Validation of the Swiss methane emission inventory by atmospheric observations and inverse modelling

. Atmospheric inverse modelling has the potential to provide observation-based estimates of greenhouse gas emissions at the country scale, thereby allowing for an independent validation of national emission inventories. Here, we present a regional-scale inverse modelling study to quantify the emissions of methane (CH 4 ) from Switzerland, making use of the newly established CarboCount-CH measurement network and a high-resolution Lagrangian transport model. In our reference inversion, prior emissions were taken from the “bottom-up” Swiss Greenhouse Gas Inventory (SGHGI) as published by the Swiss Federal Ofﬁce for the Environment in 2014 for the year 2012. Overall we estimate national CH 4 emissions to be 196 ± 18 Ggyr − 1


Introduction
Atmospheric methane (CH 4 ) acts as an important greenhouse gas (GHG) whose man-made increase from pre-industrial to present-day levels (from ≈ 700 nmol mol −1 in 1750 to 1819 nmol mol −1 in 2012) directly and indirectly contributes 0.97 (0.74-1.20) W m −2 to present-day global radiative forcing (Myhre et al., 2013). As such, its contribution to humaninduced global warming is second only to carbon dioxide (CO 2 ). Globally, natural sources (wetlands, lakes, geological seeps, termites, methane hydrates, and wild animals) and anthropogenic sources (fossil fuel extraction, distribution and combustion, rice cultivation, ruminants, and waste) each contribute about half to CH 4 emissions to the atmosphere (Kirschke et al., 2013), but larger uncertainties are connected with the natural sources. Owing to increased research efforts in recent years, uncertainties associated with these fluxes have decreased on the global and continental scale (Kirschke et al., 2013, and references therein). However, there remain open questions about the contributing processes and their temporal and spatial distributions on the regional scale (Nisbet et al., 2014).
In many developed countries, natural CH 4 sources are of limited importance (Bergamaschi et al., 2010) and anthropogenic emissions dominate. For example, ≈ 98 % of Swiss CH 4 emissions are thought to be of anthropogenic origin (Hiller et al., 2014a). Owing to its comparatively short atmospheric lifetime (≈ 10 years), CH 4 has been classified as a short-lived climate pollutant, and reducing anthropogenic CH 4 emissions has become a promising target to lower nearterm radiative forcing (Ramanathan and Xu, 2010;Shindell et al., 2012). However, the development of efficient mitigation strategies requires detailed knowledge of the source processes and the success of the mitigation measures should be monitored once put into action. The Kyoto Protocol sets legally binding GHG emission reduction targets for Annex I countries and the United Nations Framework Convention on Climate Change (UNFCCC) calls signatory countries to report their annual GHG emissions of CO 2 , CH 4 , nitrous oxide, sulfur hexafluoride, and halocarbons.
In Switzerland, the Federal Office for the Environment (FOEN) collects activity data and emission factors in the Swiss Greenhouse Gas Inventory (SGHGI) (FOEN, 2014(FOEN, , 2015 and annually reports emissions following IPCC guidelines (IPCC, 2006). According to this inventory, emissions from agriculture are the single most important source (161.5 Gg yr −1 ) in Switzerland, followed by waste handling (32.3 Gg yr −1 ) and fossil fuel distribution and combustion (12.1 Gg yr −1 ; all values refer to the 2015 reporting for the year 2012). Estimates following IPCC guidelines are derived bottom-up from source-specific information combined with activity data and other statistical data, all of which may contain considerable uncertainties. Anthropogenic CH 4 emissions in Switzerland originate from processes that may vary strongly on an individual basis (e.g. ruminants, ma-nure handling, waste treatment). Hence, at the country level they are much more difficult to quantify than anthropogenic emissions of CO 2 , which can be largely deduced from fuel statistics. As a consequence, the uncertainty assigned to total Swiss CH 4 emissions (±16 %) is much larger than that of CO 2 emissions (±3 %) (FOEN, 2015). According to the SGHGI, Swiss CH 4 emissions have decreased by about 20 % since 1990 (FOEN, 2015), but given the above uncertainties, these estimates require further validation, also in order to survey the effectiveness of the realised reduction measures. Furthermore, considerable differences exist between the SGHGI and other global-and European-scale inventories (e.g. EDGAR) both in terms of total amount and spatial distribution (Hiller et al., 2014a). Previous validation efforts of the Swiss CH 4 inventory were restricted to flux measurements either on the site scale focusing on a specific emission process (Eugster et al., 2011;Tuzson et al., 2010;Schroth et al., 2012;Schubert et al., 2012) or campaign-based flight missions (Hiller et al., 2014b) and tethered balloon soundings (Stieger et al., 2015), mainly confirming estimates of the SGHGI on the local scale. In addition, mobile nearsurface measurements were used to verify emission hotspots in a qualitative way (Bamberger et al., 2014). However, due to the limited number of studies and the focus on rather small areas, it is very difficult to employ these results for the validation of national total emission estimates.
Such an independent validation of spatially resolved national inventory data can be achieved through inverse modelling yielding a top-down estimate that uses atmospheric observations of the target species together with transport modelling in order to optimally estimate the underlying emissions (Enting, 2002;Bergamaschi et al., 2005). Early inverse modelling studies of CH 4 focused on the global-scale budget and relied on global flask sampling observations (e.g. Hein et al., 1997;Houweling et al., 1999;Bergamaschi et al., 2000;Dentener et al., 2003;Mikaloff Fletcher et al., 2004). Later studies also included continuous surface and airborne observations (e.g. Vermeulen et al., 1999;Bergamaschi et al., 2005Bergamaschi et al., , 2010Chen and Prinn, 2006;Kort et al., 2010;Manning et al., 2011;Miller et al., 2013) and provide countryspecific emissions. For data-sparse regions, the additional use of satellite-retrieved CH 4 data in atmospheric inversions has recently helped reducing uncertainties (Meirink et al., 2008;Bergamaschi et al., 2013) and increased the ability to deduce emissions with higher spatial resolution (Wecht et al., 2014;Turner et al., 2015). However, such top-down estimates were usually not made for small countries and regions like Switzerland (≈ 10 000 km 2 ), owing to the coarse spatial resolution of the inversion systems. Recent studies from the USA have shown large differences between national and regional bottom-up estimates and inverse modelling, predominantly detecting large emission underestimations in the bottom-up inventories (Wecht et al., 2014;Turner et al., 2015;Miller et al., 2013;McKain et al., 2015;Wennberg et al., 2012). These were mainly attributed to three major source pro-cesses: oil and gas extraction, ruminants, and natural gas distribution to the end user.
Here, we validate the bottom-up estimate of Swiss CH 4 emissions as given in the SGHGI by analysing continuous, near-surface observations of CH 4 from the newly established, dense CarboCount-CH measurement network in central Switzerland  and two neighbouring sites. For the first time, we apply an inverse modelling framework with high spatial resolution (< 10 km) to a relatively small area with considerable land surface heterogeneity and topographical complexity. Such modelling approaches have only recently become feasible through the use of high-resolution atmospheric transport simulations (e.g. for CH 4 ; Zhao et al., 2009;Jeong et al., 2012Jeong et al., , 2013McKain et al., 2015). The main aim of the study is to provide an independent validation of the SGHGI in terms of national total emissions (FOEN, 2015), geographical (Hiller et al., 2014a) and temporal distribution. Results in the spatio-temporal distribution shall be used to draw conclusions on the estimates of individual source processes.

Observations
The CH 4 observations used in this study are those of the CarboCount-CH 1 network (BEO, LHW, FRU, GIM) located on the Swiss Plateau and those from two additional mountain sites: Jungfraujoch and Schauinsland (see Figs. 1, S1 in the Supplement and Table 1). The Swiss Plateau, the relatively flat area between the Alps in the south and Jura Mountains in the north, covers only about one-third of the area of Switzerland but is home to two-thirds of the Swiss population and is characterised by intensive agriculture and extended urban and suburban areas. Approximately two-thirds of the Swiss CH 4 emissions are thought to stem from this area (Hiller et al., 2014a). Oney et al. (2015) characterised the transport to the CarboCount-CH sites applying the same transport model as used here. They find that all four sites are mainly sensitive to emissions from most of the Swiss Plateau during summer daytime conditions, whereas sensitivities are more localised around the sites in winter but still provide reasonable coverage of the targeted area of the Swiss Plateau.
The Beromünster (BEO) site is located on a hill in an intensively used agricultural area. It is surrounded mainly by croplands and to a smaller extent rangeland. The site itself consists of a 217 m high decommissioned radio transmission tower. Gas inlets and meteorological instrumentation are installed on the tower at five different heights above ground (12 to 212 m), whereas the gas analyser is located at the foot of the tower. A comprehensive description of the installation and the measurement system can be found in Berhanu et al. (2015). Here, only the observations from the topmost 1 http://www.carbocount.ch, last accessed 9 September 2015 inlet height (212 m) were used, since this height showed the largest extent of the relative footprint and, hence, is least influenced by local sources .
Lägern Hochwacht (LHW) is a mountaintop site on a very steep, west-east-extending crest approximately 15 km northwest of and 400 m above the city centre of Zurich, the largest city in Switzerland. The site is surrounded by forest with average tree crown heights of 20 m close to the site. The gas inlet and meteorological instrumentation is mounted on a small tower of 32 m.
Früebüel (FRU) is another mountain site and located at 982 m a.s.l. above Lake Zug on the south-eastern edge of the Swiss Plateau. Unlike Lägern Hochwacht, the site is located on a mountaintop plateau with a south-west aspect above Lake Zug and with slightly more elevated areas to the southeast. The area around the site is used as rangeland and emissions from a local dairy farm may influence the observations. In contrast to the other sites, gas samples and meteorological observations are taken close to the surface (3 m above ground). A more detailed analysis of how the observations of this site are locally influenced and how they can be compared to observations from the close-by tall tower in BEO is given in Bamberger et al. (2016). Here we only note that the influence of local emissions that cannot be accounted for in the transport model needs to be filtered from the observational data before the use in inverse modelling. We did this by removing all data (10 min resolution) with low wind speeds (< 3 m s −1 ) coming from the direction of the aforementioned farm (140 to 200 • ). These thresholds were deter- mined by comparing differences between the observations of BEO (212 m), which exhibit less local influences, and FRU as a function of wind speed and direction at FRU. At the Gimmiz site (GIM, 443 m a.s.l.) sample gases are drawn from a 32 m tall water tower. The surrounding area is flat and dominated by intensive agriculture, mostly vegetable farming and croplands. The area is a transformed wetland that used to be regularly flooded until the 1850s before the levelling of the river system (1868-1891), when former wetlands were also converted to agricultural lands (Schneider and Eugster, 2007). Although there are only two small farms in the direct vicinity, larger potential CH 4 sources are located in the town of Aarberg about 2.5 km to the southeast. Here a sugar refinery, operating a large-scale waste water treatment plant (250 000-person equivalent), a compost and soil recycling facility, and a biogas reactor for electrical power generation are located. These local sources may not be represented sufficiently well in model simulations. Therefore and as in the case of FRU, observations from GIM were filtered by wind speed and direction, excluding all 10 min averages for which wind speeds were either below 2 m s −1 or coming from directions between 90 and 150 • . Again, these thresholds were estimated by comparison to the observations at BEO. Schauinsland (SSL, 1205 m a.s.l.) is a mountaintop site in the Black Forest, Germany, to the north of the Swiss Plateau. As such it is usually situated above the stable nocturnal boundary layer of the surrounding, but at daytime it is affected by boundary layer air (Schmidt et al., 1996). The site is surrounded by forests and rangeland and no large CH 4 source is known in the direct vicinity. While not part of CarboCount-CH network, the observations from SSL provide additional constraints for the atmospheric inversion, especially at middistance from the Swiss Plateau.
The high-altitude observatory Jungfraujoch (JFJ, 3580 m a.s.l.) is located in the northern Swiss Alps on a steep mountain saddle between the two mountains Jungfrau (4158 m a.s.l.) and Mönch (4099 m a.s.l.). Although JFJ is usually located in the free troposphere, it intermittently receives polluted boundary layer air from sources both north and south of the Alps (Zellweger et al., 2003;Henne et al., 2010;Tuzson et al., 2011). The intensity of these transport events from the boundary layer can vary strongly depending on the weather condition and the transport process responsible for lifting.
At all sites, CH 4 measurements were carried out using PICARRO (Santa Clara, CA, USA) cavity ring-down spectrometers (Rella et al., 2012), which provide highfrequency (approximately 0.5 to 1 Hz) observations of CO 2 , CH 4 , H 2 O and (at BEO and LHW) CO. All instruments were calibrated against the WMO X2004 CH 4 scale  and were reporting dry air mole fractions by either applying a water vapour correction accounting for dilution and spectroscopic effects (CarboCount-CH sites and SSL) or by using pre-sample drying of sample air (JFJ). At the CarboCount-CH sites, measurements of additional target gases, not used for the calibration, give an estimate of the instruments' non-random uncertainty for CH 4 of ≈ 0.5 nmol mol −1 . At SSL observations of three additional target gases yield a combined measurement uncertainty of 0.3 nmol mol −1 . For JFJ a combined measurement uncertainty of σ = 0.31 2 + 3.61 × 10 −4 × χ 2 nmol mol −1 was reported for hourly aggregates, where χ is the observed mole fraction (Empa, 2015). For the use in the inversion 3-hourly aggregates were produced from high frequency observations for the period 1 March 2013 to 28 February 2014, the first year with a complete set of measurements for all CarboCount-CH sites. Prior to aggregation, the data filtering as described above was applied to the sites GIM and FRU. Out of the data set, only the afternoon values, covering 12:00 to 18:00 UTC (CarboCount-CH sites), were used in the atmospheric inversion. This was done in order to capture the time of day with the deepest planetary boundary layer (PBL) extent, which should also be best captured by the transport model and yield the smallest model bias (Kretschmer et al., 2014) and at the same time minimise the influence of local sources and sinks. For the elevated sites JFJ and SSL, the night-time data from 00:00 to 06:00 UTC were used instead. This is the time when the sites are least influenced by small-scale, thermally induced flow systems in the complex topography around the sites. Since the sites are situated on mountaintops no development of a shallow night-time boundary layer is expected so that the influence of local sources (if at all present) remains negligible at night. All of the following analysis and discussion is based on this filtered and aggregated data set. In addition to the absolute mole fraction, an estimate of largerscale background mole fractions, which represent conditions without recent emission input, was generated using the "robust estimation of baseline signal" (REBS) method (Ruckstuhl et al., 2012). We refer to this term as baseline mole fraction in the following. It represents a smooth curve fitted to the data, providing a baseline mole fraction for each observational time. The absolute mole fraction of the observations, χ o , can then be given as the sum of the baseline, χ o,b , and the contribution due to recent emissions, χ o,p , (1) The REBS method iteratively fits a non-parametric local regression curve to the observations, successively excluding points outside a certain range around the baseline curve. REBS was applied separately to hourly data from each site using asymmetric robustness weights with a tuning factor of b = 3.5, a temporal window width of 60 days and a maximum of 10 iterations. An estimate of the baseline uncertainty is given by REBS as a constant value for the whole time series. For JFJ the baseline uncertainty was estimated to 17.4 nmol mol −1 , whereas uncertainties for the other sites ranged between 16.2 nmol mol −1 (SSL) and 18.9 nmol mol −1 (LHW). The larger values generally reflect a larger degree of variability in the baseline and a reduced frequency of air masses not influenced by recent surface contact and emissions.

Transport models
Source sensitivities giving the direct influence of a mass emission from a source location onto the mole fraction at a receptor site were calculated with two different versions of the Lagrangian particle dispersion model (LPDM) FLEX-PART (Stohl et al., 2005), which can be run in time-inverted mode. The first represents the standard FLEXPART model (version 9.02) driven by analysis fields of the operational runs of the Integrated Forecast System (IFS) of the European Centre for Medium Range Weather Forecast (ECMWF). Input fields were available every 3 h with a horizontal resolution of 0.2 • × 0.2 • (≈ 15 km × ≈ 22 km) for the Alpine area (−4 to 16 • E and 39 to 51 • N) and 1 • × 1 • elsewhere. The second FLEXPART version is the one adapted to the use of output from the COSMO regional numerical weather prediction (NWP) model (Baldauf et al., 2011). FLEXPART-COSMO was driven by operational analysis fields as generated hourly by the Swiss national weather service, Me-teoSwiss, for western Europe (approximately −10 to 20 • E and 38 to 55 • N) with a horizontal resolution of approximately 7 km × 7 km. Hourly analysis fields are produced applying an observational nudging technique (Schraff, 1997) to near-surface and vertical profile observations of pressure, relative humidity and wind. The use of a high-resolution transport model in regional-scale inversions based on point observations is a prerequisite to reduce the representation uncertainty of the model (Tolk et al., 2008;Pillai et al., 2011). Furthermore, the use of a time-inverted LPDM is highly beneficial to this purpose as it allows an accurate transport description in the near-field of the sites below the resolution of the driving meteorology.
The main differences between FLEXPART-COSMO and standard FLEXPART-ECMWF are the internal vertical grid representation and the parameterisation of convective transport. In FLEXPART-COSMO, the native vertical grid of the COSMO model is used as the main frame of reference, which, in this case, was a height-based hybrid coordinate system (Gal- Chen and Somerville, 1975). In contrast, standard FLEXPART uses a terrain-following vertical coordinate with constant level depths up to the model top, which requires an initial vertical interpolation from the pressure-based hybrid coordinate used in the IFS. In FLEXPART-COSMO, all interpolation to particle positions is done directly from the native COSMO grid, avoiding multiple interpolation errors. In FLEXPART-ECMWF sub-grid-scale convection is treated by an Emanuel-type scheme (Emanuel and Zivkovic-Rothman, 1999;Forster et al., 2007), whereas in FLEXPART-COSMO the same modified version of the Tiedtke convection scheme (Tiedtke, 1989) as used in COSMO was implemented.
PBL heights are a critical parameter in FLEXPART since they are used as a scaling parameter for the turbulence parameterisation. We use the default implementation within FLEXPART to diagnose PBL heights applying a bulk Richardson method (Stohl et al., 2005;Vogelezang and Holtslag, 1996). In contrast to standard FLEXPART we did not use 2 m temperatures from COSMO in the PBL estimation but the lowest model level temperature (approximately 10 m above ground), because FLEXPART and COSMO PBL heights showed a positive bias when compared to PBL height observations from the sounding site Payerne on the Swiss Plateau under convective conditions and when using 2 m temperatures (Collaud Coen et al., 2014). This bias disappeared when using the first level temperatures instead.
With both model versions source sensitivities were calculated for each observation site and 3-hourly interval. For each interval and location a total of 50 000 particles was released and followed backward in time for 4 and 10 days in the COSMO and ECMWF version, respectively. Particles leaving the limited COSMO-7 domain were terminated prematurely. The limited horizontal model resolution and the complex terrain in the investigated domain lead to differences between the model surface altitude and the real site altitude. In such situations, the most representative height above model ground for particle releases in an LPDM is not well known.

S. Henne et al.: Swiss methane emissions
Therefore, we chose to release particles at two vertical locations for the CarboCount-CH sites to analyse the sensitivity of this choice. At BEO, where the model topography is relatively close to the site's altitude, these span the possible range of reasonable release altitudes by representing (1) the height above model surface as given by the inlet height of the observations and (2) the absolute altitude above sea level of the inlet. At the sites FRU and LHW the lower and higher release heights were chosen 50 m and 150 m above model ground, respectively, because height deficiencies in the model were larger there. At GIM only one release height was used because the model topography was relatively close to the true surface altitude. Also, for the more remote sites JFJ and SSL, only one release height was simulated that represents the middle between the model surface and the site altitude. Previously it was shown that such an approach works best (independent of time of day) for the mountaintop site JFJ, which shows large model topography deficits (Brunner et al., 2013). Values for all release heights are given in Table 1. Note that release heights were the same for all FLEXPART-ECMWF and FLEXPART-COSMO simulations except for JFJ and SSL were surface height differences between the models were large.
From both models, output was generated on a regular longitude-latitude grid with a horizontal resolution of 0.16 • × 0.12 • (≈ 13 km) covering western Europe and for a nested Alpine domain with a horizontal resolution of 0.02 • × 0.015 • (≈ 1.7 km). The generated output represents the summed residence time, τ i,j , of particles in a given grid box, i, j , and below a specific sampling height, h s , divided by the density of dry air in this grid cell and has units s m 3 kg −1 gridcell −1 . The sampling height was set to 50 and 100 m above ground in FLEXPART-COSMO and FLEXPART-ECMWF, respectively, coinciding with the minimal PBL height used in the models. Multiplication of τ i,j with the volume of the sampling grid cell, V i,j = A i,j · h s , and the ratio of the molar weight of the species of interest, µ s , and the molar weight of dry air, µ d , yields the desired source sensitivity, m i,j , in units of s kg −1 mol mol −1 , When m i,j is multiplied by a mass emission in the same grid box, E i,j (kg s −1 ), the product gives the effect this emission would have on the dry air mole fraction at the receptor. The sum over all grid boxes then yields the increase in mole fraction, χ p , due to recent emissions, whereas the baseline mole fraction, χ b , can be obtained as the average mole fraction over all particles at their end points in the simulation where i, j are the horizontal grid indices, χ k the mole fraction at each particle's end point, and K is the number of particles. In our FLEXPART-COSMO simulations particles were followed for 4 days backward in time. Not all particles leave the limited-area model domain during this time, so that the baseline mole fraction as given in Eq.
(3) cannot be directly translated to conditions at the domain boundaries, but may also contain contributions from within the domain and, therefore, may vary between different sites. For the inversion set-up it would be beneficial if the baseline mole fractions could be estimated from an external three-dimensional model. However, such model input was not available at the time of analysis, and thus the prior baseline mole fraction was taken as the one estimated from the observations (REBS) and further optimised in the inversion.

Inversion framework
In our inversion system the source sensitivities calculated by the transport model can be used to give a direct relationship between the simulated mole fractions and the so-called state vector, x = (x 1 . . . x K ) with a total of K elements, that primarily contains the desired gridded emissions. In matrix notation this can be expressed as where χ = (χ 1 . . . χ L ) represents the simulated mole fractions at different times and locations, l = 1, . . ., L. The sensitivity matrix M (dimensioned K × L) contains the sensitivities for each time/location towards the kth element of the state vector. In our case, the state vector contained additional parameters characterising the baseline mole fractions χ b at different times and for different sites. Hence, x contained K E elements describing the emissions and K B = K − K E elements giving baseline mole fractions, which were not estimated at each observation but at discrete time intervals (baseline nodes). Therefore, the sensitivity matrix M consists of two block matrices M E and M B giving the dependence on the emissions and baseline mole fractions, respectively. Similar to Stohl et al. (2009), elements of M B were set to represent temporal linear interpolation between the baseline mole fractions at the neighbouring baseline nodes. We estimate the baseline separately for each site in the inversion, since it does not necessarily just reflect the conditions at the boundary of the domain but may also contain contributions from within the domain (see discussion above). Different sites may therefore have different levels of within-domain influence. This is especially true for sites at different altitudes even if these are located at short distances as in our network. Since the baseline treatment is a critical part of the inversion system and may lead to attribution errors of the emissions, we present two alternative baseline estimation approaches as part of our sensitivity analysis (see Sect. 2.5.7). For our base inversion, baseline nodes were spaced equidistantly with a distance of τ B = 5 days over the observation period and were optimised separately for each site, resulting in 73 baseline elements in the state vector for each site. Prior estimates of the baseline mole fractions were REBS estimates for the site JFJ (see Sect. 2.1). Since the REBS estimate represents a smooth curve to the data, the REBS value at the time of a given baseline node was used as its prior value.
In our base set-up we target temporal average emission fluxes for the period of observations (March 2013 to February 2014) and optimise their spatial distribution. We include seasonality in the emission fluxes as part of our sensitivity analysis (see Sect. 2.5.2).
In order to reduce the size of the inversion problem, emissions were not optimised on a regular longitude-latitude grid as given by the FLEXPART simulations. Instead, a reduced grid was used that assigns finer (coarser) grid cells in areas with larger (smaller) average source sensitivities. Starting from the finest output grid resolution of 0.02 • × 0.015 • , four neighbouring grid cells were merged if their average residence time did not reach a specified threshold. This procedure was iterated up to a maximum grid cell size of 2.56 • × 1.92 • . The residence time threshold was set manually in order to reduce the number of cells in the inversion to the order of K E ≈ 1000. The overall extent of the emission grid was determined by (1) the extent of the COSMO-7 domain, (2) the existence of considerable CH 4 emissions (cut-off over the oceans) and (3) a minimum source sensitivity. Tests with larger and smaller inversion domains did not indicate significant influences on the deduction of Swiss emissions.
In Bayesian atmospheric inversion, prior knowledge of the state vector, x b , and its probability distribution is used to guide the optimisation process. Mathematically this can be expressed by formulating a cost function J that penalises deviations from the prior state and differences between simulated and observed mole fractions (e.g. Tarantola, 2005) where x describes the optimised and x b the prior state vector, and Mx − χ o is the difference between simulated and observed mole fractions. B and R give the uncertainty covariance matrices of the prior state and the combined modelobservation uncertainty. In Sect. 2.4 the structure of these matrices is discussed in more detail. Minimisation of J yields the posterior state In our implementation the inverse of S = MBM T − R , a L × L matrix, was calculated using LU factorisation (function DGESVX in LAPACK). In addition to the posterior state, its uncertainty expressed as an uncertainty covariance matrix, A, can also be given (e.g. Tarantola, 2005): The total emissions and their uncertainty from a certain region or country can then be calculated as where the vector g gives the fractional contribution of a region to an inversion grid cell and A E is the part of A that contains the uncertainty covariance of the posterior emissions. g k takes a value of 1 for a grid cell that is completely within the region and 0 for grid cells outside the region. For coarse inversion grid cells containing more than one region, g k was calculated from higher-resolution population data, weighting per region contributions by population and not by land surface area. In the case of the present CH 4 inversion and the national estimates for Switzerland this treatment was of minor importance but is more crucial for other species that exhibit sharp emission gradients more closely following the population distribution (e.g. halocarbons). In our base inversion, we used the Swiss MAIOLICA inventory (Hiller et al., 2014a), which is based on the total Swiss emissions estimated by FOEN (SGHGI) for the year 2011 and reported to UNFCCC in 2013. For areas outside Switzerland, prior emissions were taken from the Europeanscale inventory developed by TNO for the MACC-2 project (Kuenen et al., 2014) (TNO/MACC-2 hereafter) applying the same country-by-country scaling to 2011 values reported to UNFCCC in 2013.

Covariance design
This section details the construction of the uncertainty covariance matrices B and R as used in the base inversion. Parameters used to build the matrices were chosen based on experience and previous publications (see below). The sensitivity to these choices was investigated in a set of sensitivity inversions as described in Sect. 2.5.
Both uncertainty covariance matrices are symmetric block matrices. In the case of B, one block, B E , describes the uncertainty covariances of the emission vector and a second block, B B , the uncertainty covariances of the baseline mole fractions. Within each block the off-diagonal elements were allowed to be non-zero. The diagonal elements of B E were set proportional (factor f E ) to the prior emissions in the respec- For land grid cells with low emissions (below 10 % of land average) and ocean grid cells the uncertainty was set to 10 % of the average land cell uncertainty in order to avoid near-zero uncertainties. As more detailed information of the spatial uncertainty covariance structure was lacking, a spatial correlation of the uncertainty was assumed for the off-diagonal elements that decays exponentially with the distance between two grid cells (e.g. Rödenbeck et al., 2003;Gerbig et al., 2006;Thompson and Stohl, 2014): where d i,j is the distance between two grid cell centres and L the correlation length. In this set-up the total squared uncertainty of the prior emissions σ 2 E = 1 T B E 1, where 1 is a vector of all ones, only depends on the settings of L and f E . For the base inversion L was fixed to 50 km and f E was adjusted to yield fixed relative uncertainties of the national estimate for Switzerland of 16 %, which is the uncertainty given for the Swiss bottom-up estimate (FOEN, 2015). The choice of 50 km was driven by the need for sufficient constraints for neighbouring grid cells, whereas Hiller et al. (2014a) suggested a shorter length scale around 10 km based on a comparison of the spatial structures of the MAIOLICA, TNO/MACC-2 and EDGAR CH 4 inventories.
All diagonal elements of B B were set to a constant value, where σ b is an estimate of any given baseline uncertainty and f b is a scaling factor. The off-diagonal elements were set assuming an exponentially decaying correlation of the baseline uncertainty between baseline nodes at a given site where T i,j is the time difference between two nodes and τ b is the temporal correlation length. In the base inversion, σ b was obtained from the REBS fit of the JFJ observations (17.4 nmol mol −1 ), f b was set to unity, and τ b to 14 days. As for L, the choice of τ b is somewhat arbitrary but governed by the need for sufficient constraints on the posterior solution without restricting adjustments too strongly.
In the case of temporally variable emissions (see Sect. 2.5.2), the state vector x, the sensitivity matrix and the prior uncertainty matrix have to be extended. B E now should treat spatial and temporal covariance of the state vector. Individual diagonal elements of B E , B E i,i , now refer to different emission locations and time, with the index i running over both of these dimensions. The off-diagonal elements can then be given by where, in addition to Eq. (9), T i,j gives the time difference between two emission sets and τ t is the temporal correlation length scale of the prior emissions. The block matrix R contains one block for each site used in the inversion. In its diagonal elements both the observation and the model uncertainty were considered by quadratic addition: where σ o is the observation uncertainty as estimated for each 3-hourly CH 4 average (see Sect. 2.1) and the second and third term are contributions of the model uncertainty. σ min represents a constant contribution, while the third term represents an uncertainty contribution relative to the prior simulation of above-baseline concentrations, χ p,i (Brunner et al., 2012). For the base inversion, σ min and σ srr were estimated separately for each site from the model residuals (difference between simulated and observed mole fraction) of the prior simulation, χ p,i , by fitting a straight line through root mean square errors (RMSEs) calculated for separate bins along χ p,o . The choice of this method was motivated by the observation that prior model residuals tend to increase with prior mole fractions. Estimating the model uncertainty from the prior model residuals has been suggested before by Stohl et al. (2009), where σ min was estimated as the RMSE from the prior simulation, whereas σ srr was set to 0. In an additional step this constant value was then forced to yield a normal distribution of the normalised model residuals. Furthermore, Stohl et al. (2009) applied their uncertainty estimation in an iterative way using the model residuals from successive inversion runs. In our experience this may lead to underestimated model uncertainties and we did not iterate our procedure. These methods have in common that the results of the prior simulation influence the estimation of R, therefore somewhat violating the independence of prior and modelobservation uncertainties assumed in the Bayesian approach. Finally, off-diagonal elements of the model-observation uncertainty covariance matrix were assumed to follow an exponentially decaying correlation structure.
where T i,j is the time difference between two measurements and τ o is the temporal correlation length that describes the autocorrelation in the model-observation uncertainty. In the base inversion τ o was set to 0.5 days, a value previously used by other authors (e.g. Thompson et al., 2011) and associated with the inability of atmospheric transport models to correctly simulate the diurnal cycle in the PBL. The uncertainty covariances between observations from different sites were set to 0.

Sensitivity inversions
The Bayesian inversion provides an estimate of the posterior uncertainty of the state vector, which in itself should be sufficient to give an estimate of the combined top-down uncertainty. However, this analytical uncertainty tends to underpredict the true uncertainty. Optimality of the Bayesian approach requires normally distributed probability density functions, temporally uncorrelated residuals, and nonsystematic uncertainties, requirements that are difficult to meet exactly in practice. In particular, potential systematic uncertainties in model transport, which may contribute importantly to the overall uncertainty (e.g. Gerbig et al., 2008), are not accounted for. To explore the range of uncertainty beyond the analytically derived posterior uncertainty and to test the robustness of the results to different assumptions, it has therefore been proposed to perform additional sensitivity inversions (e.g. Bergamaschi et al., 2010Bergamaschi et al., , 2015. To this end, we set up a series of sensitivity inversions that vary different aspects of the inversion (transport simulations, inversion algorithm, uncertainty covariance design, prior emissions, observation selection, seasonality of emissions). An overview of these sensitivity inversions is given in Table 2 and details are described in the following.

Transport simulation
One important source of uncertainty when using observational data from elevated sites is the potential mismatch between model and real topography. The choice of the particle release height in the model can considerably change the model's performance and may lead to systematic biases in simulated concentrations. Therefore, we quantified the effect of the release height by using a "low" and "high" release case for each of the sensitivity inversions in Table 2. One is always using the lower release heights for the CarboCount-CH stations as introduced in Sect. 2.2, whereas the other uses the higher release heights. The release heights of the more remote sites JFJ and SSL were not varied because of their less direct influence on the Swiss emissions. In addition to the release height, two different versions of the atmospheric transport model were used. The base inversion was based on FLEXPART-COSMO and a sensitivity run used the results of FLEXPART-ECMWF (S-EC).

Seasonal variability
In the base inversion emissions were assumed to be constant in time. However, considerable seasonal variability of the emissions especially from the agricultural sector can be expected. To test the implication of this assumption, a sensitivity run extending the state vector to separately hold emissions for each season (S-V) was set up following the common definition of winter spanning the months December, January and February (DJF) and so forth (spring: MAM; summer: JJA; autumn: SON). The prior emissions and their uncertainty were set identical for all seasons. The correlation length scale between different emission times was set to τ t = 90 days (see Eq. 11). Reducing this time constant to 45 days had only a minor influence on the inverse emission estimate.

Inversion algorithm
An additional sensitivity test, replacing the Bayesian method by an extended Kalman filter (extKF) inversion as described in Brunner et al. (2012), was conducted (case S-K). Similar to the Bayesian inversion, a prior state vector is used by the extKF. In contrast to the Bayesian approach, the extKF assimilates the observations sequentially from time step to time step. In the extKF approach one baseline value and its tendency for each site are part of the state vector. In each step, observations from different sites but not from different times are incorporated. This allows for a more flexible temporal evolution of the emissions and the baseline values as for the Bayesian approach. Another important difference is that the extKF method of Brunner et al. (2012) estimates the logarithm of the emissions rather than the emissions themselves to enforce positive fluxes. This renders the problem non-linear and requires the use of an extended Kalman filter. As in the Bayesian inversion the extKF describes the uncertainties of the prior state and the model-observation uncer-tainty through the respective uncertainty covariance matrices B and R. In addition to these, the extKF requires an uncertainty covariance matrix Q that describes the uncertainty with which the state vector can change from one time step to the next. Accordingly, uncertainties of the state vector are allowed to grow from one time step to the next, which introduces an additional amount of prior uncertainty as compared to the Bayesian approach. The matrices B and R were parameterised according to Eqs. (9) and (12), respectively. The chosen parameter values are listed in Table 3. The forecast uncertainty matrix Q was also parameterised according to Eq. (9), notably with the same spatial correlation length. The diagonal elements of Q were set to a relative forecast uncertainty of the emissions of 0.6 % per 24 h, which resulted in fairly constant posterior emissions in time with only a small seasonal cycle.

Covariance parameters
The next set of sensitivity inversions was designed to analyse the effect of different uncertainty covariance matrices. Our base inversion is based on the prior emission uncertainty as estimated by the SGHGI, which we consider to be the best knowledge of bottom-up uncertainty in Switzerland. Since Hiller et al. (2014a) used the same by-category emissions as the SGHGI to spatially disaggregate total emissions for the MAIOLICA inventory (our prior), we extrapolated the SGHGI uncertainty information to the whole inversion domain. Next to the base inversion a set of uncertainty covariance parameters as estimated by the method of maximum likelihood (ML; Michalak et al., 2005) were used (S-ML). We estimated the covariance parameters (L, f E , τ b , and individually for each site f b , σ min , σ srr ) by minimising the negative logarithm of the likelihood estimator (Michalak et al., 2005) As a consequence of the ML optimisation, posterior model residuals and posterior emission differences should follow a χ 2 distribution. To find the minimum of L θ a multivariate optimisation routine was used. We applied the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm that is widely used for optimisation problems (see, for example, Nocedal and Wright, 2006). Initial parameter values were set equal to those used in the base inversion, but giving all sites the same σ min of 20 nmol mol −1 and σ srr of 1. To assess the robustness of the ML optimisation results, an alternative algorithm was tested (Nelder-Mead), yielding very similar parameter sets. Another sensitivity run varied the design of the modelobservation uncertainty covariance by estimating the diagonal elements of the matrix from the prior RMSE at each site σ min = RMSE (χ b − χ o ) and applying a correction for extreme residual values according to Stohl et al. (2009) (S-S). Such extreme residuals only occurred for two observations at LHW, so that essentially a constant model uncertainty was used for each site. The off-diagonal elements were calculated in the same way as in the base inversion. For the extKF inversion it was only possible to use a fixed set of parameters σ min and σ srr for all sites, because by-site treatment was not yet implemented in the current version of the code. They were selected to be close to the average values used in the reference inversion. All covariance parameters used in the base, the ML approach, the Stohl et al. (2009) approach, and the extKF inversion are compared in Table 3. In the case of the Bayesian inversions, the covariance parameters differed between the two release heights, with the high release showing larger values of σ min for the sites BEO and LHW and all applied estimation techniques.

Prior emissions
The sensitivity of the inversion result to the prior emissions was tested by using different prior inventories. In a sensitivity inversion we replaced the MAIOLICA emissions within Switzerland with those given by TNO/MACC-2 (S-T). A third sensitivity run was set up using the EDGAR (v4.2 FT2000) inventory for the base year 2010 (JRC/PBL, 2009) (S-E). In all three cases the prior uncertainty was set so that a value of σ E = 16 % was reached for the Swiss emissions, which is the uncertainty given for the SGHGI (FOEN, 2015). For individual grid cells the resulting proportionality factor was f E ≈ 30 %. However, the off-diagonal elements in B E contributed considerably to the total country uncertainty since they were especially large for small grid cells (see Fig. S2 in the Supplement).

Selection of observations
Another series of sensitivity inversions was set up using different parts of the observational data (runs S-01 to S-05, Table 2). The number and combination of sites used in each inversion was varied from using individual sites to using all six sites. For each of these sensitivity cases the inversion grid was adjusted according to the total source sensitivity of the selected sites, thereby ensuring that small grid cells only occurred in areas with large sensitivities. In the base inversion the two CarboCount-CH sites BEO and LHW and the two more remote sites JFJ and SSL were used, whereas the observations of FRU and GIM served for validation only.

Baseline treatment
As described above, the baseline mole fractions were treated as a linear interpolation between mole fractions at designated baseline nodes, the latter being optimised as part of the state vector in the inversion. The treatment of the baseline in this regional-scale inversion is critical and may introduce attribu- Table 3. Overview of parameters used for the construction of the uncertainty covariance matrices: contributions to model-observation uncertainty σ min and σ srr , baseline uncertainty factor f b , baseline correlation length τ b , prior correlation length L and prior Swiss emission uncertainty σ E . tion errors in the posterior emissions. Therefore, we explored two alternative methods that address certain shortcomings of our main approach. For example, there were times when the simulated smooth baseline was not able to follow apparent fast changes in the observed baseline signal. This was the case when the general advection direction towards Switzerland quickly changed from west to east, with mole fractions often being considerably elevated during easterly advection. At such transition times, use of the smooth baseline may lead to attribution errors in the emission field. Instead of a smooth baseline it would have been desirable to take the baseline directly from an unbiased state of a global-scale model, sampling the mole fractions at the FLEXPART particle end points. However, such model output was not available for the investigation period at the time of the analysis. The first alternative method (S-B1) was based on two baseline estimations -one for the eastern and one for the western part of the inversion domain -which were combined using a weighted mean depending on the end points of the model particles (here 4 days before arrival at the site). Since the initial locations of the particles were available for every 3 h interval, this approach allows for more flexible variations of the simulated baseline signal. As in the standard baseline treatment, prior baseline mole fractions were taken from the REBS baseline at JFJ, applied here to both the eastern and western baselines. The second alternative baseline method (S-B2) extended the approach to a three-dimensional grid of baseline mole fractions accounting not only for east-west but also for north-south and vertical gradients. Again, the initial positions of the model particles within the grid as obtained from each FLEXPART simulation were used to determine the baseline concentration at the site as a weighted average. Different from methods B and S-B1, however, only one common set of gridded baseline mole fractions was estimated and applied to all sites. Only a very coarse (3×3×2) grid, covering the inversion domain, with a 15-day temporal resolution was used in order to limit the size of the state vector. In the vertical, the grid was separated between heights 3000 m below and above ground level. The latter was chosen to ensure that average initial sensitivities were similar for both vertical layers. Prior baseline values in the upper vertical layer were again taken from the REBS baseline at JFJ, whereas the lower layer was initialised with the REBS baseline at BEO. This ensures a negative vertical gradient in CH 4 baseline mole fractions, since estimates for BEO were generally larger than those for JFJ.

Results
In the following the results of the emission inversions are presented, first in a more detailed fashion for the base inversion and second in a less exhaustive way for the sensitivity inver- sions highlighting the differences from the base case. Note that the base inversion does not necessarily represent the best inversion set-up and most likely or best estimate of the posterior emissions. Rather, it is used as a starting point to analyse the sensitivity to different inversion settings. Although there might be a best inversion set-up in the sense that its results are closest to the truth, this best set-up is not known (as little as the true emissions are known). The ML method applied as an alternative is an objective method to tune the free parameters of an inversion, but this does not necessarily correspond to the best set-up since it cannot account for potential biases arising from transport errors or the problem in representing the release height of the particles.

Base inversion
Average source sensitivities as calculated with FLEXPART-COSMO on the reduced grid are shown in Fig. 1 for the base inversion as the combined sensitivity of the four sites BEO, LHW, SSL, and JFJ. Source sensitivities were largest close to the sites and in general for the Swiss Plateau (see Oney et al., 2015, for a detailed discussion of source sensitivities of the CarboCount-CH sites). The pronounced south-west to north-east orientation of the maximal source sensitivities is a result of the flow channelling between the Alps and the Jura Mountains (Furger, 1990). South of the Alps and outside Switzerland, source sensitivities quickly declined with generally larger values for westerly compared with easterly directions. Source sensitivities towards the south-east were especially small, reflecting the shielding effect of the Alps.
In Switzerland prior emissions amounted to 178 Gg yr −1 . After mapping the high-resolution emission data to the reduced inversion grid (Fig. 2a) and applying Eq. (8), Swiss prior emissions were quantified at 183 Gg yr −1 . The difference of 2 % can be explained by mapping artefacts along the Swiss border, where inversion grid cells overlap with neighbouring countries, wrongly attributing some emissions from these to the Swiss total. The distribution of the prior emissions (Fig. 2a) in Switzerland clearly emphasises the dominant role of emissions from the agricultural sector. Emission maxima are located in the canton of Lucerne in close vicinity to BEO and in the north-eastern part of the country towards Lake Constance in the cantons of Thurgau and Saint Gallen. All these areas are characterised by intensive agriculture with a focus on cattle farming. Emissions from the urban centres of Zurich, Basel, Bern and Geneva, in contrast, are not especially pronounced in the MAIOLICA inventory. Within the high Alpine area, and to a smaller degree within the Jura Mountains, MAIOLICA emissions are significantly smaller, but are large again in the north Italian Po Valley and also in south-western Germany.
Simulated CH 4 time series for the sites used in the base inversion with low model release heights (B low) are compared with the observations in Fig. 3. Most of the time the Note that the y axes were scaled for each site separately. All data represent 3-hourly averages.
prior simulations were closely following the observed variability, underlining the very good performance of the transport model. However, during some periods the prior simulations considerably underestimated the observed mole fractions. This was especially true for the BEO and LHW sites and a period in March/April as well as during episodes in October and November 2013. Some of the observed temporal variability was common for all sites, suggesting an important influence from large-scale weather systems, whereas at other times the signals from different sites were little correlated. The two sites on the Swiss Plateau showed the most common behaviour, while, as expected, the high-altitude observations at JFJ were most decoupled from the other observations. Also as expected, peak mole fractions were larger for the sites closer to the emissions (BEO, LHW) and smaller for the higher-altitude sites (SSL and especially JFJ). The transport model captured this general tendency very well. Except for JFJ, prior baseline mole fractions (based on the JFJ REBS estimate) were smaller than most observed mole fractions.
The model's skill considerably improved for the posterior simulations showing greater correlations and lower biases. The simulations more closely followed the observed variability and the bias was reduced (Fig. 3). Partly, this was achieved through changes in the baseline mole fractions. Posterior baselines were generally greater than the prior at the BEO, LHW and SSL sites, whereas they were lower than the prior at JFJ. Largest baseline increases occurred during extended periods of elevated CH 4 (e.g. March 2013). These periods were characterised by easterly advection on the south-easterly side of high pressure systems with centres over north-western to central Europe. In these situations the limited model domain and the relatively short backward integration time of 4 days were likely insufficient to capture all recent emission accumulation above the baseline. As a consequence, the inversion adjusted the baseline upward.
The quality of the simulated time series is summarised in Fig. 4, where coefficients of determination, R 2 , are given for all sites, for both prior and posterior simulations and separately for the complete (Fig. 4a) and above-baseline signal (Fig. 4b). The performance in the prior simulations ranged from R 2 = 0.25 for the site FRU to R 2 = 0.5 for the site GIM and the complete signal. The coefficients of determination for the above-baseline signal were slightly lower, but showed the same ranking between the sites: largest at GIM followed by the sites SSL, LHW, BEO and JFJ and smallest for FRU. Posterior coefficients of determination consider- ably increased for all sites used in the inversion (R 2 = 0.58-0.69) and slightly increased for FRU but slightly decreased for GIM. Improvements were seen both for the complete signal as well as for the above-baseline signal. The ranking between the sites remained similar after the inversion.
An overall quality indicator, which not only accounts for the correlation but also for a correct representation of the amplitude of the variability, is the Taylor skill score (Taylor, 2001) where R is the Pearson correlation coefficient and R 0 the maximal attainable Pearson correlation of a "perfect" simulation, which is still limited by factors such as observation and representativeness uncertainty and was set to 0.9. σ f = σ m /σ o is the simulated standard deviation normalised by the observed standard deviation. S takes the value of 1 for a perfect simulation, but would take a value of 0.65 for perfectly correlated simulations that under/overestimate the observed variability by a factor of 2. The prior value of σ f was well below 1 for all sites (0.43 to 0.71), indicating generally underpredicted peak heights, but increased in the posterior simulation to values between 0.65 to 0.8, except for GIM, where it remained at 0.44. Posterior values of S for all sensitivity inversions and all sites are given in Table 4. For the base inversion S ranged from 0.78 to 0.91 for the sites used in the inversion and was smaller for the sites FRU and GIM (0.77 and 0.50). Note, however, that for the latter two sites the baseline was not adjusted by the inversion, which may explain part of the weaker posterior performance. In the case of GIM it is remarkable that the correlation was comparatively large but the normalised standard deviation was very small. This may indicate that the general transport to the site was well captured by the model (correlation), but that either local boundary layer heights or local emissions were overestimated or underestimated, respectively, so that the model was not able to simulate the observed amplitudes correctly. Taylor skill scores were very similar for posterior simulations of the base inversion using the high particle releases (B high in Table 4). Also, the prior simulation's performance was similar for low and high release heights, with lower release heights usually performing slightly better in terms of amplitude of the simulated variability and higher release heights showing slightly improved correlations. No clear preference for the lower or higher release height could be deduced from these results.
As an additional validation parameter the RMSE and its reduction from prior to posterior simulations are shown in Fig. 4c and d. For sites used in the inversion the prior RMSE was between 20 and 40 nmol mol −1 and decreased by 15 to 25 % in the posterior simulations. For the near-surface sites FRU and GIM the RMSE did not significantly decrease after the inversion. At both sites simulated mole fractions were smaller than observed, especially at GIM. Even when using only afternoon values and when filtering for wind conditions with possibly large local influences (as done here), the transport model was not able to reproduce the amplitude of the observed variability at these sites. A reason for this poor model performance in FRU is most likely the inlet height being very close to the surface and the associated high sensitivity to local emissions that cannot be captured at the resolution of the transport model. In GIM local emissions or mismatches in the local boundary layer height seem to be the main problem since the timing of the temporal variability was captured very well. The effect of including the sites GIM and FRU in the inversion is further discussed in Sect. 3.7.
We used observations from sites in more complex terrain and closer to emission sources than used in other regionalscale inversion studies of CH 4 surface fluxes for the European and East Asian domain Manning et al., 2011;Thompson et al., 2015). This should result in more complex variability at the sites. Nevertheless, our model performance parameters are well within the range reported previously by the above studies.
The posterior CH 4 emissions and their differences from the prior emissions are shown in Fig. 2b-d. The largest, though still modest, absolute changes (Fig. 2c) were estimated for the region south-west of BEO. In this region with Table 4. Overview of results of sensitivity inversions. E A and E B are the total Swiss CH 4 prior and posterior emissions (Gg yr −1 ), respectively, and S is the posterior Taylor skill score for the individual sites. The settings of the sensitivity inversions are given in Table 2 Fig. S1 for a map of the Swiss cantons) and in large parts of western Switzerland. In contrast, larger than prior emissions were obtained for north-eastern Switzerland in the cantons of Saint Gallen and Appenzell and also beyond the border in southwestern Bavaria. Emissions in northern Italy were increased but due to the weak sensitivity for this region these posterior results are subject to larger uncertainties than those on the Swiss Plateau. Relative emission increases (Fig. 2d) of up to 30 % were detected for the Appenzell region and the bordering Vorarlberg region in Austria. However, relative emission reductions appeared for the southern Black Forest. Similar patterns emerged for the base inversion when using the high release heights (see Fig. S3 in the Supplement), but posterior emissions were generally larger in this case. In this base inversion Swiss total emissions were estimated at 179 ± 7 Gg yr −1 (1σ ) and 195.0 ± 7.3 Gg yr −1 for the low and high particle release heights, respectively. Both values are not significantly (two-sided Welch t test) different from their prior value, indicating a high level of consistency between the bottom-up estimate of the MAIOLICA inventory and our top-down estimate. Furthermore, analytical uncertainties of the posterior were considerably reduced by about 75 %. However, the difference ±15 Gg yr −1 in total Swiss emissions resulting from the choice of the particle release height suggests a relatively large additional contribution to the overall uncertainty due to the inversion set-up, which is not included in the analytical uncertainty.
Next to an improved reproduction of the measurement time series, the reduction of uncertainty in the emission field provides information on the quality of the inversion. Uncertainty reductions were largest close to the observation sites (Fig. 5). For the sites with larger surface sensitivities (LHW and BEO), uncertainty reductions in their vicinity were larger than for the more remote sites (SSL and JFJ). It is interesting to note that uncertainty reductions were largest in the area Figure 5. Uncertainty reduction between prior and posterior fluxes given in % relative to prior uncertainty (1 − σ B /σ A ) for the base inversion with low particle release height.
around and west of BEO, where emission reductions were also the largest. Uncertainty reductions were smaller for the area east of LHW, where considerable emission reductions were also established. For north-eastern Switzerland, where the inversion produced large emission increases, uncertainty reductions were relatively small. The associated emission increases are thus less well constrained, which in turn may indicate temporally variable emissions or increased transport uncertainties for the associated flow direction.

Seasonal cycle
When allowing seasonal variability of the emission fluxes (S-V), distinct differences between the seasons are visible, although no seasonal variability was included in the prior (Figs. 6 and S4 in the Supplement). Wintertime posterior emissions were strongly reduced especially in agricultural areas. Posterior emissions during the other seasons tended to be slightly larger than their prior values.
Also, the estimated emission patterns changed from season to season. In spring and summer increased posterior emissions were estimated for eastern Switzerland, the canton of Lucerne (around BEO) and generally the pre-Alpine area, whereas there was a tendency for smaller than prior emissions in western Switzerland. The strong increase around the station FRU (not used in the inversion) is consistent with the observation that the posterior model performance for the site FRU was considerably enhanced compared to the prior simulation. Performance was also enhanced compared to the posterior simulation of the base inversion both in terms of correlation and RMSE reduction, although Taylor skill scores were similar in both inversions (see Table 4). However, during autumn higher than prior emissions were present in north-western and eastern Switzerland, and for small areas south of BEO and east of LHW posterior emissions were below prior estimates.
For the low model release height, total Swiss emission rates were smallest during winter (152.2 ± 9.7 Gg yr −1 ) but were relatively similar and close to the prior estimates during the other seasons (206.5 ± 12, 182.1 ± 13, and 202.7 ± 11 Gg yr −1 for spring, summer and autumn, respectively). The annual total Swiss emissions for S-V were 185.9 ± 6.5 Gg yr −1 , very close to those of the base inversion. Wintertime emission rates were 18 % smaller than the annual mean. For the high model release heights, a similar but less pronounced annual cycle was derived, which featured total annual emissions of 197 ± 7 Gg yr −1 and wintertime emission rates of 171 ± 10 Gg yr −1 (13 % lower than annual mean).

Extended Kalman filter inversion
The extended Kalman filter inversion using low particle release heights (S-K low) yielded similar annual mean posterior emissions as the base inversion (Figs. 7 and S5 in the Supplement). Several features of the posterior emission differences obtained by the base inversion are also visible in the extKF inversion: reductions west of BEO, increases in northeastern Switzerland, small changes in the Alpine area, small increase in the region close to GIM (shifted south-westerly as compared to base inversion). No emission reductions were, however, deduced for the area east of LHW. Overall the posterior model performance using the extKF inversion was superior (S between 0.84 and 0.95) compared to the base inversion (Table 4), which is most likely related to the timevariable posterior emission field and to a smaller degree to the different treatment of baseline mole fractions.
Total Swiss emissions were estimated at 193 ± 13 and 217±14 Gg yr −1 by the extKF inversion for the low and high particle release height, respectively. These values are considerably larger (8 and 15 %) than those of the base inversion but fall well within the range of values reported by the other sensitivity inversions using the Bayesian approach. The difference in total emissions between the low and high release case of 24 Gg yr −1 was considerably larger than in the base inversion (Table 4). Uncertainty estimates of the posterior emissions remained larger in the extKF case than in the base inversion, despite the fact that similar prior uncertainties and model-observation uncertainties were used in both systems. The main reason for this observation is that the uncertainties of the state vector are allowed to grow in the extKF from one time step to the next in order to account for the forecast uncertainty, which introduces an additional amount of prior uncertainty.

Influence of transport model
In the sensitivity case S-EC the source sensitivities were derived from FLEXPART-ECMWF instead of FLEXPART-COSMO (see Sect. 2.2). On the one hand, FLEXPART-ECMWF may be less suitable to resolve the complex flow in the Swiss domain due to its coarser horizontal resolution. On the other hand, FLEXPART-ECMWF is a well-validated model code and has been widely used for inverse modelling (e.g. Stohl et al., 2009;Thompson and Stohl, 2014;Thompson et al., 2015). Using the same inversion settings, FLEXPART-ECMWF simulations yielded generally similar posterior emissions as the base inversion (Figs. 8 and S6 in the Supplement). Common features were again the decrease west of BEO and east of LHW and the increase in northeastern Switzerland with respect to the prior emissions. In contrast to the base inversion, large emission reductions were also assigned to most of the western part of the country towards Lake Geneva. For the low release height, the model performance at the observation sites was only slightly lower compared to the base inversion as indicated by the posterior Taylor skill scores (Table 4). In contrast, posterior Taylor skill scores were slightly larger in the high release case than in the base inversion. An exception was the GIM site, for which skill scores were strongly reduced using FLEXPART-ECMWF. This may reflect the growing inability of a coarser transport model to simulate the local CH 4 contribution to the site.
Although FLEXPART-ECMWF's performance at the sites was of similar quality to the base inversion, the uncertainty reductions of the posterior emissions (Fig. 8b) were not as pronounced in the S-EC cases (low and high) as compared to the base inversion. This can partly be attributed to the larger model uncertainty assigned in the ECMWF case (especially low particle release case) compared to the base inversion (compare Table 3). Total Swiss posterior emissions in the S-EC case were 171.1 ± 8.0 and 182.1 ± 7.6 Gg yr −1 in the low and high particle release case, respectively, slightly smaller than in the base inversion. One possible explanation may be the coarser and, hence, potentially less dispersive behaviour of FLEXPART-ECMWF. Mesoscale flow patterns in complex terrain may contribute to effective dispersion (Rotach et al., 2013). The coarser resolution of FLEXPART-ECMWF likely results in larger under-representation of mesoscale flow in the complex Swiss terrain.

Influence of prior emissions
Two additional spatially explicit sets of prior emissions were used to explore the effect of the prior emissions on the inversion results. The sensitivity run based on EDGAR (S-E) starts off from considerably larger prior emissions for Switzerland (228 Gg yr −1 ) and also deviates strongly in the spatial allocation of these emissions, putting more emphasis on the population centres than the MAIOLICA inventory (Hiller et al., 2014a). This can be traced back to EDGARv4.2 containing about 25 Gg yr −1 larger emissions from the gas distribution network (IPCC category 1B2: fugitive emissions from oil and gas; 32 vs. 8 Gg yr −1 in MAIOLICA), while other emission categories are similar. However,the remaining emissions are also more closely following the distribution of population density when compared with the MAIOLICA inventory, which is due to less detailed geographical information in the EDGARv4.2 inventory (Hiller et al., 2014a). Differences between the TNO inventory (S-T) and the MAIOLICA inventory are more subtle and amount to only 5 Gg yr −1 for the Swiss total.
In all three inversions (B, S-E and S-T) posterior emissions were very similar both in their distribution (see Figs. S3, S7, S8 in the Supplement) and the national total. The latter only differed by 5 Gg yr −1 for S-T and 10 Gg yr −1 for S-E despite the fact that prior emissions were 45 Gg yr −1 larger in the latter (Table 4). This indicates that the posterior emissions were well constrained by the observations and not solely governed by the prior emissions for which relatively small uncertainties were assigned. The strong posterior emission increase in north-eastern Switzerland was also prominent in S-E. The posterior to prior differences for S-E showed a strong emission reduction in the larger urban areas (mainly Basel and Zurich, but also Lucerne, Bern and Geneva), suggesting that the strong attribution of emissions to urban centres in the EDGAR inventory is unrealistic (Fig. 9a). In contrast to the base inversion, uncertainty reductions in the S-E case were also large for the urban areas (Fig. 9b), lending credibility to the associated emission reductions.

Influence of uncertainty covariance treatment
The inversion results using the model-observation uncertainty as estimated by the method of Stohl et al. (2009) (S-S) were smaller than in the base inversion in the low release case but differed only slightly in the high release case (see Table 4). In S-S an almost constant value (see Sect. 2.4) was given to the model-observation uncertainty of each site, while in the base inversion uncertainties tended to be larger for large above-baseline mole fractions. However, model uncertainties were mostly smaller for the base inversion except for 10 to 20 % of the observations in the "low" and less than 10 % in the "high" release case. Despite these differences in the applied model uncertainty, the distribution of posterior fluxes was similar to that of the base inversion, with two exceptions: emission reductions were more pronounced in the area west of BEO and east of LHW in the S-S case and additional reduction occurred around the BEO site itself (see Fig. S9 in the Supplement). The distinct posterior increase in north-eastern Switzerland was also present in S-S.
In comparison with the base inversion, all parameters describing the uncertainty covariance matrices showed increased values when they were estimated by the maximum likelihood method (Table 3). The uncertainty of the baseline, as described by parameter f b , in particular was strongly increased for all sites, but the model uncertainties were also generally larger (parameters σ min and σ srr ). In addition, the ML method yielded an increased uncertainty of the prior emissions, resulting in a total uncertainty for Switzerland of about 30 %, indicating that the bottom-up estimate of 16 % may be too optimistic. The spatial correlation length of the prior emissions remained very close to the L = 50 km used in the base inversion. The resulting posterior emissions were distributed similarly as in the base inversion. However, emission reductions were more pronounced (see Fig. S10 in the Supplement). As for the S-S sensitivity, emission reductions were also estimated for the region between BEO and LHW and only a small local increase around the BEO site remained. The total posterior emissions for Switzerland were only 158±13 and 169±13 Gg yr −1 for the low and high particle release case, respectively. Due to the larger baseline uncertainty as estimated by the ML optimisation, adjustments of the posterior baseline were larger than in the base inversion. As a result, baseline mole fractions were raised for the sites BEO and LHW during periods of increased CH 4 observations, hence reducing the need for increased emissions at these times and lowering the overall posterior emissions. The increased prior and model uncertainties resulted in relatively large posterior uncertainties as compared with the base inversion. The overall posterior model performance was similar to that of the base inversion. However, a larger part of the simulated variability was attributed to variations in baseline signal.

Influence of observation selection
For almost all sensitivity inversions with different subsets of observational data (S-O1 to S-O5 in Table 2) the emission reduction west of BEO could be confirmed (see Figs. S11, S12, S13, S14, S15 in the Supplement). In contrast, the reduction east of LHW was only evident in those runs that also used the observations from LHW. Similarly, the increase in north-eastern Switzerland was more pronounced if the observations from BEO were used. Relatively large emission changes were obtained at mid-range (100 to 500 km) from the sites on the Swiss Plateau when the more remote sites SSL and JFJ were not used in the inversion (S-O1 to S-O3). The larger emission changes in S-O1 to S-O3 were likely the result of attribution errors. The BEO and LHW sites were only sensitive to these more distant areas when they were also sensitive to closer emission sources. Hence, the inversion assigned increased emissions to these distant areas located behind the real emission sources. Using observations from additional sites with a different sensitivity pattern can solve this problem as it did in our base inversion, where the elevated sites JFJ and SSL with distinctly different sensitivity patterns were included.
Swiss CH 4 emissions for this set of sensitivity inversions were larger than in the base inversion (Table 4). Largest emissions (214.3 ± 11 Gg yr −1 in the low release case) were obtained when only the site LHW was used (S-O2), resulting in large emission increases in western Switzerland, whereas posterior emissions remained similar to the base inversion close to the BEO and LHW sites. This pattern is most likely due to the problem of shadowing effects.
S-O5, the inversion using all six sites, resulted in comparatively large total emissions for Switzerland as well (208.8 ± 6 Gg yr −1 in the low release case). Emissions were largely increased around the site GIM and further west as a result of the large mole fractions observed at GIM. As discussed earlier, it seems likely that large local emissions around GIM could not properly be accounted for by the inversion system and were spread out over a larger area, resulting in overall larger national emissions.
It is interesting to note that including the additional observations from GIM and FRU only slightly reduced the overall uncertainty of the national emission estimate in comparison to the base inversion (from 7.0 to 6.0 Gg yr −1 for the low release case). In contrast, using the two sites LHW and BEO in combination instead of either one of them individually reduced the uncertainty from about 11 to 7.9 Gg yr −1 . Hence, the additional gain in terms of uncertainty reduction was relatively small when adding the sites GIM and FRU, which would have been expected from their more localised sensitivity as compared to the other sites.
Of the sensitivity inversions with differing observation data the results of the case using only observations from BEO (S-O1) was closest to those of the base inversion, both in terms of total emissions and of geographic distribution. This supports the expectation that a tall tower site should be best suited for inverse modelling (as can also be seen by the dominating role of BEO in the uncertainty reduction; Fig. 5). However, the estimation of other Swiss GHG fluxes using observations from this site alone will strongly depend on our ability to correctly assign baseline values and the question of whether shadowing effects can be neglected.

Influence of baseline treatment
As mentioned above, the treatment of baseline mole fractions is critical in order to avoid attribution errors in the emission field. When varying the prior baseline uncertainty in our base inversion, considerable changes in posterior emissions indicated this sensitivity. Doubling (halving) the prior baseline uncertainty results in −19 Gg yr −1 (+31 Gg yr −1 ) total Swiss emissions as compared to the base inversion (low particle release height). In both cases the obtained posterior baselines did not seem very reasonable (too smooth, too closely following the observed short-term variability), so that these cases can be seen as the extreme range of the baseline influence. Nevertheless, by exploring different baseline treatments, the sensitivity to baseline assumptions was further documented. Comparing the inversion results of the two inversions with alternative baseline treatment (S-B1 and S-B2; see Sect. 2.5 for details) with the base inversion did not reveal any large differences in terms of geographical distribution (see Figs. S16 and S17 in the Supplement). In the case of S-B2 the reductions in the western part of Switzerland were confined to the area between GIM and BEO, and the reductions north of BEO (as seen in the base inversion) were also turned into increases. S-B2 in particular yielded enhanced model performance that was mainly due to a more detailed description of the temporal variability of the baseline (Table 4). Total Swiss emissions for S-B1 remained very similar to the base inversion but were considerably larger for S-B2 (195.1 ± 6.9 and 223.6 ± 6.9 Gg yr −1 for low and high particle release height, respectively). In S-B2, where a coarse three-dimensional grid of baseline mole fractions was optimised, their posterior values were largest for the eastern and low grid cells and during the previously highlighted period in March 2013 and again in the winter 2013/14. Furthermore, vertical gradients were smaller during the summer months than during the winter (see Fig. S18 in the Supplement). This general distribution is in line with our expectations (higher mole fractions towards surface and more continental areas) and lends credibility to this kind of baseline estimation. One further advantage of analysing a common baseline grid for all sites is its possible use for the validation sites as well. Indeed, a larger improvement in posterior performance at the sites FRU and GIM can be seen for S-B2 than in any other sensitivity inversion in which the sites were used for validation only.

National total emissions
The main result of the present study is summarised in Fig. 10 in terms of a histogram of total Swiss CH 4 emissions for the investigation period March 2013 to February 2014 taken from all sensitivity inversions. The estimates from the individual sensitivity inversions almost follow a normal distribution. A clear average difference between sensitivity runs using the high and low particle release heights of 20 Gg yr −1 is apparent. This difference is larger than the one between the results taken from the two employed transport models FLEXPART-ECMWF and FLEXPART-COSMO (12 Gg yr −1 , 5 %). The latter supports the large degree of consistency between the two transport models and the underlying meteorology. In an inverse estimate of HFC-134a emissions from the continental USA, Hu et al. (2015) had observed a somewhat larger emission difference (20 %) when using source sensitivities obtained from two different dispersion models (HYSPLIT-NAM12, STILT-WRF) with similar horizontal resolution.
To derive an average national emission over all sensitivity inversions, we assigned the same weight to each sensitivity run and calculated a straightforward mean over all sensitivity inversions. This is a rather pragmatic approach, since some sensitivity inversions using, for example, only one site cannot be expected to be equally good as the base inversion with four sites. However, we are lacking a more Atmos. Chem. Phys., 16, 3683-3710, 2016 www.atmos-chem-phys.net/16/3683/2016/  (Table 5). Please note that Swiss emissions are reported annually for the reporting period 1990 to 2 years before the submission date. Methodological updates from one year to another usually influence the whole reporting period (FOEN, 2014(FOEN, , 2015. We refer here to the emissions reported for the year 2012, since estimates for this year are available from the 2014 and 2015 reporting. According to the 2015 reporting, emission changes from 2012 to 2013 were small (−0.14 Gg yr −1 ) (FOEN, 2015). The estimate of CH 4 emissions submitted to the UNFCCC in 2014 for the year 2012 was 176 ± 28 Gg yr −1 . Our prior was based on these estimates plus a small contribution from natural emissions of 3 Gg yr −1 . Our posterior estimates were slightly but not significantly larger. This is true for the mean obtained from the two base inversions (187 ± 10 Gg yr −1 ) as well as for the mean over all sensitivity inversions (196 ± 18 Gg yr −1 ). The latter value should be seen as our best estimate of the Swiss CH 4 emissions. It is closer to the bottom-up estimate of 206 ± 33 Gg yr −1 reported in 2015 (FOEN, 2015) than to the one reported previously. The differences in the reporting are due to updated emission factors and methodologies in the national inventory. Our inversion results support these updates. Our overall uncertainty estimate is based on the standard deviation of all sensitivity inversions and is considerably larger than any of the uncertainty estimates of the individual inversions (Table 4). Despite this fact, the overall posterior uncertainty remains smaller than the prior uncertainty. One possible reason for the relatively small posterior uncertainty of individual inversions may be seen in the small prior uncertainty of 16 % for the national total. Similarly, when applying the ML method, considerably larger prior uncertainties in the range of 30 % were suggested (see Sect. 3.6). However, pos-terior uncertainties of the ML sensitivity runs (S-ML in Table 4) were still considerably smaller than our overall uncertainty. Another reason for small posterior uncertainties could be an underestimated model-observation uncertainty, placing too much confidence in the simulation of the observations and in turn reducing posterior uncertainties. However, model-observation uncertainties were optimised in the same step as prior uncertainties with the ML method and were not estimated to be considerably different from the base set-up (see Table 3). These considerations lead to the conclusion that the enhanced posterior uncertainty over all sensitivity runs needs to be seen as the contribution of systematic uncertainties that are introduced by the specific set-up of the inversion system and cannot be fully covered by the analytical estimate of the Bayesian analysis, a result that has also been obtained in previous inversion studies (e.g. Bergamaschi et al., 2010Bergamaschi et al., , 2015Ganesan et al., 2014).

Spatio-temporal emission patterns
Considerable emission differences were observed between the seasons, with wintertime emissions being 13 to 18 % lower than the annual average. Since the largest wintertime reduction was deduced for areas with large cattle density, it seems very likely that the estimated reductions are connected with the agricultural sector. This observation was also true for the north-eastern part of Switzerland, where, although annual emissions were increased, these increases were largest in spring and summer (see Fig. 6). When compared to the prior emissions from the agricultural sector only (150 Gg yr −1 ; FOEN, 2014), the estimated seasonal posterior variability would be around 22 %. The latter is well in line with Gao et al. (2011), who estimated the seasonal variability of CH 4 emissions from a dairy cow farmstead in northern China. A major contribution to the annual variability may stem from CH 4 emissions from manure handling and storage, which strongly depends on temperature. Zeitz et al. (2012) speculated that Swiss CH 4 emissions from manure handling should be lower than estimated by FOEN (2014), since their observed emission factors were significantly smaller than those suggested by IPCC and used by FOEN (2014). However, their results were based on laboratory experiments that still need to be validated in the field. Furthermore, Zeitz et al. (2012) suggest that emissions from manure handling should be significantly reduced or even cease during winter, considering the average temperatures in Switzerland. Accounting for the temperature of the manure storage, which may be well above the ambient temperature, in the emission calculation, a 50 % wintertime reduction was estimated in the bottomup inventory (FOEN, 2015). Furthermore, seasonal variability in emissions from ruminants may be induced by seasonal variability in productivity, especially of dairy cows. In Switzerland it is common practice to time the calving date in the spring so that the cows reach their largest productivity at the point of largest feed availability (spring/summer). Since productivity and CH 4 emissions are roughly proportional, direct ruminant emissions should also follow a seasonal cycle with a minimum in the winter months (FOEN, 2015). The temporal variability in our inversion results largely agrees with these considerations and, hence, fits well with our understanding of the main agricultural emission processes in Switzerland. Furthermore, we had seen that mean annual posterior emissions were about 10 to 20 % lower in agricultural areas in our base inversion (B low). Taking the mean over all sensitivity inversions this reduction is around 5 to 15 % as compared to the prior, which was based on the 2014 reporting. Considering the larger emissions from agriculture in the 2015 reporting, our mean posterior emissions in agricultural areas suggest that the revised bottom-up inventory (FOEN, 2015) overestimates agricultural emissions by 10 to 20 %. From the inferred seasonality we conclude that this is most likely because emissions from manure handling are overestimated. Our findings are in line with recent inversion results (covering the period 2009 to 2011) for Europe that indicate emissions similar to or lower than in EDGAR (Alexe et al., 2015;Turner et al., 2015;Ganesan et al., 2015), whereas for the USA a number of studies suggest a significant underestimation of ruminant emissions in the EDGAR-v4.2 and US EPA inventories (Miller et al., 2013;Wecht et al., 2014;Turner et al., 2015).
Our posterior results depend little on the prior emission distribution (B vs. S-E and S-T) and corrected the large emissions in urban areas given by the EDGARv4.2 inventory downwards. Hence, we conclude that the emissions from natural gas distribution and use in the SGHGI/MAIOLICA inventory is more realistic than in EDGARv4.2. The SGHGI emissions from natural gas distribution of 8 Gg yr −1 correspond to < 0.4 % of the Swiss natural gas consumption (FOEN, 2015). This is in contrast to recent studies from the USA, where a large underestimation of fugitive emissions was established in the inventories for different metropolitan areas (Wennberg et al., 2012;McKain et al., 2015) and fractional loss rates between 2.5 and 6 % were established. How-ever, these results may not be representative of the USA as a whole. According to the SGHGI, fugitive emissions were reduced in Switzerland by 36 % since 1990 mainly due to a gradual replacement of cast-iron pipes by polyethylene pipes (FOEN, 2015). Our results support the reductions documented in the SGHGI and, thus, the success of this emission reduction measure. This also highlights that large reduction potentials can be expected for other countries as well when modernisation of the infrastructure is promoted. CH 4 emissions from composting and anaerobic digestion (IPCC 5B), mainly in the conversion of biogenic waste to biogas in small-scale facilities, were amended from 5 to 16 Gg yr −1 from the 2014 to the 2015 reporting (Table 5). In our prior inventory, these emissions were not explicitly localised (Hiller et al., 2014a). Since our prior was based on the earlier 5 Gg yr −1 estimate, an increase in regions with intensive biogas production should have been detectable. However, the biogas and composting plants are approximately evenly distributed across the Swiss Plateau in areas of dominating agricultural use. Hence, it is impossible to finally attribute any of the observed posterior emission differences to this emission process. Similarly, and as already indicated by Hiller et al. (2014a), emissions from waste water treatment were probably underestimated in previous FOEN estimates. In the most recent reporting from 2015, these emissions were 6.77 Gg yr −1 , which is an increase by a factor of 15 compared to previous reports. The spatial distribution of CH 4 emissions from waste water treatments should mainly follow the population density. Although our inversion results do not support increased emissions in densely populated areas, the relatively small emission revision (compared to the total emissions) may be very difficult to detect.

Unidentified source in north-eastern Switzerland
The largest emission changes that were localised by the inversion and were present in almost all sensitivity inversions were those in the north-eastern part of Switzerland in the cantons of Saint Gallen and Appenzell. These areas are also dominated by agriculture and, hence, the estimated increase contradicts the reductions in other agricultural regions. The area contributed about 16.3 % to the national emissions in our prior inventory. This contribution was increased to 22.5 % in the posterior estimate of the base inversion, an increase of 6.2 Gg yr −1 . One possible reason for the increase could be systematic biases in the transport simulations and in the balance between baseline and emission adjustment. One argument against this possibility is that the increase was also observed when using FLEXPART-ECMWF instead of FLEXPART-COSMO (see Sect. 3.4) and it seems unlikely that the same systematic bias would be inherent to both meteorological inputs. Furthermore, FLEXPART-ECMWF calculations were not as restricted by the limited model domain as FLEXPART-COSMO simulations (see discussion above). However, all inversions using any one of the three different methods to adjust the baseline yielded similar increases in north-eastern Switzerland. Another possible reason for the increased emissions could be an emission source close to the observational sites that could not be described correctly by the limited model resolution and whose contributions were wrongly assigned to the respective area. Again, this seems unlikely, since the increase was present in sensitivity inversions using either one of the sites on the Swiss Plateau (S-O1, S-O2). In conclusion, and although we cannot completely rule out inversion artefacts, it seems likely that the estimated increase represents a real emission source that is not present or underestimated in our prior inventory.
This raises the question which processes may be responsible for the detected emissions. A possible candidate is an erroneous spatial distribution of ruminant emissions within Switzerland. However, in Switzerland the number of ruminants by animal species needs to be reported at the farm level and this information, aggregated to communities, was used for distributing agricultural emissions in the prior inventory (Hiller et al., 2014a). Different cow breeds may have different CH 4 emissions factors. The dominant breeds in Switzerland are Brown Swiss and Holstein, for which similar emissions factors have been reported (Felber et al., 2015, and references therein). Different manure management methods (e.g. Owen and Silver, 2015) and diet types (e.g. Klevenhusen et al., 2011) may also lead to variations in per head emission factors. To our knowledge, detailed investigations of emission factors under real Swiss farming conditions and their spatial variability are currently not available. The large emission factors given by Owen and Silver (2015) for manure storage in anaerobic lagoons do not apply to Switzerland, since this storage type does not exist here (FOEN, 2015). Therefore, effects of spatial variability of herd composition and management cannot be excluded, although it seems unlikely that these could fully explain the differences estimated by the inversion. A typical farming practice in Switzerland is moving grazing cows towards elevated Alpine pastures during the summer months. This was considered in the prior by redistributing 4 % of the national ruminant emissions to Alpine pastures (Hiller et al., 2014a). Although there are extended areas of Alpine pastures present in north-eastern Switzerland, these are not more prominent than in other Alpine areas where we did not observe increased posterior emissions. Furthermore, increased emissions in north-eastern Switzerland were also observed by the inversion for the winter and spring periods, when the Alpine pastures are unoccupied. Possible additional sources of anthropogenic CH 4 in north-eastern Switzerland may stem from biological treatment of waste in composting and anaerobic digestion facilities, solid waste disposal, waste water treatment, and natural gas distribution. Currently we have no indication that any of these processes show a specifically high density in the given area.
This leaves the possibility of an underestimated or unaccounted natural CH 4 source. The net natural emissions accounted for by Hiller et al. (2014a) were very small (≈ 3 Gg yr −1 ) compared to their anthropogenic counterpart (≈ 180 Gg yr −1 ). Emissions from wetlands and lakes are thought to be the largest natural source in Switzerland (4.6 Gg yr −1 ). Although there are a number of small wetlands and lakes situated in the canton of Appenzell, their fractional coverage and total area is not larger than in other areas (for example, Entlebuch south-west of BEO). Furthermore, we have no indication that climate variability within the domain could have impacted the drivers of wetland emissions (precipitation, temperature) in an inhomogeneous way to explain large regional differences. Aerobic soils (forest and agricultural) are generally thought to be CH 4 sinks and were estimated to contribute a negative CH 4 flux of −4.3 to −2.8 Gg yr −1 (Hiller et al., 2014a). Nevertheless, under anaerobic conditions, methanogenesis may dominate in deep organic soils, which can be found in wetland or peatland areas. When former peatlands are re-wetted (due to either accidental flooding or renaturation) they have been shown to become a significant CH 4 source depending on water table depth, the abundance of vascular vegetation transporting CH 4 from the root space to the atmosphere and the amount of available carbon in plant litter (Couwenberg and Hooijer, 2013). Organic soils were not considered as CH 4 sources in our prior. One large area of deep organic soils in Switzerland is located in the Alpine Rhine Valley (Wüst-Galley et al., 2015), only slightly east of the area of our largest posterior increase. However, this possible source remains uncertain since the area in question is used for agriculture and should be well drained throughout most of the year. The only other large area of converted peatland in Switzerland is the Seeland region around the GIM site, possibly contributing to the large CH 4 concentrations observed there (see Sects. 2.1 and 3.1). Admittedly, river re-routing and drainage systems should keep the water table low in this area. In conclusion, we cannot explicitly determine which process may have caused the increased posterior emissions in north-eastern Switzerland. Additional studies using data from more recent observations and/or additional sites will be needed to clarify these open questions.

Conclusions
We applied a high-resolution atmospheric transport model to simulate the CH 4 observations of the CarboCount-CH network and used inversion techniques to estimate total Swiss CH 4 emissions and their geographical distribution for the period March 2013 to February 2014. A series of sensitivity inversions (varying the treatment of temporal variability of the emissions, the transport model, the inversion algorithm, the prior emissions, the uncertainty covariance matrices, the selected observations, and the baseline treatment) confirm the robustness and independent character of our results.
Our best estimate of total Swiss CH 4 emissions (196 ± 18 Gg yr −1 ) largely supports the bottom-up estimate as reported by the Swiss Federal Office for the Environment (206±33 Gg yr −1 , reported to UNFCCC in 2015 for the year 2012). The overall uncertainty as obtained from all sensitivity inversions (10 %) was larger than the analytical uncertainty of any individual sensitivity inversion but still considerably reduced the uncertainty associated with the bottomup estimate (16 %). Our results support the effectiveness of a well informed bottom-up inventory, calibrated to local to regional emission processes. A similar conclusion was drawn by Zavala-Araiza et al. (2015), who designed an updated bottom-up inventory for a gas production area in Texas, using locally observed emission factors. Although their bottomup estimates were at least 2 times larger than conventional bottom-up estimates, they largely agreed with top-down estimates in the same area.
The inversion results indicate a redistribution of CH 4 as compared to the spatially explicit bottom-up inventory. Large wintertime posterior emission reductions in regions dominated by agricultural emissions suggest that these are overestimated on an annual basis by 10 to 20 % in the most recent bottom-up inventory and that manure handling may be the responsible process. Our findings agree with recent inverse modelling of European-scale CH 4 emissions that suggest emission rates similar to or lower than in the EDGAR inventory. This is in contrast to recent studies from the USA that suggested considerably larger emissions from ruminants than reported in bottom-up inventories (Miller et al., 2013;Wecht et al., 2014;Turner et al., 2015). An area of increased posterior emissions in north-eastern Switzerland could not be assigned to a single most likely source process. Emissions from previously drained peatlands may be responsible for this observation. However, this suggestion needs further investigation.
Bottom-up estimates indicate that Swiss national emissions decreased by about 20 % since the 1990s, mainly due to a reduction in livestock numbers and improvements in the gas distribution network (FOEN, 2015). The latter can be supported by our study, which did not assign large emissions to densely populated areas and strongly corrected such emissions when present in the prior estimate (EDGAR inventory). This again is in contrast to recent studies from the USA that showed, at least for two metropolitan areas, larger than expected emissions from natural gas distribution (Wennberg et al., 2012;McKain et al., 2015) and provides evidence for the efficiency of comparatively simple modernisation efforts to reach greenhouse gas reduction targets.
Our results also demonstrate the feasibility of using highresolution transport models and continuous atmospheric observations to deduce regional-scale surface fluxes with a horizontal resolution required to retrace the underlying emission/uptake processes. This conclusion is especially encouraging when considering the complex topography of the study area and for future inverse modelling studies of the two other trace gases observed within CarboCount-CH: carbon dioxide and carbon monoxide. Inversion results using data from two sites on the Swiss Plateau and two elevated sites (base inversion) were consistent with a sensitivity inversion that used only the tall tower observations of Beromünster (212 m a.g.l.). The latter emphasises the special value of tall tower observations in deriving regional-scale fluxes. Sustaining a dense observational network like CarboCount-CH will allow for independent monitoring of future climate agreements.
The Supplement related to this article is available online at doi:10.5194/acp-16-3683-2016-supplement.