We develop an existing EnKF framework that has been used to estimate CO2 (Feng et al., 2009, 2011, 2016) and CH4 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 CO2 and CH4 at location x and time t as fpgx,t=f0gx,t+∑icigBFig(x,t), where g denotes CO2 or CH4 tracer gas and f0gx,t describes the a priori estimates of CO2 or CH4 fluxes. Following Fraser et al. (2014), our basis function set BFig(xt) is defined as the pulse-like (monthly) CO2 or CH4 fluxes from different sectors over predefined geographic regions. The coefficients cig for both the CO2 and CH4 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 perturbations of the coefficients ΔC: P=ΔCΔCT, where T represents the matrix transpose. The a posteriori coefficient estimates are given by ca=cf+Kyobs-Hcf, where ca, cf are the prior and posterior estimates, respectively; yobs 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): K≈ΔCΔYT[ΔYΔYT+R]-1, where R is the observation error covariance, and ΔYT=HΔC projects the flux perturbation (coefficients) ensemble ΔC 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 HOx-NOx-Ox chemistry simulation to describe the main oxidation sink of CH4 (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, 2016)

Where possible, we use consistent emission inventories for CO2 and CH4: 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 CO2 variations, we also use monthly-resolved climatological ocean fluxes (Takahashi et al., 2009) and 3-hourly terrestrial biosphere fluxes (CASA; Olsen and Randerson, 2004). To describe atmospheric CH4 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 2009, 2010, and 2011 (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 CH4 (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 distinguish CO2 fluxes between four categories: (1) ocean fluxes; (2) anthropogenic emissions; (3) biomass burning; and (4) terrestrial biospheric fluxes. For CH4 fluxes, we distinguish between six categories: (1) ocean fluxes; (2) anthropogenic emissions from coal mining; (3) anthropogenic emissions from oil and gas production, fossil fuel combustion, and others; (4) biomass burning; (5) natural fluxes from wetlands and rice paddies; and (6) natural fluxes from termites, hydrates, and others. In total, we have 143 monthly basis functions for CO2 and 231 monthly basis functions for CH4.

We assume an a priori uncertainty of 60 % for the coefficients corresponding to the natural CO2 and CH4 fluxes, and for CH4 emissions from coal mines. We assume an a priori uncertainty of 40 % for CO2 anthropogenic emissions, CO2 and CH4 ocean fluxes, and anthropogenic emission of CH4 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 (Feng et al., 2016). We assume that fire emissions of CO2 and CH4 are correlated with a correlation coefficient of 0.5, accounting for the variation and uncertainty of the fire emission factors (Parker et al., 2016).

We assimilated GOSAT XCH4 : XCO2 retrievals and in situ surface observations of CO2 and CH4 mole fraction. We use version 6 of the proxy GOSAT XCH4 : XCO2 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 % (Parker et al., 2015, 2011). In our experiments, we globally remove this 0.3 % bias from the GOSAT proxy data. We assume that each single GOSAT proxy XCH4 : XCO2 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 CO2 and CH4 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 (Dlugokencky et al., 2015). We assume uncertainties of 0.5 ppm and 8 ppb for the in situ observations of CO2 and CH4, respectively. We also assume a model error of 1.5 ppm and 15 ppb for CO2 and CH4, respectively. We adopt a larger percentage for the CH4 model error to account for difficulties in modelling chemical sinks of CH4 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 CO2 and CH4 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.

We use independent observations of atmospheric CO2 and CH4 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 CO2 and CH4 (Wunch et al., 2011). We use the bias-corrected TCCON XCO2 and XCH4 data at all available sites from the recent GGG2014 release of the TCCON data set (Wunch et al., 2015). 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. Blumenstock et al., 2014; 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., 2014, 2016; Kivi et al., 2014; Morino et al., 2014a, b; Notholt et al., 2014 Sherlock et al., 2014a, b; Strong et al., 2014; Sussmann and Rettinger, 2014; Te et al., 2014; Warneke et al., 2014; Wennberg et al., 2014a, 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 pole-to-pole observations (HIPPO) that provide latitude–altitude cross sections of tropospheric mole fractions of CO2 and CH4 (and other tracers) covering dates from 2009 to 2011 (Wofsy et al., 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); (3) bi-weekly aircraft measurements (surface to 4 km) collected from 2010 to 2012 at four sites over Brazil by IPEN (Instituto de Pesquisas Energéticas e Nucleares) over the Amazon rainforest (AMAZONICA; Gatti et al., 2014): Rio Branco (RBA), Tabatinga (TAB), Alta Floresta (ALF), and Santarém (SAN); and (4) aircraft measurements conducted by IPEN for the FAPESP/NERC-funded Amazonian Carbon Observatory (ACO; Webb et al., 2016) close to two of the AMAZONICA 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 XCH4 and XCO2 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 XCH4 : XCO2 data are shown below.

Figure 2 shows that the in situ only and the ratio inversions result in similar annual net CO2 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 CO2 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 CO2 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 CH4 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 CH4 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 CH4 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 CH4 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.

In general, the ratio inversion shows the best agreement with independent CH4 observations, particularly over lower latitudes. A posteriori improvements to the CO2 simulation are relatively small. We find that both the model CO2 and CH4 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 XCH4 and XCO2 variations. Over most TCCON sites, the a posteriori XCO2 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 XCH4 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 CO2 and CH4 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 CO2 and CH4 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 (Gatti et al., 2014; Alden et al., 2016). And third, we report new aircraft profile measurements from the ACO (Webb et al., 2016) that was designed specifically to evaluate GOSAT column observations of CH4 and CO2 (Sect. 3).

Figure 6 shows that the a posteriori monthly CH4 and CO2 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 CO2 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 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 regional-scale AMAZONICA aircraft observations (Gatti et al., 2014; 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 CH4 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 XCH4 : XCO2 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 CH4 emissions and/or lower CO2 fluxes. The two closest in situ sites to the locus of XCH4 : XCO2 variability (RPB and ABP) do not reproduce this change. Consequently, the in situ inversion may not accurately describe these CH4 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 CO2 and CH4 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 CO2 and CH4 inferred from the in situ data. Figure 7 shows that for CO2 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 impact of GOSAT XCH4 : XCO2 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 CH4 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 CO2. After 2012, the ratio inversion shows a positive bias at the two ACO sites (SAH and RBH). Assimilating the XCH4 : XCO2 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.