CTE-CH4 is an atmospheric inverse model that optimizes global surface CH4 emissions region-wise based on an EnKF (Evensen, 2003) used to minimize a cost function: J=x-xbTP-1x-xb+y-HxTR-1(y-Hx),E=GxEb, where x (dimension N) is a state vector that contains a set of scaling factors that multiply the CH4 surface emissions (E, dimension 360 × 180, latitude × longitude degrees) that we wish to optimize, starting from a prior estimate of these emissions (Eb [360 × 180]) and scaling factors xb[N]. P [N×N] is the covariance matrix of the state vector, y (dimension M) is a vector of atmospheric CH4 observations, R [M×M] is a covariance matrix of the observations y, and H is an observation operator [M×N]. The operator G transforms the regionally estimated scaling factors x to a 1∘×1∘ global map, which are used to scale prior emissions E. The cost function in Eq. (1) is minimized using an EnKF (Evensen, 2003) with 500 ensemble members, and the TM5 chemistry transport model (Krol et al., 2005) was used as an observation operator that transforms emissions E into simulated atmospheric CH4 (H(x)). The emissions E were optimized weekly, with an assimilation window smoother length of 5 weeks.

In this study, anthropogenic and biospheric emissions were optimized, while emissions from other sources (fire, termites, and oceans) were not optimized (see Sect. 2.3). The optimal weekly mean CH4 fluxes (Ftot), in region r and time (week) t, were calculated as follows: Ftot(r,t)=λbio(r,t)×Fbio(r,t)+λanth(r,t)×Fanth(r,t)+Ffire(r,t)+Fterm(r,t)+Foce(r,t), where Fbio, Fant, Ffire, Fterm, Foce, are the prior emissions from the biospheric, anthropogenic activities, fire, termites and oceans, respectively.

The optimization regional definition of CTE-CH4 is defined based on modified TransCom (mTC) (Fig. 1) and land-ecosystem regions (Fig. S4). Land-ecosystem regions in a 1∘×1∘ grid were defined based on Prigent et al. (2007) and Wania et al. (2010), as in the LPJ-WHyME vegetation model (Spahni et al., 2011), and contain six land ecosystem types (LETs): inundated wetland and peatland (IWP), wet mineral soil (WMS), rice (RIC), anthropogenic land (ANT), water (WTR) and ice (ICE). Large lakes, the Mediterranean Sea, and other large bay areas were defined as WTR, similarly to Peters et al. (2007). ICE corresponds to the ice region in the mTC definition. The remainder of the land-ecosystem regions were defined according to the fraction of IWP, WMS and RIC used in LPJ-WHyME. To limit the number of degrees of freedom, only one dominant LET was assigned to each grid cell. In the following cases, the LET with the largest fraction was chosen. For grid cells where the fraction of IWP, WMS or RIC was larger than 0.1, either IWP, WMS or RIC was assigned. IWP or WMS was assigned for grid cells where the fraction of IWP or WMS were smaller than 0.1, and the prior anthropogenic emission estimates (EDGARv4.2 FT2010, see Sect. 2.3) including emissions from rice fields were zero. Furthermore, if the LPJ-WHyME biospheric emission estimates exceeded the EDGARv4.2 FT2010 emission estimates by more than 200 %, either IWP or WMS was assigned. However, if the EDGARv4.2 FT2010 emission estimates were much larger than the LPJ-WHyME biospheric emission estimates, either ANT, RIC or WTR was assigned.

In one of the two model configurations referred to as L62 (see also Table 1 for an overview of configurations), anthropogenic emissions were optimized in optimization regions where LETs are RIC, ANT or WTR (i.e. λbio(r,t)=0), and biospheric emissions were optimized in optimization regions where LETs are either IWP or WMS (i.e. λanth(r,t)=0). This mutually exclusive approach resulted in 28 biospheric regions and 34 anthropogenic optimization regions, i.e. 62 scaling factors λ(t)=(λbio(t),λanth(t)) to be optimized per week globally. This number of scaling factors was smaller than theoretically expected (20 mTCs × 5 land-ecosystem regions = 100 scaling factors) because some mTCs contain less than five ecosystem types. In the second configurations referred to as L78, both λbio(r,t) and λanth(r,t) were optimized in each optimization region. In that case, the regional definition of the scaling factors for biospheric emissions was based on the combination of mTCs and land-ecosystem regions, but oceans were treated as one region instead of five (i.e. 58 biospheric regions). The mTCs (20 regions) were used for the anthropogenic emissions. This resulted in 78 scaling factors to be optimized per week globally. Note that scaling factors were optimized based on sensitivities in the EnKF (represented in Kalman Gain matrix), and thus there is no explicitly prescribed system for choosing which of the scaling factors (λbio(r,t) or λanth(r,t)) are adjusted more in each optimization region. A discussion of the application of land-ecosystem distribution maps and their effect on CH4 emission inversions for a short period during summer 2007 is also included in the Supplement of this study.

For the prior uncertainty, variance of the scaling factors was set to 0.8 for all optimization regions, except for the “Ice” region (Fig. S4), which was set to 1×10-8. Emissions from the “Ice” region contribute only 0.02 % of the global total emissions, and we did not expect the inversions to be able to optimize the emissions well. For L62, an informative covariance matrix was used; the scaling factors for biospheric and anthropogenic emissions were assumed to be independent, and biospheric scaling factors were assumed to be correlated among mTCs based on the distance between the centres of the optimization regions (see Supplement for further details). For L78, a non-informative covariance matrix was used, i.e. all optimization regions were assumed to be independent.

The atmospheric chemistry transport model TM5 (Krol et al., 2005) was used as an observation operator. TM5 was run with a 1∘×1∘ (latitude × longitude) zoom region over Europe (24–74∘ N, 21∘ W–45∘ E), framed by an intermediate zoom region of 2∘×3∘, and a global 4∘×6∘ degree resolution, driven by 3-hourly ECMWF ERA-Interim meteorological fields with 25 vertical layers. The atmospheric chemical loss, i.e. oxidation of CH4 initiated by reaction with OH, chlorine (Cl) and an electronically excited state of oxygen (O(1D)), was pre-calculated based on Houweling et al. (2014) and Brühl and Crutzen (1993), and it was not adjusted in the optimization scheme. The atmospheric lifetime of CH4 estimated from the global total annual mean atmospheric chemical loss during 2000–2012 was about 9.7 years. Interannual variability was not applied in the removal rates of the CH4 sinks.

To establish reasonable initial conditions for the global distribution of CH4 abundance, TM5 was run twice consecutively for 1999, starting from a uniform abundance of 1600 ppb globally using prior emission estimates. Using the final values, CTE-CH4 was run for 2000, and the third run was used to define the initial CH4 values at the beginning of 2000. Since atmospheric CH4 concentrations did not increase significantly in 2000, it was assumed that this condition represents well-mixed initial atmospheric CH4 for the experiments presented in this study.

In this study, two different convection schemes were used in TM5: Tiedtke (1989) (hereafter T1989) and Gregory et al. (2000) (hereafter G2000). The two versions differ mainly in vertical mixing in the troposphere: mixing is faster, and atmospheric CH4 at the surface in the Northern Hemisphere (NH) is expected to be smaller with G2000 compared to T1989. Moreover, G2000 produces faster vertical mixing near the surface and also has a faster IH exchange time compared to T1989.

Five prior emission fields were used in this study and represented CH4 release from anthropogenic, biospheric, fire, termite, and oceanic sources. Anthropogenic emissions accounted for about 60 % of total global annual CH4 emissions during 2000–2012. For prior anthropogenic emissions, the Emissions Database for Global Atmospheric Research version 4.2 FT2010 (EDGAR v4.2 FT2010) inventory was used. The original inventory data coverage extends to 2010; for 2011–2012, emission fields were assumed to be the same as 2010. Turner et al. (2016) suggested that a large increase in anthropogenic emissions from the United States contributed significantly to the global growth in CH4 emissions during 2002–2014. Although the 2010–2012 increase was not included in the prior, such an increase is expected to be seen in the CTE-CH4 after optimization. A seasonal cycle was not included in the EDGAR v4.2 FT2010 estimates. Emission estimates from the biogeochemistry model LPX-Bern v1.0 (Spahni et al., 2013) were used as prior biospheric emissions, which accounted for about 30 % of prior global total emissions. Emission estimates from rice fields were excluded from the prior biospheric emissions because they were already included in the prior anthropogenic emissions. In addition, consumption of CH4 by methanotrophic bacteria in soils was estimated by LPX-Bern, and included as surface sinks in CTE-CH4. GFEDv3.1 (Randerson et al., 2012; van der Werf et al., 2010) was used for emission estimates from large-scale biomass burning rather than the EDGARv4.2 FT2010 inventory. GFEDv3.1 emission estimates accounted for about 3 % of prior global total emissions. The original data coverage is up to 2011, so the 2011 and 2012 emission fields were assumed to be unchanged from the last year available. However, global fire emissions in 2012 were about 2 Tg CH4 yr-1 larger than in 2011, mainly due to an increase in emissions in northwest Russia during the summer (GFEDv4.1; Giglio et al., 2013). Therefore, we must be aware of an additional uncertainty in the spatial distribution of the emission sources, especially for 2012. Prior termite emissions are based on estimates from Ito and Inatomi (2012) for 2000–2006, which accounted for about 4 % of prior global total emissions. The 2006 estimate was also used for 2007–2012. The estimates by Ito and Inatomi (2012) are about 10 Tg CH4 yr-1 smaller than the estimates reported by Sanderson (1996) that were used in Bergamaschi et al. (2007), for example. Prior emission estimates from “natural” open ocean were calculated assuming a supersaturation of CH4 in the seawater of 1.3 (Lambert and Schmidt, 1993), which accounted for about 1 % of prior global total emissions. ECMWF ERA-Interim sea surface temperature, sea ice concentration, surface pressure and wind speed (Dee et al., 2011) were used to calculate the solubility and the transfer velocity (Bates et al., 1966; Tsuruta et al., 2015). No special treatment was applied to coastal emissions of the “natural” ocean. In addition to the “natural” ocean emission estimate, an “anthropogenic” ocean emission estimate from EDGAR v4.2 FT2010 was added to the prior. Sources of anthropogenic ocean emissions are mainly from ships and other “non-road” transportation. This includes emissions around coastlines. Prior fluxes from land and ocean anthropogenic sources, and from land biospheric sources, were optimized. Fluxes from fire, termites and natural ocean sources were not optimized.

Atmospheric observations of CH4 abundance (reported in units of dry-air mole fraction) collected from the World Data Centre for Greenhouse Gases (WDCGG) were assimilated in CTE-CH4. The set of observations consisted of discrete air samples and continuous measurements from several cooperative networks (Table 2). The observations were filtered based on observation flags provided by each contributor to avoid the influence of strong local signals on the inversions. For continuous observations, daily means from selected hours were assimilated; afternoon observations (12:00–16:00 LT) were selected for most sites, but for the high altitude sites, night-time observations (00:00–04:00 LT) were selected. These choices of sampling hours reflect a preference for well-mixed conditions that represent large source areas, and are also better captured by the TM5 transport model. Day–night selection was not applied to discrete observations. For each site, model–data mismatches (MDMs) were defined considering both the observation error and the transport model error, i.e. the ability of the transport model to simulate the observations. Note that the latter error is often much larger than the former. For the marine boundary layer (MBL) and the high latitude Southern Hemisphere (HLSH) sites, MDM was set to 4.5 ppb. For sites that capture both land and ocean signals, MDM was set to 15 ppb. For sites that capture signals from the land, MDM was set to 25 ppb. For sites with a large variation in observations due to local influences, MDM was set to 30 ppb, and for the sites that appeared problematic in the inversions, MDM was set to 75 ppb. Although the values of MDM are somewhat arbitrary, they are based on a previous study by Bruhwiler et al. (2014) and typically reflect the model forecast skill well. During assimilation, rejection thresholds were set as 3 times MDM, except for the MBL and HLSH sites. For these sites, rejection thresholds were set to 20 times MDM because assimilation of these observations is important in the characterization of background atmospheric CH4. In this study, the observation covariance matrix was assumed diagonal, i.e. no temporal or spatial correlation between observations was taken into account.

Aircraft profiles of CH4 abundance with altitude provide information about atmospheric CH4 in general, but also specifically on vertical transport. Aircraft data from regular profiling that operated within the European CarboEurope project at Orléans (France), Bialystok (Poland), Hegyhatsal (Hungary) and Griffin (UK) during 2006–2012, which is a part of the European Union-funded IA (Integrating Activity) project within the Integrated non-CO2 Greenhouse gas Observation Systems (InGOS), were used for evaluation (Table 3). In addition, data from an aircraft campaign performed within the Infrastructure for Measurement of the European Carbon Cycle (IMECC) project were used. The IMECC campaign deployed a Learjet 35a with multiple vertical profiles from close to the surface up to 13 km near several TCCON sites in central Europe. For details on the airborne CH4 measurements the reader is referred to Geibel et al. (2012). Aircraft observations were not assimilated in the inversions.

In addition to the aircraft profiles and surface CH4 measurements at in situ stations, XCH4 from the TCCON network and the TANSO-FTS instrument on board the GOSAT spacecraft (Kuze et al., 2009) were used for evaluation. XCH4 data provided additional information in regard to long-range transport and helped to assess the quality of the global simulations. TCCON retrievals from the GGG2014 release (Wunch et al., 2015) were used, and daily means were compared to simulated XCH4 at each site. For GOSAT retrievals, the product reported by Yoshida et al. (2013) was used, and the regional daily mean for each mTC was compared to the corresponding simulation. The XCH4 datasets were not assimilated in the inversions.

To facilitate a fair comparison, posterior XCH4 were calculated using global 4∘×6∘×25 (latitude, longitude, vertical levels) daily 3-dimensional (3-D) atmospheric CH4 fields. For each retrieval, the global 3-D daily mean gridded atmospheric CH4 estimates were horizontally (latitude, longitude) interpolated to the location of the retrievals to create the vertical profile of simulated CH4. For comparison with GOSAT and TCCON retrievals, the retrieval-specific averaging kernels (AKs) were applied to model estimates based on Rodgers and Connor (2003): C^=ca+h∘aT(x-xa), where C^ is the quantity for comparison, i.e. XCH4. The scalar ca is the prior XCH4 of each retrieval, h is a vertical summation vector, a is an absorber-weighted AKs of each retrieval, x is a model profile, and xa is the prior profile of the retrieval. For the TCCON retrievals, one prior profile was provided each day, which was scaled to get the observed profiles that optimize the spectral fit (Wunch et al., 2011). Prior profiles of GOSAT retrievals were provided for each retrieval (Yoshida et al., 2013). Model-estimated XCH4 values were calculated for each site for the comparison with TCCON XCH4, while the spatial mean of XCH4 for each mTC was used for comparison with the GOSAT retrievals.

In this study, three inversions were performed, which differed in number of parameters and TM5 convection schemes: (L62T) using L62 configuration with the T1989 convection scheme, (L78T) using L78 configuration with the T1989 convection scheme, and (L62G) using L62 configuration with the G2000 convection scheme (Table 1). Prior and posterior CH4 abundance was estimated with TM5 using prior and posterior emission estimates, respectively. Posterior CH4 was also estimated using the respective convection schemes in the forward runs.

Atmospheric CH4 values simulated using prior fluxes (prior atmospheric CH4) increase continuously during 2000–2012, and quickly exceed observed atmospheric CH4 levels, especially in the NH (Figs. 2, 3). The seasonal cycle of prior atmospheric CH4 values agrees poorly with the observations, with a positive bias from winter to summer in the NH and around the end of each year in the Southern Hemisphere (SH) (Fig. 2). Furthermore, prior atmospheric CH4 values are negatively biased compared to the observations in the SH during 2002–2004 (Fig. 2). This is likely due to an underestimation in the prior emissions in the SH. Posterior atmospheric CH4 values generally match the observations to a level close to the expected model–data mismatch, indicating a proper choice of observation covariance. A seasonal bias remains in the NH (especially in L62T), and the decrease in atmospheric CH4 in the SH around 2002–2004 also remains in the posterior, although shorter in duration and of smaller magnitude than in the prior (Fig. 2). The negative bias in posterior atmospheric CH4 around the equator remains unresolved throughout the study period in all inversions, and mainly originates from the sites Bukit Koto Tabang, Indonesia (BKT), (-25 to -27 ppb), and Mt. Kenya, Kenya (MKN) (-18 to -23 ppb). The posterior atmospheric CH4 values are especially low relative to observations during June–October. The bias became smaller when CH4 emissions were increased in the South American tropical mTC region, although this led to compensating fluxes and mismatches with observations elsewhere (not shown). Posterior emissions for the South American tropical region (mTC3) remain similar to the prior, and the inversion does not significantly decrease the uncertainty of the prior emission estimates in this mTC (see Sect. 3.4.4 and 4.2).

Agreement between simulated CH4 and surface observations is slightly better in L78T and L62G than in L62T (Fig. 2), as indicated by the root mean square error (RMSE), which is about 0.5 ppb smaller. In addition, the biases in annual amplitude are about 1–2 ppb smaller. The negative bias in the SH from 2002 to 2004 is seen in all inversions, but is most prominent in L62T. Although the difference in the average RMSE is small, it is significant as it is calculated from all the observations assimilated in the study period. In addition, differences are significant when the ensemble distributions of posterior atmospheric CH4 are considered. The spread (1 standard deviation (SD)) of ensembles is less than 5 ppb for most sites and less than 1 ppb for MBL sites, mostly located in the SH.

Further evidence of poorer performance in L62T than in other runs is seen in its global fluxes. L62T produced the smallest total global emission estimates for 2002–2004, which in turn led to the largest increase in the total global emission estimates from 2001–2006 to 2007–2012. Based on previous studies (e.g. Bergamaschi et al., 2013; Bousquet et al., 2006; Bruhwiler et al., 2014; Fraser et al., 2013), the increases in L78T and L62G are more reasonable (see Sect. 3.4.1). The differences in RMSE and bias between the latter inversion estimates are small near 30∘ N, where many observations are located. However, the RMSE and bias in L78T are about 1 and 2 ppb smaller at high northern latitudes (60–75∘ N), and about 3 and 6 ppb larger around the equator (EQ–15∘ N) than in L62G, respectively. Moreover, low atmospheric CH4 values in the SH during 2002–2004 are not as prominent in the prior when the G2000 convection scheme is used (Fig. 2), probably due to enhanced transport between the NH and SH in L62G. Mean Chi-squared statistics (Michalak et al., 2005) of the observations are typically between 0 and 2, and follow normal distributions (not shown), which again indicates that the MDM estimates are appropriate at most of the sites.

In contrast to the prior, the growth rate (GR) of posterior XCH4 does not change strongly before 2007, but increases after 2007 (Fig. 3). All inversions show an increase in XCH4 by about 6 ppb yr-1 after 2007, with some seasonal and interannual variations (Fig. 3). The timing of the change in posterior XCH4 GR is in line with the GR calculated from the global network of NOAA MBL observations (Dlugokencky et al., 2011) and with the retrieved XCH4 GR at Park Falls (Fig. 3). This indicates that the GR of prior XCH4 is too large throughout 2000–2012 (see also Fig. 2), and this can only result from overestimated emissions or underestimated loss of CH4. Note that the NOAA MBL observations compared in Fig. 3 are calculated from surface observations.

Posterior atmospheric CH4 generally agrees well with independent vertical profiles from aircraft. The average RMSE decreased from 80 ppb in the prior to 24 ppb in the posterior (Fig. 4, Table 3). The RMSE between posterior and observed atmospheric CH4 values is smallest for Griffin, UK (GRI) (< 12.9 ppb), and largest for Orléans, France (ORL) (> 37.4 ppb) (Fig. 4). The model performance at in situ sites near GRI is good, i.e. the correlations between assimilated observations and posteriors are high, and the RMSE is equal to or smaller than the MDM (Fig. 5). This suggests that emission estimates are well constrained, at least in the NH, although the RMSE is much larger than those at surface sites due to vertical transport. The model performance at in situ sites near ORL is poor, and the bias in the ORL profiles extends up to 2 km, which was also seen in Bergamaschi et al. (2015). The comparison with IMECC observations from central Europe shows the effect of the convection scheme on the profiles above 2 km. Negative biases are seen in the inversion estimates using the T1989 scheme at 2–10 km. The bias in the inversion estimates using the G2000 scheme is small at around 2–10 km, but is positive in the upper troposphere and lower stratosphere, where the estimates using T1989 better match the observations. This could however be due to diffusive transport near the tropopause simulated by the 25 vertical layers in TM5. The use of a higher vertical resolution of TM5 might improve the agreement with observations at higher altitudes for both convection schemes.

XCH4 provides additional information about the spatial distribution of atmospheric CH4. TCCON and GOSAT XCH4 retrievals were not assimilated in the inversions, so the following comparisons also allow an assessment of model performance at independent locations and times.

For many TCCON sites in the NH, the XCH4 in L62T and L78T is slightly lower than observed, but the trend and seasonal variability are generally well captured. However, the 2007–2012 trends at Izaña (Spain), Park Falls (USA) and Lamont (USA) are much stronger than in the retrievals (Fig. 6). Since the emission estimates at similar latitudes would affect the XCH4 estimates, this could be an effect of the strongly increasing northern temperate emission estimates after 2007 (Sect. 3.4.2). The RMSE between the estimates and retrievals is smallest in L62G at all sites, except at Garmisch, Germany (Table 4). Garmisch is a mountain site (altitude 734 m a.s.l.), and the mean of observed XCH4 is statistically significantly lower than at nearby sites, e.g. Karlsruhe, Germany, and Bialystok, Poland (Figs. 6, S5).

For the SH TCCON sites, a strong negative bias is found in all inversions (Figs. 6, S5). Agreement is especially poor for Wollongong, which has the largest RMSE (more than 30 ppb) among all TCCON sites in all inversions (Table 4). As the site is located in the city of Wollongong, where the influence of local emissions is high, it is difficult for models to reproduce XCH4 well (Fraser et al., 2013). The comparison with the nearest in situ site, Cape Grim, Australia (CGO) shows that the negative bias is much smaller (-6 to -11 ppb) compared to Wollongong (-32 to -35 ppb), and the correlation with the retrievals is high (> 0.85). In addition, the negative bias in XCH4 is much smaller (-12 to -15 ppb) at background site Lauder, New Zealand (LAU) and the correlation at the LAU in situ site is again strong (> 0.85) in all inversions. The disagreement at Darwin is probably due to little constraint of the emissions. Although in situ observations at Gunn Point, Australia (GPA) were assimilated, the inversion probably did not benefit significantly from these observations because data were available only after mid-2010, and the MDM was set high (75 ppb). Furthermore, emissions from the tropics also affect the XCH4 estimates in Australia. Our emission estimates for the tropics (30∘ S–30∘ N) are about 10–20 Tg CH4 yr-1 smaller than the estimates by Houweling et al. (2014), for example. When the prior emission estimates for the South American tropical region (mostly between 15∘ S–15∘ N) were increased (see Sect. 3.1), agreement in the SH improved (not shown). The comparison with GOSAT XCH4 also supports the finding from the comparison with the TCCON retrievals, showing a mean negative bias of 13 ppb in the SH (Fig. S6). We currently do not have sufficient information to correct the errors that affected the SH XCH4 in our system, or to identify the exact cause.

Spring peaks seen in GOSAT XCH4 in global, ocean and the Asian tropical mTC region point to an important role of the vertical mixing scheme, which are well captured in L62G, but not in L62T and L78T (Figs. 7, S6). The difference is statistically significant considering the ensemble distribution. Monthly emission estimates in L62G are generally larger than in L62T and L78T during November–April, especially in the northern-latitude temperate regions (35–60∘ N, Fig. S7). This suggests that winter emissions in the northern latitude temperate regions, enhanced in the model by faster vertical mixing around the surface, play an important role to reproduce the XCH4 seasonal cycle in the tropics well.

Although GOSAT retrievals are valuable for evaluating model performance, it is important to keep in mind that the satellite retrievals do not always agree with ground-based TCCON retrievals. GOSAT XCH4 has been evaluated against TCCON retrievals, but biases in the GOSAT products remain, especially in the latitudinal gradient (Yoshida et al., 2013). This is probably one of the reasons for the positive model bias in the NH compared to GOSAT (Fig. S6). Furthermore, the seasonal amplitude of GOSAT XCH4 is much smaller than that of the posterior estimates, especially in the SH (Fig. S6). This is not in line with the TCCON comparison (Figs. 6, S5), which suggests that disagreement with GOSAT XCH4 in the latitudinal gradient and the seasonal amplitude may not only be due to problems in the inversions.

Interannual variability of emission estimates is often stronger in L78T than in L62T and L62G. Differences are mainly seen in the Asian temperate region, where the proportion of biospheric emissions to total emissions is much smaller in L78T than in L62T and L62G. Anthropogenic emission estimates for the Asian tropical region in L78T show strong interannual variability, although the biospheric emission estimates in L78T are similar to the L62T and L62G estimates. The ratio of biospheric to anthropogenic emission estimates in the Asian temperate and Asian tropical regions changes from year to year in L78T. The dominant sources are similar in L62T and L62G, but sometimes different in L78T. For example, in the Asian temperate region, biospheric emissions are larger than anthropogenic emissions during 2003–2005 in L62T and L62G, but lower in L78T. Only small differences are found in the posterior values of XCH4 in L62T and L78T. Agreement with in situ CH4 observations is better in L78T than in L62T, i.e. the negative bias in the SH is less pronounced in L78T. The emission estimates in the SH are often larger in L78T than in L62T, where differences are mainly seen in the anthropogenic emission estimates. This means that the land-ecosystem distribution used in this study generally represents the division of the source areas well, although some revision may be needed for Asia and the SH, e.g. Australia.

As expected, interannual variability of emissions in L62T and L62G is similar. This shows that the different convection schemes do not have a large effect on the interannual variability of the emission estimates in L62 configuration. The north–south gradient of emissions shows that NH emissions are about 10 Tg CH4 yr-1 larger, and SH emissions about 10 Tg CH4 yr-1 less when the G2000 scheme is used. (Tables 6, S1). In all mTCs, estimates of emissions from the major sources (either biospheric or anthropogenic) are more strongly affected by the convection schemes than the estimates of minor sources (L62T and L62G). In L78T, the effects of the convection schemes are not assessed in a strictly comparable setup, but similar results are expected (for a fair comparison assessed on a short time period, see Supplement). Note that L78T and L78G-K have significant differences in their annual total emission estimates and their interannual variability in Asian temperate and Asian tropical regions (Fig. 8), but the different convection schemes are not the main cause. Although the emission estimates for the SH are smaller in L62G than in L62T, SH posterior surface atmospheric CH4 and XCH4 are larger in L62G than in L62T, due to faster mixing and larger emission estimates in the NH. Agreement with independent observations is best in L62G among the inversions. NH surface atmospheric CH4 in L62G is in good agreement with observations at in situ stations, and L62G XCH4 also agrees best with the TCCON XCH4 globally. Although NH XCH4 in L62G is larger than in GOSAT retrievals, the results suggest that CTE-CH4 performed better in TM5 when the G2000 scheme is used rather than T1989. It can be assumed that if GOSAT retrievals were assimilated in CTE-CH4, emission estimates would decrease in the NH and increase in the SH compared to this study. Also, the assimilation of satellite-based retrievals may reduce differences in the estimates between the L62T and L62G setups. However, the assimilation of GOSAT XCH4 requires further development as previous studies (Houweling et al., 2014; Pandey et al., 2016; Bergamaschi et al., 2013) have shown that the biases in the GOSAT XCH4 products could misrepresent the distribution and seasonal cycle of the optimized surface emissions.

The smallest uncertainties in the posterior total annual emissions are generally seen in L62T, and the largest in L78T. We expected that L78T would have larger uncertainties than L62T and L62G. The prior uncertainties in L78T are the sum of both prior anthropogenic and biospheric uncertainty estimates for each optimization region, whereas the uncertainty in L62T and L62G is from either anthropogenic or biospheric emissions. Although the differences are small (< 0.1 %), uncertainties in the emission estimates in L62G are slightly larger than those in L62T in most of the optimization regions for both anthropogenic and biospheric emissions. It could be that there is more mixing of the surface signals in G2000, thereby producing a wider range of ensemble atmospheric CH4 values, and thus L62G may have less flux sensitivity at surface sites. However, the difference in the ensemble standard deviation of atmospheric CH4 values between inversions is small. Furthermore, this cannot be explained by the number of assimilated observations. The uncertainty is larger in L62G than in L62T, while the number of rejected observations is smaller in L62T than in L62G (6.6 and 6.9 %). Similarly, the anthropogenic emission uncertainty is smaller for the Eurasian boreal region than for north-east Europe, which also cannot be explained purely by the number of observations within the region.