All UNFCCC parties “shall” periodically update and submit their national greenhouse gas (GHG) inventories of emissions by sources and removals by sinks to the convention parties. Annex I countries have submitted their national inventory reports (NIRs) and common reporting format (CRF) tables every year with a complete time series starting in 1990. Non-Annex I parties have been required to submit their national communications (NCs) roughly every 4 years after entering the convention and submit biennial update reports (BURs) every 2 years since 2014. Currently, there are in total nearly 400 submissions of NCs and over 100 submissions of BURs (Fig. 1).

We collected the greenhouse gas emissions data from the national inventories submitted to the UNFCCC. For Annex I countries, data collection is straightforward, as their reports are provided as Excel files under a common reporting format (CRF). For non-Annex I countries, the data were directly extracted from the original reports provided in Portable Document Format (PDF) files. Data from successive reports for the same country were extracted, except when they relate to the same years, in which case only the latest version is considered. While Annex I countries are required to compile their inventory following IPCC 2006 guidelines and the subdivision between sectors established by a UNFCCC decision (dec. 24/CP.19), non-Annex I countries are allowed to follow the older 1996 IPCC guidelines, with different approaches and sectors. Consequently, the methods used and the reported sectors may be different among NC and BUR reports.

Atmospheric inversions derive net total CH4 emissions at the surface. It is difficult for them to disentangle overlapping emissions from different sectors at the pixel/regional scale based on the information contained in atmospheric CH4 observations only. However, six of the eight modeling systems solve for some source categories owing to different spatio-temporal distributions between the sectors. For each inversion, monthly gridded posterior flux estimates were provided at a 1∘ × 1∘ grid resolution for the net flux at the surface (Enetinv); the soil uptake at the surface (Esoilinv); the total source at the surface (Etotinv); and five emitting sectors – agriculture and waste (EAgWinv), fossil fuel (EFFinv), biomass and biofuel burning (EBBinv), wetlands (EWetinv), and other natural (EOthinv) emissions. Considering the soil uptake a “negative source”, the following equation applies: 2Enetinv=Etotinv+Esoilinv=EAgWinv+EFFinv+EBBinv+EWetinv+EOthinv+Esoilinv. For inversions solving for net flux only, the partition to source sectors was created based on using a fixed ratio of sources calculated from prior flux information at the pixel scale. For inversions solving for some categories, a similar approach was used to partition the solved categories to the five aforementioned emitting sectors. Such processing can lead to significant uncertainties if not all sources increase or change at the same rate in a given region/pixel. National values have been estimated using the country land mask described in the CO2 section; thus offshore emissions are not counted as part of inversion results unless they are in a coastal grid cell.

Four methodologies were used to separate CH4 anthropogenic emissions from inversions (EAnthinv) in order to compare them with national inventories (EAnthni). The calculations of anthropogenic emissions by each method were performed separately for GOSAT inversions and in situ inversions. The first method consists in using the inversion partitioning as defined in Saunois et al. (2020):

We subtracted estimates of natural N2O sources from the N2O emission budget (Etotinv) of each inversion in order to provide inversions of anthropogenic emissions (Eantinv) that can be compared with national inventories (Eantni). 6Eantinv=Emanagedlandinv-Enataq-EwildfiresGFED⇔Eantni For this study, intact forest areas (that are unmanaged, by definition) from Potapov et al. (2017) and lightly grazed grassland areas from Chang et al. (2021a) were removed from the N2O totals in proportion to their presence in each inversion grid box. Lightly grazed grasslands (Chang et al., 2021a) include ecosystems with wild grazers and with extensive grazing by domestic animals, mainly in steppe and tundra regions (Fig. S1). We assumed the intact forest areas and lightly grazed grassland areas approximate unmanaged land, where the fluxes are not reported in the NGHGIs. We verified that the inversion grid box fractions classified as unmanaged do not contain point source emissions from the industry or energy and diffuse emissions from the waste sector to make sure that we do not inadvertently remove anthropogenic sources by masking those unmanaged areas.

To do so, from the EDGAR v4.3.2 inventory (Janssens-Maenhout et al., 2019), we checked that N2O from waste water handling covers a relatively large area that might be partly located in unmanaged land. But the emission rates are more than 1 order of magnitude smaller than those from agriculture soils. For other sectors, only very few of the unmanaged grid boxes contain point sources, and none of them has an emission rate that is comparable with agricultural soils (managed land). Thus, our assumption that emissions from these other sectors are primarily located over managed land is solid (other sectors include power industry; oil refineries and transformation industry; combustion for manufacturing; aviation; road transportation, no resuspension; railways, pipelines, and off-road transport; shipping; energy for buildings; chemical processes; solvents and product use; solid waste incineration; waste water handling; and solid waste landfills). Therefore, our masking of unmanaged land inversion grid boxes gives us Emanagedlandinv in Eq. (6). The flux Enataq is the natural emissions from freshwater systems in Eq. (6) given by a gridded simulation of the DLEM (Yao et al., 2019) describing pre-industrial N2O emissions from N leached by soils and lost to the atmosphere by rivers in the absence of anthropogenic perturbations (considered the average of 1900–1910). Natural emissions from lakes were estimated only at a global scale by Tian et al. (2020) and represent a small fraction of rivers' emissions. Therefore, they are neglected in this study. The flux EwildfiresGFED is based on the GFED4s dataset (van der Werf et al., 2017) using their reported dry matter burned and N2O emission factors. Because the GFED dataset reports specific agricultural and waste fire emissions data and we assume that those fires (on managed lands) are reported by NGHGIs, they were not counted in EwildfiresGFED. Note that there could also be a background natural N2O emission from soils over managed lands (Emanagedlandsoil). We did not try to subtract this flux from managed land emissions because we assumed that, after a land use change from natural to fertilized agricultural land, background emissions decrease and become very small compared to N-fertilizer-induced anthropogenic emissions. In a future study, for Emanagedlandsoil we could use the estimate given by simulations of pre-industrial emissions from the NMIP ensemble of dynamic vegetation models with carbon–nitrogen interactions (number of models, n, is 7), namely, its simulation S0 in which climate forcing is recycled from 1901–1920, CO2 is at the level of 1860, and no anthropogenic nitrogen is added to terrestrial ecosystems (Tian et al., 2019).

Another important point to ensure a rigorous comparison between inversions and NGHGI data is whether anthropogenic indirect emissions (AIEs) of N2O are reported in NGHGI reports. UNFCCC parties should report these in their NGHGIs according to the IPCC guidelines, but we found that this is not always the case. For example, South Africa's BUR3 did not report the indirect GHG emissions. AIEs arise from anthropogenic nitrogen from fertilizers leached to rivers and anthropogenic nitrogen deposited from the atmosphere to soils. AIEs typically represent 20 % of direct anthropogenic emissions and cannot be ignored in a comparison with inversions. For Annex I countries, AIEs are systematically reported, generally based on ad hoc emission factors since these fluxes cannot be directly measured, and it is assumed that indirect emissions only occur on managed land. For non-Annex I countries, we checked manually from the original NC and BUR documents if AIEs were reported or not by each non-Annex I country. If AIEs were reported by a country, they were used as such to compare NGHGI data with inversion results and grouped into the agricultural sector. If they were not reported or if their values were outside plausible ranges, AIEs were independently estimated by the perturbation simulation of N-fertilizer leaching, CO2, and climate on rivers and lakes fluxes in the DLEM (Yao et al., 2019) and by the perturbation simulation of atmospheric nitrogen deposition on N2O fluxes from the NMIP model ensemble (Tian et al., 2019). Table S2 lists the non-Annex I countries among the top 20 N2O emitters if they have reported AIEs to the UNFCCC from national inventories.

The categories of fluxes estimated by inversions and NGHGI sectors are different (Table S3). The bottom-up inventories are compiled based on activity data (statistics) following the IPCC 1996 and 2006 guidelines (IPCC, 1997, 2006), with detailed information of sub-sectors. But the top-down inversions can only distinguish very few sectors. Thus, in this study, we aggregated sectors into some larger sectors to make inversions and inventories comparable for each GHG gas (Table 1).

For CO2, the inversions are divided into two aggregated sectors: (1) fossil fuel and cement CO2 emissions and (2) land flux. Inversions use a prior gridded fossil fuel dataset as summarized in Sect. 2.2; thus, in this study we compare only the land flux between inversions and inventories. The adjusted land flux (NEE) from each inversion is calculated by subtracting the national total fossil emissions from the total CO2 flux, where the fossil emissions are from the Global Carbon Project annual dataset (Friedlingstein et al., 2020), consistent with the prior fossil emission maps proposed to inversion modellers and used by them, except for the inversion of Feng et al. (2009, 2016) (see Table A4 of Friedlingstein et al., 2020, for details). For processing NGHGIs, we subtracted fossil emissions of the sectors of energy and industrial processes (or industrial processes and product use) from the total net CO2 emissions to obtain NEE CO2 fluxes over managed ecosystems. Note that transportation and residential CO2 emissions are reported under the energy sector.

For CH4, we compare inversions and national inventories based on three emission groups: fossil, agriculture and waste, and total anthropogenic. For NGHGIs, we group the sectors of energy and industrial processes (and product use) into fossil, excluding biofuel burning (reported under the energy sector); group sectors of agriculture and waste into agriculture and waste; and aggregate fossil, agriculture and waste, and biofuel burning into total anthropogenic.

For N2O, we derived anthropogenic emissions by Eq. (6) by subtracting natural emissions from rivers from Yao et al. (2019) after masking unmanaged grasslands and intact forest areas.

We selected 12 countries (counting the EU27 and UK as 1 country) for the analysis, the selection being different for CO2, CH4, and N2O anthropogenic fluxes, based on the following criteria. Each selected country should have a large enough area because small countries cannot be constrained using coarse-spatial-resolution inversions and, if possible, some coverage by the in situ global network. The country with the smallest area is Venezuela (916 400 km2), selected for CH4 because it is a large oil and gas emitter and its emissions can still be constrained by inversions using GOSAT satellite observations, except inversions using the NIES column CH4 product that has very few observations in the wet season over Venezuela and Nigeria for instance (see Table S1 and Fig. S2 for GOSAT satellite sounding coverage). For CO2, we selected the top 10 fossil fuel CO2 emitters because, even if inversions do not resolve those emissions which are used as a fixed prior, it is important to compare the magnitude of their CO2 sinks with their fossil CO2 emissions. We also selected two large boreal countries (i.e., Russia and Canada); two tropical countries with important areas of forests (i.e., Brazil and the Democratic Republic of Congo); two large countries with in situ stations (i.e., Mongolia and Kazakhstan); and two large dry Southern Hemisphere countries with a high rank in the fossil fuel CO2 emitters (i.e., South Africa and Australia), which both have atmospheric stations to constrain their land CO2 flux. Altogether, the 12 countries account for >90 % of the global land CO2 sink given by NGHGIs. For CH4, we ranked countries or groups of countries in decreasing order of total anthropogenic, fossil, and agricultural emissions. The criteria of large areas and having atmospheric stations are important for in situ inversions. For satellite inversions, the advantage of GOSAT is that it provides observations where the surface network is very sparse, such as the tropics, so that countries with no or only a few ground-based observations can still obtain reliable top-down estimates. The inversion resolution is what dictates if small countries can be reliably estimated. Thus, this study includes China, India, the USA, the EU, Russia, and Indonesia, which are among the top fossil and top agricultural emitters and have vast territories, and excludes small countries considering the coarse spatial resolution. Altogether, the selected countries for CH4 represent ∼60 % of the global anthropogenic CH4 emission given by NGHGIs, ∼15 % of the fossil emissions, and ∼40 % of agriculture and waste emissions. For N2O, we chose the top 12 emitters based on NGHGI reports. In most of them, anthropogenic N2O emissions are dominated by the agricultural sector, whose share (including indirect agricultural emissions) of total NGHGI emissions ranges from 6 % in Venezuela to 95 % in Brazil. Altogether, the selected countries represent ∼55 % of the global anthropogenic N2O emissions given by NGHGIs.

Figure 4 shows the variations in CH4 anthropogenic emissions from 2000 to 2019 (up to 2017 for inversions), defined by summing the sectors of agriculture and waste, fossil fuels, and biofuel burning for the 12 selected countries (see Sect. 2.4). The distribution of emissions is strongly skewed even among the top 12 emitters, with the largest and most populated countries forming a group of super-emitters and other countries having much smaller emissions and thus being more difficult to quantify by inversions. According to GOSAT inversions, China (CHN) has the largest emissions of around 53 Tg CH4 yr-1, followed by India (IND) with 28 Tg CH4 yr-1, the USA with 26 Tg CH4 yr-1, Brazil (BRA) with 23 Tg CH4 yr-1, the EU27 and UK (EUR) with 20 Tg CH4 yr-1, Russia (RUS) with 18 Tg CH4 yr-1, and Indonesia (IDN) with 11 Tg CH4 yr-1, and the other countries has emissions of only around 5 Tg CH4 yr-1. Note the asymmetric range around the median of inversions for BRA in Fig. 4. The data in Fig. 4 indicate a large spread between inversions, owing to differences in model settings and transport. Differences due to different methods used to separate anthropogenic from natural emissions are smaller than this spread, and we discuss them in Sect. 6.2. We observed on average a smaller range of GOSAT inversions (number of inversions, n is 11) than in situ inversions (n=10) in countries emitting more than 10 Tg CH4 yr-1. The median emissions from GOSAT inversions are systematically lower than from in situ inversions, except in CHN where GOSAT inversions are on average 21 % larger than in situ ones during 2010–2017. Ranges overlap between the two inversion ensembles. Generally, the difference between NGHGIs and inversions is of the same sign based on GOSAT and in situ inversions, which gives us some confidence for evaluating NGHGIs because the GOSAT observations are different and independent from in situ networks. Ex ante, we trust more GOSAT-based inversions over most countries because GOSAT has a better observation coverage, except for in EUR and the USA where the in situ network is dense (Fig. S2). From the result shown in Fig. 4 that GOSAT and in situ inversions are on the same side compared to NGHGIs, we can thus be more confident of results provided by in situ inversions over the full time period.

For China (CHN), during 2000–2017, the median of anthropogenic emissions from in situ inversions is 44 Tg CH4 yr-1. This is lower than the NGHGI reports (53 Tg CH4 yr-1, average of four communications in 2005, 2010, 2012, and 2014). The median of GOSAT inversions (53 Tg CH4 yr-1) is close to that of NGHGIs (54 Tg CH4 yr-1) in the 2010s (Fig. 4). The trend of emissions is consistent between inversions and NGHGI data, although the increasing trend is larger in GOSAT than in in situ inversions after 2010. For the USA, the median of inversions is close to the NGHGI-reported value during the whole study period. The trend of in situ inversions in the USA is positive, with an increase of 0.3 Tg CH4 yr-1 from 2000 to 2017, in contrast to the small decrease of 0.1 Tg CH4 yr-1 in the NGHGI data. The GOSAT inversions also show a positive trend of 0.1 Tg CH4 yr-1 from 2010 to 2017. This different trend between inversions and the US NGHGIs might be attributed to CH4 leakage from unconventional oil and gas extraction that may not be fully accounted for in NGHGIs (Allen, 2016). This type of oil and gas production became important after the mid-2000s and has emission factors that are twice larger than current values from the US Environmental Protection Agency (EPA) currently used in the NGHGIs, as shown by local and regional measurement campaigns (Alvarez et al., 2018; Sargent et al., 2021).

For the EU27 and UK (EUR), the decreasing trend of anthropogenic CH4 emissions diagnosed by inversions is consistent with NGHGI estimates, but the median of inversions is higher than the NGHGI data by 2 Tg CH4 yr-1 for the study period from 2010 to 2017. This result is consistent with the EU synthesis results of Petrescu et al. (2021b) although they used a different method to subtract natural emissions based on regional estimates of peatlands and inland water natural emissions. Positive differences between inversions and NGHGI reports are found for Russia (RUS), India (IND), Brazil (BRA), Argentina (ARG), and Australia (AUS). In Russia (RUS), emissions are larger in inversions than in the NGHGI data, and this result is robust to the choice of the method to separate natural from anthropogenic sources (see Figs. S5 and 10). Note however that RUS wetland emissions are partly concentrated in the region of western Siberia (northern Ob river basin) just to the south of a major basin of gas extraction (Yamal), and these two sources are difficult to separate from each other in global inversions. Note that methane emissions from fires in Russia are smaller than fossil and wetland emissions, and fires cannot explain why inversions give larger emissions than the NGHGIs.

In Brazil (BRA), the result that inversions give systematically larger CH4 emissions than NGHGIs is also robust due to the method used to separate wetlands from anthropogenic emissions (Fig. S5), but our inversions did not use in situ data in the interior of the country (Fig. S1) and the coverage of GOSAT is sparse due to clouds (Fig. S2), especially in the wet season, which makes the estimation of the total CH4 source uncertain over this country. In India (IND), both the in situ and the GOSAT inversions also give a higher anthropogenic emission than the NGHGI data and the share of emissions from natural wetlands is much smaller than in RUS and BRA, reducing the risk of aliasing between anthropogenic and natural emissions and suggesting a lower estimation by the NGHGIs. In Indonesia (IDN) the median of inversions is slightly higher than the NGHGI data with the separation method used in Fig. 4 but close to NGHGIs with other methods (Figs. 10 and S5). All inversions give a large positive anomaly of CH4 emissions during the 2015 El Niño, when abnormal peat fire emissions occurred (Heymann et al., 2017; Yin et al., 2016), with a biomass burning event being attributed to an anthropogenic source by our aggregation of inversion results (Sect. 2) but likely not included by the NGHGIs. In AUS, the anthropogenic emissions mainly from the coal extraction and cattle sector of the NGHGIs are found to be very close to the inversion median, across both in situ and GOSAT inversions. In Pakistan (PAK) and Iran (IRN), NGHGI values show good consistency with the in situ inversions; however, in Pakistan (PAK) the GOSAT inversions are 18 % higher than the in situ inversions. Mexico (MEX) is the only country whose NGHGIs are higher than the inversions among the 12 selected countries, which is mainly attributed to the difference between inversions and inventories in the agriculture and waste sector (see below).

Figure 5 presents the CH4 emissions for the top 12 emitters from the fossil sector. The largest emitter is China (CHN), mainly from the sub-sector of coal extraction (85 % in 2014), followed by Russia (RUS) and the United States (USA). The range of inversions relative to median values is larger for fossil emissions than for total anthropogenic emissions, reflecting the fact that the uncertainty in inversions increases through their separation of fossil from other sources. Here, GOSAT inversions in which fossil sector emissions were separated from the total emissions in each grid cell using the share provided by a prior differ from in situ inversions where different sectors correspond to specific tracers, in particular for CHN where the choice of a prior to separate fossil emissions from other emissions is critical (Liu et al., 2021). In China (CHN), both in situ and GOSAT inversions find on average significantly smaller emissions than the NGHGIs, by 50 % (13 Tg CH4 yr-1) for in situ inversions and 24 % (6 Tg CH4 yr-1) for GOSAT inversions in the 2010s, consistent with Liu et al. (2021). In Russia (RUS), in situ and GOSAT inversions both have fossil emissions of nearly 6 Tg CH4 yr-1 larger than NGHGIs, with a diverging trend of an increase in inversions and a decrease in the NGHGIs. This mismatch is possibly due to aliasing between wetland emissions and gas extraction industries that occur in roughly the same region or because of accidental leaks from ultra-emitters that are ignored in the NGHGIs. The ultra-emitters defined by Lauvaux et al. (2022) are namely all short-duration leaks from oil and gas facilities (e.g., wells, compressors) with an individual emission >20 t CH4 h-1, each event lasting generally less than 1 d. The contribution of these ultra-emitters is discussed in Sect. 4.3.1. In the USA, fossil emissions from in situ inversions are smaller than in NGHGIs by 26 % until 2011 and then aligned. Differences between NGHGIs and inversions may be due to (1) under-reported emissions (Alvarez et al., 2018) in inventories from the shale gas extraction industry, which today represent 68 % of the total USA oil and gas production (EIA, 2021b), and (2) excluded oil and gas offshore emissions in the fossil sources' top-down budget through the land masking applied to the inversions. We note that although the emissions from the offshore sector might be underestimated (Gorchov Negron et al., 2020), they produce only about 3 % of the total US natural gas production (EIA, 2021c). In EUR, similar fossil emissions values are found from in situ inversions and NGHGIs before 2010, but both in situ and GOSAT inversions show higher emissions than NGHGIs from 2010 to 2017. The decreasing trend in fossil emissions between 2000 and 2010 is very consistent between inversions and NGHGI reports in EUR. In India (IND), fossil emissions mainly come from fugitive emissions (∼60 % from natural gas and 30 % from solid fuels in 2010 from MoEFCC, 2015). Only three years are available from NGHGIs, and they report similar values to GOSAT inversions with constant emissions from 2010. On the contrary, in situ inversions suggest continuously increasing emissions.

In major oil- and gas-extracting countries that have negligible agricultural and wetland emissions like Kazakhstan (KAZ), grouped in this study with Turkmenistan (TKM) into KAZ&TKM; Iran (IRN); and Persian Gulf countries (GULF), fossil emissions should be easier to separate by inversions and thus to be compared with NGHGIs. We found that GULF and KAZ&TKM fossil emissions are on average 4 and 2 times higher than diagnosed by in situ and GOSAT inversions, respectively, compared to NGHGI reports. The reasons for the lower GULF reports of emissions could be because of ultra-emitters not included in the NGHGIs, a point further examined in Sect. 6. Note that Saudi Arabie (SAU) emissions seem to be lower than for other GULF countries according to inversions, but SAU is not separated well by inversions from neighboring countries. More ultra-emitters and larger emission budgets from ultra-emitters (see Sect. 6) were also found in Qatar, Kuwait, and Iraq than in SAU (Lauvaux et al., 2022). Similarly, KAZ is downwind of Turkmenistan (TKM), which has a high share of ultra-emitters (Lauvaux et al., 2022), and global inversions working at a rather coarse resolution could misallocate to KAZ emissions coming from TKM. The emitting countries in the Persian Gulf area have no atmospheric CH4 in situ station coverage, while KAZ has two stations. In contrast, the sampling of atmospheric column CH4 by GOSAT is rather dense in all those countries, thanks to frequent cloud-free conditions. Thus GOSAT inversions could be viewed as more accurate than in situ inversions for IRN, SAU, and KAZ, and we note that GOSAT inversions give lower emissions than in situ inversions. We also compared inversions and NGHGIs with annual CH4 emissions data compiled by PRIMAP-hist (Gütschow et al., 2016) for the energy sector and found that this dataset produces much larger emissions than both NGHGIs and the median of inversions for GULF and KAZ&TKM (Fig. S6). The methodology of PRIMAP-hist interpolates and extrapolates UNFCCC values using trends of EDGAR v4.2, an inventory which is known to overestimate fossil CH4 emissions (Thompson et al., 2015; Patra et al., 2016; Ganesan et al., 2017). The higher values of PRIMAP-hist may thus be due to the extrapolation of temporally sparse national inventories for those countries, and this dataset should not be considered similar to NGHGIs for the fossil fuel CH4 sector.

In Nigeria (NGA) and Venezuela (VEN), where nearly half of the oil and gas industry is offshore or near the coast (NAPIMS, 2021), we found that fossil CH4 emissions are smaller in inversions than in the NGHGIs. This result should be considered with caution as those countries have a small size and thus emissions that are difficult to constrain by global inversions. The presence of clouds further reduces the number of GOSAT soundings, and anthropogenic and natural CH4 emissions are collocated with fossil ones. Finally, for Mexico (MEX), GOSAT and in situ inversions show good agreement with respect to NGHGIs. However, this apparent agreement might stem from both an overestimation of offshore emissions (not included here in inversions due to land masking) and an underestimation of inland fossil fuel emissions by the NGHGIs (Zavala-Araiza et al., 2021). Possible reasons could include the following: (1) in MEX, roughly 80 % of oil production and 60 % of gas production is from offshore shallow water wells. Emission inventories seem to be overestimating offshore emissions of CH4 by about an order of magnitude (Zavala-Araiza et al., 2021). (2) Emission factors used in bottom-up inventories are generic (not specific to Mexican types of well, reservoir, technology, age of technology, etc.). (3) Due to the elongated shape of Mexico, and because it is surrounded by water, the spread of the inversions is higher compared to in other countries.

Figure 6 presents the CH4 emissions of the agriculture and waste sector for the top 12 emitters. Like in Fig. 5, the relative spread of inversions (min–max range divided by mean) is larger for this sector than for the total of all anthropogenic sectors. We observed that the median of GOSAT inversions is close to the median of in situ inversions within ±0.3 Tg CH4 yr-1 over the period 2009–2017 across the countries in Fig. 6. The values from NGHGIs also show good consistency with the inversions. In China (CHN), agriculture and waste emissions from the most recent NGHGI reports in the 2010s (28 Tg CH4 yr-1) are between the GOSAT inversions (29 Tg CH4 yr-1) and in situ inversions (27 Tg CH4 yr-1). The trend in agricultural emissions is consistent between inversions and NGHGIs for CHN. In India (IND), inversions give systematically higher emissions than NGHGIs by 50 % for GOSAT and 38 % for in situ inversions, with GOSAT and in situ inversions being similar in 2010 (∼24 Tg CH4 yr-1) and showing thereafter a decreasing trend in GOSAT (-0.1 Tg CH4 yr-1) compared to an increasing trend in in situ (+0.3 Tg CH4 yr-1) inversions. In IND, from the national inventory, enteric fermentation is the major CH4 source of the agriculture and waste sector, contributing 61 % of emissions with 20 % for rice cultivation and 16 % for waste. A similar result is found in Bangladesh (BGD), where agricultural emissions are dominated by rice production (48 % in 2012) and enteric fermentation (42 % in 2012), with GOSAT inversions giving emissions that are nearly double those of the NGHGI reports during 2001 and 2012. The large differences between the inversions and NGHGIs for IND and BGD could be due to the potential underestimation of livestock CH4 emissions by NGHGIs. NGHGIs used the Tier 1 method and associated emission factors from the 2006 IPCC Guidelines for National Greenhouse Gas Inventories (IPCC, 2006), while a recent study (Chang et al., 2021b) found that the estimates using the revised Tier 1 or Tier 2 methods from the 2019 Refinement to the 2006 IPCC Guidelines for National Greenhouse Gas Inventories (IPCC, 2019) are 48 %–60 % and 42 %–61 % higher for IND and BGD by 2010, respectively, and match better the inferred emissions from inversions. In Brazil (BRA), both GOSAT and in situ inversions are systematically larger than the NGHGIs by 34 % and by 29 %, respectively, but show a consistent increasing trend over their study periods. In the USA, the medians of GOSAT and in situ inversions are slightly higher than those of the NGHGIs, while NGHGIs show a slowly decreasing trend over the study period. In Indonesia (IDN), Pakistan (PAK), and Argentina (ARG), the medians of in situ inversions have a good consistency with NGHGI-reported values, while GOSAT inversion emissions in the 2010s are on average 19 % higher in Pakistan and 24 % higher in Argentina but 9 % lower in Indonesia compared to the NGHGI reports. In the EU27 and UK (EUR), emissions from agriculture and waste are found to have significantly decreased over time in the NGHGI data, mainly from solid waste disposal (Petrescu et al., 2021a), a trend that is captured by inversions and is close to the NGHGIs over the study period. In contrast, emissions from agriculture and waste in Russia (RUS) are reported to have a positive trend after 2010, contributed mainly by the solid waste disposal (crosses vs. circles in Fig. 6), whereas in situ inversions produce a consistent trend from 2000 to 2014 but a decrease thereafter, and the GOSAT inversions produce stable values, lower than the NGHGIs after 2010. Last, in Mexico (MEX), the inversion data in Fig. 6 indicate consistently lower agricultural and waste emissions than the NGHGIs, by 1.6 Tg CH4 yr-1 across in situ inversions and by 1.0 Tg CH4 yr-1 in the GOSAT inversions. Inversions produce stable emissions in the period after 2010, whereas the NGHGIs give an increase at a rate of 2 % yr-1, mainly from solid waste disposal (∼60 %) and livestock (∼40 %). Note that livestock CH4 emissions in Mexico increased by more than 20 % during 2000–2018 (from ∼2.0 to ∼2.4 Tg CH4 yr-1) from all methodologies used by Chang et al. (2021b) (2006 Tier 1, 2019 Tier 1, and Mixed Tier), suggesting that the increase in the national inventory agricultural emissions shown in Fig. 6 is consistent with more recent methodologies.

Figure 8 presents fossil fuel and cement emissions, the net land CO2 flux, and the net flux from the sum of the land flux and fossil emissions. Fossil CO2 emissions are obtained by re-aggregating to national totals the emission maps provided by each modeling group. These emissions are not optimized by inversions and may differ from UNFCCC NGHGIs because most non-Annex I countries do not have annual emission estimates and because inversions use as fixed priors gap-filled annual data from CDIAC and BP statistics for non-Annex I countries (Friedlingstein et al., 2020), whereas the red circles in Fig. 8 show the average of emissions from available BUR or NC reports in each period (thus, for each period only data of available years of national inventories are used to calculate the average). For Annex I countries, the prior fossil CO2 emission maps prescribed to the inversions from Jones et al. (2021) match by construction national totals from the UNFCCC. For non-Annex I countries, the prior fossil CO2 emission map is based mainly on CDIAC national emissions (Friedlingstein et al., 2020). The data presented in Fig. 8 show differences between NGHGI data and inversion priors, possibly due to (1) international bunker fuel emissions from ships and aviation counted in inversions as surface emissions but not included in UNFCCC national registers, (2) interpolation or regridding by inversion modelers of gridded fossil fuel emissions, or (3) our aggregation processing of national emissions from coarse-resolution inversions back to national totals (see Sect. 2.3). Residual differences have been corrected when presenting in Fig. 8 the land sink to match the emissions of Friedlingstein et al. (2020), but these inconsistencies of emissions between inventories and what is prescribed as prior fossil emissions in inversions should be kept in mind for future studies.

There is a striking consistency in Fig. 8 between means for each 6–7-year period of NGHGI land carbon sinks and inversions, after the adjustments presented in Sect. 2, for all major emitters. Although the range of inversions is large compared to the small uncertainties reported by NGHGI reports, the median value of inversions is within 37 % of NGHGIs for China (CHN), the USA, India (IND), and Brazil (BRA). Inversions give a larger sink compared to NGHGI data for several countries, however, such as Russia (RUS, by 85 %), the EU27 and UK (EUR, by 113 %), Australia (AUS, by >600 %), and Canada (CAN, >10000 %). On the one hand, NGHGIs could potentially report lower estimation of carbon sinks in their managed lands due to incomplete estimation of environmental factors (e.g., CO2 fertilization effect) and incomplete reporting, especially for the soil pool (many of them assume that, e.g., mineral grassland soils are neutral, whereas this is probably not the case); however, the larger sink from inversions may also stem from prescribing bunker fuel aircraft emissions at the surface in the atmospheric transport models, which may imply a larger compensatory land CO2 sink. For CHN, given the large amount of fossil emissions, there is an aliasing effect between the choice of a prior emission estimate and the magnitude of the inferred national land sink (Saeki and Patra, 2017). For CAN and AUS, our proxy for unmanaged lands may explain systematically lower sink estimates in inventories compared to inversions. It should also be noted that Canada uses relatively old growth functions that do not capture much of the recent transient impact of environmental changes such as rising CO2 and longer growing seasons. AUS considers all forest as formally “managed”, but the vast majority (100 Mha of “other native forest”) is assumed to be in carbon equilibrium in the AUS NGHGIs. Thus with this assumption there is no biomass loss because the wood removal is zero, whereas old-growth forest may comprise carbon sinks.

In this study, we applied a mask of unmanaged forests to inversion gridded CO2 fluxes, which has mainly the effect of reducing CO2 uptake over the countries that have a large fraction of unmanaged forests, namely by 14 % in RUS, 30 % in CAN, 16 % in BRA, and 16 % in COD. BRA is a specific case because although large fractions of the Brazilian Amazon forest are slightly disturbed by “management” activities, it contains a significant fraction of protected areas and indigenous territories (23 % of the total forest area in BRA) (Alejo et al., 2021; IWGIA, 2021) which are counted as managed land by a political decision on land use. Thus, there is a large mismatch between nationally reported areas of unmanaged land (316 Mha in 2010 according to Table 3.109 from MCTI, 2016) and the intact forest mask that we used (166 Mha in 2010, ∼33 % of the national forest cover). According to Table 3 in the Supplement of Grassi et al. (2021), the share of total forest comprising intact forest was around 40 % in CAN and BRA and 20 % in RUS. This share depends on the threshold used to define forest, but in BRA, our intact forest area (16 %) used to exclude the inversion fluxes from unmanaged land seems to be too small. In comparison, the land carbon removals from NGHGIs are compiled based on the national communication reports of Brazil that say for instance that about half of Brazil's forest is unmanaged. We also note that we did nothing to mask unmanaged grasslands and rangelands for CO2 fluxes, even though these systems are thought to be larger CO2 sinks per unit area than managed grasslands (Chang et al., 2021a). In the future, it should be possible to mask inversions using the area simulated as managed grasslands by Chang et al. (2021a), that is, 1650 Mha or a fraction of 33 % of the global grassland area from their study. The masking of inversions' fluxes over unmanaged forests in the USA, CHN, and EUR has a negligible impact on the net land CO2 flux from inversions given their small/negligible share of forest being declared as unmanaged.

Regarding the effect of CO2 fluxes caused by lateral processes, which do not result in national carbon stock changes, the correction that we applied to inversions (Sect. 2) is equivalent to reproducing the rules of accounting by countries, where wood products harvested (also biofuels) are considered to be emitted where they have been produced, even though these products can be exported and CO2 emitted elsewhere. On the other hand, domestically produced and consumed wood, which comprises the majority of wood use in most countries, will induce subnational patterns of CO2 sources and sinks, assumed to be captured by inversions and not considered explicitly here as an inversion adjustment. To our knowledge, no country is accounting for carbon in traded crop products (as it is not a stock change) or for carbon transferred from soils to rivers and outgassed, buried in aquatic sediments, or transferred to the ocean. In inventories, observed soil carbon stock changes should implicitly include carbon leached or eroded from soils. However, since very few inventories are based on actual soil carbon change estimates but rather use assumptions or models that ignore the river loop of the carbon cycle, it is possible that the amount of carbon remaining in soils is overestimated by these approaches (Lauerwald et al., 2020). We found that altogether, the correction of inversions by CO2 fluxes induced by the lateral transport from river, crop, and wood products goes from a net source of 19 Tg C yr-1 in Sudan (mainly crop import) to a net sink of 169 Tg C yr-1 in Brazil (mainly lateral export). The river correction always makes the inversion net land CO2 flux a smaller sink, whereas the trade of crop and wood can be a net CO2 source or a sink, depending on the balance of exports and imports. We found that these trade fluxes are a source of CO2 in the net-importing countries China, the EU27 and UK, and Japan and a CO2 sink in wood- and food-exporting countries like the USA, Brazil, and Argentina. We outline the fact that most of the carbon lost by soils to rivers in a country is outgassed in territorial waters (see Sect. 2.3). Inversion results should partly include this source, although without prescribing it in an explicit manner (e.g., in their prior), but part of this CO2 source could also be misallocated to other countries in the flux increment of inversions. The same remark holds true for CO2 fluxes induced by crop and wood product growth, harvest, and trade. Although there is uncertainty about the share of unmanaged land as well as the lateral fluxes, we still make our efforts to narrow the gap between NGHGIs and inversions by excluding flues in unmanaged land and adjusting lateral fluxes from inversions. However, more profound and systematic analysis and comparisons are called for to harmonize the different scopes between national inventory compilations and inverse models.

Uncertainty in anthropogenic CH4 emissions using the inversion method is suggested not only by the spread between models (due to transport models and other inversion specific settings) but also by the method chosen to separate anthropogenic from natural emissions. The data shown in Fig. 9 compare the results of the four different separation methods presented in Sect. 2. They show that the uncertainty due to the separation method is generally much smaller than the spread between different models, derived from the fact that inversion vertical ranges appear large relative to differences due to the separation procedure. In China (CHN), the between-method range of median inversion estimates of anthropogenic emissions is 4 Tg CH4 yr-1, compared to the mean model spread (interquartile) of 46–60 Tg CH4 yr-1. The range between the median of different methods is 10 Tg CH4 for the USA, 6 Tg CH4 for the EU27 and UK (EUR), and 3 Tg CH4 for Russia (RUS). In Brazil (BRA), methods 3/1 and 3/2 based on ecosystem models of wetland emissions to diagnose natural emissions give much larger anthropogenic emissions. This is likely because these models report lower natural emissions (Sawakuchi et al., 2014); e.g., they do not have emissions from flooded forests (Pangala et al., 2017), from the open river itself, or from palm swamps and peat complexes (Winton et al., 2017), which comprise an important CH4 source in BRA (Melack et al., 2004). Method 1, which is based on the original separation of natural vs. anthropogenic emissions from inversions, is not systematically different from other methods, but its results differ markedly due to its different use of data sources in each natural/anthropogenic part (see Sect. 2.4). Method 1 gives slightly higher anthropogenic emissions than other methods by 4 Tg CH4 yr-1 on average for EUR and by 3 Tg CH4 yr-1 for the USA and a smaller value than other methods by 1 Tg CH4 yr-1 for RUS. The positive difference between method 1, chosen for this study, and other methods (Fig. S5) implies a better match of inversions with respect to NGHGIs for EUR than if other methods were used. For the USA, if we were using method 2, the anthropogenic CH4 emissions would be smaller by 2 Tg CH4 yr-1, which would further accentuate lower estimations of inversion emissions compared to the NGHGIs, especially before 2010. For RUS, even if other methods were used to compare with NGHGIs, our result of a lower estimation of anthropogenic CH4 emissions by the NGHGI report remains valid. In CHN, our result that inversions produce systematically smaller anthropogenic CH4 emissions than NGHGI data is also robust to the choice of method.

Figure 10 compares the share of the different sectors for anthropogenic CH4 emissions across a selection of 12 top emitting countries (selected countries from top anthropogenic and top fossil CH4 emitters). Generally, inversions partition agricultural and waste emissions consistently with NGHGIs within the respective uncertainties in both approaches. Inversions provide, however, larger biomass burning emissions than reported by NGHGIs, partly because we assumed that all biomass burning and biofuel emissions were anthropogenic in inversion results, whereas countries report only fire emissions on managed lands and emissions of biofuel burning used for house heating and cooking. Inversions tend to produce higher CH4 emissions than NGHGIs for all major oil- and gas-emitting countries (except CHN), in particular the USA, Russia (RUS), and Kazakhstan and Turkmenistan (KAZ&TKM). This under-reporting (also discussed in Sect. 4.2) can be due to the fact that inventories and emission factors do not consider CH4 leaks from ultra-emitting events consisting of very large and sporadic emissions, like accidental leaks (Cusworth et al., 2018). Here, we used the first global quantitative estimate of ultra-emitters derived by Lauvaux et al. (2022) from S5P-TROPOMI measurements, namely all short-duration leaks from oil and gas facilities (e.g., wells, compressors) with an individual emission >20 t CH4 h-1, with each event lasting generally less than 1 d. Using the event duration obtained by fitting a local dispersion model to observed S5P-TROPOMI methane plumes, all ultra-emitting events in each country were aggregated during the period from January 2019 to December 2020 (Table S3). Assuming that those large leaks are not reported by NGHGIs, they were added to NGHGI reports of fossil CH4 emissions as plain red stacked bars in Fig. 10. Doing so reduces the misfit with inversions, especially in RUS and KAZ&TKM. Ultra-emitters represent 85 % (1.4 Tg CH4 yr-1) of NGHGI fossil emissions for KAZ&TKM, 14 % (0.9 Tg CH4 yr-1) for RUS, and 2 % (0.03 Tg CH4 yr-1) for the countries grouped in the GULF region. We also considered emissions derived from S5P-TROPOMI measurements at the scale of regional extraction basins for oil, gas, and coal. Four major oil and gas basins were considered (Fig. S7) as they are specific areas where many individual wells and storage facilities are concentrated, each of them with a probability of emitting CH4 and forming a clear regional enhancement of CH4 detected in S5P-TROPOMI and imaged and assimilated with a regional inversion into a regional CH4 emission budget (see Table S3, Supplement, and Kayrros Methane Watch, https://www.kayrros.com/methane-watch/, last access: 30 July 2021). Such basin-scale emissions were diagnosed from regional inversions using S5P-TROPOMI atmospheric measurements. Here, we assumed that those basins are already counted as part of the national CH4 budgets from in situ and GOSAT inversions. Thus, they are shown here for the share of total national fossil emissions that they represent in inversions (dark red bars, part of total fossil emissions in inversion results displayed in Fig. 10). In the USA, the Permian basin emissions represent between 21 % (in situ, S) and 24 % (GOSAT, G) of the total national fossil CH4 estimates from inversions. Alone, the Permian basin contributed 16 % of the total gas and 35 % of the oil extracted in the USA in 2019 (EIA, 2021a). Our average 2019–2020 emission estimate in the Permian basin is 2.3 Tg CH4 yr-1 from S5P-TROPOMI data, which is consistent with an estimate of 2.7 Tg CH4 yr-1 from O&G industries in the Permian basin reported by Zhang et al. (2020) but contrasts with the 1.4 Tg CH4 yr-1 emission estimate for the entire USA reported by EPA (2020). In the GULF, emissions from the basin comprising Iraq and Kuwait represent 32 % (S)–46 % (G) of the total estimated fossil emissions of this region. This basin estimation encompasses four of the highest-oil-producing fields in the world, and its oil production accounts for 31.5 % of all the countries in the GULF region (EIA, 2021a). The basin estimation from inversions for IRN (2.3 Tg CH4) represents 55.2 % (S)–71.0 % (G) of estimated fossil fuel emissions and 94.8 % of the national total NGHGI estimates.

As shown in Sect. 5, the estimation of N2O emission fluxes by emission inventories is challenging, and currently some non-Annex I countries (e.g., COD) have no estimates available. Figure 11 compares inversions (CAMS, GEOS-Chem, and INVICAT) to available NGHGI-reported N2O emission fluxes. Because emission sectors of NGHGIs and inversions are limited and do not coincide with each other, the comparison of N2O emission sectors between these two data sources can only be accomplished partially. The main innovation proposed in this study has been to separate total inversion fluxes into unmanaged and managed lands so that the emissions over managed lands minus the natural inland water emissions can be compared with inventories (Sect. 2). We can see in the data presented in Fig. 12 that natural emissions (natural fluxes from lakes and rivers plus fluxes from unmanaged lands) account for 32 % of the mean inversion total in BRA, 47 % in COD, and 57 % in AUS. In temperate industrialized countries with a smaller fraction of unmanaged land, the magnitude of natural fluxes relative to anthropogenic ones is smaller. In comparison to emissions from unmanaged lands, the natural emissions from rivers are always of a very small magnitude. In general, removing natural emissions tends to improve the agreement with inventories in non-Annex I countries. In Annex I countries, it tends to make inversion-based emissions smaller than those of NGHGIs. The main uncertainty is in the area of grasslands and forests assumed to be unmanaged from our masks and how well they correspond to the unmanaged areas used by each country. A large area of extensively grazed land, e.g., in Mongolia and Kazakhstan, is considered here natural, whereas those countries may consider them under management, even though the nitrogen cycle and N2O emissions are close to natural conditions for extensive grazing. The consistent pattern of higher emissions in inversions than NGHGIs among the three model inversions for non-Annex I countries suggests possible improvements in inventory compilation including adopting country-specific emission factors or re-assessing and reporting indirect emissions when this is not the case (Table S2). On the other hand, for the USA and CHN, the median of inversion emissions is smaller than in inventories and CAMS is higher than the two other inversions considered. Concerning smaller inversion estimates for CHN and the USA compared to NGHGIs, this could be because the Tier 1 used by NGHGIs assumes static EFs, whereas EFs may change (become smaller or larger) depending on cropland nitrogen use efficiency (NUE) and climate. The USA improved its NUE in the 1990s compared to the 1980s considerably (Lassaletta et al., 2014), but if the EFs used are based on flux measurements in the 1980s, these could be too high. A recent data-driven model of direct cropland N2O emissions (Q. Wang et al., 2020) using non-linear EF and regional N-fertilizer input data found emissions smaller than those found by Tier 1 methods, which would be in better agreement with inversions. Another source of uncertainty in the N2O inversions is the prior estimates for land versus ocean. Since the ocean is not well constrained in the inversions, having a too high ocean prior will mean the land total will be underestimated and vice versa.

Table 3 compares the results of the global inversions used in this study with regional inversion results compiled from the literature, generally obtained with higher-resolution regional transport models and sometimes using atmospheric data not assimilated by global inversions. Global inversion results are given without and with adjustments for CO2 fluxes due to lateral transport and for anthropogenic emissions estimated using equation method 1 for CH4 and Eq. (6) for N2O (Sect. 2). The purpose of introducing a CO2 flux correction (Sect. 2.3) was to make an accurate comparison with inventories, but since regional CO2 inversions did not use such an adjustment, here we focus on comparing regional inversions with global ones without adjustment.

For CO2 fluxes in CHN, except for the large uptake found by the inversion (J. Wang et al., 2020), all previous regional inversion results fall within the range of our global inversion ensemble for their period of overlap, indicating no systematic bias of global inversions. Note that J. Wang et al. (2020) provide a global inversion using new Chinese stations data and a discretization of fluxes into smaller sub-regions within China. In BRA, the range of global inversions also covers regional inversion results yet with global inversions being a small CO2 source in 2010 (194 Tg C yr-1) and regional inversions a large source in that year. The regional inversions from Gatti et al. (2014) and Van der Laan-Luijkx et al. (2015) using aircraft CO2 and CO profiles in the Amazon also give a larger flux change between 2010 (a dry year, a CO2 source in the Amazon) and 2011 (a wet year, a CO2 sink in the Amazon) than global inversions that do not assimilate these aircraft data. For EUR, the range of regional inversions (Petrescu et al., 2021a) is similar to the one of global inversions. For North America, however, regional inversions give a higher average CO2 uptake than global ones, although within their range.

For CH4 emissions in CHN, the results of all regional inversions (Miller et al., 2019; Thompson et al., 2015) are consistent with our global inversion ensemble, although the inversion of Miller et al. (2019) is in the upper range. For BRA or the Amazon basin, interestingly, regional inversions (Tunnicliffe et al., 2020; Wilson et al., 2016) provide systematically higher CH4 emissions than global in situ inversion estimates, but regional inversions include wetlands and rivers, which can explain their higher values. If natural emissions were removed from regional inversions, then their values would be consistent with global results; i.e., Tunnicliffe et al. (2020) estimated that CH4 emissions from BRA are 33.6±3.6 Tg CH4 yr-1 with 19.0±2.6 Tg CH4 yr-1 from anthropogenic sources, falling within the range of our estimates for anthropogenic emissions from global inversions (19–36 Tg CH4 yr-1). In the EU and the USA or North America, the regional inversions in Table 3 which have higher-resolution transport models give higher CH4 emissions than global inversions, even when only anthropogenic emissions are considered in regional inversions. This suggests that global models may systematically underestimate CH4 emissions from those two high emitters. For N2O, we have several regional inversions for North America, all producing higher emissions than the median of global inversions by a factor of 4, on average. The only regional N2O inversion over Europe is also about 2 times higher than the median of global inversions.