). And third, we report new aircraft profile measurements from the ACO  that was designed specifically to evaluate GOSAT column observations of CH 4 and CO 2 (Sect. 3). Figure 6 shows that the a posteriori monthly CH 4 and CO 2 flux estimates over tropical South America from the ratio inversion are significantly different from the in situ inversion, as expected given the in situ surface data coverage. However, monthly a posteriori CO 2 fluxes from the ratio inversion are not always statistically different from the a priori, reflecting the large a priori uncertainties associated with fluxes over this region. The in situ inversion typically has larger uptake during the dry season (May to September) and smaller emissions during the wet seasons than the ratio inversion. Because the  Figure 6. The same as Fig. 3 but for CO 2 and CH 4 fluxes over tropical South America (Fig. 1).
in situ flux estimates over this geographical region rely on observation far away, they are particularly sensitive to a priori uncertainties, as expected. We find that assuming a global a priori uncertainty that is 50 % smaller than our control run results in an additional net emission of 0.4 GtC a −1 over tropical South America in 2010. Including the GOSAT ratio data into that sensitivity inversion leads to a smaller net decrease (of 0.13 GtC a −1 ) in emissions. Table 3 shows that the a posteriori annual fluxes inferred by the ratio inversion are significantly larger than the in situ inversion in 2010, 2011, and 2012 by about 0.7, 0.4, and 0.5 GtC, respectively. A posteriori fluxes from the ratio inversion show net emissions are smaller in 2013 and 2014 than in 2010 or 2012, which is due to larger uptake in the dry season and smaller emissions in the wet seasons (Fig. 6). This result reveals the continental-scale impact of the severe droughts in 2010 and 2012 over tropical Southern America. Our result for 2010 is consistent with recent studies based on regionalscale AMAZONICA aircraft observations van der Laan-Luijkx et al., 2015;Alden et al., 2016). The in situ inversion fails to reproduce this increase in net emissions during the 2010 dry season, instead showing a large uptake (Fig. 6).
A posteriori CH 4 fluxes from the ratio inversion are systematically higher than the in situ inversion (Fig. 6). This discrepancy is particularly large from October 2013 to March 2014 when the in situ inversion is lower than typical seasonal values observed during previous years. Figure 5 shows that XCH 4 : XCO 2 ratio measurements over the southwest Amazon increase from 4.55 ppb ppm −1 to about 4.65 ppb ppm −1 between October-December 2013 and January-March 2014. This is a small but significant change in the ratio that suggests either enhanced CH 4 emissions and/or lower CO 2 fluxes. The two closest in situ sites to the locus of XCH 4 : XCO 2 variability (RPB and ABP) do not reproduce this change. Consequently, the in situ inversion may not accurately describe these CH 4 flux changes over the continental interior. Figures 7 and 8 show that a posteriori fluxes from the ratio inversion generally decrease the mean model difference against independent AMAZONICA and ACO aircraft observations of CO 2 and CH 4 over the Amazon Basin, but with only small improvements to the associated standard deviations. At some sites, the fluxes from the ratio inversion significantly mute the rapid variations in atmospheric CO 2 and CH 4 inferred from the in situ data. Figure 7 shows that for CO 2 the greatest improvement is for the central basin sites of RBA and RBH (after 2012), where the bias reduced from −0.62 ppm to 0.01 ppm with an accompanying reduction in standard deviation from 3.7 to 2.6 ppm. We find similar but smaller reductions at another AMAZONICA site (TAB). Over other AMAZONICA and ACO sites, the im- 67.0 (11.6) 59.5 (11.3) 54.6 (11.6) 52.9 (11.9) 59.5 (11.2) Ratio 74.4 (3.6) 78.6 (3.8) 74.0 (3.5) 73.4 (3.2) 73.1 (3.9) pact of GOSAT XCH 4 : XCO 2 ratios are even smaller. The coarse resolution of our model that allows us to exploit efficiently the GOSAT and in situ data is one possible explanation for the large standard deviations (van der Laan-Luijkx et al., 2015;Gatti et al., 2014). Figure 8 shows that overall the ratio inversion better reproduces the AMAZONICA and ACO CH 4 data than the in situ inversion. The ratio inversion does best at SAN. It also shows a better agreement over RBA as it does for CO 2 . After 2012, the ratio inversion shows a Figure 8. The same as Fig. 7 but for comparison of the monthly mean partial CH 4 columns (in ppb) of the model simulations with AMAZONICA and ACO observations. Due to availability, CH 4 observations for 2012 have not been included.
positive bias at the two ACO sites (SAH and RBH). Assimilating the XCH 4 : XCO 2 data reduces the standard deviations (by about 4 to 11 ppb) over ALF, TAB, and RBA (RBH after 2012), and slightly (by about 1 ppb) increase the standard deviations at SAN and SAH.

Summary
Building on the previously reported theory, we simultaneously inferred regional CO 2 and CH 4 fluxes from the proxy GOSAT XCH 4 : XCO 2 retrievals in 2010-2014, inclusive, anchored by geographically sparse in situ mole fraction data. The main advantage of using these data directly is that the ratio is less compromised by systematic bias on spatial scales greater than typical model grid resolution (< 1000 km) and less than large-scale variations captured by ground-based networks (< 10 000 km), which represents a limiting factor to using full-physics XCO 2 measurements. Inferring CO 2 and CH 4 fluxes together provides a self-consistent methodology. We showed that a posteriori fluxes inferred from the GOSAT data generally outperformed the fluxes inferred only from in situ data, as expected given their greater measurement coverage. GOSAT CH 4 and CO 2 fluxes are consistent with global growth rates for CO 2 and CH 4 reported by NOAA and are generally more consistent than the results based on in situ surface data with a range of independent data collected throughout the global troposphere (e.g. aircraft profiles and ground-based total column measurements) and include new profile measurements (0-7 km) over the Amazon Basin that were collected specifically to help validate GOSAT over this geographical region.
We found that large-scale multi-year annual a posteriori CO 2 fluxes inferred from GOSAT data are similar to those inferred from the in situ surface data but with smaller uncertainties, particularly over the tropics where in situ surface data are sparse. However, we found that GOSAT data are consistent with smaller peak-to-peak seasonal amplitudes of CO 2 than either the a priori or in situ inversion, particularly over tropical and the southern extratropics, where the annual means are similar. Over the northern extratropics, GOSAT data infer a larger uptake than supported by the a priori but a smaller uptake than the corresponding in situ data. Using the individual annual means and seasonal variations during 2010-2014, we found evidence from GOSAT that the carbon balance of tropical South America was perturbed following the droughts of 2010 and 2012 when this region was a large annual source of CO 2 (0.5-0.6 PgC a −1 ) to the atmosphere, with net annual fluxes not returning to an approximate annual balance until 2013.
We showed that GOSAT data results in significant changes with respect to a priori spatial distribution of CH 4 emission with a 40 % increase over tropical South America and tropical Asia and smaller (partially compensating) decrease over Eurasia and temperate South America. We find no evidence from GOSAT that tropical South American CH 4 fluxes were dramatically affected by the two large-scale Amazon droughts in 2010 and 2012. However, we reported that GOSAT data are consistent with double seasonal peaks in fluxes that are reproduced over the 5 years we studied: a small peak in January to April and a larger peak in June to October. Currently, we have no explanation for this phenomenon, but it is likely due to superimposed emissions from different geographical regions.
While the sensitivity of our results to model error and to the temporal and spatial resolution of fluxes requires further investigation, our analysis, in the wider context of other studies, supports the adoption of using space-borne observations of CO 2 and CH 4 to better understand the carbon cycle on the continental scale. Well-known weaknesses of these data (e.g. biases in spatial and temporal coverage) can be partially overcome by integrating them with information from other networks and by judicious use of atmospheric chemistry transport models. The next obvious step is to understand how we can improve source attribution of CO 2 and CH 4 without necessarily resorting to the assumption, as used here and elsewhere, that a priori fossil fuel emission estimates are correct. Source attribution can be sometimes achieved by exploiting knowledge of spatial distributions of different sources, but techniques that allow more rigorous exploitation of multi-gas correlations must be developed and incorporated into data assimilation systems that will eventually form the backbone to operational systems (e.g. EU Copernicus Atmospheric Monitoring Service to atmospheric CO 2 ).
Data availability. The University of Leicester GOSAT Proxy XCH 4 v6.0 data are available from http://www.leos.le.ac.uk/data/ GHG/GOSAT/v6.0/. The password can be provided by R. Parker on request. A description of this data set can be found in Buchwitz et al. (2017). These data are also part of the ESA GHG-CCI Climate Research Data Package v3 (http://www.esa-ghg-cci. org/, Buchwitz et al., 2017). AMAZONICA data are available from http://www.ccst.inpe.br/projetos/lagee/ . TCCON data were obtained from the TCCON data archive, hosted by the Carbon Dioxide Information Analysis Center (CDIAC) at Oak Ridge National Laboratory, Oak Ridge, Tennessee (US), doi:10.14291/tccon.archive/1348407 . CARIBIC CO 2 and CH 4 data are available on request from A. Zahn.

Appendix A: Wider geographical model evaluation
We use independent observations to evaluate the a posteriori model concentrations that correspond to the flux estimates, acknowledging limitations associated with sparse observation coverage and atmospheric transport model errors (Chevallier et al., 2014). We sample the GEOS-Chem atmospheric chemistry transport at the time and location of each individual observation. Figures A1 and A2 show that the ratio inversion is marginally more consistent with HIPPO XCO 2 data than the in situ inversion, but the spatial error structure is qualitatively similar. The ratio inversion has a positive bias of 0.2 pm and standard deviation of 1.3 ppm compared to the in situ inversion that has a positive bias of 0.3 ppm and standard deviation of 1.3 ppm. The largest standard deviations (up to 0.8 %) reflect the ability of models to reproduce small-scale variations, particularly at the lowest (the planet boundary layer) and the highest (the upper troposphere and lower stratosphere) altitudes. We find small differences (generally within 1 ppm) below 4-6 km between 40 • S and 40 • N, and much larger differences (up to 2 ppm) in the upper troposphere and in the lower stratosphere north of 45 • N. The ratio and in situ inversions show similar spatial structure to HIPPO XCH 4 data. We find a small negative bias (0-15 ppb) in the middle and lower troposphere between 40 • S and 40 • N and a larger positive bias (by over 20 ppb) in the extratropical upper troposphere/lower stratosphere. We find the largest discrepancies between model and observed XCH 4 in the higher-latitude lower stratosphere, in agreement with previous studies (e.g. Alexe et al., 2015 andPandey et al., 2016), which is mainly due to difficulties in modelling stratospheric chemical processes. As a result, the ratio inversion and the in situ inversions have similar biases of 0.6 and 0.1 ppb, respectively, as well as similar standard deviations of 27.7 versus 27.5 ppb, respectively. Figure A2 shows that the two a posteriori models reproduce the hemispheric CO 2 gradient, typical for boreal spring months, observed by the HIPPO-3 experiment. Compared to the in situ inversion, the ratio inversion has a larger negative bias (−0.8 versus −0.4 ppm) around 20 • N, in contrast to a slightly larger positive bias over most of the Southern Hemisphere. We find that the overall model bias and associated standard deviation of the gridded partial CO 2 columns are very small (biases < 0.01 ppm and standard deviation < 0.6 ppm). Figure A2 shows that the two a posteriori models also reproduce the hemispheric CH 4 gradient observed by the HIPPO-3 experiment. Compared to the in situ inversion, the proxy GOSAT XCH 4 : XCO 2 data significantly reduce the negative bias of the CH 4 concentrations (by up to 10 ppb) over the tropical regions. The overall bias for the gridded CH 4 partial columns is reduced from −5.6 ppb for the in situ inversion to −1.5 ppb for the ratio inversion.  Figure A3 shows that the two a posteriori models reproduce the observed annual trend of CO 2 monthly means and the observed seasonal cycle with smaller amplitude. Underestimation of the seasonal cycle of the upper-tropospheric CO 2 concentrations is well documented, and believed to be caused by a deficiency in modelling vertical transport (Stephens et al., 2007). Figure A3 also shows that the a posteriori models reproduce the observed trend and seasonal variation of atmospheric CH 4 in the tropical middle/upper troposphere. The ratio inversion has a smaller bias (−0.37 ppb) than the in situ inversion (−8.27 ppb) but has only modestly improved the associated standard deviation by 15 % from 7.55 to 6.48 ppb. Figure A4. Mean multi-year statistics (2010-2014) of the differences between TCCON (top) XCO 2 and (bottom) XCH 4 measurements and the a posteriori models. Blue and red bars denote the standard deviations between TCCON and the in situ and ratio a posteriori model, respectively. Black circles and green triangles denote the mean deviation of the TCCON and the in situ and ratio a posteriori models. Figure A4 shows that the two a posteriori models have a similar level of agreement with 24 independent TCCON XCO 2 retrievals. For most of these sites, the model XCO 2 bias is well within 1.0 ppm, and the standard deviation is between 0.6 and 1.5 ppm. The two exceptions are sites around Los Angeles, CA, USA: cj (34.1 • N, 118.1 • W) and jf (34.2 • N, 118.2 • W), where the models underestimate atmospheric XCO 2 by 1.5-2.0 ppm, which we attribute to our coarse model resolution. Figure A4 also shows that assimilating GOSAT XCH 4 : XCO 2 proxy data significantly reduces the model XCH 4 bias by up to 10 ppb over low-latitude TCCON sites. The GOSAT data also help to reduce the standard deviations over most of the 24 sites.

A3 TCCON
Author contributions. L. Feng and P. I. Palmer designed the experiments and wrote the paper; H. Bösch, R. J. Parker, and Alex Webb provided the GOSAT XCO 2 and XCH 4 data; N. M. Deutscher, D. G. Feist, R. Kivi, I. Morino, O. Uchino, F. Hase, R. Sussmann, and K. Strong provided access to TCCON XCO 2 and XCH 4 data; A. Zahn provided access to CARIBIC CO 2 and CH 4 mole fraction data. L. V. Gatti, E. Gloor, C. S. C. Correia, L. G. Domingues, and J. B. Miller provided access to aircraft data (AMAZONICA and ACO) over the Amazon Basin. J. Wang and Y. Liu provided a preliminary evaluation of CO 2 and CH 4 fluxes over China. All co-authors provided comments and suggestions on the manuscript.
Competing interests. The authors declare that they have no conflict of interest.
Acknowledgements. Work at the University of Edinburgh was partly funded by the NERC National Centre for Earth Observation (NCEO) and the European Space Agency Climate Change Initiative (ESA-CCI). P. I. Palmer gratefully acknowledges funding from the NCEO and his Royal Society Wolfson Research Merit Award. NCEO and the European Space Agency Climate Change Initiative funded work at the University of Leicester. H. Bösch and R. J. Parker are supported by the ESA Climate Change Initiative (ESA-CCI). R. J. Parker was also funded by an ESA Living Planet Fellowship. We thank NERC and FAPESP for their joint funding of the Amazonian Carbon Observatory Project (NERC reference NE/J016284/1). M. Gloor was financially supported by the NERC consortium grant AMAZONICA (NE/F005806/1) which we also thank for providing access to additional aircraft profiles. The TCCON network is supported by NASA's Carbon Cycle Science Program through a grant to the California Institute of Technology. The TCCON stations from Bialystok, Orleans, and Bremen are supported by the EU projects InGOS, GAIA-CLIM, and ICOS-INWIRE, and by the Senate of Bremen. The TCCON station at Sodankylä is supported by the EU project GAIA-CLIM. N. Deutscher is supported by an Australian Research Council -Discovery Early Career Researcher Award (DE140100178). TCCON measurements at Eureka were made by the Canadian Network for Detection of Atmospheric Composition Change (CANDAC) with additional support from the Canadian Space Agency. TCCON operation at the Tsukuba and Rikubetsu sites is supported in part by the GOSAT project. Works by J. Wang and Y. Liu are funded by Helmholtz-CAS joint research groups (HCJRG-307). We also thank the HIPPO team for their observations (http://hippo.ucar.edu/) that were used in our model evaluation. We thank G. J. Collatz and S. R. Kawa for providing NASA Carbon Monitoring System land surface carbon flux products (http://nacp-files.nacarbon.org/nacp-kawa-01/).
The authors would like to thank the two anonymous reviewers for their insightful comments, which helped to improve the manuscript significantly.
Edited by: R. Müller Reviewed by: two anonymous referees