Country-Scale Analysis of Methane Emissions with a High-Resolution Inverse Model Using GOSAT and Surface Observations

: We employed a global high-resolution inverse model to optimize the CH 4 emission using Greenhouse gas Observing Satellite (GOSAT) and surface observation data for a period from 2011–2017 for the two main source categories of anthropogenic and natural emissions. We used the Emission Database for Global Atmospheric Research (EDGAR v4.3.2) for anthropogenic methane emission and scaled them by country to match the national inventories reported to the United Nations Framework Convention on Climate Change (UNFCCC). Wetland and soil sink prior ﬂuxes were simulated using the Vegetation Integrative Simulator of Trace gases (VISIT) model. Biomass burning prior ﬂuxes were provided by the Global Fire Assimilation System (GFAS). We estimated a global total anthropogenic and natural methane emissions of 340.9 Tg CH 4 yr − 1 and 232.5 Tg CH 4 yr − 1 , respectively. Country-scale analysis of the estimated anthropogenic emissions showed that all the top-emitting countries showed di ﬀ erences with their respective inventories to be within the uncertainty range of the inventories, conﬁrming that the posterior anthropogenic emissions did not deviate from nationally reported values. Large countries, such as China, Russia, and the United States, had the mean estimated emission of 45.7 ± 8.6, 31.9 ± 7.8, and 29.8 ± 7.8 Tg CH 4 yr − 1 , respectively. For natural wetland emissions, we estimated large emissions for Brazil (39.8 ± 12.4 Tg CH 4 yr − 1 ), the United States (25.9 ± 8.3 Tg CH 4 yr − 1 ), Russia (13.2 ± 9.3 Tg CH 4 yr − 1 ), India (12.3 ± 6.4 Tg CH 4 yr − 1 ), and Canada (12.2 ± 5.1 Tg CH 4 yr − 1 ). In both emission categories, the major emitting countries all had the model corrections to emissions within the uncertainty range of inventories. The advantages of the approach used in this study were: (1) use of high-resolution transport, useful for simulations near emission hotspots, (2) prior anthropogenic emissions adjusted to the UNFCCC reports, (3) combining surface and satellite observations, which improves the estimation of both natural and anthropogenic methane emissions over spatial scale of countries.


Introduction
Climate change, a matter of global concern, is driven by the increasing anthropogenic emissions of greenhouse gases (GHGs), currently, in particular, from developing countries. Methane (CH 4 ), a major greenhouse gas, has the global warming potential of about 28 times (over a time span of 100 years) higher than carbon dioxide (CO 2 ) [1] and a tropospheric lifetime of about 8-11 years. The anthropogenic sources of CH 4 are almost 50% larger than the natural sources and are estimated to be around 360 (334-375) Tg yr −1 during 2008-2017 [2]. Methane is oxidized by photochemical reactions to carbon monoxide (CO), carbon dioxide (CO 2 ), water (H 2 O), and formaldehyde (CH 2 O). These reactions consume the hydroxyl radical ( • OH) and are the biggest sink of methane in the atmosphere. The reaction involves a set of several other trace gases, including ozone (O 3 ) (see, for example, Dzyuba et al. 2012 [3]). Atmospheric methane affects the earth's radiative balance in several ways. Its oxidation produces other important greenhouse gases (such as CO 2 and H 2 O), it contributes to global warming through its infrared absorption spectrum, and it controls the lifetime of many other climate-relevant gases, such as ozone. Methane is also a precursor of tropospheric ozone, which itself is a short-lived greenhouse gas and a pollutant having adverse impacts on human health (e.g., [4]) and ecosystem productivity [5]. Therefore, reducing methane emissions brings, besides supporting climate change mitigation, added safety and health and energy-related benefits (e.g., [4]). For constituting an effective strategy for mitigation, it is essential to independently verify the national emission reports, the accuracy of which has been widely debated [6]. One way of accomplishing this is by analyzing the variations in atmospheric concentrations of methane and link them to emissions. Due to a heterogeneous network of surface observations, missing in some key regions, satellite observations have been widely used in such studies (e.g., [7,8]), owing to the advantage of the global coverage high-frequency observation.
On the country level, the CH 4 budget depends on the ecosystem types and socio-economic development of a country. Methane is emitted into the atmosphere from a variety of individual sources, whose intensity varies largely with space and time (e.g., rice fields, enteric fermentation of livestock, manure, wetlands, crop residue burning, coal production, waste disposal, etc.). Methane is mainly emitted by anthropogenic activities and natural biogenic processes, followed by minor contributions from other natural sources-biomass burning, oceans, inland water bodies, and geological reservoirs. The prime anthropogenic sources are fugitive emission from solid fuels, leaks from gas extraction Remote Sens. 2020, 12, 375 3 of 24 and distribution facilities, agriculture, and waste management. During the period 2000-2007, the atmospheric growth rate of CH 4 was nearly stalled, implying a balance between the sources and sinks. However, since 2007, the growth rate has become positive again ( [9][10][11]). Methane has been growing after 2014 at an unprecedented rate (e.g., 12.7 ± 0.5 ppb yr −1 ) since the 1980s ( [12]). The reasons for the observed atmospheric CH 4 trend are highly debated (e.g., [13]).
Recently, significant developments of inverse modeling methods have improved our understanding of the spatial and temporal distributions of CH 4 sources and sinks (e.g., [14][15][16][17]). Inverse models are able to reproduce the observed atmospheric CH 4 trends and variability within the uncertainty of the processes involved (e.g., [18][19][20]). However, further reduction in the posterior emission uncertainty of inverse modeling results depends on a better quantification of the errors in the prior emissions and sinks and on error reductions in forward modeled atmospheric transport.
Bottom-up inventories, which are often used as a priori information on emission in inverse modeling, also have several uncertainties. The statistical data on activities, causing emissions, emission factors, and emission measurements, all have associated uncertainties. Thus, the uncertainty of an emission inventory varies as a function of the uncertainties in each of these factors. It is preferable, as far as possible, to distinguish between uncertainties in activity data and emission factors in order to obtain an assessment as accurate as possible, and at a later stage be able to seek specific inventory improvements. The verification of national GHG emission inventories is necessary for building confidence in the emission estimates and trends. Verification techniques include quality checks, inter-comparison of inventories and their error estimates, comparison with activity data, comparison with concentration/source measurements, and transport modeling studies. Currently, efforts to compare the national inventories to inverse model estimates are relying upon inverse models using regional high-resolution Lagrangian transport models ( [21,22]). The major reason to use high-resolution transport models for analyzing anthropogenic methane emissions is the need to resolve high concentration events associated with emission plumes, which lower resolution models resolve less well and thus underestimate. Here, we reported the results of our analysis using a high-resolution global Eulerian-Lagrangian coupled inverse model of methane using national reports of anthropogenic methane emissions to the United Nations Framework Convention on Climate Change (UNFCCC) ( [23]) as prior anthropogenic fluxes and evaluated the posterior emissions optimized in two emission categories of natural and anthropogenic on a country scale. This study is an extension to one by Wang et al. (2019) [24], where they compared methane emissions for 2010-2012 for large regions with UNFCCC reports using either Emission Database for Global Atmospheric Research (EDGAR) or UNFCCC reported values as prior, whereas, in this study, we reported results for country-scale analysis of methane emissions for 2011-2017, with more detailed discussion and use of independent validation for India using optimized forward simulations of aircraft CH 4 observations.

Data
In this analysis, we used methane observations from the surface observation network and satellite. The details are described in the following sections.

Greenhouse Gas Observing Satellite (GOSAT) Observations
The Greenhouse gases Observing Satellite (GOSAT) is a sun-synchronous satellite that observes column-averaged dry-air mole fractions of methane in the shortwave infrared band (SWIR) ( [25,26]). Observations are made around 13:00 local time with a surface footprint diameter of about 10 km. In the default observation mode, it has a repeat cycle of every three days, and in the target mode, special observations are made over regions of interest. GOSAT is providing observations since June 2009 with no significant degradation of data quality ( [27]). In this study, we used XCH 4 retrieved from the GOSAT at the National Institute for Environmental Studies, Japan (NIES Level 2 product, v.02.72; [28]) Remote Sens. 2020, 12, 375 4 of 24 for the period 2011-2017 to constrain methane emissions. Data uncertainty for the GOSAT retrievals were set to 60 ppb, with the rejection threshold of 30 ppb. Such a large data uncertainty was applied to the GOSAT retrievals due to the volume of GOSAT observations being much larger than that of ground-based observations. Using a smaller uncertainty could result in an over-fit to the GOSAT data, although measurement precision is higher for the ground-based observations. The averaging kernel of GOSAT retrievals was not applied in this study because it did not affect the results in sensitivity tests.

Surface, Aircraft, and Ship Observations
Along with the GOSAT XCH 4 observations, ground-based weekly or continuous atmospheric CH 4 observations from a global network of stationary stations (Figure 1), aircraft and ship tracks were used in the inversions. In order to increase the representativeness of the measurements by using observations during well-mixed atmospheric conditions, the continuous observations were averaged to daily values using 12:00-16:00 local time. For mountain sites, 00:00-04:00 local time was instead used for the effects of upslope transport of local emissions due to daytime heating. For the observations from surface sites, data uncertainties were defined based on the root mean squared error (RMSE) with its prior forward simulations. A minimum threshold value of 6 ppb was set in order to allow more freedom for the inversion in the Southern Hemisphere. The rejection criteria for the surface, aircraft, and ship observations were decided based on the variance in the data (double its magnitude). Details of the data used are given in Table A1.

Surface, Aircraft, and Ship Observations
Along with the GOSAT XCH4 observations, ground-based weekly or continuous atmospheric CH4 observations from a global network of stationary stations (Figure 1), aircraft and ship tracks were used in the inversions. In order to increase the representativeness of the measurements by using observations during well-mixed atmospheric conditions, the continuous observations were averaged to daily values using 12:00-16:00 local time. For mountain sites, 00:00-04:00 local time was instead used for the effects of upslope transport of local emissions due to daytime heating. For the observations from surface sites, data uncertainties were defined based on the root mean squared error (RMSE) with its prior forward simulations. A minimum threshold value of 6 ppb was set in order to allow more freedom for the inversion in the Southern Hemisphere. The rejection criteria for the surface, aircraft, and ship observations were decided based on the variance in the data (double its magnitude). Details of the data used are given in Table A1.

Aircraft Observations over India for Validation
Airborne CH4 measurements were performed during Cloud Aerosol Interaction and Precipitation Enhancement Experiment (CAIPEEX) airplane campaigns around two urban areas in India ( [29,30]). The measurements were done by deploying in an airplane an online in-situ cavity ring-down spectroscopy (CRDS) technique-based analyzer (G2401-m; Picarro Inc., USA). For calibration of the measurements against the World Meteorological Organization (WMO) (X2004A) scale, we measured prior to take-off three working secondary standard gasses (provided by National Oceanic and Atmospheric Administration (NOAA), Boulder, CO, USA) for 20 min each. The analyzer was monitored for pressure stability during vertical sounding. Details of the analyzer are similar to the ones reported in Chen et al. (2010) [31]. More details of observation methods could be found in Tiwari et al. 2019 [32].

Aircraft Observations over India for Validation
Airborne CH 4 measurements were performed during Cloud Aerosol Interaction and Precipitation Enhancement Experiment (CAIPEEX) airplane campaigns around two urban areas in India ( [29,30]). The measurements were done by deploying in an airplane an online in-situ cavity ring-down spectroscopy (CRDS) technique-based analyzer (G2401-m; Picarro Inc., USA). For calibration of the measurements against the World Meteorological Organization (WMO) (X2004A) scale, we measured prior to take-off three working secondary standard gasses (provided by National Oceanic and Remote Sens. 2020, 12, 375

of 24
Atmospheric Administration (NOAA), Boulder, CO, USA) for 20 min each. The analyzer was monitored for pressure stability during vertical sounding. Details of the analyzer are similar to the ones reported in Chen et al. (2010) [31]. More details of observation methods could be found in Tiwari et al. 2019 [32].

Prior Fluxes
Prior methane fluxes used in the model included anthropogenic emissions, natural emissions from wetlands, soil sink, emissions from biomass burning, and other natural sources from the ocean, geological reservoirs, and termites. Annual anthropogenic emission was from the Emissions Database for Global Atmospheric Research (EDGAR v4.3.2) at a spatial resolution of 0.1 • ×0.1 • ( [33]) scaled to match the country reports to the UNFCCC. The scaling was applied on each grid cell based on the fractional difference in country total emissions between EDGAR and UNFCCC. The top fifteen emitting countries based on EDGAR v4.3.2 estimate for 2012 and other four countries Germany, France, United Kingdom, and Japan were selected to adjust the inventory according to UNFCCC reports (see Table A2). These nineteen countries emit 66% of the global total methane for the year 2012 ( [24]). The new gridded prior emission based on the UNFCCC reports was produced by scaling the annual total to EDGAR v4.3.2 values. Beyond 2012, we used the EDGAR values for 2012. More details on the data preparation could be found in [24]. Monthly variability was incorporated using the emission seasonality data available for one year for 2010 from EDGAR. Emissions from rice cultivation were taken from EDGAR.
Emission from wetland and soil sink were estimated by Vegetation Integrative Simulator of Trace gases (VISIT, [34]) terrestrial ecosystem model simulation at 0.5 • , which uses Global Lakes and Wetlands Database (GLWD; [35]) wetland area with corrections to the inundated area based on analyzed rainfall and temperature. These data were remapped from 0.5 • to the model grid of 0.1 • using GLWD globally, and for India using PROBA-V 100 m wetland area map from Copernicus Global Land Service ( [36]), since we found several wetlands with small areal extent were missing in GLWD wetland fraction when comparing to the Indian Space Research Organization wetland atlas ( [37]). Soil sink data were remapped to 0.1 • resolution using the gross primary productivity (GPP) maps by MODIS MOD17 GPP product ( [38]).
Emission from biomass burning was taken from Copernicus Atmosphere Monitoring Service (CAMS) Global Fire Assimilation System (GFASv1.2, [39]) daily data at 0.1 • resolution. GFAS assimilates fire radiative power (FRP) observations from satellite-based sensors to produce daily estimates of biomass burning emissions. It has been extended to include information about injection heights derived from fire observations and meteorological information from the operational weather forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF). FRP observations currently assimilated in GFAS are the National Aeronautics and Space Administration (NASA) Terra and Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) active fire products (http://modis-fire.umd.edu/). Data are available globally on a regular latitude-longitude grid with a horizontal resolution of 0.1 degrees.
Other emissions included annual oceanic, geological, and termite emissions. The emission from termites was from Fung et al. (1991) [40]. The emissions due to oceanic exchange were distributed over the coastal region ( [41]), and mud volcano emissions were based upon Etiope and Milkov (2004) [42].
The meteorological data used for the transport model, which is described in Section 2.2.1, were obtained from the Japanese Meteorological Agency (JMA) Climate Data Assimilation System (JCDAS; [43,44]), which provides the required parameters, such as three-dimensional wind fields, temperature and humidity at 1.25 • × 1.25 • spatial resolution, 40 vertical hybrid sigma-pressure levels, and a temporal resolution of 6 h.

NIES-TM-FLEXPART-VAR (NTFVAR) Inverse Modeling System
This study utilized a global Eulerian-Lagrangian coupled model NTFVAR that consists of the National Institute for Environmental Studies (NIES) model as a Eulerian three-dimensional transport model, and FLEXPART (FLEXible PARTicle dispersion model) [45] as the Lagrangian particle dispersion model (LPDM). The forward transport model and model development were reported by Ganshin et al. (2012) [46] and Belikov et al. (2016) [47]. Our transport model was a modified version of the one described in [47]. The coupled model combines NIES-TM v08.1i with a horizontal resolution of 2.5 • and 32 hybrid-isentropic vertical levels described by Belikov et al. (2013) [48], and FLEXPART model v.8.0 ( [45]) run in backward mode with surface flux resolution of 0.1 • (resolution of available surface fluxes limits resolution of the Lagrangian model). The changes in the current version with respect to the study by [47] include revision in the transport matrix, indexing and sorting algorithms to allow efficient memory usage for handling large matrixes of Lagrangian responses to surface fluxes required when using GOSAT data in the inversion. More details could be found in [24].

The Inverse Modeling Scheme
We used a high-resolution version of the transport model and its adjoint described by Belikov et al. (2016) [47], which was combined with the optimization scheme proposed by Meirink et al. (2008) [49] and Basu et al. (2013) [50]. Following the approach by [49], flux corrections were estimated independently for two categories of emissions viz. anthropogenic and natural. Variational optimization was applied to obtain flux corrections as two sets of scaling factors to monthly varying prior uncertainty fields at 0.1 • ×0.1 • resolution separately for anthropogenic and natural wetland emissions with a bi-weekly time step. Corrections to the anthropogenic emission were according to the monthly climatology of emissions provided by EDGAR, and wetland emissions were proportional to the monthly climatology of wetland emissions by the VISIT model, both given as prior uncertainty fields. The grid-scale flux uncertainty was defined as 30% of EDGAR climatology for the anthropogenic flux category and 50% of VISIT climatological emissions for the wetland emission category. No optimization was applied to other natural flux categories, such as emissions from biomass burning, geological sources, termites, and soil sink, as their amplitude is an order of magnitude less than that of wetlands. A spatial correlation length of 500 km and a temporal correlation of two weeks were used to provide smoothness on the scaling factors. The inverse modeling problem was formulated ( [49,51]) as the solution for the optimal value of x -vectors of corrections to prior fluxes at the minimum of a cost function J(x): where H is the atmospheric transport operator, r is the difference between observed concentration and forward simulation made with prior fluxes without correction, R is the covariance matrix of observations, and B is the covariance matrix of fluxes. In the B matrix design, we followed [49] in representing B matrix as multiple of non-dimensional covariance matrix C and the diagonal flux uncertainty D as C matrix is commonly implemented as a band matrix with non-diagonal elements declining as ∼ exp −l 2 /d 2 with distance l between the grid cells and d the correlation distance. The optimal solution, as the minimum of the cost function J, was calculated iteratively with an efficient Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, as implemented by [52]. More details on the implementation could be found in [24,53].

Posterior Uncertainties
Posterior flux uncertainties were calculated from a set of five simulations by randomly perturbing the observations and the prior fluxes, as in the method described by [54]. Pseudo-observations were prepared by perturbing the observations with its uncertainty at each site. Also, prior monthly EDGAR and VISIT fluxes were prepared, applying random scaling factors separately for each global carbon project (GCP) region and month. Inversions were carried out using the perturbed pseudo-observations and the perturbed fluxes (perturbed EDGAR and VISIT combined with non-perturbed soil sink, biomass burning, and other natural emissions from the ocean, geological sources, and termites) as the prior fluxes and calculating the standard deviation of the inversion results.

Posterior Fluxes and Flux Corrections
In this study, two categories of fluxes, viz. natural and anthropogenic, were optimized by the inverse model. The annual mean (for the entire study period) global total natural prior was 209.15 Tg CH 4 [2] (215 Tg). In the case of anthropogenic emissions, the prior was 342.57 Tg CH 4 yr −1 , and the posterior was 340.92 Tg CH 4 yr −1 , which was between 319 and 357 Tg estimated by [55] and [2], respectively. The global total methane emission prior and posterior were 551.73 and 573.40 Tg CH 4 yr −1 , respectively; the total posterior emission was close to the estimate of 572 Tg by [2]. Figure 2 presents the comparison of surface methane observations, prior forward simulation and optimized forward for six surface measurement sites, including Fraserdale (Canada), Sinhagad (India), Hateruma (Japan), Mauna Loa (United States), Le Puy (France), and Ryori (Japan). Fraserdale is a continental site with large CH 4 variability due to local wetland emissions. Sinhagad is a mountain site, whose CH 4 concentration is influenced by maritime air in summer and inland emissions during winter due to seasonal reversal of wind patterns. Mauna Loa is considered as a global background station, and Hateruma and Ryori are influenced by emissions from East Asia. The inversion optimized fluxes brought down the RMSE and bias compared to the prior forward simulations. On a regional scale, anthropogenic emissions were found to increase in posterior compared to the prior over North America, tropical South America, Western Europe, tropical Africa, and Southeast Asia. Reductions were observed mainly over eastern Europe, China, Middle East countries, Japan, temperate South America, and southern parts of Southern Africa. These were in conformity with some studies, for example, the overestimation of Chinese coal emissions and the oil and gas sector in the Middle East in EDGAR ( [56]), although we did not attribute these differences to any source sectors. The posterior fluxes in the natural emission category increased over tropical South America, contiguous and central North America, Southern Africa, parts of India, China, and Southeast Asia, and eastern parts of Russia. Amazonia is the largest natural tropical source of methane, still have large uncertainty in the emission ( [57]), and some studies have reported upward revision in the inverse analysis (e.g., [58]). Tropical Africa is also a natural methane emitter (12% of global wetland emission, [59]) where the sources are wetlands, flood plain, riverine ecosystems, etc. Due to the seasonal migration of the intertropical convergence zone (ITCZ), the inundation extent is highly variable in these water bodies, and thus there is significant variability in the estimates of methane emission in this region ( [60]) and difficulty in models to capture the wetland emissions. Significant reductions were observed over boreal North America and Russia ( Figure 3). It should be noted that the administrative boundaries shown in Figures 3 and 4 are approximate and might deviate from areas for which national emissions are reported or the national boundaries defined by the countries. Detailed analysis on the country scale is described in the following section. for six surface measurement sites, including Fraserdale (Canada), Sinhagad (India), Hateruma (Japan), Mauna Loa (United States), Le Puy (France), and Ryori (Japan). Fraserdale is a continental site with large CH4 variability due to local wetland emissions. Sinhagad is a mountain site, whose CH4 concentration is influenced by maritime air in summer and inland emissions during winter due to seasonal reversal of wind patterns. Mauna Loa is considered as a global background station, and Hateruma and Ryori are influenced by emissions from East Asia. The inversion optimized fluxes brought down the RMSE and bias compared to the prior forward simulations. On a regional scale, anthropogenic emissions were found to increase in posterior compared to the prior over North America, tropical South America, Western Europe, tropical Africa, and Southeast Asia. Reductions were observed mainly over eastern Europe, China, Middle East countries, Japan, temperate South America, and southern parts of Southern Africa. These were in conformity with some studies, for example, the overestimation of Chinese coal emissions and the oil and gas sector in the Middle East in EDGAR ( [56]), although we did not attribute these differences to any source sectors. The posterior fluxes in the natural emission category increased over tropical South America, contiguous and central North America, Southern Africa, parts of India, China, and Southeast Asia, and eastern parts of Russia. Amazonia is the largest natural tropical source of methane, still have large uncertainty in the emission ( [57]), and some studies have reported upward revision in the inverse analysis (e.g., [58]). Tropical Africa is also a natural methane emitter (12% of global wetland emission, [59]) where the sources are wetlands, flood plain, riverine ecosystems, etc. Due to the seasonal migration of the intertropical convergence zone (ITCZ), the inundation extent is highly variable in these water bodies, and thus there is significant variability in the estimates of methane emission in this region ( [60]) and difficulty in models to capture the wetland emissions. Significant reductions were observed over boreal North America and Russia ( Figure 3). It should be noted that the administrative boundaries shown in Figures 3 and 4 are approximate and might deviate from areas for which national emissions are reported or the national boundaries defined by the countries. Detailed analysis on the country scale is described in the following section.  posterior for natural, anthropogenic, and total emissions for selected countries is shown in Table 1. Considering the posterior uncertainty for each country, most of the large emitting countries were found to have the inverse model corrections within the model uncertainty range, which was calculated, as mentioned in Section 2.2.3. Though in the case of India, the optimized emission was higher than the anthropogenic prior, the difference was within the inverse model uncertainty (4.1 Tg against 5.3 Tg uncertainty).

Emission from Natural Sources
In our study, though we optimized only for wetland emissions, the discussions were on total natural emissions, including other natural sources. In the case of emissions from natural sources, the largest upward corrections were for northern South American countries, such as Venezuela (2.22 Tg CH4 yr −1 ; 36.27%), Colombia (0.78 Tg CH4 yr −1 ; 32.77%), and Brazil (10.5 Tg CH4 yr −1 ; 36%) and a lower posterior emissions in Argentina (0.14 Tg CH4 yr −1 ; 3.5%) in South America. Other South American

Emission from Anthropogenic Sources
We analyzed the prior and posterior emissions for anthropogenic and natural categories and their flux corrections by the inverse model on a country scale (Figure 4). For the anthropogenic category, emission totals calculated from EDGAR prior were highest for China ( (2.25 Tg; 6.6%). Among countries having large anthropogenic emissions, emission from Brazil was having the least correction (0.1 Tg CH 4 yr −1 ; 0.61%). Anthropogenic prior total emission in Indonesia was 11.17 Tg CH 4 yr −1 , which was found to have a 5.8% upward correction of 0.65 Tg so that the posterior emission was 11.82 ± 2.5 Tg. The prior, posterior, and percentage difference in posterior for natural, anthropogenic, and total emissions for selected countries is shown in Table 1. Considering the posterior uncertainty for each country, most of the large emitting countries were found to have the inverse model corrections within the model uncertainty range, which was calculated, as mentioned in Section 2.2.3. Though in the case of India, the optimized emission was higher than the anthropogenic prior, the difference was within the inverse model uncertainty (4.1 Tg against 5.3 Tg uncertainty).

Emission from Natural Sources
In our study, though we optimized only for wetland emissions, the discussions were on total natural emissions, including other natural sources. In the case of emissions from natural sources, the largest upward corrections were for northern South American countries, such as Venezuela (2.22 Tg CH 4 yr −1 ; 36.27%), Colombia (0.78 Tg CH 4 yr −1 ; 32.77%), and Brazil (10.5 Tg CH 4 yr −1 ; 36%) and a lower posterior emissions in Argentina (0.14 Tg CH 4 yr −1 ; 3.5%) in South America. Other South American countries, such as Peru and Bolivia, also had a more than 20% increase in the posterior emissions compared to prior. Thus, there is a general tendency that the northern South American countries have lower emissions from natural sources in the prior. While the United States had 2.1 Tg CH 4 yr −1 increase, which was 8.8% of the natural prior, posterior emissions in Canada was 7.4 Tg CH 4 yr −1 (37.8%) less than prior, which was still within the uncertainty range of the prior emissions. In Asia, for India and Bangladesh, there are large positive corrections to emissions (2.48 Tg CH 4 yr −1 ; 25% and 1.89 Tg CH 4 yr −1 ; 46.9%, respectively), followed by a less but positive correction in China mainland (0.45 Tg CH 4 yr −1 ; 7.7%). The inverse model suggested an overall underestimation in the prior for equatorial African countries (Figure 4f), such as Uganda, Tanzania, Sudan, and Kenya, though the annual emissions were lower for these countries. A recent study ( [60]) using GOSAT XCH 4 observations in their inversion reported overall larger emissions compared to prior over Africa with strong exceptions in the Congo basin. However, in our analysis, we found a slight increase in our posterior emissions over the Democratic Republic of Congo. They attributed the increase in the CH 4 emissions during 2010-2015 to increase the wetland extent during this period in some regions of Sudan (Sudd wetland). Tootchi et al. (2019) [61] presented the details of the disparity in the spatial extent among different wetland datasets over this region (Figure 10 therein). In their study, the Baroste floodplain in southern tropical Africa had a wetland extent ten times that during the dry season minimum. Thus, there was potentially an underestimation in our prior wetland model over this area. More details of emission from these countries could be found in Table 1.

Case of India
As far as the methane emission from India is concerned, there are large differences in the total wetland area in different wetland area databases. For example, Adam et al. (2010) [62] addressed the issue of disparity between GLWD wetland areas and satellite-based estimation of naturally inundated areas (NIA). Their study showed that the difference between GLWD and NIA in India and Southeast Asia (among other regions in their study) covered a significant area. Though satellite-based inundation extent might be overestimated in areas where wet soils could be interpreted as inundated, in the Indian subcontinent, they showed that GLWD might be missing some waterbodies. Therefore, there is a possibility that the wetland methane emissions in India may be underestimated in the prior (as suggested by increasing the wetland emissions by optimization), and this may influence the posterior estimate of anthropogenic emissions due to the lack of freedom to increase wetland emissions because of underestimated wetland area fraction in the region. In our analysis, we found that in India, some wetlands with small areal extent were not captured in GLWD dataset, and we merged it with the PROBA-V 100 m wetland area fraction to redistribute spatially the 0.5 • wetland methane emissions from VISIT model, keeping the total India wetland emissions unchanged.
Moreover, the anthropogenic emissions for India in EDGAR v4.3.2 is around 65% higher than the UNFCCC reported data (for example, in 2010, the EDGAR estimate is 32.6 Tg, while the emission reported to UNFCCC is 19.7 Tg in first Biennial Update Report to the UNFCCC by the Government of India ( [63]) and 21 Tg in 2008 by [64]). Some of the recent studies, focusing on the region, covering some of the years in this analysis, found emission estimates between UNFCCC reports and the recent EDGAR updates. As a validation to the inverse model estimates, we prepared an independent check with aircraft observations of methane during few months for 2014 (September to November) and 2015 (July). This aircraft observation campaign was conducted by the Indian Institute of Tropical Meteorology, India (Section 2.1.3). These observations were not included in our inversion itself, but prior forward and optimized forward simulations were carried out for one-minute averaged CH 4 observations. Figure 5a shows the tracks of aircraft observations centered around the Indian city of Varanasi and the difference between the observations and simulation with fluxes optimized by the inverse model. Flight tracks of the observations around the city of Pune, which were also used in the profile averaging presented in Figure 5b, were not shown here. The vertical profiles of the aircraft CH 4 observations averaged for 300 m altitude is shown in Figure 5b. The total methane emission, both anthropogenic and natural, in India, was corrected upwards by the optimization. It could be seen in Figure 5b that the prior forward simulation showed low mixing ratios at all mean vertical levels, and the simulations with posterior emissions agreed well in the boundary layer and to a less degree above it. Overall, the validation with the surface stations was used in the inversion and the aircraft observations used for validation only, and the posterior simulations showed a better fit to the observations than the prior forward model. aircraft observation campaign was conducted by the Indian Institute of Tropical Meteorology, India (Section 2.1.3). These observations were not included in our inversion itself, but prior forward and optimized forward simulations were carried out for one-minute averaged CH4 observations. Figure  5a shows the tracks of aircraft observations centered around the Indian city of Varanasi and the difference between the observations and simulation with fluxes optimized by the inverse model. Flight tracks of the observations around the city of Pune, which were also used in the profile averaging presented in Figure 5b, were not shown here. The vertical profiles of the aircraft CH4 observations averaged for 300 m altitude is shown in Figure 5b. The total methane emission, both anthropogenic and natural, in India, was corrected upwards by the optimization. It could be seen in Figure 5b that the prior forward simulation showed low mixing ratios at all mean vertical levels, and the simulations with posterior emissions agreed well in the boundary layer and to a less degree above it. Overall, the validation with the surface stations was used in the inversion and the aircraft observations used for validation only, and the posterior simulations showed a better fit to the observations than the prior forward model.

Seasonal Variability in Emission
Besides the annual country's total emissions, we analyzed the monthly variation of the fluxes for selected countries (having total emission greater than 5 Tg yr −1 ), as presented in Figure 6. In the case of China, the peak anthropogenic emission during the spring season was reduced, and the posterior emissions peaked during the summer months. The relatively lower natural methane emissions had not been altered by the inverse model. Anthropogenic prior for India showed a very weak seasonal cycle (similar to the analysis by [65]), while the inverse model brought out the more

Seasonal Variability in Emission
Besides the annual country's total emissions, we analyzed the monthly variation of the fluxes for selected countries (having total emission greater than 5 Tg yr −1 ), as presented in Figure 6. In the case of China, the peak anthropogenic emission during the spring season was reduced, and the posterior emissions peaked during the summer months. The relatively lower natural methane emissions had not been altered by the inverse model. Anthropogenic prior for India showed a very weak seasonal cycle (similar to the analysis by [65]), while the inverse model brought out the more significant seasonal cycle with peaks during the southwest monsoon season (June to September). This was due to the fact that agricultural practices are dependent on rainy season (e.g.,~40% of rice production in low-lying rainfed land, [69]), and a slight phase shift with natural sources was found with the emission from natural sources (Figure 6), which indicates sources other than in natural emission category. Waterlogged areas increased nearly threefold during the southwest monsoon season, resulting in increased wetland CH 4 emissions ( [70]). During this season, the natural emission also increased in the posterior (e.g., [71]), both contributing to the summer peak in the total methane emission in India. Bangladesh had a very clear seasonal cycle (further enhanced by the optimization), which was mainly modulated by the methane emission from the natural sources. Pakistan had a peculiar scenario, having very small emission from natural sources with the total methane emission having distinct double peaks, a dominant one in spring and another one in summer. Most of the methane emission in Pakistan was from the agricultural sector (4 Tg in 2012, [72]). Iran also showed large influence from anthropogenic sources, and the inverse model offset the emission peak to summer months from spring. The natural methane emission in Russia was almost half of the total anthropogenic emissions, but the amplitude of the monthly variation was large compared to anthropogenic emissions, and thus the seasonality in total methane emission was modulated by natural emissions.

Desirable Future Improvements
The deficiencies of the inversion system, with respect to the application for comparison of estimated emissions with national emission reports, to be addressed in future studies include the following. The inverse model optimizes the emissions on a coarser spatial resolution than the transport defined on 0.1° because of smoothing in the flux corrections applied to the prior emissions, which is dependent on both the smoothness constraint and the number of iterations. Thus, more research is needed to find an optimal balance between the smoothness of the solution and the amount of detail in retrieved fluxes. It would potentially improve the estimated emissions for countries and regions with lower emissions. Another improvement should be the use of high-resolution meteorological fields for transport, in place of currently used data at 1.25° spatial resolution and 6 h temporal intervals ( [76,77]). Improved mapping of natural (and anthropogenic) emissions is necessary as we have identified deficiencies in the spatial distribution of wetland emissions, for example, over India, as discussed in Section 4.1. Some of the transport model biases, such as reduced vertical mixing and higher inter-hemispheric transport rate in the Eulerian transport model, used in this study were discussed in a multi-model intercomparison study by Krol et al. (2018) [78]. Currently, there is less evidence on the size of the biases and their impact on inversion results; more details would emerge after analysis of the data of GCP methane intercomparison ([2]), where multiple models could be compared to each other, including the one used in this study, and the correlations between transport model properties and reconstructed emissions could be established. Unaccounted In the Southeast Asian countries, emission from natural sources is mainly influenced by water availability due to summer monsoon (e.g., [73]). Although the anthropogenic emission is larger than the emission from natural sources in Indonesia, there are strong signals of natural emissions due to major fire events in Indonesia (e.g., anomalous peak in 2015). Total methane emission in Myanmar has two peaks in monthly emissions, one in spring and another prominent peak in summer monsoon season. Myanmar is a country influenced by southwest monsoon rainfall and is a land of rice production both irrigated and rainfed ( [74]), of which the majority of CH 4 emission (65%) is from irrigated or deep-water rice fields. Thus, the seasonality in CH 4 emissions is mainly modulated by wetland emissions. Variability in total emission follows mainly the variability in natural emissions. Methane emission in Thailand is, on the other hand, influenced mainly by anthropogenic emissions. So is the case with Vietnam, the optimization embeds a stronger annual peak during the monsoon season.
For the United States, these two categories are nearly equal in magnitude, but peaks at different seasons in the year-−natural emissions in summer and anthropogenic in winter. The main anthropogenic source of methane in the United States is from livestock and manure management. The seasonality in methane emission in Canada is driven mainly by natural emissions, which has a larger magnitude than the anthropogenic emissions [75]. The seasonal cycle in the total methane emission in Mexico is mainly contributed by the anthropogenic emissions, with more than four times the emission from natural sources. In Brazil, the seasonality in the total methane emission is mainly driven by variability in methane emissions from natural sources, and in the posterior, we found substantial upward correction in the natural emission category and thereby total methane emissions. Besides Brazil, Venezuela also is mainly contributed by emission from natural sources with a distinct peak during summer months. While seasonality in the methane emission in Colombia is influenced mainly by natural sources, the seasonal cycle in total emission in Argentina is equally modulated by natural and anthropogenic categories.
In the African continent, Nigeria, Sudan, and the Democratic Republic of Congo are the main methane emitters. Though anthropogenic emission is the major category of emission and has clear seasonality in Nigeria, the total emissions do not have a discernible seasonal pattern in emission. On the contrary, Sudan and Congo have a clear seasonal cycle due to the greater contribution from natural sources.

Desirable Future Improvements
The deficiencies of the inversion system, with respect to the application for comparison of estimated emissions with national emission reports, to be addressed in future studies include the following. The inverse model optimizes the emissions on a coarser spatial resolution than the transport defined on 0.1 • because of smoothing in the flux corrections applied to the prior emissions, which is dependent on both the smoothness constraint and the number of iterations. Thus, more research is needed to find an optimal balance between the smoothness of the solution and the amount of detail in retrieved fluxes. It would potentially improve the estimated emissions for countries and regions with lower emissions. Another improvement should be the use of high-resolution meteorological fields for transport, in place of currently used data at 1.25 • spatial resolution and 6 h temporal intervals ( [76,77]). Improved mapping of natural (and anthropogenic) emissions is necessary as we have identified deficiencies in the spatial distribution of wetland emissions, for example, over India, as discussed in Section 4.1. Some of the transport model biases, such as reduced vertical mixing and higher inter-hemispheric transport rate in the Eulerian transport model, used in this study were discussed in a multi-model intercomparison study by Krol et al. (2018) [78]. Currently, there is less evidence on the size of the biases and their impact on inversion results; more details would emerge after analysis of the data of GCP methane intercomparison ( [2]), where multiple models could be compared to each other, including the one used in this study, and the correlations between transport model properties and reconstructed emissions could be established. Unaccounted biases in the satellite observations, especially over regions where ground-based observations are missing, also might influence the results. Incorporating more ground-based observations in the inversion might help reducing biases over regions with a sparse observation network.

Conclusions
We carried out inversion of methane fluxes for seven years using GOSAT satellite observations and surface observations using a high-resolution inverse model NIES-TM-FLEXPART-VAR (NTFVAR) that couples a Lagrangian particle dispersion model FLEXPART with a global Eulerian model NIES-TM. Optimization was applied to natural (wetland only) and anthropogenic emissions on a bi-weekly time step, and the results were analyzed on a global country scale. In order to evaluate the inverse model estimates of methane emissions on a country scale, we used EDGAR anthropogenic methane emission inventory scaled to match the national reports to the UNFCCC. Our results showed that largest correction to the wetland emissions were for Bangladesh having an upward revision of around 46 , with all differences being within emission uncertainty range. The inversion results for India were validated against aircraft data over two north Indian urban regions, and the posterior fit to the observations showed a clear improvement, especially in the boundary layer. The application of an inversion system based on high-resolution transport using prior anthropogenic emission field adjusted to the UNFCCC emission reports, and with the combination of surface and satellite observations, enabled us to study the natural and anthropogenic methane emissions over a spatial scale of countries and to compare with the national methane emission reports. However, improvements in the resolution of the model and meteorological fields, fixing source allocations in emission sources used as priors, refinements to reduce model and observation biases, and inclusion of more observations are desirable targets for future improvement. Funding: This research was supported by the GOSAT project at the National Institute for Environmental Studies, Japan.

Acknowledgments:
We thank all the people and institutes who procured and provided the observation data used in this study. We are grateful to Emilio Cuevas, Juha Hatakka, Petri Keronen, Elena Kozlova, Tuomas Laurila, Zoe Loh, Nikolaos Mihalopoulos, Simon O'Doherty, Ray Wang, Damiano Sferlazzo, and other contributors making the methane observations and data available for the Global Carbon Project. We thank the Ministry of the Environment, Japan, for the financial support for the GOSAT project. The simulations were carried out using the Supercomputer System of the National Institute for Environmental Studies (NIES). We thank Dr. Thara Prabhakaran, CAIPEEX Project Head, and team of scientists involved in this project for supporting GHGs monitoring during the airplane campaign. The CAIPEEX project is funded by the Ministry of Earth Sciences, Government of India.

Conflicts of Interest:
The authors declare no conflict of interest.