Top-down estimates of European CH 4 and N 2 O emissions based on four different inverse models

. European CH 4 and N 2 O emissions are estimated for 2006 and 2007 using four inverse modelling systems, based on different global and regional Eulerian and Lagrangian transport models. This ensemble approach is de-signed to provide more realistic estimates of the overall uncertainties in the derived emissions, which is particularly important for verifying bottom-up emission inventories. We use continuous observations from 10 European stations (including 5 tall towers) for CH 4 and 9 continuous stations for N 2 O, complemented by additional European and global discrete air sampling sites. The available observations mainly constrain CH 4 and N 2 O emissions from north-western and eastern Europe. The inversions are strongly driven by the observations and the derived total emissions of larger countries show little dependence on the emission inventories used a priori. Three inverse models yield 26–56 % higher total CH 4 emissions from north-western and eastern Europe compared to bottom-up emissions reported to the UNFCCC, while one model is close to the UNFCCC values. In contrast, the inverse modelling estimates of European N 2 O emissions are in general close to the UNFCCC values, with the overall range from all models being much smaller than the UNFCCC uncertainty range for most countries. Our analysis suggests that the reported uncertainties for CH 4 emissions might be under-estimated, while those for N 2 O emissions are likely overestimated.


Introduction
Atmospheric methane (CH 4 ) and nitrous oxide (N 2 O) are the second and third most important long-lived anthropogenic greenhouse gases (GHGs), after carbon dioxide (CO 2 ). CH 4 and N 2 O have large global warming potentials of 28 and 265, respectively, relative to CO 2 over a 100-year time horizon (Myhre et al., 2013). Globally averaged dry-air mole fractions of CH 4 reached 1819 ± 1 ppb in 2012, 160 % above the pre-industrial level (1750) of ∼ 700 ppb, while N 2 O reached 325.1 ± 0.1 ppb, ∼ 20 % higher than pre-industrial level (270 ppb) (WMO, 2013). CH 4 and N 2 O contributed ∼ 18 % and ∼ 6 %, respectively, to the direct anthropogenic radiative forcing of all long-lived GHGs in 2012, relative to 1750 (NOAA Annual Greenhouse Gas Index (AGGI), http://www.esrl.noaa.gov/gmd/aggi/). CH 4 also has significant additional indirect radiative effects due to its feedback on global OH concentrations, tropospheric ozone, and stratospheric water vapour, and the generation of CO 2 as the final product of the CH 4 oxidation chain (Forster et al., 2007;Shindell et al., 2005). These indirect effects are reflected in the CH 4 emission-based radiative forcing of 0.97 (0.74 to 1.20) Wm −2 , which is about twice the concentrationbased radiative forcing of 0.48 (0.43 to 0.53) Wm −2 (Myhre et al., 2013). In addition to its significant contribution to global warming, N 2 O plays an important role in the depletion of stratospheric ozone, with its current ozone depletion potential-weighted emissions being the largest of all ozonedepleting substances (Ravishankara et al., 2009).
On the European scale, combined emissions of CH 4 and N 2 O contributed 15.4 % to total GHG emissions (in CO 2equivalents) reported under the United Nations Framework Convention on Climate Change (UNFCCC) by the EU-15 countries for 2012 (16.3 % for EU-28) (EEA, 2014). The large reductions of both CH 4 and N 2 O emissions since 1990 (CH 4 by 33 %; N 2 O by 34 %) reported by the EU-15 contributed significantly to the reduction of its total GHG emissions by 15.1 % (2012 compared to 1990).
GHG emissions reported to the UNFCCC are based on statistical activity data and source-specific and country-specific emission factors (IPCC, 2006). For CH 4 and N 2 O however, such "bottom-up" emission inventories have considerable uncertainties, mainly due to the large variability of emission factors, which for many CH 4 and N 2 O sources are not very well characterized (e.g. CH 4 emissions from landfills, gas production facilities and distribution networks, or N 2 O emissions from agricultural soils (e.g. Karion et al., 2013;Leip et al., 2011)).
Complementarily to "bottom-up" approaches, emissions can be estimated using atmospheric measurements and inverse modelling. This "top-down" technique is widely used to estimate GHG emissions on the global and continental scale (e.g. Bergamaschi et al., 2013;Bousquet et al., 2006;Hein et al., 1997;Houweling et al., 1999;Kirschke et al., 2013;Mikaloff Fletcher et al., 2004a, b for CH 4 andHirsch et al., 2006;Huang et al., 2008;Thompson et al., 2014 for N 2 O). With the availability of quasi-continuous GHG measurements and the increasing number of regional monitoring stations, especially in Europe and North America, various inverse modelling studies have estimated emissions also on the regional to country scale (e.g. Bergamaschi et al., 2010;Corazza et al., 2011;Kort et al., 2008;Manning et al., 2011;Miller et al., 2013), demonstrating the potential of using such top-down methods for independent verification of bottomup inventories (Bergamaschi, 2007). The use of atmospheric measurements and inverse modelling for verification has also been recognized by the IPCC (2006).
Currently, only anthropogenic GHG emissions are reported to UNFCCC. In many specific cases, such as the European CH 4 and N 2 O emissions discussed in this study, the contribution of natural emissions is considered to be relatively small. Nevertheless, quantitative comparison between inverse modelling and bottom-up estimates also requires estimates of natural emissions.
A further challenge with inverse modelling, particularly for its use in verifying bottom-up estimates, is the provision of realistic uncertainties for the derived emissions. Although various studies attempt to take account of estimates of the model representation and transport errors, such estimates are typically based on strongly simplified assumptions. As a complementary approach, the range of results from an ensemble of models can be analysed and may be considered a more realistic estimate of the overall uncertainty, provided the applied models are largely independent and represent well the range of current models. Furthermore, detailed model comparisons, and verification with independent validation data, allow the model characteristics to be analysed in detail and potential model deficiencies to be identified. Comparisons of global inverse models have been performed for CO 2 (e.g. Peylin et al., 2013;Stephens et al., 2007), CH 4 (Kirschke et al., 2013) and N 2 O (Thompson et al., 2014), focusing on the global and continental scale. Here, we present for the first time a detailed comparison of inverse models estimating European CH 4 and N 2 O emissions. We use four inverse models, based on different global and regional Eulerian and Lagrangian transport models. The inversions are constrained by a comprehensive data set of quasi-continuous observations from European monitoring stations (including five

Atmospheric measurements
The European monitoring stations used in the CH 4 and N 2 O inversions are summarized in Table 1. The monitoring stations include 10 sites with quasi-continuous measurements for CH 4 (i.e. providing data with hourly or higher time resolution), and 9 sites with quasi-continuous N 2 O measurements. Five of these stations are equipped with tall towers (Cabauw, Bialystok, Ochsenkopf, Hegyhatsal, and Angus), with uppermost sampling heights above the surface by 97-300 m. The measurements at the tall towers were set up or improved within the EU project CHIOTTO ("Continuous High-precision Tall Tower Observations") (Popa et al., 2010;Thompson et al., 2009;Vermeulen et al., 2007Vermeulen et al., , 2011. Additional quasi-continuous measurements are from the AGAGE (Advanced Global Atmospheric Gases Experiment) network (Cunnold et al., 2002;Rigby et al., 2008) at Mace Head, from the operational network of the German Federal Environment Agency (UBA) at Schauinsland, from the Finnish Meteorological Institute at Pallas (Aalto et al., 2007), from the Swiss Federal Laboratories for Materials Science and Technology (EMPA) at Jungfraujoch, and from the Royal Holloway University of London (RHUL) in London. Furthermore, we use CH 4 and N 2 O discrete air samples from the NOAA Earth System Research Laboratory (ESRL) global cooperative air sampling network at 10 European sites (and for the global inverse models, additional global NOAA sites) (Dlugokencky et al., 1994(Dlugokencky et al., , 2003, and CH 4 discrete air samples from the French RAMCES (Réseau Atmosphérique de Mesure des Composés à Effet de Serre) network  at 5 European sites. Finally, discrete air samples from the Max-Planck-Institute for Biogeochemistry at the Shetland Islands, and from the Italian National Agency for New Technologies, Energy and Sustainable Development (ENEA) at Lampedusa were used. Both quasi-continuous and discrete air sample measurements are based on gas chromatography (GC) using flame ionization detectors (FIDs) for CH 4 , and electron capture detectors (ECDs) for N 2 O. Measurements are reported as dry air mole fractions (nmol mol −1 , abbreviated as ppb).
For CH 4 , we generally apply the NOAA04 CH 4 standard scale (Dlugokencky et al., 2005). AGAGE CH 4 data were converted to NOAA04 using a scaling factor of 1.0003 (Prinn et al., 2000), and RAMCES CH 4 data were scaled by 1.0124 from CMDL83 to NOAA04 (Dlugokencky et al., 2005). CH 4 comparisons of high-pressure cylinders performed in the frame of the European projects MethMoniteur, IMECC, Geomon andCHIOTTO, andWMO between 2004 and2010 showed that the CH 4 measurements of the CHIOTTO, NOAA, RAMCES, UBA, and RHUL networks agreed within 2 ppb. Furthermore, comparison of the quasi-continuous measurements at Pallas, Mace Head, Ochsenkopf, and Hegy-hatsal with NOAA discrete air samples (using measurements coinciding within 1 h, and the additional condition that the quasi-continuous measurements show low variability within a 5 h time window) showed annual average absolute CH 4 biases of less than 4 ppb during 2006 and 2007, the target period of this study.
While the merged CH 4 data set used in this study can, therefore, be considered reasonably consistent, this is not the case for N 2 O, for which significant offsets are apparent between different monitoring laboratories, even though most laboratories use N 2 O primary standards from NOAA/ESRL. These offsets exceed the compatibility goal of ±0.1 ppb (1σ ) recommended by WMO GAW (WMO, 2012) (Table 7). We, therefore, adopt the approach developed by Corazza et al. (2011) to correct for these calibration offsets in the inversion (see also Sect. 3), using the NOAA discrete air samples (which are reported on the NOAA-2006 scale; Hall et al., 2007) as a common reference. Corazza et al. (2011) showed that the N 2 O bias correction derived in the inversion agreed within 0.1-0.2 ppb (N 2 O dry-air mole fraction) with the bias derived from the comparison of quasi-continuous measurements with parallel NOAA discrete air samples. We emphasize that this bias correction assumes that the bias remains constant during the inversion period (yearly for TM5) and, therefore, cannot correct for changes of the systematic bias on shorter timescales.
For validation, CH 4 measurements of discrete air samples from three European aircraft profile sites in Scotland, France, and Hungary are used, operated within the European Car-boEurope project. The analyses of these samples were performed at LSCE, in the same manner as the RAMCES surface measurements.

Modelling protocol
The modelling protocol used in this study prescribed mainly the basic settings for the inversions, such as a priori emission inventories, observational data sets, time period, and requested model output. Atmospheric sinks were not prescribed. For both CH 4 and N 2 O, two types of inversions were performed: (1) the base inversions, S1-CH 4 and S1-N 2 O, respectively, using detailed bottom-up emission inventories for anthropogenic and natural sources as a priori emission estimates, and (2) the "free inversions", S2-CH 4 and S2-N 2 O, which do not use these bottom-up inventories. The objective of these "free inversions" is to explore the information content of the observations in the absence of detailed a priori information.
The CH 4 and N 2 O emission inventories applied in S1-CH 4 and S1-N 2 O are summarized in Tables 3 and 4, (2006)(2007). "ST" specifies the sampling type ("CM": quasicontinuous measurements, providing data with hourly time resolution; "FM": discrete air measurements with typically weekly sampling frequency). "CH 4 " and "N 2 O" indicate which stations have been used in the CH 4 and N 2 O inversions, respectively. (as 2005 is the most recent available year in EDGARv4.1). For S2-CH 4 and S2-N 2 O, a homogeneous distribution of emissions over land and over the ocean was used as starting point for the optimization (i.e. a "weak a priori" for TM5-4DVAR and TM3-STILT), with global total CH 4 and N 2 O emissions over land and over the ocean, respectively, close to the total emissions over land and over the ocean of the detailed a priori inventories (Bergamaschi et al., 2010;Corazza et al., 2011), hence effectively limiting the emissions that can be attributed to the ocean. For the NAME-INV model, no separation was made between land and ocean. Moreover, the NAME-INV model started from random emission maps rather than a homogeneous distribution of emissions. Inversions S2 were not available for LMDZ-4DVAR.

ID
For the European limited domain models NAME-INV and STILT, background CH 4 and N 2 O mixing ratios were calcu-   175.0 Wild animals (Houweling et al., 1999) 5.0 Termites (Sanderson, 1996) 19.3 Ocean (Lambert and Schmidt, 1993) 17.0 Soil sink (Ridgwell et al., 1999 (Bouwman et al., 1995) 0.6 Natural Natural soils (Bouwman et al., 1995) 7.2 Ocean (Bouwman et al., 1995)  All models used the same observational data set described in Sect. 2 (with the exception of a few stations that are outside the domain of the limited domain models). For the continuously operated monitoring stations in the boundary layer, measurements between 12:00 and 15:00 LT were assimilated, when measurements (and model simulations) are usually representative of large regions and much less affected by local emissions. In contrast, for mountain sites night-time measurements (between 00:00 and 03:00 LT) were used to avoid the potential influence of upslope transport on the measurements, which is frequently observed at mountain stations during daytime. Different from this sampling scheme (applied in TM5-4DVAR, LMDZ-4DVAR, and TM3-STILT), the NAME-INV model used observations at all times, but with local contributions excluded as in Manning et al. (2011).
For the N 2 O inversions, bias corrections for the N 2 O observations from different networks or institutes were calculated within the 4DVAR optimization of the TM5-4DVAR and LMDZ-4DVAR models, as described by Corazza et al. (2011). For NAME-INV and TM3-STILT, the bias corrections calculated by TM5-4DVAR (Table 7) were applied.

Atmospheric models
The atmospheric models used in this study are summarized in Table 2 and briefly described in the following.

TM5-4DVAR
The TM5-4DVAR inverse modelling system is described in detail by Meirink et al. (2008). It is based on the two-way nested atmospheric zoom model TM5 (Krol et al., 2005). In this study we apply the zooming with 1 • × 1 • resolution over Europe, while the global domain is simulated at a horizontal resolution of 6 • (longitude) × 4 • (latitude). TM5 is an offline transport model, driven by meteorological fields from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis (Dee et al., 2011). The 4-dimensional variational (4DVAR) optimization technique minimizes iteratively a cost function using the adjoint of the tangent linear model and the m1qn3 algorithm for minimization (Gilbert and Lemaréchal, 1989). We apply a "semiexponential" description of the probability density function for the a priori emissions to force the a posteriori emissions to remain positive (Bergamaschi et al., 2009(Bergamaschi et al., , 2010. In inversion S1-CH 4 , four groups of CH 4 emissions are optimized independently: (1) wetlands, (2) rice, (3) biomass burning, and (4) all remaining sources (Bergamaschi et al., 2010). For S1-N 2 O the following four groups of N 2 O emissions are optimized: (1) soil, (2) ocean, (3) biomass burning, and (4) all remaining emissions . In S2-CH 4 and S2-N 2 O, only total emissions are optimized. We assume uncertainties of 100 % per grid-cell and month for each source group and apply spatial correlation scale lengths of 200 km in S1-CH 4 and S1-N 2 O. In the "free inversions" S2-CH 4 and S2-N 2 O, smaller correlation scale lengths of 50 km, and larger uncertainties of 500 % per grid-cell and month are used to give the inversion enough freedom to retrieve regional hot spots (Bergamaschi et al., 2010;Corazza et al., 2011). The temporal correlation timescales are set to zero for the source groups with significant seasonal variations, and 9.5 months for the "remaining" CH 4 and N 2 O sources (which include major anthropogenic sources that are assumed to have no or only small seasonal variations) in S1-CH 4 and S1-N 2 O, and 1 month for the total emissions optimized in S2-CH 4 and S2-N 2 O.
The photochemical sinks of CH 4 (due to OH in the troposphere, and OH, Cl, and O( 1 D) in the stratosphere) are simulated as described in Bergamaschi et al. (2010). The stratospheric sinks of N 2 O (photolysis and reaction with excited oxygen O( 1 D)) are modelled as in Corazza et al. (2011).
The observation errors were set to 3 ppb for CH 4 , and 0.3 ppb for N 2 O. The model representation error is estimated as a function of local emissions and 3-D gradients of simulated mixing ratios (Bergamaschi et al., 2010), resulting in overall (combined measurement and model representation) errors in the range between 3 ppb and up to ∼ 1 ppm for CH 4 , and between 0.3 ppb and up to several ppb for N 2 O. For the N 2 O inversions we optimize bias parameters for the N 2 O observations from different networks or institutes (see Table 7), as described by Corazza et al. (2011).

LMDZ-4DVAR
The LMDZ-4DVAR inverse modelling framework is based on the offline and adjoint models of the Laboratoire de Météorologie Dynamique, version 4 (LMDZ) general circulation model (Hourdin and Armengaud, 1999;Hourdin et al., 2006). The offline model is driven by archived fields of winds, convection mass fluxes, and planetary boundary layer (PBL) exchange coefficients that have been calculated in prior integrations of the complete general circulation model, which was nudged to ECMWF ERA-Interim winds (Dee et al., 2011). In this study, LMDZ is used with a zoom over Europe at a resolution of approximately 1.2 • × 0.8 • and decreasing resolution away from Europe to a maximum grid size of approximately 7.2 • ×3.6 • . LMDZ has 19 hybrid pressure levels in the vertical dimension. The optimal fluxes were found by solving the cost function using the adjoint model and the Lanczos algorithm for N 2 O and the m1qn3 algorithm for CH 4 .
Details about the inversion framework for CH 4 are given in Pison et al. (2009Pison et al. ( , 2013. Only the total net emissions of methane are optimized, at the resolution of the grid-cell for 8-day periods. Prior uncertainties in each grid-cell are set to 100 % of the maximum flux over the grid-cell and its P. Bergamaschi et al.: Top-down estimates of European CH 4 and N 2 O emissions 721 eight neighbours (so as to allow for a misplacement of the sources). Correlation scale lengths are used to compute the off-diagonal terms in the error covariance matrix: they are set at 500 km on land and 1000 km on sea (land and sea are not correlated); there are no time correlations. The "observation" errors include the estimates of the errors due to the transport model and to the representativity of the grid-cell compared to the measurement (combined measurement and model error ranging between 3 ppb and up to 450 ppb). Note that the OH fields are inverted simultaneously to the methane emissions, with constraints from methyl-chloroform (Pison et al., 2009;2013).
Details about the inversion framework for N 2 O can be found in Thompson et al. (2011). For N 2 O, only total emissions were optimized. Prior uncertainties in each grid-cell were set to 100 % and correlation scale lengths of 500 km over land, 1000 km over ocean, and 3 months were used to form the full error covariance matrix, which was subsequently scaled to be consistent with a global total uncertainty of 3 TgN yr −1 (approximately 18 %). The error of the N 2 O observations was set to 0.3 ppb. Model representation errors incorporated an estimate of aggregation error, i.e. distribution of emissions within the grid-cell (Bergamaschi et al., 2010), and horizontal advection errors (Rödenbeck et al., 2003), resulting in total model errors ranging from about 0.2 ppb to 1 ppb. In addition to the emissions, bias parameters for the N 2 O observations from different networks or institutes were optimized, similarly to TM5-4DVAR .

TM3-STILT
In the Jena inversions, the coupled system TM3-STILT is used for regional-scale high-resolution inversions. TM3-STILT (Trusilova et al., 2010) is a combination of the coarse-grid global 3-dimensional atmospheric offline transport model TM3 (Heimann and Koerner, 2003) and the finescale regional Stochastic Time-Inverted Lagrangian Transport model STILT Lin et al., 2003). The models are coupled using the two-step nesting scheme of Rödenbeck et al. (2009), which allows the use of completely independent models for the representation of the global and the regional transport. The variational inversion algorithm of the Jena inversion scheme, applied in the global as well as in the regional inversion step, is described in detail in Rödenbeck (2005). In this study, the global transport model TM3 is used with a spatial resolution of 4 • × 5 • and 19 vertical levels. STILT is driven by meteorological fields from ECMWF operational analysis, used here with a spatial resolution of 0.25 • × 0.25 • and confined to the lowest 61 vertical layers. The regional TM3-STILT inversions are conducted in this study on a 1 • × 1 • horizontal resolution grid covering the greater part of Europe (12 • W-35 • E, 35-62 • N). Regional inversion results for CH 4 were obtained directly by the TM3-STILT system. For the regional N 2 O inversions the same modular nesting technique is applied to couple STILT with a baseline provided by TM5-4DVAR (Bergamaschi et al., 2010;Corazza et al., 2011) and the regional inversion step is performed in the Jena inversion system. The latter combination is referred to as TM5-STILT in the presentation of the N 2 O inversion results. In all regional inversions we optimize the total emissions. Uncertainties of 100 % per grid-cell and month, with a spatial correlation scale length of 600 km and a temporal correlation timescale of 1 month, are assumed in the regional S1-CH 4 and S1-N 2 O inversions. In both S2 inversions the uncertainties are set to 500 % with a correlation scale length of 60 km and correlation timescale of 1 month. The observation errors were set to 3 ppb for CH 4 and 0.2 ppb for N 2 O. Model representation errors are assigned to the individual sites according to their location with respect to continental, remote or oceanic situations (Rödenbeck, 2005), resulting in overall (combined measurement and model representation) errors in the range of 10-30 ppb for CH 4 , and 0.8 and 2.4 ppb for N 2 O. For N 2 O the bias parameters estimated by TM5-4DVAR (see Table 7) are applied in the regional inversions.

NAME-INV
The NAME-INV inverse modelling system is described in Manning et al. (2011) using one station to estimate UK and Northern European emissions of various trace gases and in Athanassiadou et al. (2011) for multiple stations across Europe. The transport of CH 4 and N 2 O from sources to observations is performed using the UK Met Office Lagrangian model NAME (Jones et al., 2007). Thousands of particles are released from each measurement for each 2 h period in 2006 and 2007, and these are tracked backwards in time over a period of 13 days (long enough for the majority of particles to leave the domain of interest). The 13-day timeintegrated concentrations only include contributions from 0 to 100 m a.g.l., representative of surface emissions. The meteorological fields needed to run NAME are from the global version of the Met Office Unified Model (UM) at a resolution of 0.56 • × 0.37 • and 31 vertical levels from surface to about 19 km (see Table 2). The domain used for the inversion extends from 14.63 • W to 39.13 • E and from 33.81 • N to 72.69 • N, with a resolution of 0.42 • × 0.27 • in the longitudinal and latitudinal directions respectively. The inversion is initialized either from the modelling protocol a priori or from a random emissions field as in Manning et al. (2011). In the latter case, the cost function used in the optimization is the same as in Manning et al. (2011). In S1, when the inversion is initialized and guided by the a priori emission inventory, a modified version is used (original cost function + root mean square error (RMSE) between modelled values and a priori). To account for the imbalance in the contribution from different grid boxes (i.e. the grids more distant from the observations are expected to contribute less than those that are closer), grid boxes are progressively grouped together In all inversions, the total annual emissions are optimized without any partitioning to various sectors. The background values used for CH 4 and N 2 O are from TM5-4DVAR following the two-step scheme of Rödenbeck et al. (2009). Observations at all times have been used (i.e. not only in the time windows specified in Sect. 3.1), but excluding local contributions . An estimate of the uncertainty in the emissions is obtained from the 5th and 95th percentiles of 52 independent inversion solutions (the mean of these being the final solution). The independent inversion solutions are considered to simulate uncertainties in the meteorology, dispersion and observations. For each inversion a different time series of random noise is applied to the observations. The random element at each observation is multiplicative and taken from a lognormal distribution with mean 1 and variance, arbitrarily, set to one fifth of the standard deviation of baseline observations about a smoothed baseline value as in Manning et al. (2011). For this project the baseline standard deviation values 9.5 ppb (CH 4 ) and 0.194 ppb (N 2 O) were used. Figures 1 and 2 show maps of derived CH 4 emissions (average 2006-2007) for inversions S1-CH 4 and S2-CH 4 , respectively. Guided by the a priori emission inventory in inversion S1-CH 4 , TM5-4DVAR, TM3-STILT and LMDZ-4DVAR largely preserve the "fine structure" of the a priori spatial patterns, but calculate some moderate emission increments on larger regional scales (determined by the chosen spatial correlation scale lengths, ranging between 200 and 600 km). Larger emission increments are apparent for inversion S1-CH 4 of NAME-INV, with generally lower CH 4 emissions across Europe, compared to the a priori and the a posteriori emissions of the other three models.

Inverse modelling of European CH 4 emissions
Inversion S2-CH 4 , which is not constrained by a detailed a priori emission inventory, shows in general a smoother spatial distribution than S1-CH 4 . While the NAME-INV model does not use any a priori information in S2-CH 4 , TM5-4DVAR and TM3-STILT assume that CH 4 emissions are mainly over land. Consequently, NAME-INV attributes much larger emissions over the sea than TM5-4DVAR and TM3-STILT, especially over the North Sea and the Bay of Biscay. All three models show consistently high CH 4 emissions over the Benelux countries and north-western Germany (especially over the highly populated and industrialized Ruhr area). Apart from these hotspot emission areas, TM5-4DVAR and TM3-STILT overall show relatively similar distributions over land, while the NAME-INV inversion differs significantly, for example, over Spain and south-eastern France / north-western Italy, where NAME-INV attributes much lower emissions compared to TM5-4DVAR and TM3-STILT.
It is interesting to compare the inversions S2-CH 4 and the a priori used for S1-CH 4 , representing completely independent emission estimates, top-down and bottom-up respectively. Both approaches show coherently elevated CH 4 emissions over Benelux/north-western Germany, and southern UK. The S2-CH 4 inversions also show somewhat elevated emissions per area in southern Poland, where large coal mines are located. However, the inversions are not able to reproduce the very pronounced CH 4 emission hotspot of the bottom-up inventory in this area. This is probably largely due to the limitations of the inversion's ability to resolve point sources accurately (also given the limitation of the sparse atmospheric measurement network) but could also point to a bottom-up overestimate of the CH 4 emissions from the coal mining in this area. In fact, the EDGARv4.2 estimate of CH 4 emissions from coal mines in Poland (1.71 Tg CH 4 yr −1 ) is about 4 times higher than that reported under UNFCCC (0.43 Tg CH 4 yr −1 ; see Table 6). However, it should be pointed out that the bottom-up emissions have large uncertainties, estimated to be 49 % for UNFCCC, and 83 % for EDGARv4.2 for the coal mines in Poland.
In the following discussion, we analyse the CH 4 emissions per country for the countries whose emissions are reasonably well constrained by the available observations. These are mainly north-western and eastern European countries (Fig. 3), while southern European countries are poorly constrained. For smaller countries, we present aggregated emissions (e.g. Benelux), as they are considered more robust than emissions of individual small countries. The normalized range of derived CH 4 emissions (defined as (E max − E min )/(E max + E min )) is between ±16 and ±44 % for the analysed countries (or combined countries), and ±25 % for the total CH 4 emissions of all north-western and eastern European countries shown in Fig. 3 (inversion S1-CH 4 ). For some countries, the range of emission estimates from all four models is close to the uncertainties estimated for the individual inversions (e.g. Poland), but there are also several countries with much larger emission ranges (e.g. France). This shows that there are systematic differences between the inversions, which are not covered by the uncertainty estimates of the individual inversions.
The country totals of the "free" inversion S2-CH 4 are in general very close to those of S1-CH 4 for most countries, demonstrating the strong observational constraints. Apparently, the above-mentioned differences in the smaller-scale "fine structure" in the spatial patterns between S1-CH 4 and S2-CH 4 (see Figs. 1 and 2) are largely compensated by aggregating emissions on the country scale. The fact that in several cases the emission ranges of the S2-CH 4 inversions are smaller than for S1-CH 4 is probably mainly due to fewer models being available (three instead of four).  For most countries, the NAME-INV model yields lower emissions compared to the other three models. This is most clearly visible in the total emission of all north-western and eastern European countries, which NAME-INV estimates to be 10.7-11.7 Tg CH 4 yr −1 (annual totals for 2006 and 2007, for S1-CH 4 and S2-CH 4 ), compared to estimates of 16.0-19.4 Tg CH 4 yr −1 from TM5-4DVAR, LMDZ-4DVAR and TM3-STILT.
The reasons for the generally lower emissions derived by NAME-INV remain unclear. One factor that may contribute Table 6. CH 4 emissions from EDGARv4.1, EDGARv4.2, and UNFCCC for major CH 4 source categories. For the UNFCCC emissions, the reported relative uncertainties (2σ ) per country and category and corresponding emission ranges are also compiled. Total uncertainties per country (or aggregated countries) are estimated from the reported uncertainties per category assuming no correlation between different UNFCCC categories (but correlated errors for sub-categories). "NWE" is the total of the north-western European countries Germany, France, UK, Ireland and Benelux. "NEE" is the total of the eastern European countries Hungary, Poland, Czech Republic (CZE) and Slovakia (SVK). is the use of different meteorology in NAME-INV (i.e. meteorology from the Met Office UM) and the other three models (using ECMWF meteorology, albeit different production streams). In sensitivity experiments Manning et al. (2011) found differences of ∼ 10-20 % (with different signs for different years) in derived emissions from the UK and northwestern Europe, when using ECMWF ERA-Interim instead of Met Office UM meteorology. Hence, differences in the applied meteorological data sets can have a significant impact, but probably explain only part of the differences between NAME-INV and the other models.

P. Bergamaschi et al.: Top-down estimates of European CH 4 and N 2 O emissions
In the case of S2-CH 4 , the difference in the CH 4 emissions attributed to European countries could be partly due to the higher emissions allocated by NAME-INV to the sea (Figs. 2 and 4). In the absence of any a priori constraint, NAME-INV allocates 4.5-4.9 Tg CH 4 yr −1 over the Euro-pean seas (of which ∼ 1 Tg CH 4 yr −1 over the North Sea), while sea emissions are largely suppressed in TM5-4DVAR and TM3-STILT in S2-CH 4 (< 0.2 Tg CH 4 yr −1 over the European seas). In the case of S1-CH 4 , the range of CH 4 emissions attributed to the sea by the different models is generally much smaller, 0.6-2.2 Tg CH 4 yr −1 , due to a priori constraints.
In this study we use the same country mask (from EDGAR) for all models to enable a consistent comparison among all models. This country mask accounts only for emissions over land (in the case of coastal grid-cells, the total emissions of this grid-cell are attributed to the land). In contrast, previous NAME-INV inversion studies used different country masks, taking into account also offshore emissions at some further distance from the coastlines . . Phys., 15, 715-736  It is important to note that the inverse modelling estimates the total of the anthropogenic and natural emissions. According to the bottom-up inventories applied in our study, however, it is estimated that natural CH 4 emissions play only a minor role for the countries considered here (shown by the dashed/dotted lines in Figs. 3 and 4). This is important when comparing the CH 4 emissions derived by the inverse models with anthropogenic CH 4 emissions reported to the UNFCCC (shown by black lines in Fig. 3). The range of CH 4 emissions estimated by the inverse models overlaps for most countries with the uncertainty range of the UNFCCC emissions. Nevertheless, there is a clear tendency to higher CH 4 emissions derived by three of the inverse models (TM5-4DVAR, LMDZ-4DVAR, TM3-STILT) compared to UNFCCC, while NAME-INV is in most cases close to UNFCCC. For comparing different approaches, realistic uncertainty estimates are For each year, the left yellow box shows the results for inversion S1-CH 4 , and the right yellow box for S2-CH 4 . The grey-shaded area is the range of UNFCCC CH 4 emissions (based on reported uncertainties, as compiled in Table 6). Figure 3. European CH 4 emissions by country and aggregated region. For each year, the left yellow box shows the results for inversio CH 4 , and the yellow right box for S2-CH 4 . The grey-shaded area is the range of UNFCCC CH 4 emissions (based on reported uncerta as compiled in Table 6).   Comparison of modeled and observed CH4 at stations: correlation coefficients (top) and root mean square (RMS) differences (bottom) for inversion S1-CH4. "All" denotes the mean correlation coefficient and RMS difference, averaged over those stations, for which results were available from all models.

Figure 5.
Comparison of modelled and observed CH 4 at stations: correlation coefficients (top) and rms differences (bottom) for inversion S1-CH 4 . "All" denotes the mean correlation coefficient and rms difference, averaged over those stations, for which results were available from all models. essential to evaluate their consistency. Under the UNFCCC, European countries report uncertainty estimates for individual source categories, taking account of uncertainty estimates for activity data and for emission factors (both for CH 4 and for N 2 O usually the latter is the dominant term). Since uncertainties of total emissions are usually not reported, we estimate these assuming that the uncertainties of different IPCC/UNFCCC source categories are uncorrelated (but fully correlated for sub-categories). Furthermore, we assume correlated errors when aggregating individual source categories from different countries (as different countries usually apply similar approaches). Table 6 shows the UNFCCC uncertainty estimates for the six major CH 4 source categories and our derived estimates of the total uncertainty per country (and aggregated countries). Overall the estimated total uncertainties are surprisingly low: between 17 and 26 % for the countries considered and about 20 % for the total CH 4 emissions of all north-western and eastern European countries.  (Table 6). However, there are considerable differences, in particular for solid fuels (i.e. coal mining) and oil and natural gas, for which EDGARv4.2 estimates 1.4 and 1.9 Tg CH 4 yr −1 higher emissions, respectively, for the NWE + NEE total than UNFCCC. For single countries, the largest differences are for solid fuels from Poland (EDGARv4.2: 1.71 (0.29-3.21) Tg CH 4 yr −1 ; UN-FCCC: 0.43 (0.22-0.64) Tg CH 4 yr −1 ) and oil and natural gas from France (EDGARv4.2: 1.49 Tg CH 4 yr −1 ; UNFCCC: 0.05 (0.04-0.06) Tg CH 4 yr −1 ). Since uncertainty estimates are not standardly available for each sector and country in EDGARv4.2, a strict comparison cannot be made. However, the large differences between the two bottom-up estimates highlight the large uncertainties for fugitive emissions related to production (and transmission/distribution) of fossil fuels.
For TM5-4DVAR, LMDZ-4DVAR and TM3-STILT, the derived emissions are in general closer to the total emissions from EDGARv4.2 than those from UNFCCC, while NAME-INV, as already mentioned, is relatively close to UNFCCC.
Our inverse modelling estimates of the total emissions per country do not account for offshore emissions. According to EDGARv4.2, about 0.8 Tg CH 4 yr −1 is emitted offshore over the European seas (mainly from oil and gas production), while natural CH 4 emissions of about 0.4 Tg CH 4 yr −1 over the European seas are estimated from our bottom-up inventories (total between 35 • and 62 • N and between 12 • W and 35 • E; see Fig. 4). For comparison, Bange (2006) estimates natural CH 4 emissions from European coastal areas to be in the range 0.5 to 1.0 Tg CH 4 yr −1 (including the Arctic Ocean, Baltic Sea, North Sea, northeastern Atlantic Ocean, Mediterranean Sea and Black Sea).  The statistics of the assimilated observations are summarized in Fig. 5. Overall, all the models show relatively similar performance, with an average correlation coefficient between 0.7 and 0.8 and an average root mean square (rms) difference between observed and assimilated CH 4 mixing ratios between ∼ 25 and ∼ 35 ppb.
All models have been validated against regular aircraft profiles performed within the CarboEurope project at three European monitoring sites (Fig. 6). These aircraft data have not been used in the inversion. However, for two aircraft sites (Griffin, Scotland and Hegyhatsal, Hungary) the corresponding surface observations have been assimilated (tall towers Angus (TT1) and Hegyhatsal (HU1)), while the surface observations at Orléans (France) were not used (since they started only in 2007), but the observations from Gifsur-Yvette, about 100 km north of Orléans, were included. Hence, while surface mixing ratios are well constrained at these three aircraft sites, the comparison of observed and modelled vertical gradients allows the model-simulated vertical transport to be validated, which is of critical importance to the inversions. Figure 6 shows that all models reproduce the average observed vertical gradient in the lower troposphere relatively well, indicating overall realistic vertical mixing. In general, the four models show a relatively consistent picture for S1-N 2 O, with moderate N 2 O emission increments on larger regional scales, while largely preserving the spatial "fine structure" of the a priori emission inventory. As for S1-CH 4 , however, NAME-INV, yields lower N 2 O emissions than TM5-4DVAR, LMDZ-4DVAR and TM3-STILT.

Inverse modelling of European N 2 O emission
In Fig. 8, the three available free N 2 O inversions for S2-N 2 O consistently show elevated N 2 O emissions over Benelux, but none derive the chemical industry hotspots. For S2-N 2 O, the N 2 O emissions attributed to the sea by NAME-INV are significantly larger (0.26-0.31 Tg N 2 O yr −1 ; Fig. 10) than in S1-N 2 O (0.06-0.07 Tg N 2 O yr −1 ), while they remain relatively low in TM5-4DVAR and TM3-STILT (due to the a priori assumption of low emissions over the sea compared to land in these two inversions, which suppresses the attribution of emissions to the sea). Independent studies about N 2 O emissions from European seas provide very different estimates. Bange (2006) estimated a net source of N 2 O to the atmosphere of 0.33-0.67 Tg N yr −1 (equivalent to 0.52-1.05 Tg N 2 O yr −1 ), using measured N 2 O saturations of surface waters and air-sea gas exchange rates based on Liss and Merlivat (1986) and Wanninkhof (1992). Bange (2006) attributes the major contribution to estuarine/river systems and not to open shelf areas. In contrast, Barnes and Upstill-Goddard (2011) estimate only 0.007 ± 0.013 Tg N 2 O yr −1 for European estuarine N 2 O emissions, claiming that mean N 2 O saturation and mean wind speed for European estuaries might be overestimated in the study of Bange (2006). Figure 9 shows the total N 2 O emissions per country derived by the different inversions, and their comparison with UNFCCC bottom-up inventories. Similar to CH 4 , the contribution of natural N 2 O emissions (derived from the bottomup inventories of natural N 2 O sources compiled in Table 4 Table 8), we take account of the non-symmetric nature of errors above 100 %, assuming zero emissions for the specific category as the lowermost boundary for any relative error larger than 100 %. Figure 9 shows that the range of the inverse modelling estimates is much smaller than the UNFCCC uncertainty range for most countries (including the total emissions from north-western and eastern Europe). This finding is consistent with the analysis of error statistics of bottom-up inventories by Leip (2010), suggesting that the current UNFCCC uncertainty estimates of N 2 O bottom-up emission inventories are likely too high.
It is important to note, however, that significant biases in N 2 O measurements exist between different laboratories that require corrections (Table 7). The bias corrections calculated by TM5-4DVAR and LMDZ-4DVAR are within ∼ 0.3 ppb compared to the bias determined for those stations for which parallel NOAA discrete air measurements are available (for stations with at least 10 coinciding hourly measurements per year). This is somewhat worse than the agreement of 0.1-0.2 ppb reported by Corazza et al. (2011) and may indicate some limitations of the applied bias correction scheme, which does not account for potential changes of the bias within the inversion period (TM5-4DVAR: 1 year, LMDZ-4DVAR: 2 years). Figure 11 shows the correlation coefficients and rms differences between (bias-corrected) observed and simulated N 2 O mixing ratios at the monitoring stations used in inversion S1-N 2 O. The mean correlation coefficients for the four models are in the range between 0.6 and 0.7 (averaged over all stations), which is somewhat lower than for CH 4 (average correlation coefficients between 0.7 and 0.8; Fig. 5). This is probably mainly due to the lower atmospheric N 2 O variability compared to CH 4 , but may be partly also due to the mentioned limitations of the quality of the N 2 O data. Figure 11. Comparison of modeled and observed N2O at stations: correlation coefficients (top) and root mean square (RMS) differences (bottom) for inversion S1-N2O (after bias correction of observations). "All" denotes the mean correlation coefficient and RMS difference, averaged over those stations, for which results were available from all models. Figure 11. Comparison of modelled and observed N 2 O at stations: correlation coefficients (top) and rms differences (bottom) for inversion S1-N 2 O (after bias correction of observations). "All" denotes the mean correlation coefficient and rms difference, averaged over the stations for which results were available from all models.

Conclusions
We estimated European CH 4 and N 2 O emissions for 2006 and 2007 using four different inverse modelling systems that were constrained by quasi-continuous observations from various European monitoring stations (including five tall towers), complemented by further European and global discrete air sampling sites. Although the range of CH 4 emissions estimated by the inverse models overlaps for most countries with the uncertainty range of the UNFCCC emissions, three of four models show a clear tendency to higher emissions compared to the anthropogenic emissions reported under UN-FCCC for the total of north-western and eastern European countries (range of TM5-4DVAR, LMDZ-4DVAR and TM3-STILT after correction for natural sources 26-56 % higher than UNFCCC), while NAME-INV yields estimates of country totals very close to UNFCCC. This analysis suggests that (1) CH 4 emissions reported to UNFCCC could be underestimated for some of the European countries analysed in this study, or (2) natural CH 4 emissions are underestimated, or (3) atmospheric models may have significant biases. Although the flux inversions do not allow direct conclusions about specific source categories, the comparison between UNFCCC and EDGARv4.2 shows the critical importance of fugitive emissions from fossil fuels (coal mining, oil production, and production, transmission and distribution of natural gas), for which large differences are apparent between UNFCCC and EDGARv4.2 inventories, outside the estimated UNFCCC uncertainties for some countries. In addition, it is important that natural CH 4 emissions are better quantified in the future, especially CH 4 from wetlands and wet soils. Isotope analysis (δ 13 C and δD) could provide some additional information on the relative contribution of different sources; however, the constraints on the European scale might be limited by overlapping isotopic signatures of the sources.
Furthermore, the transport models need better validation. Although the presented validation against independent aircraft CH 4 observations suggests that vertical mixing is realistically modelled overall, we emphasize the need to extend this validation to more sites and to include further diagnostics such as 222 Rn and boundary layer height dynamics. These are currently being investigated in more detail in the framework of the InGOS ("Integrated Non-CO 2 Greenhouse Gas Observing System"; http://www.ingos-infrastructure. eu/) project. In addition, it would be useful to include more models in future comparisons to allow more robust estimates of the "inter-model" uncertainties.
The N 2 O emissions derived by the inverse models are in general very close to the UNFCCC values, with the range of the inverse modelling estimates being much smaller than the UNFCCC uncertainty range for most countries. This finding suggests that atmospheric observations and inverse modelling can probably constrain N 2 O emissions better than bottom-up approaches, and/or that UNFCCC uncertainties (which are dominated by the uncertainties for N 2 O emissions from agricultural soils) might be overestimated. However, we emphasize the limitations of the atmospheric N 2 O data set used (with biases between different laboratories exceeding the WMO compatibility goal of ±0.1 ppb), which required significant bias corrections. A major effort is currently being undertaken within the InGOS project to improve and harmonize the European N 2 O measurements, which should improve N 2 O inversions in the future. A fundamental chal-lenge for the atmospheric measurements of N 2 O, however, remains the generally much lower signal in N 2 O compared to CH 4 , owing to lower N 2 O emissions and the long atmospheric lifetime of N 2 O (∼ 130 years compared to ∼ 9 years for CH 4 , Prather et al., 2012).
This study demonstrates the general feasibility of independent top-down verification of bottom-up inventories. This is particularly important for CH 4 and N 2 O because of the large uncertainties (and variability) of emission factors for major CH 4 and N 2 O source categories. Future, post-Kyoto international agreements on reductions of GHG emissions would strongly benefit from comprehensive and independent verification to monitor the effectiveness of the emission reduction measures and to ensure the reliability of the reported emissions. However, the application of inverse modelling in this context requires high-quality long-term monitoring of GHGs in the atmosphere with increased density of the monitoring stations, improved atmospheric transport models, and a realistic quantification of uncertainties, in both bottom-up and top-down emission estimates.