The consolidated European synthesis of CH4 and N2O emissions for the European Union and United Kingdom: 1990–2017

Abstract. Reliable quantification of the sources and sinks of greenhouse gases, together with trends and uncertainties, is essential to monitoring the
progress in mitigating anthropogenic emissions under the Paris Agreement. This study provides a consolidated synthesis of CH4 and
N2O emissions with consistently derived state-of-the-art bottom-up (BU) and top-down (TD) data sources for the European Union and UK
(EU27 + UK). We integrate recent emission inventory data, ecosystem process-based model results and inverse modeling estimates over the period
1990–2017. BU and TD products are compared with European national greenhouse gas inventories (NGHGIs) reported to the UN climate convention UNFCCC secretariat
in 2019. For uncertainties, we used for NGHGIs the standard deviation obtained by varying parameters of inventory calculations, reported by the
member states (MSs) following the recommendations of the IPCC Guidelines. For atmospheric inversion models (TD) or other inventory datasets (BU), we defined
uncertainties from the spread between different model estimates or model-specific uncertainties when reported. In comparing NGHGIs with other
approaches, a key source of bias is the activities included, e.g., anthropogenic versus anthropogenic plus natural fluxes. In inversions, the
separation between anthropogenic and natural emissions is sensitive to the geospatial prior distribution of emissions. Over the 2011–2015 period,
which is the common denominator of data availability between all sources, the anthropogenic BU approaches are directly comparable, reporting mean
emissions of 20.8 Tg CH4 yr−1 (EDGAR v5.0) and 19.0 Tg CH4 yr−1 (GAINS), consistent with the NGHGI estimates of
18.9 ± 1.7 Tg CH4 yr−1. The estimates of TD total inversions give higher emission estimates, as they also include natural
emissions. Over the same period regional TD inversions with higher-resolution atmospheric transport models give a mean emission of
28.8 Tg CH4 yr−1. Coarser-resolution global TD inversions are consistent with regional TD inversions, for global inversions with
GOSAT satellite data (23.3 Tg CH4 yr−1) and surface network (24.4 Tg CH4 yr−1). The magnitude of natural
peatland emissions from the JSBACH–HIMMELI model, natural rivers and lakes emissions, and geological sources together account for the gap between
NGHGIs and inversions and account for 5.2 Tg CH4 yr−1. For N2O emissions, over the 2011–2015 period, both BU approaches
(EDGAR v5.0 and GAINS) give a mean value of anthropogenic emissions of 0.8 and 0.9 Tg N2O yr−1, respectively, agreeing with the
NGHGI data (0.9 ± 0.6 Tg N2O yr−1). Over the same period, the average of the three total TD global and regional inversions
was 1.3 ± 0.4 and 1.3 ± 0.1 Tg N2O yr−1, respectively. The TD and BU comparison method defined in this study can be
operationalized for future yearly updates for the calculation of CH4 and N2O budgets both at the EU+UK scale and at the national
scale. The referenced datasets related to figures are visualized at https://doi.org/10.5281/zenodo.4590875 (Petrescu et al., 2020b).



Introduction
The global atmospheric concentration of methane (CH 4 ) has increased by 160 % and that of nitrous oxide (N 2 O) by 22 % since the pre-industrial period (WMO, 2019), and they are well documented as observed by long-term icecore records (Etheridge et al., 1998;CSIRO). According to the NOAA atmospheric data (https://www.esrl.noaa.gov/ gmd/ccgg/trends_ch4/, last access: June 2020) the CH 4 concentration in the atmosphere continues to increase and, after a small dip in 2017, has an average growth of 10 ppb yr −1 , representing the highest rate observed since the 1980s 1 (Nisbet et al., 2016(Nisbet et al., , 2019. This increase was attributed to anthropogenic emissions from agriculture (livestock enteric fermentation and rice cultivation) and fossil-fuel-related activities, combined with a contribution from natural tropical wetlands (Saunois et al., 2020;Thompson et al., 2018;Nisbet et al., 2019). The recent increase in atmospheric N 2 O is more linked to agriculture in particular due to the application of nitrogen fertilizers and livestock manure on agricultural land (FAO, 2020(FAO, , 2015IPCC, 2019b;. 1 The rapid development of the gas industry in the 1980s in the former USSR. National greenhouse gas inventories (NGHGIs) are prepared and reported on an annual basis by Annex I countries 2 based on IPCC Guidelines using national activity data and different levels of sophistication (tiers) for well-defined sectors. These inventories contain annual time series of each country's greenhouse gas (GHG) emissions from the 1990 base year 3 until 2 years before the year of reporting and were originally set to track progress towards their reduction targets under the Kyoto Protocol (UNFCCC, 1997). Non-Annex I countries provide some information in biennial update reports (BURs) as well as national communica-tions (NCs), but neither BURs nor NCs report annual time series or use harmonized formats. The IPCC tiers represent the level of sophistication used to estimate emissions, with Tier 1 based on global or regional default values, Tier 2 based on country-specific parameters, and Tier 3 based on more detailed process-level modeling. Uncertainties in NGHGIs are calculated based on ranges in observed (or estimated) emission factors and variability of activity data, using the error propagation method (95 % confidence interval) or Monte Carlo methods, based on clear guidelines (IPCC, 2006).
NGHGIs follow principles of transparency, accuracy, consistency, completeness and comparability (TACCC) under the guidance of the UNFCCC (UNFCCC, 2014). Methodological procedures are taken from the 2006 IPCC Guidelines (IPCC, 2006). The IPCC 2019 Refinement (IPCC, 2019a), which may be used to complement the 2006 IPCC Guidelines, has updated sectors with additional sources and provides guidance on the possible and voluntary use of atmospheric data for independent verification of GHG inventories. Complementary to NGHGIs, research groups and international institutions produce estimates of national GHG emissions, with two families of approaches: atmospheric inversions (top-down, TD) and GHG inventories based on the same principle as NGHGIs but using different methods and input data (bottom-up, BU). These complementary approaches are necessary. First, TD approaches act as an independent check on BU approaches and facilitate a deeper understanding of the scientific processes driving different GHG budgets. Second, NGHGIs only cover a subset of countries, and it is therefore necessary to construct BU estimates independently for all countries. The BU estimates are often used as input data for TD estimates and to track emissions over time, either globally or on the country level, such as in the UNEP Emissions Gap Report (UNEP, 2019). There is no guideline to estimate uncertainties in TD or BU approaches. The uncertainties are usually assessed from the spread of different estimates within the same approach, though some groups or institutions report uncertainties for their estimates using a variety of methods -for instance, by varying parameters or input data. However, this gets complicated when dealing with complex process-based models.
NGHGI official numbers are not always straightforward to compare with other independent estimates. Independent estimates often have different system boundaries and a different focus. BU estimates often have a lot of overlap in terms of methods and other input data, and through harmonization the differences between BU estimates and NGHGIs can be bridged. On the other hand, TD estimates are much more independent and provide the best independent check on NGHGIs. While NGHGIs go through a review process, the UNFCCC procedures do not incorporate mandatory independent, large-scale observation-derived verification but allow the use of atmospheric data for external checks within the data quality control, quality assurance and verification process (2006 IPCC Guidelines, chap. 6: QA/QC procedures).
So far, only a few countries (e.g., Switzerland, the UK, New Zealand and Australia) have used atmospheric observations (TD) to complement their national inventory data (Bergamaschi et al., 2018a).
A key priority in the current policy process is to facilitate the global stocktake exercise of the Paris Agreement, the first one coming in 2023, and to assess collective progress towards achieving the near-and long-term objectives, considering mitigation, adaptation and means of implementation. The global stocktake is expected to create political momentum for enhancing commitments in nationally determined contributions (NDCs) under the Paris Agreement. Key components of the global stocktake are the NGHGIs submitted by countries under the enhanced transparency framework of the Paris Agreement. Under the framework, for the first time, developing countries will be required to submit their inventories and also commit to provide regular reports to UNFCCC, alongside developed countries, which will continue to submit also on an annual basis. Some developing countries will face challenges to provide and then update inventories.
The work presented here represents dozens of distinct datasets and models, in addition to the individual country submissions to the UNFCCC for all European countries (NGHGIs), which while following the general guidance laid out in IPCC (2006) still differ in specific approaches, models and parameters, in addition to differences underlying activity datasets. A comprehensive investigation of detailed differences between all datasets is beyond the scope of this paper, though attempts have been previously made for specific subsectors (e.g., agriculture, Petrescu et al., 2020) and in dedicated gas-specific follow-ups to this paper. As this is the most comprehensive comparison of NGHGIs and research datasets (including both TD and BU approaches) for the European continent to date, we focus here on the following rich set of questions that such a comparison raises without necessarily offering detailed solutions. How can we compare the detailed sectoral NGHGI to the observation-based estimates? Which new information are the observation-based estimates likely to bring (mean fluxes, trend, ensemble variability)? What can we expect from such a complex study and how do we proceed going forward?
We compare official anthropogenic NGHGI emissions with research datasets and wherever needed harmonize research data on total emissions to ensure consistent comparisons of anthropogenic emissions. We analyze differences and inconsistencies between emissions and make recommendations towards future actions to evaluate NGHGI data. While NGHGIs include uncertainty estimates, individual spatially disaggregated research datasets of emissions often lack quantification of uncertainty. Here, we use the median 4 and minimum/maximum (min/max) range of different Inland water (lakes, rivers and reservoirs) fluxes (non-wetland inland waters_ULB) a For consistency with the NGHGIs, here we refer to the five reporting sectors as defined by the UNFCCC and the Paris Agreement decision (18/CMP.1), the IPCC Guidelines (IPCC, 2006) and their 2019 Refinement (IPCC, 2019a), with the only exception that the latest IPCC refinement groups together the agriculture and LULUCF sectors in one sector (agriculture, forestry and other land use -AFOLU). b The term "natural" here refers to unmanaged natural CH 4 emissions (wetlands, geological, inland waters) not reported under the UNFCCC LULUCF sector. c Anthropogenic (managed) agricultural soils can also have a level of natural emissions. d Natural soils (unmanaged) can have both natural and anthropogenic emissions.
research products of the same type to get a first estimate of uncertainty.

CH 4 and N O data sources and estimation approaches
We analyze CH 4 and N 2 O emissions in the EU27 + UK from inversions (TD) and anthropogenic emissions from various BU approaches that cover specific sectors. These data (Table 2) span the period from 1990 and 2017, with the same data available for shorter time periods. The data are from peer-reviewed literature and from unpublished research results from the VERIFY project (Table 1 and Appendix A).
They are compared with NGHGI official submissions up to 2017 and supplemented by the UNFCCC-NRT inventory to capture 2018 estimates (near real time, EEA 2019). References are given in Table 2 and the detailed description of all products in Appendices A1-A3. For both CH 4 and N 2 O BU approaches, we used inventories of anthropogenic emissions covering all sectors (EDGAR v5.0 and GAINS) and inventories limited to agriculture (CAPRI and FAOSTAT). For CH 4 we used one biogeochemical model of natural peatland emissions (JSBACH-HIMMELI), as well as literature data for geological emissions on land (excluding marine seepage) (Etiope et al., 2019;Hmiel et al., 2020) and for lakes and reservoirs (Del     Eisma et al. (1995), Vermeulen et al. (1999), Vermeulen et al. (2006) Global inversions from the Global Carbon Project CH 4 and N 2 O budgets (Saunois et al., 2020; TD  Sontro et al., 2018). Emissions from gas hydrates and termites are not included as they are close to zero in the EU27 + UK (Saunois et al., 2020). Biomass burning emissions of CH 4 from the land use, land use change and forestry (LULUCF) sector account for 3 % of the total emissions in the EU27 + UK. These estimates are described in Sect. 2.2. From TD approaches, we used both regional and global inversions, with the latter having a coarser spatial resolution. These estimates are described in Sect. 2.3. For N 2 O emissions, we used the same global BU inventories as for CH 4 and natural emissions from inland waters (rivers, lakes and reservoirs) Lauerwald et al., 2019). In this study, about 66 % of the N 2 O emitted by Europe's natural rivers is considered anthropogenic indirect emissions, caused by leaching and runoff of N fertilizers from the agriculture sector. We did not account for natural N 2 O emissions from unmanaged soils (Tian et al., 2019, estimated pre-industrial soil emissions in Europe at a third of the level of the most recent decade -emissions that in preindustrial times may have been influenced by human management activities or based on natural processes that have been abolished since). For N 2 O inversions, we used one regional inversion (FLEXINVERT_NILU) and three global inversions (Friedlingstein et al., 2019;. Agricultural sector emissions of N 2 O were presented in detail by Petrescu et al. (2020). In this current study these emissions come from the CAPRI model and FAOSTAT, with the latter additionally covering non-CO 2 emissions from biomass fires in LULUCF. Fossil-fuel-related and industrial emissions were obtained from GAINS (see Appendix A1). Table A2 in Appendix A presents the methodological differences of the current study with respect to Petrescu et al. (2020).
The units used in this paper are metric tonnes (t) (1 kt = 10 9 g; 1 Mt = 10 12 g) of CH 4 and N 2 O. The referenced data used for the figures' replicability purposes are available for download at https://doi.org/10.5281/zenodo.4590875 (Petrescu et al., 2020). Upon request, we can provide the codes necessary to plot precisely the style and/or layout of the figures. We focus herein on the EU27 + UK. In the VERIFY project, we have constructed in addition a web tool which allows for the selection and display of all plots shown in this paper (as well as the companion paper on CO 2 , Petrescu et al., 2021) not only for the regions but for a total of 79 countries and groups of countries in Europe. The data, located on the VERIFY project website (http://webportals.ipsl.jussieu.fr/VERIFY/FactSheets/, last access: February 2021) are free but accessible with a username and password distributed by the project. Figure 1 includes also data from countries outside the EU but located within geographical Europe (Switzerland, Norway, Belarus, Ukraine and the Republic of Moldova).

CH 4 and N 2 O anthropogenic emissions from
NGHGIs UNFCCC NGHGI (2019) emissions are country estimates covering the period 1990-2017. They were kept separate to be compared with other BU and TD data. We supplemented the NGHGI estimates with the member state (MS) near-realtime inventory (MS-NRT; EEA, 2019) to capture one additional year with preliminary estimates 5 . MS-NRT represents the approximated GHG inventory (also referred to as "proxy estimates") with an early estimate of the GHG emissions for the preceding year, as required by Regulation (EU) 525/2013 of the European Parliament and of the Council.
Anthropogenic CH 4 emissions from the four UNFCCC sectors (Table 1, excluding LULUCF) were grouped together. As anthropogenic NGHGI CH 4 emissions from the LULUCF sector are very small for the EU27 + UK (2.6 % in 2017 including biomass burning), we exclude them in Fig. 4 but include them in the total UNFCCC estimates from Figs. 1-3, 5 and 6. Only a few countries 6 under the NGHGIs volunteered to report wetland emissions, following the recommendations of the 2014 IPCC wetlands supplement (IPCC, 2014), and these emissions were not included in the NGHGI total, following the IPCC (2006) Guidelines as the reference for NGHGIs and in the absence of a detailed description of what they cover. According to NGHGI data between 2008 and 2017, the wetland emissions in the EU27 + UK reported under LULUCF (CRF Table 4(II) accessible for each EU27 + UK country 7 ) include only managed wetlands which represent one-fourth of the total wetland area in the EU27 + UK (Giacomo Grassi, personal communication, 2019) and sum up to 0.1 Tg of CH 4 (Petrescu et al., 2020a).
Anthropogenic N 2 O emissions are predominantly related to agriculture (for the EU27 + UK, 69 % in 2017) but are also found in the other sectors . In addition, N 2 O has natural emissions, which are defined as the pre-industrial background, that is, before the use of synthetic N fertilizers and intensive agriculture, and derive from natural processes in soils but also in lakes, rivers and reservoirs Lauerwald et al., 2019;. We used four global CH 4 and N 2 O BU anthropogenic emissions inventories: CAPRI, FAOSTAT, GAINS and EDGAR v5.0 (Tables 2 and 3). These estimates are not completely independent from NGHGIs (see Fig. 4 in Petrescu et al., 2020a) as they integrate their own sectorial modeling with the UN-FCCC data (e.g., common activity data and IPCC emission factors) when no other source of information is available.
Anthropogenic emissions from these datasets follow and can be matched to Table 1 sectors. The CH 4 biomass and biofuel burning emissions are included in NGHGIs under the UNFCCC LULUCF sector, although they are identified as a separate category by the Global Carbon Project CH 4 budget synthesis (Saunois et al., 2020). For both CH 4 and N 2 O, CAPRI (Britz and Witzke, 2014;Weiss and Leip, 2012) and FAOSTAT (FAO, 2020) report only agricultural emissions. None of the BU inventories reported uncertainties, except for the 2015 values of EDGAR v5.0 (Solazzo et al., 2021) and for an earlier FAOSTAT dataset only up to 2010 (Tubiello et al., 2013, and Appendix B).
The CH 4 natural emissions belong to "peatlands" and "other natural emissions", with the latter including geological sources and inland waters (lakes and reservoirs), following Saunois et al. (2020). For peatlands, we used the JSBACH-HIMMELI framework and the ensemble of 13 monthly gridded estimates of peatland emissions based on different land surface models as calculated for Saunois et al. (2020), all described in Appendix A2. In EU27 + UK, geological emissions were calculated by scaling up the regional emissions from Etiope et al. (2019) (37.4 Tg CH 4 yr −1 ) to the global ratio of emissions from Hmiel et al. (2020) (see Appendix A2, geological fluxes), obtaining an estimate of 1.3 Tg CH 4 yr −1 (marine and land geological). Marine seepage emissions were excluded. This rescaled geological source represents 24 % of the total EU27 + UK natural CH 4 emissions. Inland waters (lakes and reservoirs, based on Lauerwald et al., 2019, andDel Sontro et al., 2018) (Appendix A2) are the largest natural component (48 %), with the rest (28 %) being attributed to peatlands. Overall, in the EU27 + UK the natural emissions thus accounted for 5.2 Tg CH 4 yr −1 .
The N 2 O anthropogenic emissions from BU datasets belong predominantly to two main categories, as presented in Table 2: (1) direct emissions from the agricultural sector where synthetic fertilizers and manure were applied, as well as from manure management; and (2) indirect emissions on non-agricultural land and water receiving anthropogenic N through atmospheric N deposition, leaching and runoff (also from agricultural land). Furthermore, emissions from industrial processes are declining over time but originate from fossil fuel combustion, air pollution abatement devices, specific chemical reactions, wastewater treatment and land use change. In this study, we do not consider the natural emissions from soils, since these emissions are relatively small for temperate regions, including Europe, and cannot be singled out in landscapes largely dominated by human activities. Therefore, the only "natural" fluxes considered in this study are emissions from inland waters (lakes, rivers and reservoirs, Maavara et al., 2019;Lauerwald et al., 2019, Appendix A3) even if more than half of the emissions (56 % globally, , and 66 % for Europe this study) are due to eutrophication following N fertilizer leaching to inland waters. Emissions from natural soils in this study are considered anthropogenic because, according country-specific national inventory reports (NIRs), all land in the EU27 + UK is considered to be managed, except 5 % of France's EU territory.
2.3 CH 4 and N 2 O emission data from top-down inversions Inversions combine atmospheric observations, transport and chemistry models, and estimates of GHG sources all with their uncertainties to estimate emissions. Emission estimates from inversions depend on the dataset of atmospheric measurements and the choice of the atmospheric model, as well as on other settings (e.g., prior emissions and their uncertainties). Inversion outputs were taken from original publications without evaluation of their performance through specific metrics (e.g., fit to independent cross-validation atmospheric measurements (Bergamaschi et al., 2013(Bergamaschi et al., , 2018Patra et al., 2016). Some of the inversions solve explicitly for sectors; others solve for all fluxes in each grid cell and separate sectors using prior grid-cell fractions (see details in Saunois et al., 2020, for global inversions).
For CH 4 , we use 9 regional TD inversions and 22 global TD inversions listed in Table 2. These inversions are not independent from each other: some are variants from the same modeling group, many use the same transport model and most of them use the same atmospheric data. Different prior data are generally used in models, which produce a greater range of posterior emission estimates (Appendix B3, Table B4). The subset of InGOS inversions (Bergamaschi et al., 2018a) belongs to a project where all models used the same atmospheric data over Europe covering the period 2006-2012. The global inversions from Saunois et al. (2020) were all updated to 2017.
The regional inversions generally use both higherresolution a priori data and higher-resolution transport models, and, e.g., TM5-JRC runs simultaneously over the global domain at coarse resolution and over the European domain at higher resolution, with atmospheric CH 4 concentration boundary conditions taken from global fields. For CH 4 , 11 global inversions use GOSAT for the period 2010-2017, 8 global inversions use surface stations (SURF) since 2000, 2 global inversions use SURF since 2010 and 1 global inversion uses SURF since 2003 (see Appendix 4 Table in Saunois et al., 2020, and Table 2 below). All regional inversions use observations from SURF stations as a base of their emission calculation.
For N 2 O, we use one regional inversion (FLEXIN-VERT_NILU for 2005-2017 period) and three global inversions for the period 1998-2016 from Thompson et al. (2019), listed in Table 2. These inversions are not completely independent from each other since most of them use the same input information (Appendix B, Table B4). The regional inversion uses a higher-resolution transport model for Europe, with atmospheric N 2 O concentration boundary conditions taken from global fields. As all inversions derived total rather than anthropogenic emissions; emissions from inland waters (lakes, rivers and reservoirs) estimated by Maavara et al. (2019) and Lauerwald et al. (2019) were subtracted from the total emissions. Note that the estimates of Maavara et al. (2019) and Lauerwald et al. (2019) include anthropogenic emissions from N fertilizer leaching accounting for 66 % of the inland water emissions in the EU27 + UK. In 2016, emissions from rivers represent 2.2 % of the total UNFCCC NGHGI (2019) N 2 O emissions. The natural N 2 O emissions are small but should be better quantified in the future to allow for a more accurate comparison between BU (anthropogenic sources only) and TD estimates.
The largest share of N 2 O emissions comes from the agricultural soils (direct and indirect emissions from the applications of fertilizers, whether synthetic or manure) contributing in 2017 69 % of the total N 2 O emissions (excluding LULUCF) in the EU27 + UK. Table B3 in Appendix B1 presents the allocation of emissions by activity type covering all agricultural activities and natural emissions, following the IPCC classification. We notice that each data product has its own particular way of grouping emissions and does not necessarily cover all emissions activities. Main inconsistencies between models and inventories are observed with activity allocation in the two models (ECOSSE and DayCent). ECOSSE only estimates direct N 2 O emissions and does not estimate downstream emissions of N 2 O, for example indirect emissions from nitrate leached into water courses, which also contributes to an underestimation of the total N 2 O emissions. Field burning emissions are also not included by most of the data sources.

Results and discussion
3.1 Comparing CH 4 emission estimates from different approaches 3.1.1 Estimates of European and regional total CH 4 fluxes We present results of the total CH 4 fluxes from the EU27 + UK and five main regions in Europe: north, west, central, east (non-EU) and south. The countries included in these regions are listed in Appendix A, Table A1. Figure 1 shows the total CH 4 fluxes from NGHGIs for both the base year 1990 and mean of the 2011-2015 period. This period was the common denominator for which data were available, including 2 years of the Kyoto Protocol first reporting period (2011/12) and reaching the year of the Paris Agreement was adopted. We aim with the selection of this period to bring together all information over a 5-year period for which values are known in 2018. In fact, this can be seen as a reference for what we can achieve in 2023, the year of the first global stocktake, where for most UN Parties the reported inventories will be known until 2021. Given that the global stocktake is only repeated every 5 years, a 5-year average is clearly of interest.
The total NGHGI estimates include emissions from all sectors, and we plot and compare them with fluxes from global datasets, BU models and inversions. We note that for all five regions, the NGHGI-reported CH 4 emissions decreased by 21 % in southern Europe, by up to 54 % in eastern Europe and by 35 % for the European Union with respect to the 1990 value. This is encouraging in the context of meeting EU commitments under the PA (at least 50 % and towards 55 % compared with 1990 levels stated by the amended proposal for a regulation of the European Parliament and of the council on establishing the framework for achieving climate neutrality and amending Regulation (EU) 2018/1999 (European Climate Law) (https://ec.europa.eu/clima/sites/ clima/files/eu-climate-action/docs/prop_reg_ecl_en.pdf, last access: November 2020) and reaching carbon neutrality by 2050). It also shows that the emissions from BU (anthropogenic and natural) and TD estimates agree well with reported NGHGI data despite the high uncertainty observed in the TD models not only at the EU27 + UK level but also at the regional European level. This uncertainty is represented here by the variability in the model ensembles and denotes the range of the extremes (min and max) of estimates within each model ensemble. From Fig. 1 we clearly note that northern Europe is dominated by natural (wetlands) emissions while western, central and southern European emissions are dominated by anthropogenic sectors (e.g., agriculture).
The EDGAR v5.0 estimate for northern Europe is twice as high when compared to NGHGI and GAINS, and this is because of CH 4 emissions from the fuel production and distribution (IPCC sector 1B) and waste sectors. Most Scandinavian countries rely for their power and heat supply on biogenic fuels, which introduces more uncertainty in the use of activity data and emission factors. The allocation of autoproducers as explained in Sect. 3.2 could be another reason for differences. The waste sector emissions for Norway, Sweden, Finland and Estonia are different but still consistent with the landfill emissions from EDGAR v4.3.2, which are known to be up to twice as high as the nationally reported value (Janssens-Maenhout et al., 2019). For eastern Europe we note that BU anthropogenic estimates have the same magnitude as the TD. One possible explanation is linked to the fact that for TD estimates (i.e., using atmospheric inversions) the fluxes are strongly constrained by the density of observa- Figure 1. Five-year-average (2011Five-year-average ( -2015 total CH 4 emission estimates (including LULUCF) for the EU27 + UK and five European regions (north, west, central, south and east non-EU). The eastern European region does not include European Russia, and the UNFCCC uncertainty for the Republic of Moldova was not available. Northern Europe includes Norway. Central Europe includes Switzerland. The data belong to the UNFCCC NGHGI (2019) submissions (grey) and base year 1990 (black star), two BU inventories (GAINS and EDGAR v5.0), natural unmanaged emissions (sum of peatland, geological and inland water emissions), and three TD total estimates (regional European inversions -excluding InGOS unavailable for 2013-2015 -and GOSAT and SURF estimates from global inverse models). The relative error on the UNFCCC value represents the UNFCCC NGHGI (2018) reported uncertainty computed with the error propagation method (95 % confidence interval): 9.3 % for the EU27 + UK, 10 % for eastern Europe non-EU, 7.8 % for northern Europe, 10.9 % for southern Europe, 16.1 % for western Europe and 11 % for central Europe. The uncertainty for EDGAR v5.0 was calculated for 2015 and represents the 95 % confidence interval of a lognormal distribution.
tions. Where there are few or no observations, the fluxes in the inversion will stay close to the prior estimates, since there is little or no information to adjust them.
In line with Bergamaschi et al. (2018a) we highlight the potential significant contribution from natural unmanaged sources (peatlands, geological and inland water), which for the EU27 + UK accounted for 5.24 Tg CH 4 yr −1 (Fig. 1). Taking into account these natural unmanaged CH 4 emissions and adding the to the range of the anthropogenic estimates (19-21 Tg CH 4 yr −1 ), the total BU estimates become broadly consistent for all European regions with the range of the TD estimates (23-28 Tg CH 4 yr −1 ).
The data in Fig. 2 show anthropogenic CH 4 emissions and their change from one decade to the next, from UNFCCC NGHGI (2019), with the contribution from different UN-FCCC sectors. In 2017, NGHGIs report CH 4 from agricultural activities to be 52 % (± 10 %) of the total EU27 + UK CH 4 emissions, followed by emissions from waste, 27 % (± 23 %). The large share of agriculture in total anthropogenic CH 4 emissions also holds at the global level (IPCC, 2019a). Between the 1990s and the 2000s, the net −17.7 % reduction originates largely from energy and waste, with IPPU (metal and chemical industry) and LULUCF having negligible change. Between the 2000s and 2010-2017, the −15.5 % reduction is distributed more evenly across sectors, with waste having the largest contribution and industry showing no change. The two largest sectors composing total EU27 + UK emission are the agriculture and waste sectors, but the energy and waste sectors have shown higher reductions over the last decade.
The reduction observed in the waste sector is partly due to the adoption of the first EU methane strategy published in 1996(COM(96), 1996. EU legislation addressing emissions in the waste sector proved to be successful and brought about the largest reductions. Directive 1999/31/EC on the landfill of waste (also referred to as the Landfill Directive) required the members states (MSs) to separate waste, minimizing the amount of biodegradable waste disposed untreated in landfills, and to install landfill gas recovery at all new sites. Based on the 1999 directive, the new 2018/1999 EU regulation on the governance of the Energy Union requires the European Commission to propose a strategic plan for methane, which will become an integral part of the EU's long-term strategy.  (1990-1999, 2000-2009 and 2010-2017), and percentages represent the contribution of each sector to the total reduction percentages (black arrows) between periods.
In the waste sector, the key proposal included the adoption of EU legislation requiring the installation of methane recovery and use systems at new and existing landfills. Other suggested actions included measures aimed at the minimization, separate collection and material recovery of organic waste (Olczak and Piebalgs, 2019).

NGHGI estimates compared with bottom-up inventories
The data in Fig. 3 present the total anthropogenic CH 4 emissions from four BU inventories and UNFCCC NGHGI (2019) excluding those from LULUCF. According to NGHGIs, anthropogenic emissions from the total EU27 + UK of the four UNFCCC sectors (Table 1, excluding LULUCF) amounted to 18.2 Tg of CH 4 in the year 2017, which is 10.7 % of the total GHG emissions in CO 2 eq. In Fig. 3a, we observe that EDGAR v5.0 and GAINS show consistent trends with NGHGIs (excluding LULUCF), but GAINS reports consistently lower estimates (10 %) and EDGAR v5.0 consistently higher estimates (8 %) compared to NGHGIs. In contrast to the previous version, EDGAR v4.3.2, which was found by Petrescu et al. (2020a) to be consistent with NGHGI (2018) data, EDGAR v5.0 reports higher estimates but within the 9.4 % UNFCCC uncertainty range. The trends in emissions agree better between the two BU inventories and NGHGIs over 1990-2015, with linear trends of −1.5 % yr −1 in NGHGIs compared to −1.5 % yr −1 in GAINS and −1.4 % yr −1 in EDGAR v5.0. Sectoral time series of anthropogenic CH 4 emissions (excluding LULUCF) and their means are shown in Fig. 3be. For the energy sector (Fig. 3b), both EDGAR v5.0 and GAINS match the NGHGI trend well thanks to updated methodology that derives bottom-up emission factors and accounts for country-specific information about associated petroleum gas generation and recovery, venting, and flaring (Höglund-Isaksson, 2017). After 2005, GAINS reports consistently lower emissions than UNFCCC due to a phasedown of hard coal production in the Czech Republic, Germany, Poland and the UK; a decline in oil production in particular in the UK; and declining emission factors reflecting reduced leakage from gas distribution networks as old town gas networks are replaced. The consistently higher estimates (+6 % compared to the UNFCCC mean) of EDGAR v5.0 might be due to the use of default emission factors for oil and gas production based on data from the US (Janssens-Maenhout et al., 2019). Next to that, several other reasons could be the cause for the differences (e.g., use of Tier 1 emission factors for coal mines, assumptions for material in the pipelines (in the case of gas transport) and the activity data). EDGAR v5.0, for example, uses the gas pipeline length as a proxy for the activity data; however, this may not be appropriate for the case of the official data, which could consider the total amount of gas being transported or both methods according to the countries. Using pipeline length may overestimate the emissions because the pipeline is not always at 100 % capacity; thus, a larger amount of methane is assumed to be leaked. For coal mining, emissions are a function of the different types of processes being modeled.
The IPPU sector (Fig. 3c), which has only a small share of the total emissions, is not reported in GAINS, while EDGAR v5.0 estimates are less than half of the emissions reported by NGHGI 2019 in this sector. The discrepancy for this sector has a negligible impact on discrepancy for the total CH 4 emission. However, we identified that the low bias of EDGAR v5.0 could be explained by fewer activities included in EDGAR v5.0 (e.g., missing solvent, electronics and other manufacturing goods), accounting for 5.5 % of the total IPPU emissions in 2015 reported to UNFCCC. The reason for the remaining difference could be explained by the allocation of emissions from auto-producers 8 in EDGAR v5.0 to the energy sector (following the IPCC 1996 guidelines), while in NGHGIs they are reported under the IPPU sector (following the 2006 IPCC Guidelines).
As CAPRI and FAOSTAT just report emissions from agriculture, we only included them in Fig. 3d. The data show that the four data sources (EDGAR v5.0, GAINS, CAPRI and FAOSTAT) show good agreement, with CAPRI at the lower range of emissions (Petrescu et al., 2020a) and on average 3 % lower than UNFCCC and EDGAR v5.0 at the upper range. The reason for EDGAR v5.0 having the highest estimate (contrary to Petrescu et al., 2020a, where NGHGIs were the highest and EDGAR v4.3.2 the second highest) is likely due to the activity data updates in EDGAR v5.0 based on FAOSTAT values, compared to EDGAR v4.3.2. When look-ing at the time series mean, EDGAR v5.0, GAINS and FAO-STAT show a similar value, +5 % higher than the NGHGI. This shows good consistency between the three BU estimates and UNFCCC likely due to the use of similar activity data and emission factors (EFs); cf. Fig. 4 in Petrescu et al. (2020a).
For the waste sector ( Fig. 3e) EDGAR v5.0 shows consistent higher estimates compared to the NGHGI data, while GAINS emissions have an increasing trend after 2000 (mean 1990-2015 value 6 % higher than NGHGIs). The two inventories, EDGAR v5.0 2020 update for landfills and GAINS, used an approach based on the decomposition of waste into different biodegradable streams, with the aim of applying the methodology described in the 2019 Refinement to the 2006 IPCC Guidelines for National Greenhouse Gas Inventories and the IPCC waste model (IPCC, 2019b) using the firstorder-decay (FOD) method. The main differences between the two datasets come from (i) sources for total waste generated per person, (ii) assumption for the fraction composted and (iii) the oxidation. The two inventories may have used different strategies to complete the waste database when inconsistencies were observed in the EUROSTAT database or in the waste trends in UNFCCC.

Regional inversions
Figure 4 compares TD regional estimates with NGHGI anthropogenic data for CH 4 and with natural BU emissions. We present TD estimates of the total emissions ( For the common period 2006-2012, the four inverse models give a total CH 4 emissions mean of 25.8 (24.0-27.4) Tg CH 4 yr −1 compared to anthropogenic total of 20.3 ± 1.9 Tg CH 4 yr −1 in NGHGIs (Fig. 4a). The large positive difference between TD and NGHGIs suggests a potentially significant contribution from natural sources (peatlands, geological sources and inland waters), which for the same period report a total mean of 5.2 Tg CH 4 yr −1 . However, it needs to be emphasized that wetland emission estimates have large uncertainties and show large variability in the spatial (seasonal) distribution of CH 4 emissions, but for Europe their inter-annual variability is not very strong (mean of 13 years from JSBACH-HIMMELI peatland emissions 1.4 ± 0.1 Tg CH 4 yr −1 ). Overall, they do represent an important source and could dominate the budget assessments A. M. R. Petrescu et al.: European synthesis of CH 4 and N 2 O emissions for the EU27 andUK: 1990-2017 in some regions such as northern Europe (Fig. 1). We also note that the TD trends do not necessarily match those of NGHGIs, and this might be due to strong seasonality of emissions coming from the natural fluxes used as input to the inversions (Saunois et al., 2020).
The natural emissions from inland waters (based on Lauerwald et al., 2019; see Appendix A2) contribute 2.53 Tg CH 4 yr −1 , or 48 % of the total natural CH 4 emissions (sum of lake and reservoir, geological, and peatland emissions). Peatlands (Raivonen et al., 2017, andSusiluoto et al., 2018) account for 1.38 Tg CH 4 yr −1 , i.e., 27 % of the total natural CH 4 emissions, and geological sources sum up to 1.27 Tg CH 4 yr −1 , i.e., 25 % of the total natural CH 4 emissions. It should be noted that geological emissions are an important component of the EU27 + UK emissions budget, although not of concern for climate warming if their source strength has not changed since pre-industrial times (Hmiel et al., 2020). According to the 2006 IPCC Guidelines (IPCC, 2006) CH 4 emissions from wetlands are reported by the MS to the NGHGIs under the LULUCF sector and considered anthropogenic. They are included in the total LULUCF values (Figs. 1, 2, 4 and 5), and in 2017 only eight EU countries (Germany, Denmark, Spain, Estonia, Finland, Ireland, Latvia and Sweden) reported CH 4 emissions from wetlands, accounting only for 11.2 kt CH 4 yr −1 .
In an attempt to quantify the anthropogenic CH 4 component in the European TD estimates, in Fig. 4b we subtract from the total TD emissions the BU peatland emissions from the regional JSBACH-HIMMELI model and those from geological and inland water sources. It remains however uncertain to perform these corrections due to the prior inventory data allocation of emissions to different sectors (e.g., anthropogenic or natural), which can induce uncertainty of up to 100 % if for example an inventory allocates all emissions to natural emissions and the correction is made by subtracting the natural emissions. The inversion that simulates the closest anthropogenic estimate to the UNFCCC NGHGI (2019) is FLExKF-TM5-4DVAR_EMPA. In 2017, it reports 19.4 Tg CH 4 yr −1 , while NGHGIs report 18.5 Tg CH 4 yr −1 . Regarding trends, only FLExKF-TM5-4DVAR_EMPA shows a linear decreasing trend of −2.1 % yr −1 , compared to the NGHGI data trend of −1.3 % yr −1 over their overlap period of 2005-2017, while other inversions show no significant trend. From this attempt we clearly note that few of the inversions showed the clear decline of NGHGIs. As NGHGI emissions are dominated by anthropogenic fluxes and decline by almost 30 % compared to 1990, this should also be seen in the corrected anthropogenic inversions. Therefore, we need to further investigate how well the NGHGIs reflect reality or how well the TD estimates capture the trends. Figure 5 compares TD global estimates with NGHGI data and gives information on the wetland emissions from global wetland models (Saunois et al., 2020). We present TD estimates of the total emissions ( Fig. 5a) as well as estimates of anthropogenic emissions (Fig. 5b). The global inversion models were split according to the type of observations used, with 11 of them using satellites (GOSAT) and 11 using surface stations (SURF). Wetlands emissions provided by 22 global TD inversions from the Global Methane Budget (Saunois et al., 2020) are post-processed with prior ratio estimates for wetland CH 4 emissions (Appendix B, Table B4).

Global inversion estimates
For the common period 2010-2016 for the EU27 + UK, the two ensembles of regional and global models give a total CH 4 emission mean (Fig. 5a) of 22.6 Tg CH 4 yr −1 (GOSAT) and 23.7 Tg CH 4 yr −1 (SURF) compared to 19.0 ± 1.7 Tg CH 4 yr −1 for NGHGIs (Fig. 5a). The mean of the natural wetland emissions from the global inversions is 1.3 Tg CH 4 yr −1 and partly explains the positive difference between total emissions from inversions and NGHGI anthropogenic emissions.
In an attempt to quantify the European TD anthropogenic CH 4 component, in Fig. 5b we subtract from the total TD CH 4 emissions once again the peatland emissions from the regional JSBACH-HIMMELI model and those from geological and inland water sources. The reason for correcting both regional and global inversions with the European peatland emissions from the JSBACH-HIMMELI model lies in the fact that they are in the range of the global wetland emission estimates for Europe (Saunois et al., 2020). Their median for all years (1.43 Tg CH 4 yr −1 , averaged over 2005-2017) is close to the BU estimates of peatland emissions from the JSBACH-HIMMELI model (1.44 Tg CH 4 yr −1 , averaged over [2005][2006][2007][2008][2009][2010][2011][2012][2013][2014][2015][2016][2017]. For the 2010-2016 common period, the two ensembles of regional and global models give an anthropogenic CH 4 emission mean ( Fig. 5b) of 17.4 Tg CH 4 yr −1 (GOSAT) and 23.7 Tg CH 4 yr −1 (SURF) compared to 19.0 ± 1.7 Tg CH 4 yr −1 for NGHGIs (Fig. 5b). For the same period, total CH 4 emissions ( Fig. 5a) from the SURF and GOSAT ensemble decrease by 0.5 % and 4.6 %, respectively. For anthropogenic CH 4 emissions ( Fig. 5b), the SURF and GOSAT ensemble show a decrease of 1.1 % and 6.3 %, respectively, compared to 7.3 % for the NGHGIs from 2010 to 2016.
In 2017, the TD ensemble that simulates the closest anthropogenic estimate (Fig. 5b) to the UNFCCC NGHGI (2019) is GOSAT, with the median of GOSAT inversions (16.4 Tg CH 4 yr −1 ) falling within the uncertainty range of UNFCCC (18.4 ± 1.7 Tg CH 4 yr −1 ). The total UNFCCC estimates include emissions from all sectors. We plot these and compare them with fluxes from global datasets, BU models and TD inversions. We note that for all five regions the N 2 O emissions decreased between 29 % (northern Europe) and 43 % (western Europe) and for the EU27 + UK 37 % with respect to the NGHGI 1990 value. It also shows that at the regional European level the emissions from BU (anthropogenic and natural) and TD estimates agree well with reported NGHGI data within the high uncertainty reported by UNFCCC (∼ 80 %) or observed in the TD model range (for the EU27 + UK global inversions show a min/max range of 25 %-32 %, while regional inversions show a variability range of 9 %-11 % compared to the mean 2011-2015 value). This TD uncertainty is represented here by the variability in the model ensembles and denotes the range of the extremes (min and max) of estimates within each model ensemble. There is significant uncertainty in northern Europe, where the TD estimates indicate either a source or a sink (Fig. 6). The current observation network is sparse, Figure 6. Five-year-average (2011Five-year-average ( -2015 N 2 O emission estimates for the EU27 + UK and five European regions (northern, western central, southern and eastern non-EU). The eastern European region does not include European Russia, and the UNFCCC uncertainty for the Republic of Moldova was not available. Northern Europe includes Norway. Central Europe includes Switzerland. The data belong to UNFCCC NGHGI (2019) submissions (grey) and base year 1990 (black star), two BU inventories (GAINS and EDGAR v5.0), natural unmanaged emissions (sum of peatland, geological and inland waters emissions), and three TD total estimates (regional European inversions and GOSAT and SURF estimates from global inverse models). The relative error on the UNFCCC value represents the UNFCCC NGHGI (2018) MS-reported uncertainty computed with the error propagation method (95 % confidence interval): 80.0 % for the EU27 + UK, 50.3 % for eastern Europe non-EU, 26.6 % for northern Europe, 91.6 % for southern Europe, 51.9 % for western Europe and 46.0 % for central Europe.  (1990-1999, 2000-2009 and 2010-2017), and percentages represent the contribution of each sector to the total reduction percentages between periods.
which currently limits the capability of inverse models to quantify GHG emissions at the country or regional scale.
For all other regions BU anthropogenic emissions agree well with NGHGIs given uncertainties, though we note consistently higher estimates from TD regional and global mod-els estimates. The difference is too high to be attributed to the natural emission, which is related here to inland waters as the only source and which ranges for all five regions between 0.2-1.3 kt N 2 O yr −1 . The blue bar representing the natural emissions has a lower value estimates Lauerwald et al., 2019), while the maximum value was calculated according to Yao et al. (2020). The higher values in Yao et al. (2020) are primarily due to N 2 O emissions from small streams, which are not included in Maavara et al. (2019), while both studies agree fairly well regarding N 2 O emissions from larger rivers .
The data in Fig. 7 show anthropogenic CH 4 emissions and their change from one decade to the next, from UN-FCCC NGHGI (2019), with the contribution from different UNFCCC sectors. In 2017, NGHGIs reported anthropogenic emissions from the EU27 + UK for the four UNFCCC sectors (excluding LULUCF) (Table 1) to be 0.8 Tg N 2 O yr −1 . The agricultural N 2 O emissions accounted for 76 % (± 107 %) of the total EU27 + UK emissions followed by emissions from the energy sector with 12 % (± 23 %). We exclude fire emissions as they only account for 1.8 % of the total N 2 O emissions in the EU27 + UK.
Between the 1990s and the 2000s, the net −17.7 % reduction originates largely from the IPPU and agriculture sectors, which contributed −13.5 % and −4.2 %, respectively. For the period between the 2000s and 2010-2017, the net −15.2 % reduction was again mainly attributed to the IPPU sector (−14.1 %), despite very small increases from the LU-LUCF and waste sectors (+0.6 %).
We note that in 2017 the amount of emissions from the IPPU sector had already decreased by 98 % compared to 1990 and was only 3.5 kt N 2 O yr −1 . Although the IPPU sector contributes in 2017 only 4 % to the total N 2 O emissions, it was the sector with the largest reduction. IPPU sector emissions are mainly linked to the production of nitric acid (e.g., used in fertilizer production) and adipic acid (e.g., used in nylon production). In the late 1990s and early 2000s the five European adipic acid plants were equipped with efficient abatement technology, cutting emissions by 95 %-99 %, largely through voluntary agreements of the companies. Much of the remaining IPPU emissions, from nitric acid plants, were cut in a similar manner around 2010, a development that has been connected with the introduction of the European Emission Trading System that made it economically interesting for companies to apply emission abatement technologies (catalytic reduction of N 2 O in the flue gas) to reduce their emissions. Figure 8 compares the six bottom-up inventories with UN-FCCC NGHGI (2019) data and shows that all of them fall on the NGHGI line (Fig. 8a), noting that GAINS only provides emissions every 5 years. Each inventory shows a very good agreement with each other and the NGHGI estimates until 2005. After 2005 the slight increased trend is influenced by the IPPU (Fig. 8c) and waste (Fig. 8e) (Petrescu et al., 2020a). In contrast, ECOSSE estimates do not use the FAO fertilizer application rate database but instead calculate ideal fertilizer application rates from the nitrogen demand of the crops. This means that it can severely underestimate the applied fertilizer amounts for some areas (e.g., the Netherlands, Denmark or northwestern Germany), and the results are more indicative of emissions under idealized fertilizer application rates. Additionally, as mentioned above, the model simulates only the direct emissions.

NGHGI estimates compared with bottom-up inventories
In the NGHGI (2018) submissions, the EU27 + UK Tier 1 total uncertainty (based on the IPCC chap. 3 error propagation method described in detail by Petrescu et al., 2020a) for the waste sector was 626 %. The sectoral activity responsible for this high uncertainty was the wastewater treatment and discharge (913 %), and this remains one of the most uncertain sources of N 2 O having the highest emissions in the waste sector. Emissions are known to vary markedly in space and time even within a single wastewater treatment plant , a fact that only recently has been properly accounted for in the inventory guidelines (IPCC, 2019a). However, the total emissions from the waste sector account for only 4.4 % of the total EU27 + UK N 2 O emissions (excluding LULUCF).    For the N 2 O we do not present the corrected anthropogenic value because the only natural flux, from inland waters, is very low (2.7 kt N 2 O yr −1 ), and when subtracted from the four inversions the change is almost negligible. Part of the inland water natural estimate is considered anthropogenic in Europe and is due to the leaching of N fertilizers from agriculture. In this study, it accounts for 66 % of the total inland waters emissions.

Data availability
All data files reported in this work which were used for calculations, and figures are available for public download at https://doi.org/10.5281/zenodo.4590875 (Petrescu et al., 2020b). The data we submitted are reachable with one click (without the need for entering login and password) and downloadable with a second click, consistent with the twoclick access principle for data published in ESSD (Carlson and Oda, 2018). The data and the DOI number are subject to future updates and only refer to this version of the paper. The raw gridded data, according to the VERIFY consortium governing document, will be made publicly available 12 months after their publication in ESSD. However, they could be released earlier, upon request to the specific author.
Please also see Table 2 for an overview of data sources for CH 4 and N 2 O emissions used in this study.

Summary and concluding remarks
This study represents the first comprehensive European verification that compares total and sectoral European CH 4 and N 2 O emission estimates from BU (anthropogenic and natural) with TD estimates in order to assess their use for verification purposes with the UNFCCC NGHGI reporting. Above, in the results sections, we discussed differences between estimates. Identification of source-specific uncertainty is key in understanding these differences and will lead to the reduction of the overall uncertainty in GHG inventories. More specifically, we present the first EU27 + UK and European regional 2011-2015 averaged results for CH 4 (Fig. 1) and N 2 O (Fig. 6) compared to the NGHGI emissions (including LULUCF) for the same period and the one reported in 1990, in the framework of the future global stocktake estimate.
Regarding sources of inconsistencies between CH 4 BU estimates and NGHGI data (Fig. 3), at the EU27 + UK level they are mainly caused by the use of different methodologies in calculating emissions as highlighted in Petrescu et al. (2020a). Both BU inventories and the NGHGIs use similar activity data, and the default EFs reported in the 2006 IPCC Guidelines make all data sources agree rather well; thus, inventory spread may not be indicative of the uncertainty. For global consistency purposes, EDGAR v5.0 mostly uses Tier 1 approaches in calculating emissions and uncertainties, a fact which triggers differences with other data sources (GAINS for all sectors and CAPRI for agriculture). Within the UNFCCC reporting process, the two most important emission sectors after agriculture are energy and waste and contribute to the highest reduction percentages (see Fig. 1).
Another reason for small inconsistencies between datasets is the allocation of emissions to different sectors, with different data sources using different versions of IPCC Guidelines (e.g., EDGAR v5.0).
For N 2 O anthropogenic emissions, all BU data sources show good agreement with the UNFCCC NGHGI (2019) data in both trends and means (Fig. 8), and agriculture remains the largest emitter (e.g., urea fertilizers). The uncertainties reported by NGHGIs are very large and will need further improvement.
Regarding the TD estimates, our exercise shows that the comparison between CH 4 inversion estimates and NGHGIs is highly uncertain because of the large spread in the inversion results. As TD inversions do not fully distinguish between all emission sectors used by NGHGIs and report either total emissions or a coarse sectorial partitioning, their comparison to NGHGIs is only possible for total emissions. It is also necessary to make an adjustment for natural emissions, which are included in TD inversions but not reported by the NGHGIs. However, the natural N 2 O emissions do not explain the difference between BU and TD (452 kt N 2 O), and more research is needed to identify the source of discrepancies.
Some studies (Fronzek et al., 2018) show that model ensembles work well in simulating highly uncertain variables. In general regional inversions show less spread than the global inversions as they used recent updates of transport models and higher-resolution transport. Total CH 4 from regional inversions shows a minimum-maximum range of 8.7 Tg CH 4 yr −1 compared to 12.4 Tg CH 4 yr −1 from global GOSAT inversions and 13.5 Tg CH 4 yr −1 from global SURF inversions (Figs. 4 and 5). The global models use fewer observations for Europe compared to the European regional inversions and thus are expected to have larger uncertainties for the European fluxes. In addition, the global models are at coarser resolution and thus likely have larger model representation errors compared to the regional ones, which may contribute to further systematic uncertainty for the European fluxes.
A key challenge for the inversion CH 4 community remains the separation of emissions in specific source sectors, as derived total emissions may also include natural emissions (or removals), while in the case of N 2 O this will not be possible due to the use of definitions (e.g., "natural" N 2 O emissions are defined as the level of emission in the pre-industrial period). It is therefore not possible to separate between N 2 O from natural or anthropogenic sources because natural (or unmanaged) soils can have both natural and anthropogenic emissions, while anthropogenic (managed) agricultural soils can also have a level of natural emissions according to the definition of natural. Therefore, the goal of TD inversions for estimating N 2 O emissions should mainly focus on the trends. Furthermore, the accuracy of derived emissions and the spatial scales at which emissions can be estimated depend on the quality and density of measurements and the quality of the atmospheric models (Bergamaschi et al., 2018b). Significant further developments of the global observation system and the top-down methods would be required to support the implementation of the Paris Agreement.
We provide for the EU27 + UK a consolidated synthesis of the relatively uncertain CH 4 and N 2 O emissions making use of consistently derived BU and TD estimates over the region of Europe, which might illustrate the importance of regional consistent analyses that form the basis of the multilateral facilitative consideration of progress under the enhanced transparency framework of the Paris Agreement. However, the implementation of the Paris Agreement requires accurate quantification of GHG emissions in order to track the progress of all parties with their nationally determined contributions and to assess collective progress towards achieving the purpose of this agreement and its long-term goals (stocktake). As this will be mainly achieved and build upon BU methodologies developed by the IPCC, we need to take into consideration the potential to quantify GHG emissions by using top-down methods (inverse modeling) (Bergamaschi et al., 2018b). One advantage of the inverse estimate is that it provides total emission estimates. Therefore, the capability to quantify anthropogenic emissions depends on the magnitude of natural sources and sinks and the capability to quantify them.
As stated in the introduction, our aim was to identify in this synthesis the issues which cause the differences between NGHGIs, BU and TD to further improve and build a pathway to a verification system (BU use of activity data, emission factor and emission allocation (CH 4 ), very large NGHGI reported uncertainties which need to be reassessed (N 2 O) and higher TD estimates compared to inventories (CH 4 and N 2 O). Additionally, we advocate the need of analyzing the seasonality of emissions, which is of great importance for CH 4 (wetland emission estimates have large uncertainties and show large variability in the spatial (seasonal) distribution) and N 2 O (agriculture fertilizer application), included mostly in the TD prior information but not included in the reported IPCC Guidelines. In the climate mitigation process these seasonal variations may play an important role for a better quantification of sector-specific uncertainties.

VERIFY project
VERIFY's primary aim is to develop scientifically robust methods to assess the accuracy and potential biases in national inventories reported by the parties through an independent pre-operational framework. The main concept is to provide observation-based estimates of anthropogenic and natural GHG emissions and sinks as well as associated uncertainties. The proposed approach is based on the integration of atmospheric measurements, improved emission inventories, ecosystem data, and satellite observations, as well as on an understanding of processes controlling GHG fluxes (ecosystem models, GHG emission models).
Two complementary approaches relying on observational data streams will be combined in VERIFY to quantify GHG fluxes: 1. atmospheric GHG concentrations from satellites and ground-based networks (top-down atmospheric inversion models) and 2. bottom-up activity data (e.g., fuel use and emission factors) and ecosystem measurements (bottom-up models).
For CO 2 , a specific effort will be made to separate fossil fuel emissions from ecosystems fluxes. For CH 4 and N 2 O, we will separate agricultural from fossil fuel and industrial emissions. Finally, trends in the budget of the three GHGs will be analyzed in the context of NDC targets.
The objectives of VERIFY are as follows.
-Objective 1. Integrate the efforts between the research community, national inventory compilers, operational centers in Europe, and international organizations towards the definition of future international standards for the verification of GHG emissions and sinks based on independent observation.
-Objective 2. Enhance the current observation and modeling ability to accurately and transparently quantify the sinks and sources of GHGs in the land use sector for the tracking of land-based mitigation activities.
-Objective 3. Develop new research approaches to monitor anthropogenic GHG emissions in support of the EU commitment to reduce its GHG emissions by 40 % by 2030 compared to the year 1990.
-Objective 4. Produce periodic scientific syntheses of the observation-based GHG balance of EU countries and practical policy-oriented assessments of GHG emission trends and apply these methodologies to other countries.  (2019) Under the UNFCCC convention and its Kyoto Protocol national greenhouse gas (GHG) inventories is the most important source of information to track progress and assess climate protection measures by countries. In order to build mutual trust in the reliability of the GHG emission information provided, national GHG inventories are subject to standardized reporting requirements, which have been continuously developed by the Conference of the Parties (COP) 9 . The calculation methods for the estimation of greenhouse gases in the respective sectors are determined by the methods provided by the 2006 IPCC Guidelines for National Greenhouse Gas Inventories (IPCC, 2006). These guidelines provide detailed methodological descriptions to estimate emissions and removals as well as provide recommendations to collect the activity data needed. As a general overall requirement, the UNFCCC reporting guidelines stipulate that reporting under the convention and the Kyoto Protocol must follow the five key principles of transparency, accuracy, completeness, consistency and comparability (TACCC). The reporting under UNFCCC shall meet the TACCC principles.
The three main GHGs are reported in time series from 1990 up to 2 years before the due date of the reporting. The reporting is strictly source category based and is done under the common reporting format tables (CRF), downloadable from the UNFCCC official submission portal: https://unfccc. int/process-and-meetings/transparency-and-reporting/ reporting-and-review-under-the-convention/ greenhouse-gas-inventories-annex-i-parties/ national-inventory-submissions-2019 (last access: January 2021) The UNFCCC NGHGI anthropogenic CH 4 emissions include estimates from four key sectors for the EU27 + UK: (1) energy, (2) industrial processes and product use (IPPU), (3) agriculture, and (5) waste. The tier method a country applies depends on the national circumstances and the individual conditions of the land, which explain the variability of uncertainties among the sector itself as well as among EU countries. The LULUCF CH 4 emissions are very small but are included in some figures (see Table 1).
The uncertainty methodology for the NGHGI UNFCCC submissions is based on chap. 3 of the 2006 IPCC Guidelines for National Greenhouse Gas Inventories and is explained in Appendix B of Petrescu et al. (2020a).   The latest version of the EDGAR database EDGAR v5.0 contains estimated CH 4 emissions from 1970 until 2015 based fully on statistical data (https://edgar.jrc.ec.europa.eu/ overview.php?v=50_GHG, last access: January 2021). The EDGAR v5.0 updated waste emissions were quantified using the first-order-decay method, combining nationally defined inputs (for waste generation rates and compositions) and IPCC's regional default values for parameters associated with waste degradation processes (specific mass of biodegradable organic carbon, the methane volumetric fraction in the obtained landfill gas and the half-life time for each waste component). The total landfilled waste was split into six streams: food and organic waste type, paper and cardboard, textiles, rubber, wood, and sludge and similar effluents. This was done by making use of the EUROSTAT waste database (EUROSTAT, 2020) but also by employing data from waste composition for municipal/household-type waste from Silpa (Silpa et al., 2018).
Uncertainties. The methodological description is explained in detail in Appendix B Petrescu et al. (2020a) and Solazzo et al. (2021).

CAPRI
CAPRI is an economic, partial equilibrium model for the agricultural sector focused on the EU (Britz and Witzke, 2014 10 ; Weiss and Leip, 2012 11 . CAPRI stands for Com- Table A2. Main methodological changes of the current study with respect to Petrescu et al. (2020a). The sectors are highlighted in italics; the changes with respect to AFOLU (Petrescu et al., 2020a) are shown in bold. "NA" means that there are no data available. mon Agricultural Policy Regionalised Impact analysis, and the name hints at the main objective of the system: assessing the effect of CAP policy instruments not only at the EU or member state level but also at the sub-national level. The model is calibrated for the base year (currently 2012) and then baseline projections are built, allowing the ex ante evaluation of agricultural policies and trade policies on production, income, markets, trade and the environment.
Among other environmental indicators, CAPRI simulates CH 4 emissions from agricultural production activities (enteric fermentation, manure management, rice cultivation, agricultural soils). Activity data are mainly based on FAO-STAT and EUROSTAT statistics, and estimation of emissions follows IPCC 2006 methodologies, with a higher or lower level of detail depending on the importance of the emission source. Details on the CAPRI methodology for emissions calculations are referenced in the Annex Table A1.
Uncertainties are not available for the CAPRI estimates.

GAINS
Specific sectors and abatement technologies in GAINS vary by the specific emitted compound, with source sector definition and emission factors largely following the IPCC methodology at the Tier 1 or Tier 2 level. GAINS includes in general all anthropogenic emissions to air but does not cover emissions from forest fires, savannah burning and land use/land use change. Emissions are estimated for 174 countries/regions, with the possibility to aggregate to a global emission estimate and spanning a timeframe from 1990 to 2050 in 5-year intervals. Activity drivers for macroeconomic development, energy supply and demand, and agricultural activities are entered externally; GAINS extends with knowledge required to estimate "default" emissions (emissions occurring due to an economic activity without emission abatement) and emissions and costs of situations under emission control (see Amann et al., 2011). The GAINS model covers all source sectors of anthropogenic methane (CH 4 ) emissions: agricultural sector emissions from livestock, rice cultivation and agricultural waste burning; energy sector emissions from upstream and downstream sources in fossil fuel extraction and use; and emissions from handling and treatment of solid waste and wastewater source sectors. A description of the modeling of CH 4 emissions in GAINS is presented in . Generation of solid waste and the carbon content of wastewater are derived within the model in consistency with the relevant macroeconomic scenario. The starting point for estimations of anthropogenic CH 4 is the methodology recommended in the IPCC (2006 and revision in 2019) Guidelines, for most source sectors using country-specific information to allow for deriving countryand sector/technology-specific emission factors at a Tier 2 level. Consistent methodologies were further developed to estimate emissions from oil and gas systems (Höglund-Isaksson, 2017) and solid waste Gómez-Sanabria et al., 2018). Emission factors are specified in a consistent manner across countries for given sets of technology and with past implementation of emission abatement measures reflected as changes in technology structures. The resulting emission estimates are well comparable across geographic and temporal scales. The GAINS approach to calculate waste emissions is developed in consistency with the first-order-decay method recommended by IPCC (2006 and 2019 revision), applying different decay periods when estimating emissions from flows of different types of organic waste, i.e., food and garden, paper, wood, textile and other. Data on waste generation, composition and treatment are taken from EUROSTAT (https://ec.europa.eu/ eurostat/statistics-explained/index.php/Waste_statistics, last access: 2019) and complemented with national information from the UNFCCC (2019) common reporting format tables on the amounts of waste diverted to landfills of various management levels and to treatment, e.g., recycling, composting, biodigestion and incineration.
Uncertainties. Uncertainty is prevalent among many different dimensions in the estimations of emissions, abatement potentials and costs. When constructing global bottom-up emission inventories at a detailed country and source level, it is inevitable that some information gaps will be bridged using default assumptions. As it is difficult to speculate about how such sources of uncertainty affect resulting historical and future emission estimates, we instead address uncertainty in historical emissions by making comparisons to estimates by other publicly available and independently developed bottom-up inventories and various top-down estimates consistent with atmospheric measurements and inverse model results. Although existing publicly available global bottom-up inventories adhere to the recommended guidelines of the IPCC (2006), the flexibility in these is large, and results will depend on the availability and quality of gathered source information. There is accordingly a wide range of possible sources of uncertainty built into estimations in such comprehensive efforts. Having a pool of independently developed inventories, each with its own strengths and weaknesses, can improve the understanding of the scope for uncertainty, in particular when compared against top-down atmospheric measurements.

The
Food and Agriculture Organization of the United Nations (FAO) provides CH 4 emissions from agriculture available at http://www.fao.org/faostat/en/#data/GT/visualize (last access: January 2021) and emissions from land use, available at http://www.fao.org/faostat/en/#data/GL/visualize (last access: January 2021). The FAOSTAT emissions database is computed following Tier 1 2006 IPCC Guidelines for National GHG Inventories (http://www.ipcc-nggip.iges.or.jp/public/2006gl/index.html, last access: December 2019). Country reports to FAO on crops, livestock and agriculture use of fertilizers are the source of activity data. Geospatial data are the source of activity data (AD) for the estimates from cultivation of organic soils, biomass and peat fires. GHG emissions are provided by country, regions and special groups, with global coverage, relative to the period 1961-present (with annual updates, currently to 2017) and with projections for 2030 and 2050, expressed as CO 2 eq. for CH 4 , by underlying agricultural emission sub-domain and by aggregate (agriculture total, agriculture total plus energy, agricultural soils). LULUCF emissions consist of CH 4 (methane) associated with biomass and peat fires.
Uncertainties were computed by Tubiello et al. (2013) but are not available in the FAOSTAT database.

A1.2 Top-down CH 4 emission estimates FLEXPART(FLExKF-TM5-4DVAR)
FLExKF applies an extended Kalman filter (Brunner et al., 2012) in combination with backward Lagrangian transport simulations using the model FLEXPART (Stohl et al., 2005;Pisso et al., 2019). It optimizes surface-atmosphere fluxes by assimilating atmospheric observations in a sequential manner, which allows for an analytical solution for relatively large inversion problems (long time periods, number stations O(100)). Since model-observation residuals typically follow a lognormal distribution, the method optimizes logtransformed emissions, which also guarantees a positive solution. Source-receptor matrices (Seibert and Frank, 2004) were computed at 0.25 • × 0.25 • resolution with FLEXPART driven by ECMWF ERA-Interim meteorological fields in the same way as for FLEXINVERT_NILU. Backward simulations were limited to 10 d prior to each observation and to the domain 15 • W-35 • E, 30 • -75 • N. Fluxes were estimated for this domain on a monthly basis at 0.5 • × 0.5 • resolution. For the version used in this study, FLEXPART(FLExKF-TM5-4DVAR)_EMPA, the background mole fraction was taken from a global TM5-4DVAR assimilation run (Bergamaschi et al., 2018a) where the above domain was cut out following the two-step approach of Rödenbeck et al. (2009).
Uncertainties. The uncertainty in the posterior fluxes is composed of random and systematic errors. The random uncertainties are represented by the posterior error covariance matrix provided by the Kalman filter, which combines errors in the prior fluxes with errors in the observations and model representation. Systematic uncertainties primarily arise from systematic errors in modeled atmospheric transport and in background mole fractions but also include aggregation errors, i.e., errors arising from the way the flux variables are discretized in space and time.

FLEXINVERT_NILU
The FLEXINVERT_NILU framework is based on Bayesian statistics and optimizes surface-atmosphere fluxes using the maximum probability solution (Rodgers, 2000). Atmospheric transport is modeled using the Lagrangian model FLEXPART (Stohl et al., 2005;Pisso et al., 2019) run in the backwards time mode to generate a so-called source-receptor matrix (SRM). The SRM describes the relationship between the change in mole fraction and the fluxes discretized in space and time (Seibert and Frank, 2004) and was calculated for 8 d prior to each observation. For use in the inversions, FLEXPART was driven using ECMWF operational analysis wind fields. The state vector consisted of prior fluxes discretized on an irregular grid based on the SRMs (Thompson and Stohl, 2014). This grid has finer resolution (in this case the finest was 0.25 • × 0.25 • ) where the fluxes have a strong influence on the observations and coarser resolution where the influence is only weak (the coarsest was 2 • × 2 • ). The fluxes were solved at 10 d temporal resolution. The state vector also included scalars for the background contribution. The background mixing ratio, i.e., the contribution to the mixing ratio that is not accounted for in the 8 d SRMs, was estimated by coupling the termination points of backwards trajectories (modeled using virtual particles) to initial fields of methane simulated with the Lagrangian FLEXPART-CTM model, which was developed at Empa based on FLEXPART (Stohl et al., 2005;Pisso et al., 2019). In these simulations, we applied the data assimilation method described by Groot Zwaaftink et al. (2018) that constrains modeled fields with surface observations through nudging.
Uncertainties. The posterior fluxes are subject to systematic errors primarily from (1) errors in the modeled atmospheric transport; (2) aggregation errors, i.e., errors arising from the way the flux variables are discretized in space and time; (3) errors in the background methane fields; and (4) the incomplete information from the observations and hence the dependence on the prior fluxes. In addition, there is, to a smaller extent, some error due to calibration offsets between observing instruments. Uncertainties in the observation space were inflated to take into account the model representation errors

InGOS and TM5-4DVAR
The atmospheric models used within the European FP7 project InGOS (Integrated non-CO 2 Greenhouse gas Observing System) are described by Bergamaschi et al. (2018a) and their Supplement (https://doi.org/10.5194/acp-18-901-2018-supplement). The models include global Eulerian models with a close-up over Europe (TM5-4DVAR, TM5-CTE, LMDZ), regional Eulerian models (CHIMERE) and Lagrangian dispersion models (STILT, NAME, COMET). The horizontal resolutions over Europe are ∼ 1.0-1.2 • (longitude) × ∼ 0.8-1.0 • (latitude) for the global models (close-up) and ∼ 0.17-0.56 • (longitude) × ∼ 0.17-0.5 • (latitude) for the regional models. Most models are driven by meteorological fields from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis (Dee et al., 2011). In the case of STILT, the operational ECMWF analyses were used, while for NAME meteorological analyses of the Met Office United Model (UM) were employed. The regional models use boundary conditions (background CH 4 mole fractions) from inversions of the global models (STILT from TM3, COMET from TM5-4DVAR, CHIMERE from LMDZ) or estimate the boundary conditions in the inversions (NAME) using baseline observations at Mace Head as prior estimates. In the case of NAME and CHIMERE, the boundary conditions are further optimized in the inversion. The inverse modeling systems applied in this study use different inversion techniques. TM5-4DVAR, LMDZ, and TM3-STILT use 4DVAR variational techniques, which allow optimization of emissions of individual grid cells. These 4DVAR techniques employ an adjoint model in order to iteratively minimize the cost function using a quasi-Newton  or conjugate gradient (Rödenbeck, 2005) algorithm. The NAME model applies a simulated annealing technique, a probabilistic technique for approximating the global minimum of the cost function. In CHIMERE and COMET, the inversions are performed analytically after reducing the number of parameters to be optimized by aggregating individual grid cells before the inversion. TM5-CTE applies an ensemble Kalman filter (EnKF) (Evensen, 2003) with a fixed-lag smoother .
Uncertainty. In general, the estimated model uncertainties depend on the type of station and for some models (TM5-4DVAR and NAME) also on the specific synoptic situation. In InGOS the uncertainty of the ensemble was calculated as a 1σ estimate. Bergamaschi et al. (2015) showed that the range of the derived total CH 4 emissions from north-western and eastern Europe using four different inverse modeling systems was considerably larger than the uncertainty estimates of the individual models because the latter typically use Bayes' theorem to calculate the reduction of assumed a prior emission uncertainties by assimilating measurements (propagating estimated observation and model errors to the estimated emissions). An ensemble of inverse models may provide more realistic overall uncertainty estimates, since estimates of model errors are often based on strongly simplified assumptions and do not represent the total uncertainty.

InTEM-NAME
The Inversion Technique for Emission Modelling (InTEM) (Arnold et al., 2018) uses the NAME (Numerical Atmospheric dispersion Modeling Environment) (Jones et al., 2007) atmospheric Lagrangian transport model. NAME is driven by analysis 3-D meteorology from the UK Met Office Unified Model (Cullen, 1993). The horizontal and vertical resolution of the meteorology has improved over the modeled period from 40 to 12 km (1.5 km over the UK). InTEM is a Bayesian system that minimizes the mismatch between the model and the atmospheric observations given the constraints imposed by the observation and model uncertainties and prior information with its associated uncertainties. The direction-(latitude and longitude) and altitude-varying background concentration and observation station bias are solved for within the inverse system along with the spatial distribution and magnitude of the emissions. The time-varying prior background concentration for the DECC network stations is derived from the MHD observations when they are very largely sensitive only to northern Canada (Arnold et al., 2018). The prior bias (that can be positive or negative) for each station is set to zero with an uncertainty of 1 ppb. The observations from each station are assumed to have an exponentially decreasing 12 h time correlation coefficient and, between stations, a 200 km spatial correlation coefficient. The observations are averaged into 2 h periods. The uncertainty of the observations is derived from the variability of the observations within each 2 h period. The modeling uncertainty for each 2 h period at each station varies and is defined as the larger of the median pollution events in that year at that station or 16.5 % of the magnitude of the pollution event. These values have been derived from analysis of the observations of methane at multiple heights at each station across the DECC network. Each inversion is repeated 24 times; each time 10 % of the observations per year per station are randomly removed in 5 d intervals and the results and uncertainty averaged.
Uncertainty. This random removal of observations allows a greater exploration of the uncertainty, given the potential for some of the emission sources to be intermittent within the time period of the inversion.

CTE-CH 4 Europe, CTE-SURF and CTE-GOSAT
CarbonTracker Europe CH 4 (CTE-CH 4 ) (Tsuruta et al., 2017) applies an ensemble Kalman filter  in combination with the Eulerian transport model TM5 . It optimizes surface fluxes weekly and assimilates atmospheric CH 4 observations. TM5 was run at 1 • × 1 • resolution over Europe and 6 • × 4 • e resolution globally, constrained by 3-hourly ECMWF ERA-Interim meteorological data. The photochemical sink of CH 4 due to tropospheric and stratospheric OH as well as stratospheric Cl and O( 1 D) were pre-calculated based on Houweling et al. (2014) and Brühl and Crutzen (1993) and not adjusted in the optimization scheme.
Uncertainty. The prior uncertainty is assumed to be a Gaussian probability distribution function, where the error covariance matrix includes errors in prior fluxes, observations and transport model representations. The uncertainty for the prior fluxes was assumed to be 80 % of the fluxes over land and 20 % over ocean, with the correlation between grid cells or regions being 100-500 km over land and 900 km over ocean. The uncertainties for observations and transport model representations vary between observations, with the minimum aggregated uncertainty being 7.5 ppb for surface observations and 15 ppb for GOSAT data. The posterior uncertainty is calculated as the standard deviation of the ensemble members, where the posterior error covariance matrix is driven by the ensemble Kalman filter.

MIROC4-ACTM
The MIROC4-ACTM time-dependent inversions solve for emissions from 53 regions for CH 4 and 84 regions for N 2 O. The inversion framework is based on Bayesian statistics and optimizes surface-atmosphere fluxes using the maximum probability solution. Atmospheric transport is modeled using JAMSTEC's Model for Interdisciplinary Research on Climate, version 4, based on an atmospheric chemistrytransport model (MIROC4-ACTM) (Watanabe et al., 2008;Patra et al., 2018). The source-receptor matrix (SRM) is calculated by simulating unitary emissions from 53 or 84 basis regions, for which the fluxes are optimized. The SRM describes the relationship between the change in mole fraction at the measurement locations for the unitary basis region fluxes. The MIROC4-ACTM meteorology was nudged to the JMA 55-year reanalysis (JRA-55) horizontal wind fields and temperature. The calculation of photochemical losses is performed online. The hydroxyl (OH) radical concentration for reaction with CH 4 varies monthly but without any interannual variations. The simulated mole fractions for the total a priori fluxes are subtracted from the observed concentrations before running the inversion calculation (as in Patra et al., 2016, for CH 4 inversion). Both inversion results are contributed to the GCP-CH 4 and GCP-N 2 O activities (Saunois et al., 2020;Thompson et al., 2019;. Uncertainties. The posterior fluxes are subject to systematic errors primarily from (1) errors in the modeled atmospheric transport; (2) aggregation errors, i.e., errors arising from the way the flux variables are discretized in space (84 regions) and time (monthly means); (3) errors in the background mole fractions (assumed to be a minor factor); and (4) the incomplete information from the sparse observational network and hence the dependence on the prior fluxes. In addition, there is, to a much smaller extent, some error due to calibration offsets between observing instruments, which is more pertinent for N 2 O than for other GHGs. We have validated model transport in the troposphere using SF 6 for the inter-hemispheric exchange time using SF 6 and CO 2 for the age of air in the stratosphere. The simulated N 2 O concentrations are also compared with aircraft measurements in the upper troposphere and lower stratosphere for evaluating the stratosphere-troposphere exchange rates. Comparisons with ACE-FTS vertical profiles in the stratosphere and mesosphere indicate good parameterization of N 2 O loss by photolysis and chemical reactions and thus the lifetime, which affect the global total N 2 O budgets. Random uncertainties are calculated by the inverse model depending on the prior flux uncertainties and the observational data density and data uncertainty. Only 37 sites are used in the inversion, and thus the reduction in priori flux uncertainties has been minimal. The net fluxes from the inversion from individual basis regions are less reliable compared to the anomalies in the estimated fluxes over a period of time.

Global Carbon Project -Global Methane Budget (GMB)
GMB uses an ensemble of 22 top-down global inversions for anthropogenic CH 4 emissions presented in Saunois et al. (2020) for the Global Methane Budget. These inversions were simulated by nine atmospheric inversion systems based on various chemistry-transport models, differing in vertical and horizontal resolutions, meteorological forcing, advection and convection schemes, and boundary layer mixing. Surface-based inversions were performed over the period 2000-2017, while satellite-based inversions cover the GOSAT data availability over 2010-2017. The protocol established for these simulations was not stringent as the prior emission flux dataset was not mandatory, and each group selected their constraining observations. More information can be found in Saunois et al. (2020), in particular in their Tables 6 and S6.
Uncertainties. Currently there are no uncertainties reported for the GMB models. This study uses the median and the min/max as uncertainty range estimation from the 22model ensemble. In general uncertainties might be due to factors like different transport models, physical parameterizations, prior fluxes and observation datasets. The CH 4 estimate from inland waters represents a climatology of average annual diffusive and ebulitive CH 4 emissions from lakes and reservoirs at the spatial resolution of 0.1 • . The climatology is based on five alternative estimates, all relying on the high-resolution HydroLAKES database (Messager et al., 2016), and of which we report the mean and the standard deviation as a measure of uncertainty. Four of these estimates are based on predictions of CH 4 emission rates from N and P concentrations. These concentrations were computed for each lake and reservoir of the Hy-droLAKES dataset (> 1.4 millions), using the mechanisticstochastic model (MSM) of Maavara et al. (2017Maavara et al. ( , 2019 and Lauerwald et al. (2019); see methodology for inland water N 2 O emissions for further details. The four estimates result from two empirical equations relating CH 4 emissions to chlorophyll a concentrations (Deemer et al., 2016;DelSontro et al., 2018) and two equations relating chlorophyll a concentrations to nutrient concentrations (both from McCauley et al., 1989) in lakes and reservoirs. The fifth estimate is based on direct upscaling from observed CH 4 emission rates (155 lakes and reservoirs), which we have classified into rates reported for small lakes (< 0.3 km 2 ), larger (> 0.3 km 2 ) lakes and reservoirs. In addition, we applied a coarse regionalization distinguishing the boreal (> 54 • N) from the temperate to sub-tropical (< 54 • N) zone.

JSBACH-HIMMELI
The model framework, JSBACH-HIMMELI (Raivonen et al., 2017;Susiluoto et al., 2018), is used to estimate wetland and mineral soil emissions, and an empirical model is used to estimate the emissions from inland water bodies.
JSBACH-HIMMELI is a combination of two models, JS-BACH, which is the land-surface model of MPI-ESM (Reick et al., 2013), and HIMMELI, which is a specific model for northern peatland emissions of CH 4 (Raivonen et al., 2017). HIMMELI (HelsinkI Model of MEthane buiLd-up and emIssion for peatlands) has been developed especially for estimating CH 4 production and transport in northern peatlands. It simulates both CH 4 and CO 2 fluxes and can be used as a module within different modeling environments (Raivonen et al., 2017;Susiluoto et al., 2018). HIMMELI is driven with soil temperature, water table depth, the leaf area index and anoxic respiration. These parameters are provided to HIM-MELI from JSBACH, which models hydrology, vegetation and soil carbon input from litter and root exudates. CH 4 emission and uptake of mineral soils are calculated applying the method by Spahni et al. (2011) based on soil moisture estimated by JSBACH.
The distribution of terrestrial vegetation types in JSBACH-HIMMELI is adopted from CORINE land cover data and from native JSBACH land cover for the areas that CORINE does not cover. The HIMMELI methane model is applied for peatlands and the mineral soil approach for the rest. The map of inland water CH 4 emissions has been combined with the JSBACH-HIMMELI land use map so that the map of inland waters is preserved and JSBACH grid-based fractions of different land use categories are adjusted accordingly. In order to avoid double-counting the terrestrial CH 4 flux estimates have been normalized by the ratio of the two inland water body distributions.
Uncertainties. As in any process modeling, the uncertainties of the bottom-up modeling of CH 4 arise from three primary sources: parameters, forcing data (including spatial and temporal resolution) and model structure. An important source of uncertainty in the case of terrestrial CH 4 flux modeling is the spatial distribution of peatlands.
The uncertainties of JSBACH-HIMMELI peatland emissions were estimated by comparing the annual totals of measured and simulated methane fluxes at five European observation sites. Two of the sites are located in Finnish Lapland, one in middle Sweden, one in southern Finland and one in Poland.
For the sensitivity of mineral soil fluxes Spahni et al. (2011) tested two soil moisture thresholds, 85 % or 95 % of water holding capacity. Below these two thresholds, mineral soils are assumed to be only CH 4 sinks, while above these thresholds they are assumed to be only CH 4 sources. We used the higher value, 95 % of water holding capacity. The uncertainty was estimated using CH 4 flux simulations of 1 year (2005). We performed two new model runs, using the moisture threshold 95 ± 15 %, and derived the uncertainty from the resulting range in the annual emission sum.

Geological fluxes
To calculate geological CH 4 emissions we used literature data for geological emissions on land (excluding marine seepage) (Etiope et al., 2019;Hmiel et al., 2020). From the gridded geological CH 4 emissions by Etiope et al. (2019), and using the land-sea mask for the EU27 + UK (to exclude marine seepage), geological CH 4 emissions from the land of EU27 + UK are 8.83 Tg CH 4 yr −1 . Then we scaled this number by the ratio of global geological CH 4 emissions estimated by Hmiel et al.   (Saunois et al., 2020) GMB uses an ensemble of 13 monthly gridded estimates of wetland emissions based on different land surface models as calculated for Saunois et al. (2020). Each model conducted a 30-year spin-up and then simulated net methane emissions from wetland ecosystems over 2000-2017. The models were forced by CRU-JRA reconstructed climate fields (Harris, 2019) and by the remote sensing-based wetland dynamical area dataset WAD2M (Wetland Area and Dynamics for Methane Modeling). This dataset provides monthly global areas over 2000-2017 based on a combination of microwave remote sensing data from Schroeder et al. (2015) and various regional inventory datasets. More information is available in Saunois et al. (2020), and more details will be presented in a future publication led by Poulter et al. (2017) and colleagues.
Uncertainty. As described by Saunois et al. (2020) uncertainties are reported as minimum and maximum values of the available studies in brackets. They do not take into account the uncertainty of the individual estimates but rather express the uncertainty as the range of available mean estimates, i.e., the standard error across measurements/methodologies considered.

ECOSSE
ECOSSE is a biogeochemical model that is based on the carbon model RothC (Jenkinson and Rayner, 1977;Jenkinson et al., 1987;Coleman and Jenkinson, 1996) and the nitrogen model SUNDIAL (Bradbury et al., 1993;. All processes of the carbon and nitrogen dynamics are considered (Smith et al., 2010a,b). Additionally, in ECOSSE, processes of minor relevance for mineral arable soils (e.g., methane emissions) are implemented in order to represent better processes that are relevant for other soils (e.g., organic soils). ECOSSE can run in different modes and for different time steps. The two main modes are site-specific and limited data. In the later version, basis assumptions/estimates for parameters can be provided by the model. This increases the uncertainty but makes ECOSSE a universal tool that can be applied for large-scale simulations even if the data availability is limited. To increase the accuracy in the site-specific version of the model, detailed information about soil properties, plant input, nutrient application and management can be added as available.
During the decomposition process, material is exchanged between the soil organic matter (SOM) pools according to first-order rate equations, characterized by a specific rate constant for each pool, and modified according to rate modifiers dependent on the temperature, moisture, crop cover and pH of the soil. The N content of the soil follows the decomposition of the SOM, with a stable C : N ratio defined for each pool at a given pH, with N being either mineralized or immobilized to maintain that ratio. Nitrogen released from decomposing SOM as ammonium (NH + 4 ) or added to the soil may be nitrified to nitrate (NO − 3 ). For spatial simulations the model is implemented in a spatial model platform. This allows us to aggregate the input parameter for the needed resolution. ECOSSE is a onedimensional model, and the model platform provides the input data in a spatial distribution and aggregates the model outputs for further analysis. While climate data are interpolated, soil data are represented by the dominant soil type or by the proportional representation of the different soil types in the spatial simulation unit (this is a grid cell in VERIFY).
Uncertainties in ECOSSE arise from three primary sources: parameters, forcing data (including spatial and temporal resolution) and model structure.

DayCent
DayCent was designed to simulate soil C dynamics, nutrient flows (N, P, S) and trace gas fluxes (CO 2 , CH 4 , N 2 O, NO x , N 2 ) between soil, plants and the atmosphere at a daily time step. Submodels include soil water content and temperature by layer, plant production and allocation of net primary production (NPP), decomposition of litter and soil organic matter, mineralization of nutrients, N gas emissions from nitrification and denitrification, and CH 4 oxidation in nonsaturated soils.
The DayCent modeling application at the EU level is a consolidated model framework running on Land Use/Cover Area frame statistical Survey (LUCAS) points (Orgiazzi et al., 2018), which was extensively explained in previous works (Lugato et al., 2017(Lugato et al., , 2018Quemada et al., 2020) where a detailed description of numerical and geographical datasets and uncertainty estimations is reported.
Information directly derived from LUCAS (2009-2015) included the soil organic carbon content (SOC), particle size distribution and pH. Hydraulic properties and bulk density was also calculated with an empirically derived pedotransfer. Management information was derived from official statistics (EUROSTAT, https://ec.europa.eu/eurostat/ web/agriculture/data, last access: Seprember 2019) and included crop shares at the NUTS2 level. The amount of mineral N was partitioned according to the regional crop rotations and agronomic crop requirements. Organic fertilization and irrigated areas were derived from the Gridded Livestock of the World FAO dataset and the FAO-AQUASTAT product.
Uncertainty. The starting year of the simulation was set in 2009 and projected in the future. The uncertainty analysis, based on the Monte Carlo approach, was done running the model 52 times in each point and, contemporarily, randomly sampling model inputs from probability density functions for SOC pool partition, irrigation, and both mineral and organic fertilization rates. The model outputs (including uncertainties) at point level were upscaled regionally at 1 km resolution by a machine learning approach based on random forest regression.

N 2 O emissions from inland waters
The N 2 O estimate represents a climatology of average annual N 2 O emissions from rivers, lakes, reservoirs and estuaries at the spatial resolution of 0.1 • . Based on a spatially explicit representation of water bodies and point and nonpoint sources of N and P, this model quantifies the globalscale spatial patterns in inland water N 2 O emissions in a consistent manner at 0.5 • resolution, which were then downscaled to 0.1 • using the spatial distribution of European inland water bodies. The procedure to calculate the cascading loads of N and P delivered to each water body along the river-reservoir-estuary continuum and to topologically connect 1.4 million lakes (extracted from the HydroLAKES database) is described in Maavara et al. (2019) and Lauerwald et al. (2019). The methodology to quantify N 2 O emissions is based on the application of a mechanistic stochastic model (MSM) to estimate inland water C−N−P cycling as well as N 2 O production and emission generated by nitrification and denitrification. Using a Monte Carlo analysis, the MSM allows us to generate relationships relating N processes and N 2 O emissions to N and P loads and water residence time from the mechanistic model outputs, which are subsequently applied for the spatially resolved upscaling. For the estimation of N 2 O emission, we ran two distinct model configurations relying on EFs scaling to denitrification and nitrification rates: one assuming that N 2 O production equals N 2 O emissions and the other taking into account the kinetic limitation on N 2 O gas transfer and progressive N 2 O reduction to N 2 during denitrification in water bodies with increasing residence time . The model outputs from the two scenarios are used to constrain uncertainties in N 2 O emission estimates.

GAINS
Specific sectors and abatement technologies in GAINS vary by the specific emitted compound, with source sector definition and emission factors largely following the IPCC methodology at the Tier 1 or Tier 2 level. GAINS includes in general all anthropogenic emissions to air but does not cover emissions from forest fires, savannah burning and land use/land use change. Emissions are estimated for 174 countries/regions, with the possibility to aggregate to a global emission estimate and spanning a timeframe from 1990 to 2050 in 5-year intervals. Activity drivers for macroeconomic development, energy supply and demand, and agricultural activities are entered externally; GAINS extends with knowledge required to estimate "default" emissions (emissions occurring due to an economic activity without emission abatement) and emissions and costs of situations under emission control (Amann et al., 2011).
Emissions of nitrous oxide derive from energy, industry, agriculture and waste. Land use change emissions are not included. In the energy sector, certain technologies implemented to improve air quality affect N 2 O emission factors (like catalytic converters in vehicles), sometimes also negatively. That is also the case for non-selective catalytic reduction devices for NO x abatement in power plants or for fluidized bed combustion. Relevant industrial processes cover nitric acid and adipic acid, with other processes (glyoxal, if relevant, or caprolactam) included. Both processes allow for two different levels of abatement technologies, which both are relatively easily accessible and low cost. The use of N 2 O in gaseous form, often as an anesthetic for medical purposes, is associated with population numbers and scaled by availability of hospital beds. Marked emission reductions (at low costs) as well as complete phaseout of emissions (high costs) are implemented as technologies. Agricultural emissions in part derive from manure handling, where different management strategies have repercussions on emissions. The larger fraction of emission is from application of nitrogen compounds in different forms to grassland, crops and rice, with rice using a different emission factor. Application of manure and of mineral fertilizer in GAINS can be reduced by advanced computer technology such as automatic steering and variable rate application or by agrochemistry (nitrification inhibitors). The costs of implementation are considered to depend on the size of a farm; hence farm size is an important parameter. In the waste sector, composting and wastewater treatment are considered relevant sources. For wastewater treatment, GAINS also considers a specific emission reduction option when optimizing processes towards N 2 O reduction (e.g., via favoring the anammox process). All details have been reported by Winiwarter et al. (2018) in their supplementary material.
Uncertainties. The same paper provides full information on the uncertainty of N 2 O emissions in the GAINS model, which is a consequence of uncertainty provided in the activ-  EU27 andUK: 1990-2017 ity data, in the emission factors and in the actual structure of the respective management strategies that also include the share of abatement technology already implemented. Further parameters also described (on uncertainty of future projections and on costs) are not relevant here.

FAOSTAT
The Statistics Division of the Food and Agriculture Organization of the United Nations provides N 2 O emissions from agriculture (http://www.fao.org/faostat/en/#data/GT/visualize, last access: January 2021) and its sub-domains, as well as N 2 O emissions from land use linked to biomass burning (metadata: http://fenixservices.fao.org/faostat/ static/documents/GT/GT_e_2019.pdf, last access: December 2020, and http://fenixservices.fao.org/faostat/ static/documents/GL/GL_e_2019.pdf, last access: December 2020). The FAOSTAT emissions database is computed following Tier 1 of the 2006 IPCC Guidelines for National Greenhouse Gas Inventories (http://www.ipcc-nggip.iges.or.jp/public/2006gl/index.html, last access: December 2020). Country reports to FAO on crops, livestock and agriculture use of fertilizers are the source of activity data. Geospatial data are the source of AD for the estimates from cultivation of organic soils, biomass and peat fires. N 2 O emissions are provided by country, regions and special groups, with global coverage, relative to the period 1961-present (with annual updates, currently 2017) and with projections for 2030 and 2050 for agriculture only, expressed in both CO 2 eq. and N 2 O by underlying agricultural and land use emission sub-domain and by aggregate (agriculture total, agriculture total plus energy, agricultural soils). The main N 2 O emissions are reported for the following agricultural activities: manure management, synthetic fertilizers, manure applied to the soils, manure left in pasture, crop residues, cultivation of organic soils and burning crop residues. LULUCF emissions consist of N 2 O associated with burning biomass and peat fires, as well as from the drainage of organic soils.
Uncertainties were computed by Tubiello et al. (2013) but are not available in the FAOSTAT database.

A3.2 Top-down N 2 O emission estimates FLEXINVERT_NILU
The FLEXINVERT_NILU framework is based on Bayesian statistics and optimizes surface-atmosphere fluxes using the maximum probability solution (Rodgers 2000). Atmospheric transport is modeled using the Lagrangian model FLEX-PART (Stohl et al., 2005;Pisso et al., 2019) run in the backwards time mode to generate a so-called source-receptor matrix (SRM). The SRM describes the relationship between the change in mole fraction and the fluxes discretized in space and time (Seibert and Frank, 2004) and was calculated for 7 d prior to each observation. For use in the inversions, FLEX-PART was driven using ECMWF ERA-Interim wind fields.
The state vector consisted of flux increments (i.e., offsets to the prior fluxes) discretized on an irregular grid based on the SRMs (Thompson et al., 2014). This grid has finer resolution (in this case the finest was 0.5 • × 0.5 • ) where the fluxes have a strong influence on the observations and coarser resolution where the influence is only weak (the coarsest was 2 • × 2 • ). The flux increments were solved at 2-weekly temporal resolution. The state vector also included scalars for the background mole fractions. The optimal (posterior) fluxes were found using the conjugate gradient method (e.g., Paige and Saunders, 1975).
The background mole fractions, i.e., the contribution to the modeled mole fractions that is not accounted for in the 7 d SRMs, was estimated by coupling the termination points of backwards trajectories (modeled using virtual particles) to initial fields of mole fractions from the optimized Eulerian model LMDZ (i.e., the CAMS N 2 O mole fraction product v18r1) following the method of Thompson et al. (2014).
Uncertainties. The posterior fluxes are subject to systematic errors primarily from (1) errors in the modeled atmospheric transport; (2) aggregation errors, i.e., errors arising from the way the flux variables are discretized in space and time; (3) errors in the background mole fractions; and (4) the incomplete information from the observations and hence the dependence on the prior fluxes. In addition, there is, to a smaller extent, some error due to calibration offsets between observing instruments, which is more pertinent for N 2 O than for other GHGs. Random uncertainties are calculated from a Monte Carlo ensemble of inversions following Chevallier et al. (2007), and uncertainties in the observation space were inflated to take into account the model representation errors.
A3.3 Global N 2 O Budget -GCP  CAMS-N 2 O Within the GCP 2019 results, N 2 O fluxes are estimated using the atmospheric inversion framework, CAMS-N 2 O. Atmospheric inversions use observations of atmospheric mixing ratios, in this case of N 2 O, and provide the fluxes that best explain the observations while at the same time being guided by a prior estimate of the fluxes. In other words, the fluxes are optimized to fit the observations within the limits of the prior and observation uncertainties. To produce the optimized (a posteriori) fluxes a number of steps are involved: first, the observations are pre-processed; second, a prior flux estimate is prepared; third, mixing ratios are simulated using the prior fluxes and are used to estimate the model representation error; and fourth, the inversion is performed.
In total 140 ground-based sites, ship and aircraft transects are included in the inversion. The term "site" refers to locations where there is a long-term record of observations and includes ground-based measurements, both from discrete samples (or "flasks") and quasi-continuous sampling by in situ instruments, as well as aircraft measurements. A prior estimate of the total N 2 O flux with monthly resolution and inter-annually varying fluxes is prepared from a number of models and inventories. For the soil fluxes (including anthropogenic and natural) an estimate from the land surface model OCN-v1.2 is used, which is driven by observation-based climate data, N fertilizer statistics and modeled N deposition (Zaehle et al., 2011). For the ocean fluxes, an estimate from the ocean biogeochemistry model PlankTOM-v10.2 is used, which is a prognostic model . Atmospheric transport is modeled using an offline version of the Laboratoire de Météorologie Dynamique model, LMDZ5, which computes the evolution of atmospheric compounds using archived fields of winds, convection mass fluxes and planetary boundary layer (PBL) exchange coefficients that have been calculated using the online version nudged to ECMWF ERA-Interim winds.
CAMS-N 2 O uses the Bayesian inversion method to find the optimal fluxes of N 2 O given prior information about the fluxes and their uncertainty, as well as observations of atmospheric N 2 O mole fractions. The method is the same as that used in Thompson et al. (2014) Uncertainty. Uncertainties in CAMS-N 2 O simulations pertain to observation space and to state space. The uncertainty in the observation space is calculated as the quadratic sum of the measurement and transport uncertainties. The measurement uncertainty is assumed to be 0.3 ppb (approximately 0.1 %) based on the recommendations of data providers. The transport uncertainty includes estimates of uncertainties in advective transport (based on the method of Rödenbeck et al., 2003) and from a lack of subgrid-scale variability (based on the method of Bergamaschi et al., 2010). For the error in each land grid cell, the maximum magnitude of the flux in the cell of interest and its eight neighbors is used, while for ocean grid cells the magnitude of the cell of interest only is used. Posterior flux uncertainties are calculated from a Monte Carlo ensemble of inversions, based on the method of Chevallier et al. (2005).

TOMCAT-INVICAT
TOMCAT-INVICAT  is a variational inverse transport model, which is based on the global chemical transport model TOMCAT and its adjoint. It uses a fourdimensional variational (4DVAR) optimization framework based on Bayesian theory which seeks to minimize modelobservation differences by altering surface fluxes while allowing for prior knowledge of these fluxes to be retained. TOMCAT (Monks et al., 2017) is an offline chemical transport model in which meteorological data are taken from ECMWF ERA-Interim reanalyses (Dee et al., 2011). The model grid resolution, and therefore the optimized surface flux estimates, has a horizontal resolution of 5.6 • × 5.6 • . The model has 60 vertical levels running from the surface to 0.1 hPa. For each individual year's fluxes, which are optimized on a monthly basis, 30 minimization iterations are carried out.
Uncertainty. Uncertainties in TOMCAT-INVICAT N 2 O inversions are described as follows and further in Thompson et al., (2019). The uncertainty in the observations is calculated as the quadratic sum of the measurement and transport uncertainties. The measurement uncertainty for each observation is assumed to be 0.4 ppb. The transport error for each observation is assumed to be the mean difference between the observation grid cell and its eight neighbors. Prior flux errors are assumed to be 100 % or the prior estimate and are uncorrelated in space and time. Posterior flux uncertainties are not currently able to be calculated.

MIROC4-ACTM
The MIROC4-ACTM time-dependent inversion for 84 regions (TDI84) framework is based on Bayesian statistics and optimizes surface-atmosphere fluxes using the maximum probability solution (Rodgers 2000). Atmospheric transport is modeled using JAMSTEC's Model for Interdisciplinary Research on Climate, version 4, based on an atmospheric chemistry-transport model (MIROC4-ACTM) (Watanabe et al., 2008;Patra et al., 2018). The sourcereceptor matrix (SRM) is calculated by simulating unitary emissions from 84 basis regions, for which the fluxes are optimized. The SRM describes the relationship between the change in mole fraction at the measurement locations for the unitary basis region fluxes (similar to Rayner et al., 1999). The MIROC4-ACTM meteorology was nudged to the JMA 55-year reanalysis (JRA-55) horizontal wind fields and temperature.
The simulated mole fractions for the total a priori fluxes are subtracted from the observed concentrations before running the inversion calculation (as in Patra et al., 2016, for CH 4

inversion).
Uncertainties. The posterior fluxes are subject to systematic errors primarily from (1) errors in the modeled atmospheric transport; (2) aggregation errors, i.e., errors arising from the way the flux variables are discretized in space (84 regions) and time (monthly means); (3) errors in the background mole fractions (assumed to be a minor factor); and (4) the incomplete information from the sparse observational network and hence the dependence on the prior fluxes. In addition, there is, to a much smaller extent, some error due to calibration offsets between observing instruments, which is more pertinent for N 2 O than for other GHGs. We have validated model transport in the troposphere using SF6 for the inter-hemispheric exchange time and used SF6 and CO 2 for the age of air in the stratosphere. The simulated N 2 O concentrations are also compared with aircraft measurements in the upper troposphere and lower stratosphere for evaluating the stratosphere-troposphere exchange rates. Comparisons with ACE-FTS vertical profiles in the stratosphere and meso-2340 A. M. R. Petrescu et al.: European synthesis of CH 4 and N 2 O emissions for the EU27 andUK: 1990-2017 sphere indicate good parameterization of N 2 O loss by photolysis and chemical reactions and thus the lifetime, which affect the global total N 2 O budgets.
Random uncertainties are calculated by the inverse model depending on the prior flux uncertainties and the observational data density and data uncertainty. Only 37 sites are used in the inversion, and thus the reduction in priori flux uncertainties has been minimal. The net fluxes from the inversion from individual basis regions are less reliable compared to the anomalies in the estimated fluxes over a period of time. Table B1. Comparison of CH 4 results from the BU and TD methods for common periods: BU anthropogenic 1990, BU and TD natural 2005, and TD total 2006 representing the common period between all datasets and the last year available. All values are in kt CH 4 yr − 1, and uncertainties are in kilotons (kt). The UNFCCC NGHGI uncertainties represent the 95 % confidence interval; the uncertainty for EDGAR v5.0 was calculated for 2015, and the min/max values for all sectors are as follows: energy 33/37, IPPU 39/34, agriculture 18/18 and waste 32/38; it represents the 95 % confidence interval of a lognormal distribution. The other uncertainties represent the variability of the model ensembles (TD) and are the min and max of the averaged result over the time period. All values are rounded to the nearest 0.1 kt CH 4 , and therefore columns do not necessarily add up.    B3 Source-specific methodology: AD, EFs and uncertainties   (Lehner et al., 2008) and Hydro1K (USGS, https://www.usgs.gov/centers/ eros/science/usgs-eros-archivedigital-elevation-hydro1k?qt-science_center_objects=0#qt-science_center_objects, last access: June 2019) for river network, HydroLAKES for the lake and reservoir network and surface area (Messager et al., 2016); worldwide typology of estuaries by Dürr et al. (2011 Geological emissions, including marine and land geological Areal distribution activity: 1 • × 1 • maps include the four main categories of natural geo-CH 4 emission: (a) onshore hydrocarbon macro-seeps, including mud volcanoes; (b) submarine (offshore) seeps; (c) diffuse microseepage; and (d) geothermal manifestations.

B1 Overview tables
CH 4 fluxes, measurements and estimates based on size and activity 95 % confidence interval of the median emission-weighted mean sum of individual regional values. (Etiope et al., 2019, andHmiel et al., 2020) CH 4 top-down inversions  For priors please see Table B4 The uncertainty of the model ensemble was calculated as a 1σ estimate. Individual models use Bayes' theorem to calculate the reduction of assumed a priori emission uncertainties by assimilating measurements.
Detailed gridded data can be obtained by contacting the data provider: Peter Bergamaschi (peter.bergamaschi@ec.europa.eu).
Global inversions from the Global Carbon Project CH 4 budget (Saunois et al., 2020) GCP-CH 4 2019 anthropogenic and natural partitions from inversions Ensemble of inversions gathering various chemistry-transport models surface or satellite data.
For priors please see The model is a point model, which provides spatial results by using spatial distributed input data (lateral fluxes are not considered). The model is a Tier 3 approach that is applied on grid map data, polygon organized input data or study sites.  Uncertainty in the observation space is calculated as the quadratic sum of the measurement and transport uncertainties. For the error in each land grid cell, the maximum magnitude of the flux in the cell of interest and its eight neighbors is used; for ocean grid cells the magnitude of the cell of interest only is used.
Detailed gridded N 2 O data can be obtained by contacting the data provider: Rona Thompson (rlt@nilu.no).

TOMCAT-INVICAT
Variational Bayesian inverse model assimilating surface flask observations of atmospheric mixing ratios. ECMWF ERA-Interim meteorological driving data.
Uncertainty in the observation space is calculated as the quadratic sum of the measurement and transport uncertainties. For the error in each land grid cell, the maximum magnitude of the flux in the cell of interest and its eight neighbors is used. Prior emission uncertainties are 100 % and uncorrelated.
Detailed gridded N 2 O data can be obtained by contacting the data provider: Christopher Wilson (GEO) (c.wilson@leeds.ac.uk).

MIROC4-ACTM
Matrix inversion for calculation of fluxes from 53 and 84 partitions of the globe for CH 4 and N 2 O, respectively. Forward model transport is nudged to JRA-55 horizontal winds and temperature.
Fire emissions for CH 4 are taken from GFEDv4s.
A posteriori uncertainties are obtained from the Bayesian statistics model. A priori emissions uncertainties are uncorrelated.
Detailed gridded data can be obtained by contacting the data provider: Prabir Patra (prabir@jamstec.go.jp).
NA: not available.    (2012) VISIT (Ito and Inatomi, 2012) TransCom  Sanderson (1996) Author contributions. AMRP, AJD and PC designed research and led the discussions; AMRP wrote the initial draft of the paper and edited all the following versions; CQ made the figures; PC and CQ edited and commented to the first versions of the manuscript; GPP provided the Appendix B overview Fig. B1a and b and performed a very detailed review of a previous version; PP and MJM processed the original data submitted to the VERIFY portal; MJM, PP and PB designed and are managing the web portal; ES developed the methodology for the EDGAR uncertainty calculation and provided the CH 4 and N 2 O uncertainties; RLT, GJM, FNT, PB, DBa, DBr, LHI, PR, RL, WW and AJD provided in-depth advice and commented on/edited the initial versions of the manuscript; LP and DG provided advice and edited the text related to the UNFCCC and NGHGI information; RLT, PB, DBr, LHI, PR, RL, AT, WW, PKP, MK, GDO, MC, MS, TM, TA, CDGZ, YY, CW, AL, AL, JMH, AJM and JMN are data providers; all co-authors read and made changes to the subsequent versions of the manuscript and provided specific comments related to their data.
Competing interests. The authors declare that they have no conflict of interest.
Acknowledgements. FAOSTAT statistics are produced and disseminated with the support of its member countries to the FAO regular budget. The views expressed in this publication are those of the author(s) and do not necessarily reflect the views or policies of FAO.
We acknowledge the work of the entire EDGAR group (Marilena Muntean, Diego Guizzardi, Edwin Schaaf and Jos Olivier). Review statement. This paper was edited by Nellie Elguindi and reviewed by two anonymous referees.