Inverse modeling of GOSAT-retrieved ratios of total column CH 4 and CO 2 for 2009 and 2010.

. This study investigates the constraint provided by greenhouse gas measurements from space on surface ﬂuxes. Imperfect knowledge of the light path through the atmosphere, arising from scattering by clouds and aerosols, can heavily bias column measurements retrieved from space. To minimize the impact of such biases, ratios of total column retrieved CH 4 and CO 2 (X ratio ) have been used. We apply the ratio inversion method described in Pandey et al. (2015) to retrievals from the Greenhouse 5 Gas Observing SATellite (GOSAT). The ratio inversion method uses the measured X ratio as a weak constraint on CO 2 ﬂuxes. In contrast, the more common approach of inverting proxy CH 4 retrievals (Frankenberg et al., 2005) prescribes atmospheric CO 2 ﬁelds and optimizes only CH 4 ﬂuxes. inverse modeling system is used to simultaneously optimize the ﬂuxes of CH 4 and CO 2 for 2009 2010. The results are compared to proxy inversions using model-derived-XCO 2 mixing ratios (XCO model 2 ) from CarbonTracker 10 and MACC. The performance of the inverse models is evaluated using aircraft measurements from the HIPPO, CONTRAIL and AMAZONICA projects. those used in the proxy method. However, the CH 4 ﬂuxes are more realistic, because the impact of unaccounted systematic uncertainties is more evenly distributed between CO 2 and CH 4 . The ratio inversion estimates an enhanced CO 2 release from Tropical South America during the dry season of 2010, which is in accordance with the ﬁndings of Gatti et al. (2014) and Vanderlaan et al. (2015). The performance of the ratio method is encouraging, because despite the added non-linearity due to the assimilation of X ratio 5 and the signiﬁcant increase in the degree of freedom by optimizing CO 2 ﬂuxes, still consistent results are obtained. , biospheric and oceanic ﬂuxes are optimized separately. The a priori CH 4 ﬂuxes used in the study are the as used in Houweling et al. (2014), except 25 for the Anthropogenic emissions. We use the 4.2FT2010 versions of (European Commission, Joint Research Centre (JRC)/Netherlands Environmental As- sessment Agency), Houweling et al. (2014) uses 4.1 version (http://edgar.jrc. ec.europa.eu). The a priori CO 2 ﬂuxes come from CarbonTracker, CT2013B Peters et al. (2007), in which biosphere ﬂuxes are based on the Carnegie-Ames-Stanford Approach (CASA) biogeochemical model (CASA), ﬁre ﬂuxes are on Global Fire attribute such constraints to CH 4 ﬂuxes. The ratio inversion predicts an enhanced CO 2 natural source in this region during 2010 compared with the NOAA-only and a priori model. This is accordance with the ﬁndings of Gatti et al. (2014) and Vanderlaan et al. (2015), and is also supported by the AMAZONICA aircraft measurements. Overall, this study shows that the ratio method is capable of informing us about surface ﬂuxes of CH 4 and CO 2 using satellite measurements, and that it provides a useful alternative for the proxy inversion method. 5


Introduction
Detailed knowledge of the global distribution of surface fluxes of potent greenhouse gases (GHGs) such as CH 4 and CO 2 is needed to investigate the uncertain feedback of the global carbon cycle to human disturbances. Atmospheric measurements of these GHGs provide original information about surface fluxes. Inverse modeling methods, also known as top-down approaches, 10 have been developed to make use of that information to obtain improved estimates of surface fluxes. Bottom-up estimates of those fluxes are used as prior values in the top-down method, and are further improved using atmospheric measurements.
Inversions assimilating flask and/or in-situ measurements from surface networks have significantly improved our knowledge of the sources and sinks of GHGs (Bousquet et al., 2006;Bergamaschi et al., 2010;Hein et al., 1997;Houweling et al., 1999;Peters et al., 2007;Chevallier et al., 2010;Gurney et al., 2008). However, many regions with a key role in the global annual 15 budgets of CO 2 and CH 4 are not adequately covered by the surface measurement network. This is especially true for tropical regions and the Southern Hemisphere. Total column measurements of CH 4 and CO 2 (XCH 4 and XCO 2 ) by sensors onboard satellites, with near global coverage, have been used in some recent studies (Basu et al., 2013;Fraser et al., 2013;Houweling et al., 2014;Detmers et al., 2015;Basu et al., 2014).
The Greenhouse Gas Observing Satellite (GOSAT), launched in January 2009 by the Japanese Space Agency (JAXA), is 20 the first satellite dedicated to monitoring GHGs from space (Kuze et al., 2009;Yokota et al., 2009;Yoshida et al., 2011).
Onboard are the Thermal And Near Infrared Sensor for carbon Observations-Fourier Transform Spectrometer (TANSO-FTS) and a dedicated Cloud and Aerosol Imager (TANSO-CAI). TANSO-FTS measures the absorption spectra of Earth reflected sunlight in the shortwave-infrared (SWIR) spectral range, from which XCO 2 and XCH 4 are retrieved with global coverage.
Systematic errors in satellite retrievals are an important factor limiting the scientific interpretation of the data, and various methods have been proposed to mitigate their impact on the inferred surface fluxes (Bergamaschi et al., 2007;Frankenberg et al., 2005;Butz et al., 2010;Parker et al., 2015). An important source of systematic error is scattering of light by aerosols 30 and thin cirrus clouds along the measured light path. Two retrieval methods have been developed in the past to account for atmospheric scattering, referred to as the "full-physics" and "proxy" approach. The full-physics approach tries to account for scattering-induced errors by explicitly modeling the scattering process, and retrieving scattering properties from the data (Butz et al., 2010). The proxy method, first introduced by (Frankenberg et al., 2005), takes the ratio of XCH 4 and XCO 2 retrieved at nearby wavelengths ( 1562 to 1585 nm for XCO 2 and 1630 to 1670 nm for XCH 4 ) so that path length perturbations due to atmospheric scattering largely cancel out in the ratio (see equation 1). X ratio is multiplied with model-derived-XCO 2 (XCO model Here, XCH ns 4 and XCO ns 2 are retrieved assuming a non-scattering atmosphere. XCO model 2 is calculated using a transport model, normally employing CO 2 surface fluxes that have been optimized using surface measurements. The atmospheric CO 2 fields are sampled at the coordinates of the satellite measurements and converted to corresponding total columns using the retrieval-derived averaging kernels (Schepers et al., 2012). 10 Proxy XCH 4 retrievals from GOSAT have been used in many inverse modeling studies to investigate the global surface fluxes of CH 4 (Alexe et al., 2014;Monteil et al., 2013;Fraser et al., 2013;Bergamaschi et al., 2013). These studies rely on the assumption that the uncertainties and biases in XCO model 2 are relatively unimportant. Some recent studies have investigated this assumption in further detail. Schepers et al. (2012) suggested that the errors in XCH proxy

20
In an attempt to avoid the biases introduced by errors in XCO model 2 , (Fraser et al., 2014) developed the 'ratio' method, which simultaneously constrains CO 2 and CH 4 fluxes by assimilating X ratio on the sub continental scale using the ensemble Kalman filter. Pandey et al. (2015) also developed a similar ratio inversion method for jointly optimizing the surface fluxes of CH 4 and CO 2 on the model grid scale using a variational optimization method. Fraser et al. (2014) compared posterior CH 4 and CO 2 flux uncertainties derived from a ratio inversion with traditional CH 4 proxy and CO 2 full-physics inversions and reported a 25 larger reduction in uncertainty than the two in the tropics for the fluxes of both tracers.
This study extends the work of Pandey et al. (2015), by separately inverting real GOSAT measurements of X ratio and XCH proxy 4 in a consistent and comparable framework to investigate the following questions: 1) How do errors in XCO model 2 influence the results of a XCH proxy 4 inversion? 2) How does the X ratio inversion system developed by Pandey et al. (2015) perform using real data? The performance of the inversions is evaluated using independent aircraft measurements. We provide an 30 estimate of the posterior uncertainties of the X ratio inverted fluxes using the Monte-Carlo method described by Chevallier et al. (2007).
This paper is organized as follows. The following section explains the methods used in this study. Subsection 2.1 describes the inverse model and the a priori flux assumptions. Subsection 2.2 lists the measurements that are assimilated in the inversions and used for validation. Subsection 2.3 provides an overview of the inversions performed in the study. Section 3 presents the inversion results and Section 4 discusses their implications for the use of satellite retrievals in inversion studies. Finally, we give the overall conclusions of this work.

2 Method
We invert GOSAT-retrievals of X ratio , and XCH proxy

4
, each together with flask-air CH 4 and CO 2 measurements from the NOAA Global Greenhouse Gas Reference Network (GGGRN) to provide monthly surface fluxes of CO 2 and CH 4 using the TM5-4DVAR inversion system (Meirink et al., 2008). This is done as follows: 1. GOSAT-retrieved total column measurements of X ratio are compared to measured ratios of XCH 4 :XCO 2 from the Total and X ratio measurements are inverted along with surface observations and the resulting posterior surface fluxes are integrated over the TRANSCOM regions (see supplementary Figure 4).
5. The posterior flux uncertainty for all inversions is quantified using a Monte-Carlo approach (see Appendix B) for consistent comparison. 20 6. The performance of the inversions is evaluated and compared using independent aircraft measurements.
The remainder of this section explains these steps in further detail.

Inversion setup
CH 4 fluxes are optimized as a single flux category, representing the sum of all processes. For CO 2 , biospheric and oceanic fluxes are optimized separately. The a priori CH 4 fluxes used in the study are the same as used in Houweling et al. (2014) flux covariance matrix is constructed assuming relative flux uncertainties of 50%, 84% and 60% per grid box and month for the total CH 4 , biospheric CO 2 , and oceanic CO 2 categories, respectively. The fluxes are assumed to be correlated temporally using an exponential correlation function with temporal scales of 3, 3, and 6 months, respectively, and spatially with Gaussian 5 functions using corresponding length scales of 500, 500 and 3000 km for total CH 4 , biospheric CO 2 , and oceanic CO 2 , respectively.

Measurements
Here we give a brief account of the measurements that were assimilated (GOSAT and NOAA) or used for validation (TCCON and aircraft-measurements).

GOSAT
The XCH ns 4 and XCO ns 2 terms in equation 1 were taken from the RemoTec XCH 4 Proxy retrieval v2.3.5 . More information about the dataset can be found in Product User Guide on the ESA GHG CCI website (www.esa-ghg-cci.org/?q=webfm_send/ 180) The RemoTeC algorithm uses GOSAT TANSO-FTS NIR and SWIR spectra to retrieve simultaneously XCH ns 4 and XCO ns 2 assuming a non-scattering atmosphere (Schepers et al., 2012). X ratio values were translated into XCH proxy 4 using XCO model 2 15 derived from the following: 1. Monitoring Atmospheric Composition and Climate (MACC) Reanalysis CO 2 product (www. copernicus-atmosphere.eu). It uses Laboratoire de Météorologie Dynamique transport model (LMDZ) (Chevallier, 2013). The corresponding XCH proxy 4 product will be referred as XCH ma 4 . 2. CarbonTracker-2013B (http://www.esrl.noaa.gov/gmd/ccgg/ carbontracker/). These CO 2 fields are calculated using the TM5 model as used in this study. The corresponding XCH proxy 4 product will be referred to as XCH ct 4 .

20
Both data assimilation systems optimized the CO 2 fluxes using surface measurements of CO 2 . For GOSAT measurements, we only used the high-gain soundings from GOSAT under cloud free conditions from nadir mode. This was done to avoid any systematic inconsistency among the operation modes of TANSO. Figure 1 shows the spatial coverage of the GOSAT dataset used in our inversions. Systematic mismatches between NOAA-optimized and GOSAT-optimized TM5 CH 4 fields were observed by Monteil et al. (2013). We apply an additional bias correction to X ratio and XCH proxy 4 by comparing them to 25 total column CH 4 and CO 2 optimized via an inversion using TM5-4DVAR and NOAA flask-air data (see Appendix A).

TCCON
TCCON is a global network of ground-based FTS instruments, for measuring the total column abundance of several gases, including XCO 2 and XCH 4 , in the near nfrared region of the electromagnetic spectrum (Wunch et al., 2011). These measurements are the standard for validating total column retrievals from greenhouse gas observing satellites such as GOSAT. 30 We validate XCH ns 4 , XCO ns 2 , X ratio , XCO ma 2 , XCO ct 2 with corresponding values of XCH 4 , XCO 2 and XCH 4 :XCO 2 measured The numbers (1-12) refer to corresponding entries in Table 1. The size of the purple rectangles is proportional to the number of collocated high-gain GOSAT soundings by TCCON at 12 sites using the GGG2014 release of TCCON dataset (see Figure 1 and section 3.1). An albedo-based bias correction was applied to GOSAT-retrieved X ratio to account for mismatch with TCCON X ratio . (see Appendix A).

NOAA
High accuracy surface measurements of CH 4 and CO 2 were used from NOAA's GGGRN (http://www.esrl.noaa.gov/gmd/ccgg/ index.html ). The standard scales used for CO 2 is the WMO X2007 scale and for CH 4 is WMO X2004 scale. Only the sites  Figure 1 shows the location of the observation sites. 1 σ uncertainties of 0.25 ppm and 1.4 ppb were assigned to CO 2 and CH 4 measurements, respectively (Basu et al., 2013;Houweling et al., 2014). Note that our system also assigns modeling errors to each observation, depending on simulated local gradients in mixing ratio (Basu et al., 2013). 2. Comprehensive Observation Network for TRace gases by AIrLiner (CONTRAIL) from Machida et al. (2008).
HIPPO provides in-situ measurements covering the vertical profiles of CO 2 and CH 4 over the Pacific spanning a wide range in latitude (approximately pole-to-pole), from the surface up to the tropopause. We used data from the HIPPO 2 (October surements of CH 4 and CO 2 that were used have been bias corrected with flask air samples that were collected during each flight and analyzed at NOAA (Wofsy et al., 2012b).This allows us to make consistent comparison with our inversions models, as all of them assimilate NOAA flask measurements. CONTRAIL makes use of commercial airlines to measure in-situ CO 2 by continuous measurement equipment (Machida et al., 2008). For some of the CONTRAIL flights CH 4 measurements are 10 also available from flask-air samples. We use data from a lower-troposphere greenhouse-gas sampling program as part of the AMAZONICA project, over the Amazon Basin in 2010, measuring bi-weekly vertical profiles of CO 2 and CH 4 from above the forest canopy to 4.4 km above sea level at four locations: Tabatinga (TAB), RioBranco (RBA), Alta Floresta (ALF), and Santarem (SAN) (Gatti et al., 2014). The coverage of all aircraft measurements that were used in this study is shown in Figure   1. 15

Inversion Experiments
The following inversions have been performed: 1. SURF: Inversions assimilating flask air measurements of CH 4 or CO 2 to constrain surface fluxes of CH 4 or CO 2 , respectively.
2. RATIO: Inversion assimilating X ratio and flask air measurements of CH 4 and CO 2 to constrain surface fluxes of CH 4 and 20 CO 2 .
3. PR-MA: Inversion assimilating proxy XCH ma 4 and flask air measurements of CH 4 to constrain surface fluxes of CH 4 .
4. PR-CT: Inversion assimilating proxy XCH ct 4 and flask air measurements of CH 4 to constrain surface fluxes of CH 4 .
To assess the relative performance of each inversion, we validate atmospheric concentrations as simulated using the optimized fluxes from the different inversions with aircraft measurements. We define a normalized (i.e., divided by n) chi-square 25 statistic to quantify the agreement between the optimized model and aircraft measurements.
Where y is a vector of the aircraft measurements, n is the length of y. Hx is the TM5 simulation sampled at the measurement coordinates. The covariance matrix R represents the expected uncertainty in the model-data mismatch. Its diagonal elements are calculated as the sum of the model representation error of TM5 and the measurement uncertainty; all non-diagonal elements are zero.

GOSAST-TCCON comparison
TCCON measurements are used to investigate the errors in GOSAT-retrieved XCH 4 . Each term on the right hand side of 5 equation 2 contributes to the uncertainty in XCH proxy

4
. To quantify these error contributions, we compare TCCON measurements of X ratio , XCH 4 and XCO 2 to corresponding co-located GOSAT-retrievals . The validation is carried out for the time period of 1st June 2009 to 31st December 2013, for which both proxy datasets (XCH ma 4 and XCH ct 4 ) are available. Table 1 shows mean differences per TCCON station, expressed as fractional differences to facilitate the comparison of quantities with different units. As expected, the largest differences between GOSAT and TCCON are found for XCO ns 2 and XCH ns 4 . In general, XCO ns 2 10 (mean= -1.57%) shows larger relative differences than XCH ns 4 (mean =-0.95%). A latitudinal dependence can be observed, with increasing biases towards stations at higher latitudes. This can be explained by increased aerosol scattering at larger sun angles, as the light path through the atmosphere is longer. For all the stations, the mean difference is negative which is expected for aerosol scattering-induced errors at the low surface albedos of the TCCON sites (Houweling et al., 2004). The smaller bias values for X ratio than XCO ns 2 and XCH ns 4 confirm that scattering-induced errors cancel out in the ratio, which motivated the 15 proxy approach (Frankenberg et al., 2005). Overall, we observe that X ratio (mean bias = 0.59 %) is the dominant contributor to the error in XCH proxy

Station
No .

CH 4 fluxes
Optimized annual CH 4 fluxes, integrated over the TRANSCOM regions are shown in the left panel of Figure 3. The fluxes obtained with the RATIO inversion are on average more similar to fluxes from other GOSAT inversions than to the surface inversion, with a few exceptions. Differences between satellite and surface inversion are most prominent over Tropical South America, where the latter is closer to the prior, which can likely be explained by the lack of surface measurement coverage. 5 We will return to the inversion results for Tropical South America in section 3.2.6, where validation results are shown using aircraft data.
The most significant difference between the satellite inversion and SURF is found for Temperate Eurasia, where SURF reduces the CH 4 emissions from 121 Tg/y in the prior estimate to 66 Tg/y. When satellite data are added, the fluxes increase again to 100 Tg/y in the region. The large flux correction in the SURF inversion is compensated by increases in other TRANSCOM   northern wetlands, as discussed in (Spahni et al., 2011). A bias in inter-hemispheric transport in TM5 is not a likely cause, since the use of ECMWF archived convective fluxes in TM5 has been shown to lead to a realistic simulation of the north-south gradient of SF6 (Vanderlaan et al., 2015). Houweling et al. (2014) found similar CH 4 emission shifts between the hemispheres, after bringing the inter-hemispheric transport in agreement with SF6 using a parameterization of horizontal diffusion.
Next we shift focus to seasonal differences between the inversion-derived methane fluxes (see Figure 4). Also on the seasonal 5 scale, RATIO resembles the two PROXY inversions more than SURF. In Boreal North America, the satellite inversions that assimilate GOSAT soundings are in better agreement with the prior. We observe an increase in summertime CH 4 fluxes in SURF estimates for Boreal and Temperate North America. The differences in annual mean fluxes discussed earlier for Tropical South America and Temperate Eurasia do not show an important seasonal dependence. Large differences in seasonality are obtained for Australia and the African regions, which also show important differences between the two proxy inversions (see 10 Section 3.2.4). In Southern Africa, all inversions show increased CH 4 fluxes compared to the prior estimate; however, small differences can be seen between the two proxy inversions, especially in 2010. SURF remains in good agreement with PRIOR, which is expected as no surface observations are available to constrain the fluxes in this region.

CO 2 fluxes
Annual CO 2 fluxes from the SURF and RATIO inversions, integrated over TRANSCOM regions, are shown in Figure 5. 15 Overall, we find good consistency between the results from RATIO and SURF except for Temperate Eurasia, where RATIO results in a higher CO 2 uptake of 0.5 PgC/y. Corresponding reductions in CH 4 fluxes are found for this region in the RATIO inversion. This can be understood by realizing that the satellite information, that is used, consists of the ratio of CH 4 and CO 2 columns. A RATIO inversion can simultaneously reduce the CO 2 and CH 4 fluxes over a region without changing the X ratio in the atmosphere. SURF points towards a natural sink of 0.5 PgC/y in Boreal North America. RATIO and the a priori are carbon 20 neutral in this region. This agreement is also seen on the CH 4 side of the RATIO inversion. Only small differences between

2
In this Section, we analyze the differences between the two proxy retrievals (XCH ct 4 and XCH ma 4 ) and how they propagate into posterior CH 4 fluxes. Note that these differences arise only from differences in XCO model 2 , and therefore large differences between the XCH proxy 4 measurements point towards high uncertainties in the model representations of atmospheric CO 2 . Figure   6 further displays the result of these inversions. We find a mean difference between XCH ma 4 and XCH ct 4 of -2.36 ppb and a σ 5 of 4.55 ppb. This is caused by mean differences between XCO ma 2 and XCO ct 2 of -0.50 ppm and a σ of 0.97 ppm (not shown in the Figure). We find a seasonal variation in the difference with the largest amplitudes of about 10 ppb in the northern tropics. PR-CT and PR-MA yield different CH 4 fluxes in Northern Africa and Australia (see Figure 4). We plot these fluxes with the corresponding regional averaged XCH 4 values in Figure 7. For Northern Africa, the difference in XCH proxy 4 of up to 10 ppb around January 2010 gives rise to a difference in the monthly posterior flux of 1 Tg/month. In Australia, XCH ma 4 and 15 XCH ct 4 are in relatively good agreement with each other, with differences within 2 ppb. However, because the a priori emission from this region is very small, the difference in the optimized seasonal cycle of fluxes nevertheless becomes relatively large.
In particular PR-MA causes significant deviations from the a priori, with decreases in the posterior fluxes during Australian   fluxes. RATIO estimates a significantly stronger sink of CO 2 in agreement with (Basu et al., 2013) (see supplementary Figure   2). This results in lower CH 4 fluxes in the RATIO inversion (see Figure 4), demonstrating how the RATIO inversion method can avoid shortcomings in the proxy inversions in regions where CO 2 is poorly constrained by surface data.
PR-CT and PR-MA have opposite seasonal cycles, which may be due to their XCO model 2 components, which are derived using different ecosystem models. Carbontracker uses a priori natural fluxes from a CASA simulation driven by actual climatological 5 information, whereas MACC uses only the climatology of natural fluxes. Therefore, the inter-annual variability of the inverted fluxes in MACC is driven by measurements only. Since the surface network does not pose strong constraints on the Australian carbon budget, the differences are driven by the prior fluxes of the two models, which may be more realistic in Carbontracker in this case.

10
To further investigate the performance of our inversions, we validate the inversion-optimized CH 4 and CO 2 mixing ratios against independent aircraft measurements obtained during the projects described in section 2.2. The results of the HIPPO and 15 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-77, 2016 Manuscript under review for journal Atmos. Chem. Phys.   Table 1.
The difference between HIPPO and PRIOR reflects the overestimated north-south gradient that is found using a priori CH 4 fluxes, as already discussed in section 3.2.2. In addition, PRIOR shows a uniform bias of 13.5 ppb. SURF and RATIO correct 5 the north-south gradient and reduce biases to 5.56 and 6.68 ppb, respectively. All the models are performing equally well in terms of κ. The original MACC and CarbonTracker CO 2 fields have RMSD values of 1.08 and 1.09 ppm, respectively, which is lower than the RMSD of RATIO (1.64 ppm) and SURF (1.65 ppm). We suggest that CarbonTracker and MACC have a better representation of CO 2 than PR-CT, PR-MA and SURF as they assimilate a larger number of flask measurements sites and also few continuous in-situ sites. 10 Compared with the large CONTRAIL dataset of CO 2 measurements, only a limited number of CH 4 measurements are available, mostly over the Pacific Ocean (see Figure 1). We observe the same north-south gradient mismatch with PRIOR as seen in the comparison to HIPPO. PR-CT is able to improve the PRIOR κ of 6.99 to 4.56, followed in order of decreasing performance by PR-MA (4.71), SURF (5.33), and RATIO (5.47). The values of κ are larger than 1, which points to significant errors in all the inversion results. The RMSD of the different inversions are comparable. The large dataset of CONTRAIL CO 2 15 16 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-77, 2016 Manuscript under review for journal Atmos. Chem. Phys.  However, similar to the HIPPO validation, MACC (mean bias = -0.2 ppm) and CarbonTracker-derived CO 2 (mean bias = 0.11 ppm) fields are in better agreement with the CONTRAIL measurements than the other inversions.

5
Tropical South America contains the Amazon basin, which is a large reservoir of standing biomass and contains one of the largest wetlands in the world. Therefore, it plays an important role in the annual global budget of both CO 2 and CH 4 . Inversion results for the region have been validated using AMAZONICA measurements (see Supplementary Figure 5 and Supplementary   Table 1). Generally, the model results using PRIOR emissions underestimate the measured CH 4 mixing ratios (mean offset= -32.02 ppb). All inversions correct this offset, with SURF performing best (mean offset= -14.18 ppb). RATIO closely follows 10 SURF with a mean mismatch of -17.18 ppb. The proxy inversions have a higher mismatch than RATIO and SURF, with means of -20.30 and -24.11 ppb respectively for PR-MA and PR-CT. The κ values for the AMAZONICA CH 4 measurements (see Figure 9) again show that fluxes from RATIO lead to lower mismatches than those from PR-CT and PR-MA. RATIO predicts this region as a significantly high CH 4 source for the first half of 2010 (see Figure 4), and is in good agreement with aircraft measurements. 15 To check whether this is caused by errors in XCO model 2 , we perform similar comparisons using AMAZONICA CO 2 measurements. We find that the two original models represent CO 2 about equally well in terms of RMSD (see Supplementary Table 1). Therefore, the lesser performance of PR-CT and PR-MA for CH 4 is not due to a poor representation of the XCO model region. This raises the question why RATIO performs better? In sections 3.1, we observe that the error in CO model 2 is generally lower than the error in the GOSAT X ratio retrievals (see section 3.1. In proxy inversions, this retrieval error ,which is coming from X ratio (see equation 2), is directly transferred to CH 4 fluxes, whereas in RATIO it is distributed over the CH 4 and CO 2 part of the state vector. The high posterior CO 2 flux uncertainties for RATIO in the region support this further (see Figure 5).
Flux maps of the region show that the satellite inversions provide a more spatially resolved adjustment of the CH 4 fluxes 5 than SURF (see Supplementary Figure 3). The satellite inversions estimate higher fluxes in the northwest corner of the region near Columbia. Similar increases have been reported in earlier studies assimilating satellite retrieved XCH 4 (Monteil et al., 2013;Frankenberg et al., 2006). The spatial pattern of the flux adjustment suggests that the proxy inversions compensate the increase over Columbia by reducing the fluxes in the Amazon Basin, which is less well covered by satellite retrievals due to frequent cloud cover. This may explain why the proxy inversions end up underestimating the observations inside the Basin. This solution brings SURF in relatively close agreement with the measurements. RATIO also shows a flux enhancement in Columbia, but at the same time represents the Amazon Basin better than the proxy inversions, likely because of its larger number of degrees of freedom in modifying regional flux patterns of both CO 2 and CH 4 . 15 Gatti et al. (2014) and Vanderlaan et al. (2015) reported an anomalous natural source of CO 2 in the region in 2010, also using AMAZONICA aircraft measurements. In this study, RATIO predicts a more enhanced CO 2 natural source than the SURF and PRIOR. RATIO (RMSD =3.23 ppm) is also in better agreement in terms of RMSD with AMAZONICA CO 2 data than SURF (RMSD=3.31 ppm) and PRIOR (3.38 ppm). This demonstrates, like in the case of Australia, that the RATIO method is capable of informing us about the CO 2 fluxes, from which the CH 4 flux estimation benefits also.

Temperate Eurasia
As mentioned in section 3.2.2, SURF leads to a drastic emission reduction in Temperate Eurasia, whereas all satellite inversions show comparatively smaller decreases. Here, we investigate this in further detail by analyzing the inversion-optimized fits to the NOAA measurements at five surface sites located in this region ( Figure 10). We find large mismatches between the a priori simulated concentrations and the measurement at these sites, with mean offsets ranging between 29.1 ppb at Mt. Waliguan and 25 174 ppb at Shangdianzi. All inversions correct for this mismatch by decreasing the regional emissions. Surprisingly enough, the satellite inversions are able to fit the flask measurements even better than SURF, despite smaller corrections to the fluxes.
For example, the mean posterior mismatch at Shangdianzi is 24.3 ppb for SURF, and only 7.5 ppb to 9.8 ppb for the satellite inversions. A possible explanation is the double counting of surface data in the satellite inversions, because the satellite data have been bias corrected using an inversion that was already optimized using surface data. However, the bias correction is

Disscussion
We have demonstrated that the application of the ratio method to GOSAT data yields realistic solutions for CO 2 and CH 4 fluxes. Its performance is comparable, and may in some regions even be better than the proxy inversion method. This is an important finding because the X ratio retrieval approach provides a useful alternative to the full-physics method in that cloud filtering is less critical. In the case of GOSAT, it increases the number of useful measurements by about a factor of two (Butz 5 et al., 2010;Fraser et al., 2014). At the same time, the RATIO inversion method avoids using the model-derived-CO 2 fields as a hard constraint, which is the an important limitation of the proxy method.
The realistic performance of the ratio method is certainly not a trivial outcome, since it prompts the user for specification of new uncertainties influencing the way in which measurement information is shared between CH 4 and CO 2 . The joint CO 2 and CH 4 inversion problem has a larger number of degrees of freedom, as a result of which CH 4 flux adjustments can compensate 10 for errors in CO 2 and vice versa. Assimilating surface measurements helps decoupling CH 4 and CO 2 , which works best in regions that are relatively well covered by the surface network.
In other regions, the method can be improved further by accounting for correlations between a priori fluxes of CH 4 and CO 2 . This study does not specify such correlations, which corresponds to the assumption that a priori CO 2 and CH 4 flux uncertainties are independent of each other. Fraser et al. (2014) accounted for a priori uncertainty correlations for biomass burning fluxes of CO 2 and CH 4 , based on the available information about emission ratios. Imposing such a priori constraints increased posterior uncertainty reduction compared to other methods for both CH 4 and CO 2 in some regions. 5 One problem with the ratio method is the assimilation of X ratio over oceans. The uncertainty of CH 4 fluxes over the open oceans is relatively small. As a result, the model-data mismatch over the ocean is mostly accounted for by adjusting the CO 2 fluxes, which has a larger a priori uncertainty. At the same time, CO 2 fluxes over oceans tend to be very sensitive to small and systematic model-data mismatches of a few tenths of a ppm (Basu et al., 2013). Any bias in atmospheric transport, affecting both CO 2 and CH 4 is projected on the CO 2 fluxes, which may lead to rather unrealistic estimates of the annual CO 2 exchange 10 over oceanic regions. Palmer et al. (2006) proposed to account for cross correlations in the model representation error between the components of a dual tracer inversion, which could reduce this problem.
Our surface-only inversion shows a large decrease in the fluxes from Temperature Eurasia. To better understand this, we look at results of other recently published CH 4 inversion results. We group the studies into three groups: 1. Studies not using versions, as found also by Bergamaschi et al. (2013). In addition, however, these increased emissions have the largest impact on surface-only inversions assimilating measurements from the Shangdianzi site, possibly due to a nearby hot spot in EDGAR v4.2. The hotspot is located near Jiexiu in the Shanxi province (112E, 37N), and has coal emissions of 10.83 Tg/yr for the year 2010 from a 10 × 10 km grid. According to the EDGAR team (G. Meanhout, personal communication), this unrealistically high local source of CH 4 is the consequence of disaggregating large emission from Chinese coal mining using the limited 25 available information on the location of the coal mines. Thompson et al. (2015), the other study in group 3, show a large a priori mismatch with a root mean square error of 103 ppb at Shangdianzi. Their inversions reduce an a priori East Asian CH 4 emission of 82 Tg/y by 23 Tg/y, with large adjustments in the emissions from rice cultivation. Further research is needed to investigate the implications of the shortcoming of EDGAR v4.2. It is noteworthy, however, that when satellite data are assimilated in these studies, the improved regional coverage reduces the impact of this local disaggregation problem on the 30 estimated regional emissions.
20 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-77, 2016 Manuscript under review for journal Atmos. Chem. Phys. Published: 3 February 2016 c Author(s) 2016. CC-BY 3.0 License. This study investigated the use of GOSAT-retrived-X ratio for constraining the surface fluxes of CO 2 and CH 4 . First, we validated the XCH 4 , XCO 2 and X ratio retrievals, as well as the model-derived-XCO 2 fields used in the proxy methods, using TCCON measurements. This analysis confirmed that biases in non-scattering XCH 4 and XCO 2 retrievals cancel out in X ratio . X ratio has a larger mean bias than model-derived-XCO 2 from CarbonTracker and MACC, suggesting that mostly retrieval biases, rather 5 than CO 2 model errors, limit the performance of the proxy method. This is true especially at large temporal and spatial scale.
To account for biases in GOSAT-retrieved X ratio a TCCON-derived correction was applied as a function of surface albedo, resulting in a mean adjustment of -0.74%. An additional correction was applied to X ratio , XCH ct 4 and XCH ma 4 to account for a bias between NOAA-optimized-CH 4 fields in TM5 and TCCON observed XCH 4 , amounting to -0.76%, -0.80% and 0.59%, respectively.
We optimized monthly CH 4 and CO 2 fluxes for the year 2009 and 2010 by assimilating GOSAT-retrieved-X ratio data using the TM5-4DVAR inverse modeling system. Additional inversions, assimilating XCH proxy Overall, the ratio and proxy inversions show similar results for annual CH 4 fluxes. Significant seasonal differences in CH 4 15 are found between the two proxy inversions for TRANSCOM regions Northern Africa and Australia, which can be traced back to differences in XCO model 2 . The CO 2 models show a systematic difference in the seasonal cycle of CO 2 , resulting in a seasonally varying mismatch in the northern tropics. The ratio method has the advantage that it allows adjustment of the CO 2 fluxes, whereas the proxy inversions can only account for this mismatch by adjusting CH 4 . For Australia, the proxy inversions predict an anomalous CH 4 increase in the second half of 2010. This difference can be explained by errors in XCO model 2 , which 20 does not account for the anomalous carbon sink reported by Detmers et al. (2015) for lack of surface measurement coverage.
The ratio method has the build-in flexibility needed to attribute the anomaly to CO 2 instead of CH 4 and is therefore is not affected.
Inversions using satellite data show a better agreement among each other compared to the NOAA-only inversions, which use only surface data. This is true in particular for Temperate Eurasia, where the NOAA-only inversion reduces the annual CH 4 flux 25 by as much as 55 Tg/y, relative to an a priori flux of 121 Tg/y. This is traced back to a large overestimation of atmospheric CH 4 concentration in the prior model at NOAA sites in the region, especially at Shangdianzi, where the prior model overestimates the data by 179 ppb on average. When satellite measurements are assimilated, the CH 4 flux reduction for Temperate Eurasia is limited to 21 Tg/y, while accounting for the a priori mismatch in Shangdianzi.
We validated the inversion-optimized atmospheric tracer fields, as well as the CarbonTracker and MACC CO 2 fields used in 30 the proxy inversions, against three independent aircraft measurement projects. For CH 4 , the ratio and NOAA-only inversions showed a lower mismatch with HIPPO and AMAZONICA measurements than the two proxy inversions. Further analysis shows that this is not due to a better representation of atmospheric CO 2 in the ratio inversion. However, the ratio inversion accounts for inconsistent constraints from X ratio by correcting both CH 4 and CO 2 fluxes, whereas the proxy inversions can only 21 Atmos. Chem. Phys. Discuss., doi: 10.5194/acp-2016-77, 2016 Manuscript under review for journal Atmos. Chem. Phys. Published: 3 February 2016 c Author(s) 2016. CC-BY 3.0 License. attribute such constraints to CH 4 fluxes. The ratio inversion predicts an enhanced CO 2 natural source in this region during 2010 compared with the NOAA-only and a priori model. This is accordance with the findings of Gatti et al. (2014) andVanderlaan et al. (2015), and is also supported by the AMAZONICA aircraft measurements. Overall, this study shows that the ratio method is capable of informing us about surface fluxes of CH 4 and CO 2 using satellite measurements, and that it provides a useful alternative for the proxy inversion method.

Appendix A: Bias correction
We apply a two-step correction to reduce the influence of biases in our inversions: 1. TCCON-based: Residual biases in X ratio remain that are not accounted for by taking the ratio between XCH ns 4 and XCO ns 2 . The standard bias correction procedure in the RemoTeC XCH proxy 4 retrieval assumes a linear dependence on surface albedo . However, this procedure would also correct biases in XCO model 2 , which are not 5 expected to vary with surface albedo. Therefore, we apply the albedo-based bias correction only to the GOSAT-measured-X ratio . To determine the bias correction, we use GOSAT retrievals that are co-located with TCCON measurements, i.e.
they are within 5 degrees latitude and longitude and within 2 hours of TCCON measurements. The relationship between surface albedo at 1593 nm and the monthly difference between GOSAT and TCCON is shown in Figure 11 . A global bias correction function is obtained by linear regression, results in a mean adjustment of -0.74% of GOSAT X ratio . 10 23 Atmos. Chem. Phys. Discuss., doi: 10.5194/acp-2016-77, 2016 Manuscript under review for journal Atmos. Chem. Phys. Published: 3 February 2016 c Author(s) 2016. CC-BY 3.0 License. Figure 12. NOAA based bias correction applied to XCH4 in the PR-CT inversion 2. NOAA-based: A systematic mismatch between the NOAA and GOSAT-optimized TM5 CH4 fields has been discussed in Monteil et al. (2013). The cause of this problem is still unresolved, but may be explained in part by transport model uncertainties in representing XCH 4 in the stratosphere. Several other studies have reported similar biases and applied NOAA-based bias corrections, in addition to the TCCON derived retrieval corrections, in order to restore consistency between the observational constraints provided by surface and total column measurements (Alexe et al., 2014;5 Houweling et al., 2014;Basu et al., 2013). We use a similar procedure for X ratio and XCH proxy 4 data by comparing the TCCON-corrected GOSAT retrievals to the NOAA-optimized TM5 model. The mean difference is corrected using a linear function of latitude. This results in a mean adjustment of -0.76 % in X ratio , -0.59% in XCH ma 4 and -0.80% in XCH ct 4 (See Figure 12 and 13) Appendix B: Posterior Uncertainty 10 As discussed in Pandey et al. (2015), the X ratio inversion problem is weakly non-linear and is solved using the quasi-Newtonian optimizer M1QN3. The standard implementation of M1QN3 does not provide an estimate of posterior uncertainty. Therefore,

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Atmos. Chem. Phys. Discuss., doi: 10.5194/acp-2016-77, 2016 Manuscript under review for journal Atmos. Chem. Phys.  has been performed to determine the size of the ensemble needed to properly capture the 1 σ of the prior fluxes. Figure 14 shows the results of this experiment. We choose an ensemble size of 24 for our experiments which gives a 1 σ estimate with thank Debra Wunch and other TCCON PI's for making their measurements available.