Intensive coal mining activities in the Upper Silesian
Coal Basin (USCB) in southern Poland are resulting in large amounts of
methane (CH4) emissions. Annual CH4 emissions reached 448 kt
according to the European Pollutant Release and Transfer Register (E-PRTR,
2017). As a CH4 emission hotspot in Europe, it is of importance to investigate its emission sources and make accurate emission estimates.
In this study, we use satellite-based total column-averaged dry-air mole
fraction of CH4 (XCH4) from the TROPOspheric Monitoring Instrument
(TROPOMI) and tropospheric XCH4 (TXCH4) from the Infrared
Atmospheric Sounding Interferometer (IASI). In addition, the high-resolution
model forecasts, XCH4 and TXCH4, from the Copernicus Atmosphere
Monitoring Service (CAMS) are used to estimate the CH4 emission rate
averaged over 3 years (November 2017–December 2020) in the USCB
region (49.3–50.8∘ N and 18–20∘ E). The wind-assigned anomaly method is first validated using the
CAMS forecast data (XCH4 and TXCH4), showing a good
agreement with the CAMS GLOBal ANThropogenic emission (CAMS-GLOB-ANT) inventory. It indicates that the
wind-assigned method works well. This wind-assigned method is further
applied to the TROPOMI XCH4 and TROPOMI + IASI TXCH4 by using the
Carbon dioxide and Methane (CoMet) inventory derived for the year 2018. The
calculated averaged total CH4 emissions over the USCB region is about
496 kt yr-1 (5.9×1026 molec. s-1) for TROPOMI XCH4 and 437 kt yr-1 (5.2×1026 molec. s-1) for TROPOMI + IASI TXCH4. These values are very close to the
ones given in the E-PRTR inventory (448 kt yr-1) and the ones in the CoMet
inventory (555 kt yr-1), and are thus in agreement with these inventories.
The similar estimates of XCH4 and TXCH4 also imply that for a
strong source, the dynamically induced variations of the CH4 mixing
ratio in the upper troposphere and lower stratosphere region are of
secondary importance. Uncertainties from different error sources (background
removal and noise in the data, vertical wind shear, wind field segmentation,
and angle of the emission cone) are approximately 14.8 % for TROPOMI
XCH4 and 11.4 % for TROPOMI + IASI TXCH4. These results suggest
that our wind-assigned method is quite robust and might also serve as a
simple method to estimate CH4 or CO2 emissions for other regions.
Introduction
Atmospheric methane (CH4) is the second most important anthropogenic
greenhouse gas (GHG) with a larger global warming potential than carbon
dioxide (CO2) (IPCC, 2014). The globally averaged amount of atmospheric
CH4 has increased by 260 % to 1877±2 ppb from the
preindustrial era until 2019 (World Meteorological Organization, 2020).
Sources of CH4 induced by anthropogenic activities include fossil fuel
production and use (e.g., coal mining, gas/oil extraction), waste disposal,
and agriculture, which in total accounts for about 60 % of the total
CH4 emissions (Saunois et al., 2020). Although most sources and sinks
of CH4 have been characterized, their spatial–temporal variations and
relative contributions to the atmospheric CH4 level are still highly
uncertain (Kirschke et al., 2013; Saunois et al., 2020).
Approximately 33 % of the CH4 emissions from coal mining (42 000 kt yr-1) are estimated to come from the total fossil-fuel-related emissions
during 2008–2017 (Saunois et al., 2020). The CH4 is released primarily to
the atmosphere via ventilation shafts located at the surface during the
production and processing of the coal (Saunois et al., 2020; Andersen et al.,
2021). The largest contribution of CH4 emissions related with the coal
mining activities in Europe is from southern Poland – the Upper Silesian
Coal Basin (USCB) (Luther et al., 2019; Krautwurst et al., 2021). The USCB
is in the Silesian Upland, which is a plateau between 200 and 300 m above sea level (m a.s.l.) with a predominant south-west wind. The USCB within Poland covers
an area of over 5800 km2, and to its south is the Tatra Mountains ridge
with elevations larger than 2000 m a.s.l. The European Pollutant Release and
Transfer Register (E-PRTR, 2017; https://prtr.eea.europa.eu/, last access:
25 October 2021) reports that the total CH4 emissions from the USCB
region amount to 448 kt yr-1. Most of these emissions are from mining
activities and heavy industry (Kostinek et al., 2021), which makes this
region a hot spot for CH4 emissions in Europe.
To investigate the CH4 emissions from this hot spot, the Carbon Dioxide
and Methane (CoMet) campaign was performed, covering roughly 3 weeks from
May to June 2018. A variety of state-of-the-art instruments, including in situ
and remote-sensing instruments on the ground and aboard five research
aircraft, were deployed in order to provide independent observations of GHG
emissions on local to regional scale and provide data for satellite
validation (more details can be found in Luther et al., 2019; Fiehn et al.,
2020; Gałkowski et al., 2021b; Kostinek et al., 2021; Krautwurst et al.,
2021; Wolff et al., 2021). For example, Gałkowski et al. (2021b) present
results of in situ GHG measurements obtained over nine research flights of
the German research aircraft, HALO (High Altitude and LOng Range Research
Aircraft), acting as the airborne flagship of the CoMet campaign, together
with simultaneous flask measurements for the isotopic composition of CH4.
A new lidar, CHARM-F (CO2 and CH4 Atmospheric Remote Monitoring
Flugzeug), was also on board HALO and its measurements were investigated to
determine CO2 emission rates from the power plant (Wolff et al., 2021).
Many studies present similar CH4 emission estimates for the region
based on different instruments and methods. Luther et al. (2019) estimated
CH4 emissions ranging from 6±1 kt yr-1 for a single shaft up
to 109±33 kt yr-1 for a subregion of USCB covering several
shafts, by using several portable Fourier transform infrared (FTIR)
spectrometers (Bruker EM27/SUN). Active AirCore system aboard an unmanned
aerial vehicle (UAV) was used to measure CH4 downwind of a single
ventilation shaft, and emission rates ranging from 0.5 to 14.5 kt yr-1 based
on a mass balance approach and ranging from 1.1 to 9.0 kt yr-1 based on an
inverse Gaussian method were estimated (Andersen et al., 2021). Fiehn et al. (2020) analyzed aircraft- and ground-based in situ observations and reported
an emission estimate of 436±115 kt yr-1 and 477±101 kt yr-1
from two selected flights. An advanced model approach was introduced by
Kostinek et al. (2021) to investigate two research flights in the morning
and afternoon, resulting in estimated CH4 emissions of 451±77 kt yr-1 and 423±79 kt yr-1, respectively. Another emission estimate
based on the observations from the nadir-looking passive remote sensing
Methane Airborne MAPper (MAMAP) instrument accounted for 8.8 to 78.8 kt yr-1 for sub-clusters of ventilation shafts (Krautwurst et al., 2021).
A recent study (Luther et al., 2022) displays a larger emission rate of 414–790 kt yr-1 based on a network of four portable Fourier-transform spectrometer (FTS) instruments (EM27/SUN) during the CoMet campaign.
Launched in October 2017, the TROPOspheric Monitoring Instrument (TROPOMI)
on board the Sentinel-5 Precursor satellite provides an unprecedented high
spatial resolution (5.5×7 km2) of the CH4 total
column-averaged dry-air mole fraction (XCH4) (Veefkind et al., 2012;
Lorente et al., 2021a). An a posteriori method has been developed by
Schneider et al. (2022a) to obtain tropospheric XCH4 (TXCH4) by
combining observations from TROPOMI and the Infrared Atmospheric Sounding
Interferometer (IASI). This synergetic product is not influenced by the
changing tropopause height, and it offers improved sensitivity to the
tropospheric variations than the total column XCH4 data from either
sensor. The improved real-time forecast data with high resolution
(0.1∘× 0.1∘∼ 9 km × 9 km) are produced by the Copernicus Atmosphere Monitoring Service (CAMS)
(Agustí-Panareda et al., 2019; Barré et al., 2021). All data sets
provide a large spatial coverage and long-term XCH4/TXCH4
observations, which help to better estimate CH4 emissions in the USCB
region.
In Sect. 2 we present the data sets and methodology used in this study to
derive estimated CH4 emissions. The results and discussions are
presented in Sect. 3. We present a novel wind-assigned method introduced by
Tu et al. (2022), which is firstly verified by the CAMS model forecasts and
then applied to the TROPOMI XCH4 and TROPOMI + IASI TXCH4 data to
estimate the CH4 emissions in the USCB region for the time period from
November 2017 to December 2020, together with an uncertainty analysis.
Finally, the summary and conclusions are given in Sect. 4.
Data sets and method
There are over 50 active ventilation shafts in the USCB region
(49.3–50.8∘ N and 18–20∘ E),
Poland, whose emission rates range between 0.17 and 41.02 kt yr-1
(Gałkowski et al., 2021a) (Fig. 4b). Most of them
are located near Katowice and further west and southwest of Katowice.
The Integrated Forecasting System (IFS,
https://www.ecmwf.int/en/publications/ifs-documentation, last access: 27
October 2021) from the European Centre for Medium-Range Weather Forecasts
(ECMWF) is used in the CAMS atmospheric composition analysis and forecasts
system to simulate 5 d CO2 and CH4 forecasts
(Agustí-Panareda et al., 2019, Barré et al., 2021), as well as
other chemical species and aerosols (Flemming et al., 2015; Morcrette et
al., 2009). This model is also used in the operational Numerical weather
prediction (NWP) system, but with additional modules (Agustí-Panareda
et al., 2019). The forecast data used in this study are the same suit as the
data used in Barré et al. (2021), where the Cycle 45r1 IFS model cycle
was implemented. The CAMS GHGs operational data set includes analysis and
forecast data at medium and high resolution, with 137 model levels from the
surface to 0.01 hPa (Barré et al., 2021). In this study we will focus on
using the high-resolution CH4 forecasts, which have a spatial
resolution of 0.1∘× 0.1∘ and a temporal
resolution of 3 h, starting from 00:00 UTC. Here we use the daily averaged
CAMS forecasts during 09:00–18:00 UTC at each resolution grid point.
The corresponding standard deviation (SD) is considered as the noise/error.
The anthropogenic CH4 emissions used in the global CAMS forecasts are
from the CAMS-GLOB-ANT inventory (Granier et al., 2019; https://permalink.aeris-data.fr/CAMS-GLOB-ANT, last
access: 27 October 2021). The CAMS-GLOB-ANT inventory is based on the
emissions provided by the Emissions Database for Global Atmospheric Research (EDGAR) v4.3.2 inventory for the 2000–2012 time period (Crippa et al., 2018), and linearly extrapolated to 2020 using the
trends from the Community Emissions Data System (CEDA) global inventory for the 2011–2014 time period (Hoesly et al., 2018). The latest version (CAMS-GLOB-ANT v4.2) was released in March
2020, using the same setup as v4.1, except for adding the emissions in 2020.
The anthropogenic sources in the standard v4.2 are divided into 12 sectors
and the agricultural sections are split into three sectors, including
livestock, soils and waste burning (https://eccad3.sedoo.fr/, last access:
27 October 2021). The inventory is provided as a monthly mean with the same
spatial resolution (0.1∘× 0.1∘ ) as the CAMS
forecast data (Granier et al., 2019).
The monthly averages of CAMS-GLOB-ANT for
different sectors in the study area of USCB are presented in
Fig. 1. The emissions from the sectors
“agricultural soils” and “solvents” are zeros. The CH4 emitted from
ships has 19 orders of magnitude, which are much lower than the other
sectors. Thus, these three sectors are not shown here. The sources from
agricultural livestock (1.7×1025±4.0×1025 molec. s-1) amount to only 4 % of
the total emissions in this region. The dominant CH4 sources in this
region are fugitive sources from energy production and distribution (e.g.,
fuel use). With a mean value of 7.9×1026 molec. s-1 and SD of
2.2×1025 molec. s-1, they account for 82 % of the anthropogenic CH4
emissions in the CAMS-GLOB-ANT inventory (9.7×1026 molec. s-1 in total). This
becomes particularly visible in the spatially overlapping distribution
within USCB (see Fig. 2). The seasonal
emission variations of the fugitive sector are minor and can be ignored.
Therefore, we apply the 3-year mean of total emissions at grids with
significant emissions without considering seasonal variations in the simple
cone plume model (see Sect. 2.3). The total emissions amount to 9.7×1026 molec. s-1 over this study area.
Stacked area plot for different sectors of the monthly averaged
CAMS global anthropogenic emissions (>1×1020 molec. s-1) in the USCB region for 2017–2020 (https://permalink.aeris-data.fr/CAMS-GLOB-ANT, last
access: 22 December 2021, Granier et al., 2019).
Spatial distribution of (a) the CAMS global anthropogenic
emissions (CAMS-GLOB-ANT) from all sectors and (b) percentage share of the fugitive
emissions compared to the overall anthropogenic emissions over the USCB
region on a 0.1∘× 0.1∘ latitude/longitude
grid. The fugitives are the dominant CH4 sources.
TROPOMI and IASI data sets
The TROPOMI instrument is a nadir-viewing, imaging spectrometer, which uses
passive remote-sensing techniques to perform measurements of the solar
radiation reflected by and radiated from the Earth in the ultraviolet (UV), the
visible (VIS), the near-infrared (NIR), and the short-wave infrared spectral (SWIR) bands
(Veefkind et al., 2012). The instrument crosses the Equator at about 13:30 LST at each orbit with a repeat cycle of 17 d. It observes a full swath (2600 km) per second with an orbital duration of 100 min. The
algorithm for CH4 column retrieval is called the RemoTeC algorithm and it
has been extensively used to derive CO2 and CH4 retrievals from
the Greenhouse Gases Observing Satellite (GOSAT) and Orbiting Carbon
Observatory-2 (OCO-2; Boesch et al., 2011; Butz et al., 2009, 2011; Hasekamp
and Butz, 2008; Schepers et al., 2012). An updated retrieval algorithm has
been implemented by Lorente et al. (2021a) to obtain a data suit with less
scatter and a higher-resolution surface altitude database. This updated
TROPOMI XCH4 data set has been validated with the Total Carbon Column
Observing Network (TCCON) (-3.4±5.6 ppb) and GOSAT (-10.3±16.8 ppb), showing very good agreements. In this study, the TROPOMI XCH4
during November 2017 and December 2020 within the study area over the USCB
region is investigated. The data provided by Lorente et al. (2021a) include
an additional quality filter parameter (quality value, qa). The TROPOMI
XCH4 with qa=1.0 represents the data under clear-sky and low-cloud
atmospheric conditions and the problematic data points are removed as well.
This quality filter has been applied in this study and about 16 000 data are
derived over the 3-year time period considered in this study.
The IASI instrument is a nadir viewing FTS that
measures the infrared part of the electromagnetic spectrum. The IASI
measurements are performed with a horizontal resolution of 12 km and a full
swath width of about 2200 km on the ground. It is the key payload element of
the polar-orbiting METOP-A -B and -C satellites. These satellites overpass
the Equator at 09:30 LT and 21:30 LT, with
about 14 orbits per day. It provides unprecedented accurate vertical
information of atmospheric temperature and humidity, which helps to improve
NWP (Collard, 2007; Coopmann et al., 2020).
The thermal infrared nadir spectra of IASI have been successfully used in
retrieving different atmospheric trace gas profiles, and these retrievals are
especially sensitive between the middle troposphere and the stratosphere
(García et al., 2018; Diekmann et al., 2021; Schneider et al., 2022a,
2022b). By combining the IASI CH4 profiles and the TROPOMI CH4
total column, which has a higher sensitivity near ground, we are able to
detect the TXCH4 independently from CH4
at higher altitudes. The combined product cannot be obtained by either the
TROPOMI or IASI product independently. The combined product shows a weak
positive bias of about 1 % with respect to the reference data (Schneider
et al., 2022a). We refer to this product in the following as the
TROPOMI + IASI TXCH4 and it comprises about 12 000 data points for the
time period considered in this study.
Simple cone plume model and wind-assigned anomaly method
The averaged distribution of emitted CH4 over a long-term period can be
modeled simply as an evenly distributed cone-shape dispersion based on the
wind and source strength. Since CH4 is a long-lived gas, its decay is
negligible for short periods and not considered in the model. This model is
referred to as the simple cone plume model (see Fig. A1). This model is easy to apply, and the estimated emission strengths are
reasonable compared to the ones from other studies (Tu et al., 2022).
Based on the simple cone plume model, the enhanced CH4 column (ΔCH4) at the downwind side of the location xi,yi
is computed as
ΔCH4(xiyi)=εv⋅d(xi,yi)⋅α,
where the emission strength ε is the a priori knowledge from
the CAMS-GLOB-ANT data set or from the coal mine ventilation shafts in this
study (see Sect. 3.2). Their emission rates are assumed to be constant with
time from 2017 to 2020. The angle of the emission cone is α and has
an empirical value of 60∘, which has been derived from TROPOMI
NO2 measurements (Tu et al., 2022). The wind speed from ERA5, v, is the fifth generation ECMWF reanalysis product using 4D-Var data
assimilation and model forecasts in Cycle 41R2 of the ECMWF IFS model
(Copernicus Climate Change Service, C3S, 2017; Hersbach et al., 2020). The ERA5 provides hourly estimates on 137 pressure levels in the vertical covering
the atmosphere from the surface up to 0.01 hPa, with a spatial resolution of
0.25∘× 0.25∘ (Hersbach et al.,
2020). The distance between the downwind location and the CH4
emission source is denoted as d. Each individual source, either from the CAMS-GLOB-ANT
inventory or from the knowledge of the ventilation shafts, is considered as
an individual point source. The daily plume from each point source (location
at (i,j)) is averaged over daytime (08:00–18:00 UTC):
XCH4‾(i,j)=111∑t=111XCH4i,j,t.
These daily plumes are super-positioned over all point sources to obtain a
daily plume (XCH4‾daily):
XCH4daily‾=∑s=1NsXCH4i,j,s‾,
where Ns represents the number of the sources.
The wind distributions at different height levels (10, ∼330, ∼500 m) over the USCB region are presented in
Fig. 3. The wind speed increases with increasing
altitude (see Table 1). The ERA5 wind is divided
into two opposite wind regimes based on directions (e.g., 135–315∘ for SW and the rest for NE). For each wind regime, an
averaged plume is computed:
XCH4‾SW/NE=1Nd∑d=1NdXCH4‾daily,d,
where Nd is the number of days with SW wind or NE
wind.
The difference of the two plumes is therefore the wind-assigned anomaly:
wind-assignedanomaly=XCH4‾NE-XCH4‾SW.
The estimated emission strengths can be calculated by fitting the modeled
anomalies to the known anomalies from e.g., CAMS XCH4/TXCH4,
TROPOMI, and TROPOMI + IASI observations. Note that CH4 has a lifetime
of around 12 years, which results in a high background concentration
compared to the newly emitted CH4. Thus, the contributions from the
background should be removed for correctly estimating emissions (Liu et al.,
2021). The background is considered to consist of a constant value, a linear
increase with time, a seasonal cycle, a daily anomaly, and a horizontal
anomaly. For more details, see the Appendix in Tu et al. (2022). The
uncertainties (± values) in the emission estimate are determined by
considering the deficits of the background model due to the imperfect
elimination of the background and the noise in the data set.
This method was firstly used to estimate the CH4 emissions from
landfills in Madrid, Spain based on nearly 3-year spaceborne XCH4
data, and different opening angles were investigated to obtain an empirical
value (60∘) (Tu et al., 2022). The CH4 emission
strengths derived from satellite products have the same orders of magnitude
as the ones from single-day observations by ground-based instruments,
showing that this method works properly.
Number of days and the averaged wind speed (± standard
deviation) per specific wind regime during daytime (08:00–18:00 UTC)
at different vertical levels from November 2017 to December 2020 over the
USCB region. The days for the 3-year average coincide with the TROPOMI
overpass days.
NE/>315∘ or <135∘SW/135–315∘Number of daysAveraged wind speed ±Number of daysAveraged wind speed ±in total (%)standard deviation (m s-1)in total (%)standard deviation (m s-1)10 m39.13.2 ± 1.556.93.4 ± 1.6∼330 m (975 hPa)38.74.1 ± 2.256.94.3 ± 2.3∼500 m (950 hPa)38.75.0 ± 2.757.35.9 ± 3.5
Wind rose plots for daytime (08:00–18:00 UTC) from November 2017 to December 2020 for the ERA5 model wind at different vertical levels
(10, ∼330 and ∼500 m). The days for the
3-year average coincide with the TROPOMI overpass days.
Results and discussionEstimated emissions derived from CAMS forecasts (evaluation of the method)
The CAMS forecast XCH4 data from November 2017 to December 2020 within
the study area are illustrated in Fig. 4 left. The
areas with high XCH4 amounts fit well with the CAMS anthropogenic
CH4 emissions (square symbols). Similar to the CoMet inventory, high
sources in the CAMS-GLOB-ANT inventory are centered in this region, but
there are other weaker sources outside. The total emission rate of the CoMet
inventory is 555 kt yr-1 (6.6×1026 molec. s-1), which is slightly less than the
CAMS-GLOB-ANT emissions (815 kt yr-1). This is probably because the
CAMS-GLOB-ANT includes more CH4 emission sources, e.g., wastes and
combustion (residential and commercial), which account for about 20 %.
Averaged (a) CAMS forecast XCH4, (b) TROPOMI XCH4, and
(c) TROPOMI + IASI TXCH4 in the USCB region on a 0.1∘× 0.1∘ latitude/longitude grid during November 2017–December 2020. The square and triangle symbols represent the locations
of CAMS-GLOB-ANT sources (for better viewing, only the emission strengths
larger than 1×1024 molec. s-1 are shown here) and the active coal mine shafts
from the CoMet inventory (Gałkowski et al., 2021a), respectively. Different
colors denote the amount of emission rates. The white grids represent no
data from TROPOMI or the number of the points in the grid less than 5. A
zoomed version of panel (b) is shown in the appendix
(Fig. A2). Note that a different color bar has been
used in panel (c).
Based on the CAMS emissions, the wind-assigned method is applied to CAMS
XCH4. The XCH4 enhancement (raw-background) and the wind-assigned
anomalies are presented in Fig. 5a and b,
respectively. The example plumes of the enhancements for wind coming from NE
and SW are presented in Fig. A3. Note that the
CAMS XCH4 is coincided with TROPOMI XCH4 for better comparison.
Some data are thus missing here mostly due to the quality filter of TROPOMI
observations. After removing the XCH4 background, the XCH4
anomalies represent the CAMS sources well. The highest CH4 sources from the CAMS-GLOB-ANT inventory are also obviously visible in the 2D anomalies.
In addition, the spatial distributions of the three XCH4 data products
show different patterns (Fig. 4), whereas the
anomalies' (after removing background) patterns are similar
(Figs. 5a and d, 7a and d). This indicates that the background removal is of importance
for XCH4 and our method works well.
The wind-assigned anomalies for CAMS and the simple cone plume model show a very
good agreement with a slope of 1.11 and a R2 of 0.85
(Fig. 5c). Our results are derived from the CAMS
emission information, and they are in good agreement with the CAMS model data. The
estimated emission rate is about 815±1 kt yr-1 (9.7×1026±2.0×1025 molec. s-1) when using the ERA5 wind at 975 hPa (∼330 m),
and this value is quite close to CAMS-GLOB-ANT (estimated emission rate
at other levels are presented in Sect. 3.2, see Fig. 8 as well). Therefore, we use ERA5 wind at this level in the following study. Note that the points whose distances to the nearest dominant sources are
less than 10 km, are removed here, because they are very close to the
significant sources and small changes in wind (either speed or direction)
can result in high uncertainties.
The XCH4 is affected by local surface emissions and a varying stratospheric
contribution due to changes in the tropopause altitude (Liu et al., 2021;
Schneider et al., 2022a). This stratospheric contribution has to be taken
into account, in order to use XCH4 for a reliable
investigation of local surface CH4 sources and sinks (Pandey et al.,
2016). Our background removal method effectively accounts for the
stratospheric contribution. To show this, we apply the approach to CAMS
forecasts of XCH4 (which has a significant stratospheric contribution)
and TXCH4 (calculated from the CAMS forecast as CH4 averaged
from surface to 6 km, which should have a very limited stratospheric
contribution). The results are presented in Fig. 5d–f. The CAMS TXCH4 anomalies have similar distribution as CAMS
XCH4 anomalies, suggesting that our background removal approach
reliably removes the stratospheric contribution. The wind-assigned plume and
the correlation between CAMS and the wind-assigned model results are very
similar between XCH4 and TXCH4. The estimated CH4 emission
strength derived from CAMS TXCH4 is 798±15 kt yr-1 (9.5×1026±1.8×1025 molec. s-1).
CAMS XCH4 enhancement (XCH4-background) (a), the
wind-assigned anomalies (NE–SW) (b), and correlation plot of the wind-assigned
anomalies (c) between CAMS and the simple cone plume model with using the
CAMS-GLOB-ANT inventory (9.7×1026 molec. s-1 in total) and ERA5 wind at 330 m
during November 2017–December 2020 over the USCB region. The same
as for the upper panel are shown in (d–f) but for CAMS TXCH4. The square symbols represent
the locations of the CAMS-GLOB-ANT (>1×1024 molec. s-1) inventory
and different colors denote the amount of emission rates. The hatched areas
in (a)–(b) and (d)–(e) represent no data in these grids. The uncertainties
in (c) and (f) represent the mean error bars, i.e., error propagation of the
background uncertainty and the CAMS standard deviation.
Estimated emissions derived from satellite observations
The high-resolution TROPOMI XCH4 provides the ability to detect and
quantify the CH4 emissions (e.g., oil and gas sector, coal mining) on
fine and large scales (Pandey et al., 2019; Varon et al., 2019; De Gouw et al.,
2020; Schneising et al., 2020). Figure 6 illustrates
the enhanced XCH4 (raw XCH4-background in the upwind) distribution
over the USCB region on an example day (6 June 2018), in which the wind
mostly came from northeast. As expected, obvious XCH4 enhancements were
observed by TROPOMI along the downwind direction (southwest of Katowice
where most ventilation shafts are located), as well as simulated by the CAMS
forecast. The downwind-enhanced XCH4, modeled by our simple cone plume
model and based on the CAMS-GLOB-ANT inventory, also shows a similar shape of
plume. This enhancement was also observed by portable FTIR instruments
(COCCON) employed during the CoMet campaign (Fig. 4 in Luther et al.,
2019). The observations support the statement that TROPOMI is able to detect
the CH4 emission signals. In addition, the spatial pattern of the
downwind plume is similar to that of the cone-shaped plume, which implies
our cone-shape assumption is reasonable.
ΔXCH4 together with the ERA5 wind at 12:00 UTC from
(a) TROPOMI observations at 11:34 UTC, (b) CAMS forecast at 12:00 UTC, and
(c) from the simple cone plume model (averaged over the daytime) based on
the CAMS-GLOB-ANT inventory over the USCB region on an example day (6 June 2018). The “bg” in the title of (a) and (b) represents the average
background, derived from the mean XCH4 in the upwind region
(50.3–50.8∘ N, 19.5–20.0∘ E). Note that a different color bar has been used in panel
(c) for improved recognizability.
The 3-year averaged TROPOMI XCH4 observations presented in
Fig. 4b show scattered high XCH4 amounts,
whereas CAMS XCH4 is more concentrated on the center of the study area,
and those agree well with its anthropogenic emission sources (CAMS-GLOB-ANT
inventory). This might be because TROPOMI detects other real CH4
sources that are not included in the CAMS forecast model data.
For better comparison with other studies discussing the coal mine emissions
in the USCB region, we apply the CoMet inventory as the a priori known
sources in the wind-assigned method to estimate the CH4 emissions. The
results are illustrated in Fig. 7. The TROPOMI
XCH4 and TROPOMI + IASI TXCH4 anomalies show high concentrations
around the areas where the ventilation shafts are located and the region in
the northeast of Katowice. Although the anomalies of the satellite
observations are lower than the CAMS results (Fig. 5a), their spatial distributions are similar. Positive and negative plumes
can be clearly seen in Fig. 7b and e. The
correlation of the wind-assigned anomalies between the TROPOMI and simple
cone plume model has a very good agreement with an R2 value of 0.76.
Similar results are also derived from TROPOMI + IASI TXCH4 with a
R2 value of 0.62. Compared to CAMS data, higher scatter is expected,
because satellite observations suffer from observational errors and might
contain more CH4 sources (e.g., landfills, gas distribution network).
Although none of these sources have the same orders of magnitude of coal
mining emission, they might still bring some errors.
The estimated CH4 emission strengths are 496±17 kt yr-1 (5.9×1026±2.1×1025 molec. s-1) for XCH4 and 437±27 kt yr-1 (5.2×1026±3.2×1025 molec. s-1) for TXCH4, and both are close to the E-PRTR
inventory (448 kt yr-1). The TROPOMI + IASI result has a higher uncertainty
than the TROPOMI result, because (1) the vertical distribution of CH4
is in general much more difficult to measure than the total column of
CH4 and (2) the vertical distribution is derived by considering two
independent measurements, each with its own noise error. This might change
for a larger number of data points (e.g., by using data from more years or
by applying the method to IASI and TROPOMI successors on the upcoming
METOP-SG satellite, which offers much more collocated observations).
However, in our study, using TXCH4 data in addition to XCH4 data
nicely documents the robustness of the method. Important for a correct
estimation of the emission is the correct removal of the CH4 background
signal. For XCH4 the stratospheric and the tropospheric backgrounds
have to be removed, whereas only the tropospheric background has to be
removed for TXCH4. Despite this difference, we estimate very similar
emission rates from both data sets, and the emission rate uncertainties of
using XCH4 or TXCH4 are small compared to the estimated emission rates.
Figure 8 summarizes the estimated emission strengths
derived from different products based on different a priori knowledge of
inventories and wind information at different altitudes (for specific values
see Table A1). Different a priori inventories
result in 16 %–32 % changes in strength at different altitudes, which is
generally smaller than the 47 % difference in the total amount of
inventories (9.7×1026 for CAMS-GLOB-ANT and 6.6×1026 molec. s-1 for CoMet
inventory). This is probably due to the different locations of sources and
different proportions of each emission source in the total strengths in the
two inventories. When using the CAMS-GLOB-ANT inventory, CH4 emission
rates derived from CAMS XCH4 and TXCH4 are ∼37 %
and ∼56 % higher than those derived from TROPOMI XCH4
and IASI + TROPOMI TXCH4, respectively. This difference is mainly due
to the difference between the CAMS forecast and satellite products. The
strength increases with respect to the increasing wind speed at higher
altitude, while the increment is not always proportional to the wind
speed, i.e., less increase in the strength with respect to the wind speed at
higher altitude (see Sect. 3.3.1).
Similar to Fig. 5, but for TROPOMI
XCH4(a–c) and TROPOMI + IASI TXCH4(d–f). The a priori knowledge of
sources are based on the CoMet inventory (6.6×1026 molec. s-1 in total, Gałkowski et al., 2021a). The triangle symbols represent the locations of the
active coal mine shafts and different colors denote the amount of emission
rates.
Uncertainty analysis
The CH4 signal is weak compared to the background concentration which shows
an increasing trend with obvious seasonality and strong day-to-day signals.
It is necessary to remove the background signals before estimating the
emission strengths. However, the imperfect elimination of the background
introduces uncertainties, which can be determined by considering the
deficits of the background model and the noise in the background (Tu et al.,
2022). In this study, the uncertainties of the estimated strengths include
the background uncertainties.
Winds, particularly near the surface, are significantly altered by
topography, which yields uncertainties in knowing the transport pathway from
emission sources to the measurement location (Chen et al., 2016;
Babenhauserheide et al., 2020). Thus, wind is one of the most important
factors in correctly estimating the emission rates. Here, we investigate the
wind uncertainties based on the CAMS XCH4 and the CAMS-GLOB-ANT
inventory. The wind used in Sect. 3.3.2 and 3.3.3 are from ERA5 at 10 m.
Vertical wind shear
Compared to the wind at 330 m, the distributions of wind directions are
similar at lower or higher altitudes (10 and 500 m) but the wind speed
increases with higher altitude (Fig. 3). The wind
speed at 10 m is 20 % weaker than that at 330 m
(Table 1), which yields a corresponding lower
emission estimate of 613±13 kt yr-1 (7.3×1026±1.5×1025 molec. s-1,
-25 %) based on the CAMS XCH4 and CAMS emission inventory
(Fig. A4a).
Assuming that the height of the planetary boundary layer (PBL) is typically
less than a kilometer, we use the ERA5 wind at 500 m above the ground
(Fig. 3c) for describing the transport of CH4 released in the study
region. The wind speed at 500 m increases by 22 % and 37 % for NE and SW
regimes, respectively, i.e., 32 % on average, compared to the wind at 330 m. The share of SW directed winds is slightly larger at the 500 m level.
These differences result in an increase of 13 % of the estimated emission
rate (924±19 kt yr-1, 1.1×1027±2.3×1025 molec. s-1). The wind
speed is linear in the calculation of ε (Eq. 2), but the wind
speeds do not all linearly change for each grid and for each time at
different levels. This results in unequal changes between the wind speed and
the enhanced columns, and later unequal changes in the estimated emission
strength. In addition, the simple cone plume model introduces biases, i.e.,
the enhanced column in the downwind is set to zero when its location is out
of the cone angle (60∘). Slight changes in the wind
directions might result in a huge difference in the enhanced columns.
Estimated CH4 emission rates derived from the CAMS forecasts
(XCH4 and TXCH4), TROPOMI XCH4, and TROPOMI + IASI TXCH4
data based on different a priori knowledge of emission sources
(CAMS-GLOB-ANT and CoMet inventories) and on ERA5 model winds at different
altitudes (10, 330, 500 m). Square symbols represent the a priori
emission sources from the CAMS-GLOB-ANT inventory and triangle symbols
represent the a priori emission sources from the CoMet inventory. The two
horizontal lines represent the number of total emissions for the
CAMS-GLOB-ANT inventory (lavender color) and for the CoMet inventory (orange
color), respectively. Note that error bars represent the uncertainties from
background removal and noise in the data, which are much smaller than the
results and they are not visible here. For specific values see
Table A1.
Use of narrowed angular wind regimes
The long-term wind comes from all directions (0–360∘)
(Fig. 3). To define the uncertainty of wind
regimes' coverage, the wind is separated into two groups with narrow
coverage fields: NE1/4 (0–90∘)–SW1/4 (180–270∘) and NW1/4 (270–360∘)–SE1/4 (90–180∘). The
final estimated emission strength is weighted by the number of days on
which, on average, the wind blew in the respective wind regime (i.e., 115 d for NE1/4–SW1/4 and 71 d for NW1/4–SE1/4, respectively). The XCH4 anomalies and the plume for the
NE1/4–SW1/4 regime are quite similar to those with
wider-coverage NE and SW fields (Fig. 9a–c). The
wind-assigned anomalies derived from CAMS and the simple cone plume model
show very good agreement as well. Slightly less data points are found here
because of the choice of narrower wind fields, especially for NW1/4–SE1/4 wind fields. The estimated emission rate is about 773±19 kt yr-1 (9.2×1026±2.3×1025 molec. s-1) for the NE1/4–SW1/4 field. This indicates that the effect of the segment in the wind
field coverage is negligible when there are enough measurements. The use of
NW1/4–SE1/4 wind fields yields an emission strength of 1176±134 kt yr-1 (1.4×1027±1.6×1026 molec. s-1). The higher uncertainty
is probably due to less measurements in these wind fields. The weighted rate
is therefore about 927 kt yr-1 (1.1×1027 molec. s-1), 13.4 % higher than based
on the wider NE–SW wind regime (Sect. 3.1).
Similar figures to Fig. 5b–c. Results
are derived from CAMS XCH4, CAMS emission inventory and ERA5 wind at
330 m for (a)–(b) narrow wind coverage (NE1/4 and SW1/4), and
(c)–(d) narrow wind coverage (NW1/4 and SE1/4).
Investigation of different choices for wind field segmentation
The wind category here is based on the predominant wind fields over the USCB
region and is divided into two opposite regimes (SW and NE). To investigate
the effect of the segmentation on the uncertainty in the emission rate
estimation, we additionally apply another kind of segmentation: N (<90∘ or >270∘) and S (90–270∘) categories. Similar results are found and are shown in
Fig. 10. Though the 2D distribution of the plume
changes due to the new wind category, an obvious plume can be seen. The
estimated emission rate is 773±19 kt yr-1 (9.2×1026±2.3×1025 molec. s-1), which is only 5.2 % less than that using NE and SW wind
categories. The correlation of the wind-assigned anomalies derived from the
CAMS and the simple cone plume model shows a very good agreement as well,
with a similar R2 value of 0.85 to that in the NE–SW wind category.
This result demonstrates that our method is not significantly influenced by
the wind regime division.
Similar figures to Fig. 5b–c. Results
are derived from CAMS XCH4, CAMS emission inventory and ERA5 wind at
330 m, but using a new wind category (N and S).
Investigation of different choices for angle of the emission cone
The angle (α=60∘) used in the simple cone plume model is
an empirical value which affects the deduced emission strengths.
Figure 11 shows the results when α is
decreased or increased by 10∘. Changes in the spatial
distributions of wind-assigned anomalies and in the correlations derived
from CAMS and the simple cone plume model are nearly negligible when using
different angles in the model. The estimated emissions are 789±16 kt a-1 (9.5×1026±1.9×1025 molec. s-1) for α=50∘ and 832±17 kt a-1 (9.9×1026±2.0×1025 molec. s-1) for α=70∘, which are 3 % lower and 2 % higher than that using the
empirical angle (α=60∘).
Similar figures to Fig. 5b–c. Results are derived from CAMS
XCH4, CAMS emission inventory, and ERA5 wind at 330 m for (a)–(b)α=50∘, and (c)–(d)α=70∘.
The changes in the estimated emission rates for different products due to
different error sources are summarized in Table A2. Based on the error
propagation, the total uncertainty in the estimated emission rates from the
different error sources (background removal and noise in the data, vertical
wind shear at 500 m, wind field segmentation, and opening angle α=70∘) is approximately 14.7 % for CAMS XCH4,
14.8 % for TROPOMI XCH4, and 11.4 % for TROPOMI + IASI TXCH4.
Note that the use of narrowed angular wind regimes is not a preferable way
due to few amounts of data in narrowed wind regimes, and thus is not
considered an error source. In addition, the 500 m wind shear was used as a
contribution to the budget, as the 10 m wind is not expected to be
representative of the PBL.
Conclusions
Intensive mining activities are the dominant CH4 emission sources in
the USCB region, Poland, where one of the largest coal mining areas in
Europe is located. It is thus of importance to quantify the CH4
emissions from this area. In this study we use the combination of a simple
cone plume model and a novel wind-assigned model to estimate CH4
emission rates from high-resolution CAMS forecast XCH4 and TXCH4,
along with satellite data (TROPOMI XCH4 and TROPOMI+IASI TXCH4)
over the USCB region (49.3–50.8∘ N and 18–20∘ E) from November 2017 to December 2020.
Based on the CAMS-GLOB-ANT inventory, the dominant CH4 source is
emitted from energy production and distribution, and the significant sources
are spread around the city of Katowice and its southwest region. We firstly
apply the wind-assigned method to the CAMS forecasts based on the a priori
knowledge of the CAMS-GLOB-ANT inventory (815 kt yr-1, 9.7×1026 molec. s-1 in total)
and ERA5 wind at ∼330 m. We use the wind-assigned anomalies
of XCH4/TXCH4 to represent the difference of XCH4/TXCH4
between the conditions of two opposite wind fields (NE and SW). The
wind-assigned anomalies derived from CAMS XCH4/TXCH4 show very
good agreements with the output of the simple cone plume model with an
R2 value of 0.85 for CAMS XCH4 and CAMS TXCH4. This nice
correlation indicates that our background removal works well. In addition,
similar estimates are derived from CAMS XCH4 (815 kt yr-1, i.e., 9.7×1026 molec. s-1) and TXCH4 (798 kt yr-1, i.e., 9.5×1026 molec. s-1).
To investigate the CH4 emissions from this hot spot, the CoMet campaign
was performed in 2018. Locations and emission rates of the ventilation
shafts of the coal mine used in this study are based on this campaign. Based
on this knowledge, the emissions are estimated as 496 kt yr-1 (5.9×1026 molec. s-1) and 437 kt yr-1 (5.2×1026 molec. s-1) from the TROPOMI XCH4 and
combined TROPOMI + IASI TXCH4, respectively. These results are 40 %
less than that derived from the CAMS model and CAMS-GLOB-ANT inventory. It
is probably because CAMS-GLOB-ANT includes many sectors of anthropogenic
sources, like wastes, and residential and commercial combustion, which
account for about 20 %. Nevertheless, our results derived from satellite
observations are close to the E-PRTR inventory of 448 kt yr-1 and reasonable
compared to the CoMet inventory (555 kt yr-1), and to previous studies over
the USCB region (ranging from 9 to 79 kt yr-1 for a sub-cluster of
shafts (Krautwurst et al., 2021) up to 477 kt yr-1 derived from one flight
(Fiehn et al., 2020).
Similar 2D anomalies and plumes are also observed for TROPOMI XCH4 and
TROPOMI + IASI TXCH4. This nicely documents the robustness of the
method. The TROPOMI + IASI result has a higher uncertainty than the TROPOMI
result, because (1) the vertical distribution of CH4 is in general much
more difficult to measure than the total column of CH4 and (2) the
vertical distribution is derived by considering two independent
measurements, each with its own noise error. This might change for a larger
number of data points (e.g., by using data from more years or by applying
the method to IASI and TROPOMI successors on the upcoming METOP-SG
satellite, which offers much more collocated observations). Nonetheless, the
uncertainties are insignificant compared to the estimated emission rates.
Wind contains uncertainties in knowing the transport pathway from emission
sources to the measurement location and thus, we analyze the effects in
selecting wind at lower and higher altitudes (10 and 500 m), wind field
coverage, and wind category. Wind distributions at higher levels are similar
to the ones at 330 m. However, their speeds decrease by 20 % at 10 m and
increase by 32 % at 500 m, which results in changes in the emission rates
by -25 % and 13 % for CAMS XCH4, respectively. Narrower wind field
coverage (0–90∘ for the NE regime and 180–270∘ for the SW regime) and different wind segmentation (<90∘ or >270∘ for N regime and 90–270∘ for S regime) introduce uncertainties of +13.4 % and
-5.2 % for CAMS XCH4, respectively. The agreements for these
sensitivity tests of the wind-assigned anomalies derived from both the CAMS and simple cone plume models are as good as that using previous NE and
SW wind fields. The impact of a suboptimal choice for the angle (60∘) used in the simple cone plume model is also discussed. The estimation
is decreased by 3 % for α=50∘ and increased by 2 %
for α=70∘ for CAMS XCH4. This small change supports
the empirical choice for α. Based on the error propagation, the
total uncertainty in the estimated emission rates from the different error
sources (background removal and noise in the data, vertical wind shear at
500 m, wind field segmentation, and opening angle α=70∘) is approximately 14.7 % for CAMS XCH4, 14.8 % for
TROPOMI XCH4, and 11.4 % for TROPOMI+IASI TXCH4. These
results suggest that the wind-assigned method is robust and is also suitable
for estimating CH4 and CO2 emissions in other regions.
Sketch of the simple cone plume model used to explain the
CH4 emission estimation method. The CH4 at the point source is
distributed along the wind direction (wind speed: v) in the
cone-shaped area with an opening angle of α. The point source emits
the CH4 at an emission rate of ε. We assumed the CH4
molecules are evenly distributed in the dotted area A, and the distance from
area A to the point source is d. Therefore, the emitted CH4 in dt time
period equals the amount of CH4 in the area A. It yields the equation:
ε×dt≈Δcolumn×απ×π×d×v×dt. This figure is adopted from Tu et al. (2022).
A zoomed figure of Fig. 4b.
Estimated CH4 emission rates derived from CAMS forecasts
(XCH4 and TXCH4), TROPOMI XCH4, and IASI & TROPOMI
TXCH4 data based on different a priori knowledge of emission sources
(CAMS-GLOB-ANT and CoMet campaign inventories) and ERA5 model winds at
different altitudes (10, 100 and ∼500 m).
ERA5 wind at 10 m ERA5 wind at 330 m (975 hPa) ERA5 wind at 500 m (950 hPa) CAMS-GLOB-ANTCoMet inventoryCAMS-GLOB-ANTCoMet inventoryCAMS-GLOB-ANTCoMet inventory(total =(total =(total =(total =(total =(total =prior emission sources9.7×1026 molec. s-1)6.6×1026 molec. s-1)9.7×1026 molec. s-1)6.6×1026 molec. s-1)9.7×1026 molec. s-1)6.6×1026 molec. s-1)CAMS XCH47.3×1026±1.5×10256.3×1026±1.3×10259.7×1026±2.0×10258.3×1026±1.8×10251.1×1027±2.3×10259.2×1026±2.1×1025CAMS TXCH47.2×1026±1.3×10256.1×1026±1.2×10259.5×1026±1.8×10258.1×1026±1.6×10251.0×1027±2.1×10258.9×1026±1.9×1025TROPOMI XCH45.4×1026±1.8×10254.5×1026±1.5×10257.1×1026±2.4×10255.9×1026±2.1×10258.1×1026±2.8×10256.3×1026±2.3×1025IASI&TROPOMI TXCH44.7×1026±2.7×10254.0×1026±2.3×10256.2×1026±3.7×10255.2×1026±3.2×10256.8×1026±4.3×10255.5×1026±3.6×1025
The enhancements for wind coming from NE and SW.
Changes in the estimated emission rates for different
products when using different input data or under different
situations compared to their results using the default setting (wind at 330 m, NE–SW wind segmentation, α=60∘, CAMS-GLOB-ANT for
CAMS XCH4 and CoMet inventory for TROPOMI XCH4 and TROPOMI + IASI
TXCH4).
CAMSTROPOMITROPOMI +XCH4XCH4IASI TXCH4Background removal & noise in the data2.1 %3.6 %6.1 %Vertical wind shear (500 m)13.4 %6.8 %5.8 %Wind field segmentation (N–S)-5.2 %12.7 %7.7 %Angle of the emission cone (α=70∘)2.1 %0.07 %-0.02 %Total:14.7 %14.8 %11.4 %
Similar to Fig. 5 but using ERA5 wind at 10 m.
Data availability
The data are accessible by contacting the corresponding author (qiansi.tu@kit.edu). The SRON S5P-RemoTeC scientific TROPOMI CH4 data set from this study is available for download at
10.5281/zenodo.4447228 (Lorente et al., 2021b).
The MUSICA IASI data set is available for download via 10.35097/408
(Schneider et al., 2021). The CoMet inventory is available at 10.18160/3K6Z-4H73 (Gałkowski et al., 2021a).
Author contributions
QT, FH and MS developed the research
question. QT wrote the manuscript and performed the data analysis
with input from FH, MS and FK.
MS, BE and CJD provided the
combined (MUSICA IASI + TROPOMI) data and supported technically for the
analysis of these data. JN supported consultation of the
local situation and CoMet inventory. All authors discussed the results and
contributed to the final manuscript.
Competing interests
At least one of the (co-)authors is a member of the editorial board of Atmospheric Chemistry and Physics. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Special issue statement
This article is part of the special issue “CoMet: a mission to improve our understanding and to better quantify the carbon dioxide and methane cycles”. It is not associated with a conference.
Acknowledgements
The CAMS results were generated using the Copernicus Atmosphere Monitoring
Service (2017–2020) information. Neither the European Commission nor ECMWF
is responsible for any use that may be made of the Copernicus information or
data it contains. We also thank Michela Giusti and Kevin Marsh in the Data
Support Team at ECMWF for retrieving and providing comments about the CAMS
data. This research has largely benefited from funds of the Deutsche
Forschungsgemeinschaft (provided for the two projects MOTIV and TEDDY with
IDs 290612604 and 416767181, respectively). An important part of this work was
performed on the supercomputer, HoreKa, funded by the Ministry of Science,
Research and the Arts Baden-Württemberg and by the German Federal
Ministry of Education and Research. We acknowledge Emissions of atmospheric
Compounds and Compilation of Ancillary Data (ECCAD) for providing
CAMS-GLOB-ANT inventory data. We also give thanks to Claire Granier from
Laboratoire d'Aerologie, Toulouse, France for providing information about
the uncertainties of the CAMS-GLOB-ANT inventory.
The access and use of any Copernicus Sentinel data available through the
Copernicus Open Access Hub are governed by the legal notice on the use of
Copernicus Sentinel Data and Service Information, which is given here:
https://sentinels.copernicus.eu/documents/247904/690755/Sentinel_Data_Legal_Notice (last access: 8 November 2021).
We acknowledge the support by the Deutsche Forschungsgemeinschaft and the
Open Access Publishing Fund of the Karlsruhe Institute of Technology.
Financial support
This research has been supported by the Deutsche Forschungsgemeinschaft (Project MOTIV (grant no. 290612604) and Project TEDDY (grant no. 416767181)). The Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg and the Bundesministerium für Bildung und Forschung provided funds for the supercomputer HoreKa used for the MUSICA IASI retrieval work and the MUSICA IASI + TROPOMI combination calculations.The article processing charges for this open-access publication were covered by the Karlsruhe Institute of Technology (KIT).
Review statement
This paper was edited by Christoph Gerbig and reviewed by two anonymous referees.
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