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

Atmospheric methane (CH

In many developed countries, natural CH

In Switzerland, the Federal Office for the Environment (FOEN) collects
activity data and emission factors in the Swiss Greenhouse Gas Inventory
(SGHGI)

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

Overview of the location of the observational sites used in the study, including particle release heights as used in FLEXPART simulations. See text for details on release height selection.

Here, we validate the bottom-up estimate of Swiss CH

The CH

Total source sensitivity for the period March 2013 to February 2014 and the 4 sites used in the base inversion (crosses and labels in subplot – BEO: Beromünster; LHW: Lägern Hochwacht; JFJ: Jungfraujoch; SSL: Schauinsland). Source sensitivities are displayed on the reduced resolution grid that is used in the inversion. The units of the source sensitivity are given as residence times divided by atmospheric density and surface area. The locations of the two validation sites (FRU: Früebüel; GIM: Gimmiz) are given in the subplot as well.

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

Lägern Hochwacht (LHW) is a mountaintop site on a very steep, west–east-extending crest approximately 15

Früebüel (FRU) is another mountain site and located at
982

At the Gimmiz site (GIM, 443

Schauinsland (SSL, 1205

The high-altitude observatory Jungfraujoch (JFJ, 3580

At all sites, CH

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

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

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) FLEXPART

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

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

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. 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

From both models, output was generated on a regular longitude–latitude grid
with a horizontal resolution of 0.16

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,

In our case, the state vector contained additional parameters characterising
the baseline mole fractions

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.

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

In Bayesian atmospheric inversion, prior knowledge of the state vector,

The total emissions and their uncertainty from a certain region or country
can then be calculated as

In our base inversion, we used the Swiss MAIOLICA inventory

This section details the construction of the uncertainty covariance matrices

Both uncertainty covariance matrices are symmetric block matrices. In the
case of

All diagonal elements of

In the case of temporally variable emissions (see Sect.

The block matrix

Set-up of the base (B) and sensitivity inversions (S-X).

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 non-systematic 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

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

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

An additional sensitivity test, replacing the Bayesian method by an extended
Kalman filter (extKF) inversion as described in

Overview of parameters used for the construction of the uncertainty
covariance matrices: contributions to model–observation uncertainty

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

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

Another sensitivity run varied the design of the model–observation
uncertainty covariance by estimating the diagonal elements of the matrix from
the prior RMSE at each site

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

Another series of sensitivity inversions was set up using different parts of
the observational data (runs S-01 to S-05, Table

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 attribution 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 (

Observed (black) and simulated (prior: red; posterior: blue) CH

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 inversions 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.

Average source sensitivities as calculated with FLEXPART-COSMO on the reduced
grid are shown in Fig.

In Switzerland prior emissions amounted to 178

Simulated CH

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.

The quality of the simulated time series is summarised in
Fig.

Model performance parameters for simulated time series at all sites
for the base inversion with low particle release heights (B low): prior
(shaded) and posterior (filled).

Overview of results of sensitivity inversions.

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

As an additional validation parameter the RMSE and
its reduction from prior to posterior simulations are shown in
Fig.

We used observations from sites in more complex terrain and closer to
emission sources than used in other regional-scale inversion studies of
CH

The posterior CH

In this base inversion Swiss total emissions were estimated at

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.

Uncertainty reduction between prior and posterior fluxes given in

Absolute difference between posterior minus prior emission fluxes
for seasonal inversion.

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.

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

For the low model release height, total Swiss emission rates were smallest
during winter (

The extended Kalman filter inversion using low particle release heights (S-K
low) yielded similar annual mean posterior emissions as the base inversion
(Figs.

Absolute difference between posterior minus prior emission fluxes as obtained from extended Kalman filter inversion with low particle releases.

Total Swiss emissions were estimated at

In the sensitivity case S-EC the source sensitivities were derived from
FLEXPART-ECMWF instead of FLEXPART-COSMO (see Sect.

Although FLEXPART-ECMWF's performance at the sites was of similar quality to the base inversion, the uncertainty reductions of the posterior emissions
(Fig.

Absolute difference between posterior minus prior emission fluxes when using EDGAR instead of MAIOLICA prior fluxes.

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

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

The inversion results using the model–observation uncertainty as estimated by
the method of

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

For almost all sensitivity inversions with different subsets of observational
data (S-O1 to S-O5 in Table

Swiss CH

S-O5, the inversion using all six sites, resulted in comparatively large
total emissions for Switzerland as well (

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

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.

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

The main result of the present study is summarised in
Fig.

Histogram of total Swiss CH

Swiss CH

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 objective measure that would
allow us to assign quantitative weights to the different runs. Our estimates
can be compared to the bottom-up estimates that the Swiss Federal Office for
the Environment reported to the UNFCCC in the years 2014 and 2015
(Table

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

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.

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

CH

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

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

This leaves the possibility of an underestimated or unaccounted natural
CH

We applied a high-resolution atmospheric transport model to simulate the
CH

Our best estimate of total Swiss CH

The inversion results indicate a redistribution of CH

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

Our results also demonstrate the feasibility of using high-resolution
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

This study was funded by the Swiss Federal Office for the Environment (FOEN)
and by the Swiss National Science Foundation (SNSF) as part of the
“CarboCount-CH” Sinergia Project (grant number: CRSII2_136273). We thank
the International Foundation High Altitude Research Stations Jungfraujoch and
Gornergrat (HFSJG) for the opportunity to perform experiments on the
Jungfraujoch, MeteoSwiss for providing meteorological observations at the
site Lägern Hochwacht and COSMO model analysis, and Swiss FLUXNET for the
meteorological observations at Früebüel. Measurements at Jungfraujoch
were partly performed as part of the Swiss contribution to ICOS
(