The atmospheric abundance of methane (CH4) has increased by a factor of 2.6 since pre-industrial times from roughly 720 ppb (parts per billion) to about 1879 ppb in 2020 , mainly driven by anthropogenic influences e.g.,. Roughly 20% of the total global anthropogenic CH4 emissions are caused by the fossil fuel industry and an extensive source of CH4 is hard coal mining. Poland is the largest hard coal producer in the European Union with the Upper Silesian Coal Basin (USCB) as one of the largest hard coal producing regions in Europe. Several bottom-up inventories report on the total CH4 emissions for the USCB: according to the GESAPU database, the USCB emitted a total of 405 kt CH4 in 2010 . The E-PRTR (http://prtr.ec.europa.eu/, ) collects emission reports of every individual mine, yielding an aggregated total of 507 kt CH4 a-1 for the USCB. reports hard coal mining emissions of 530 kt CH4 for the USCB in 2018, and the Copernicus Atmosphere Monitoring Service regional emission inventory (CAMS-REG-GHG/AP) lists 632 kt CH4 a-1 . EDGAR v4.3.2 (Emission Database for Global Atmospheric Research) gives emissions of 675 kt CH4 a-1 for fuel exploitation emissions (EDGAR abbreviation PRO) for the USCB in the year 2012. EDGAR v6.0 states 454 kt CH4 a-1 for the sector abbreviation PRO COAL for the USCB in 2018. The extrapolated seasonal breakdown provided by EDGAR for the relevant months May and June 2018 matches the total 2018 EDGAR emission estimate for the USCB.

In addition to the bottom-up inventories, top-down approaches have examined USCB emissions. During the CoMet mission (Carbon dioxide and Methane mission 2018, from 23 May to 12 June 2018), several ground-based instruments and aircraft measured the atmospheric CH4 abundance in the USCB. In our precursor study , we used stop-and-go measurements of the column-average dry-air mole fractions of CH4 (XCH4) by a mobile, ground-based Fourier transform spectrometer (FTS) to evaluate the mining emissions of individual ventilation facilities and found similar emissions as suggested by the E-PRTR inventory. The total USCB emission estimates of and , based on airborne in situ measurements, are in broad agreement with the E-PRTR data for single flights. Using airborne imager data, found some discrepancies between their estimates and the E-PRTR inventory for small groups of ventilation facilities. The isotopic CH4 composition was measured by with ground-based in situ instruments. discusses the short-term, shaft-wise CH4 release in the USCB.

Given the magnitude of emissions and the range of estimates, CH4 in the USCB warrants further investigation. Here, we report on CH4 emission estimates derived from measurements of four stationary, sun-viewing FTSs of the type EM27/SUN arranged in a network-like pattern enclosing the USCB during the CoMet campaign activities. The setup largely mimics previous network deployments for quantifying urban greenhouse gas emissions in Berlin , Paris , St. Petersburg , Munich , Indianapolis , and other places. Our four EM27/SUN instruments were positioned in the four cardinal directions at a distance of a few tens of kilometers to the center of the USCB. We calculate differences between pairs of upwind and downwind observations to determine enhancements (ΔXCH4) in our XCH4 records attributable to sources within the USCB. Further developing the model setup of , we use the flexible Lagrangian particle dispersion model (FLEXPART) together with wind fields from the Weather Research and Forecasting model (WRF) constrained by three wind lidars to translate the observed XCH4 enhancements into emission estimates for groups of coal mine ventilation shafts. To this end, we set up an inverse estimation scheme based on Phillips–Tikhonov regularization. This setup enables careful information content analysis while not relying on estimates of a priori emission uncertainties, which are often inaccessible. This work demonstrates emission estimation of a methane-emitting hotspot based on an FTS network combined with a Phillips–Tikhonov regularized inversion approach.

Our paper first summarizes the campaign setup (Sect. ). Then, Sects.  and  detail the modeling and regularization methods. Section  reports on emission estimates for six case studies, and Sect.  discusses our results in terms of compatibility with other emission estimates and methodological strengths and weaknesses.

As part of the CoMet activities in May and June 2018, our campaign deployment of the EM27/SUN focused on the USCB, extending roughly 80×80 km2 in the southwest of Poland. Figure , adopted from our precursor study on mobile measurements , illustrates the network pattern together with the locations of the most important coal mine ventilation shafts and the wind lidars. The four stationary EM27/SUN spectrometers are positioned roughly in the four cardinal directions around the center of the basin, ensuring that at least one instrument measures upwind and one downwind of the USCB for most wind situations. Due to mainly easterly wind conditions prevailing during our deployment, the eastern station (The Glade) functions as the upwind station for all case studies discussed here. The respective downwind stations are located in the south (Pustelnik) and west (Raciborz) of the USCB. The northern station (Za Miastem) was identified as neither an upwind nor downwind station for any of the cases.

The functioning of the EM27/SUN FTS and the data reduction techniques are described in detail by , , and with a particular focus on our setup by . Generally, the EM27/SUN instruments observe spectra of direct sunlight in the shortwave infrared spectral range from which the total column concentrations of CH4, carbon dioxide (CO2), water vapor (H2O), molecular oxygen (O2), carbon monoxide (CO), and other substances can be retrieved. CH4 and O2 are of relevance here. All EM27/SUN spectrometers participating in the campaign successfully underwent the instrumental quality assurance tests required by the Collaborative Carbon Column Observing Network (COCCON) and presented in before field deployment.

We run the software package PROFFIT to retrieve the column concentrations [O2] and [CH4] from the 7765 to 8005 and 5897 to 6145 cm-1 spectral windows, respectively, using absorption line parameters by and . The respective column-average dry-air mole fractions of methane, XCH4, are calculated via normalization through [CH4][O2]×0.2094, where the atmospheric O2 mole fraction is assumed to be 0.2094. The normalization is generally recommended to lessen spurious artifacts due to pressure and solar zenith angle (SZA) dependencies. The SZAs during our measurements did not exceed 56∘, which is within the range that does not require air-mass-dependent bias correction . Slightly deviating from the processing recipe and in line with our precursor study , our CH4 retrievals only scale the CH4 concentrations in the layers below 1700 m a.g.l. where we expect elevated methane due to the localized sources at the ground. Further, we extract the a priori CH4 profiles from a dedicated ECHAM/MESSy Atmospheric Chemistry simulation described by and .

For network deployments such as undertaken here, it is common practice to cross-calibrate the network nodes by side-by-side measurements in order to exclude spurious gradients when conducting upwind–downwind analyses. We calibrated the four instruments through side-by-side measurements on 23 and 26 May 2018 at the southern location Pustelnik. Figure  shows the raw and calibrated XCH4 records, and Table lists the respective calibration factors. These instrument-specific empirical calibration factors have been applied to the XCH4 campaign data discussed in the following. After calibration, the mean absolute instrument-to-instrument difference is roughly 1 ppb, which is compatible with , who state the instrument-to-instrument difference for an EM27/SUN ensemble as 0.8 ppb for XCH4. We estimate the precision for XCH4 as 0.6 ppb for 1 min integration time from measurements sampled during the campaign in the rather variable methane field of the USCB, which is consistent with the precision stated by . Based on measurements of the eastern and northern instruments (The Glade – E and Za Miastem – N) observed from 07:00 to 10:00 UTC on 28 May 2018 (upper panel Fig. ), we calculated the precision as the standard deviation of the observations averaged between the two instruments during this period. We chose this period, since the two timelines are not affected by any strong methane sources in the vicinity.

In addition to the EM27/SUN network, we also operated three Leosphere Windcube 200S Doppler wind lidars marked as red stars in Fig.  and as detailed in and . The measured wind profiles (10 min time interval) reach up to 4 km a.g.l. and are assimilated into the WRF simulations to improve the modeled wind fields as discussed in Sect. .

Our simulations of methane dispersion in the USCB are partitioned into two steps, largely adopting the basic setup reported by : first (Sect. ), the wind fields are modeled by a two-domain WRF setup including assimilation of the wind lidar observations. Second, the WRF wind fields drive the particle dispersion in the Lagrangian particle dispersion model FLEXPART (Sect.  ).

In order to estimate the shaft emissions from the mismatch between measured and simulated methane enhancements ΔXCH4, we use a Phillips–Tikhonov inverse method. We set it up such that the state vector x consists of m dimensionless factors that scale the emissions of each coal mine ventilation shaft considered by the FLEXPART simulations. We assume the scaling factors to be constant for each day of measurement; i.e., we impose the assumption of the source strength being constant over the time of a day. FLEXPART is the forward model K (m×n) relating the emissions of the n shafts to m ΔXCH4 measurements. The measurement vector y contains the ΔXCH4 enhancements, observed at 1 min intervals, translated from units of parts per billion (ppb) into total mass column enhancements (kgm-2). The Phillips–Tikhonov inverse method then delivers the estimated state vector xλ by minimizing a two-term cost function consisting of a measurement term and an a priori term : 1xλ=argmin‖Sϵ-12(Kx-y)‖22+λ2‖W(x-xa)‖22, with Sϵ the error covariance matrix, λ the regularization parameter, W the weighting operator, xa the a priori state vector, and ||⋅||2 representing the L2 norm. Sϵ contains the averaged standard deviation of the FLEXPART simulation ensemble summed in quadrature with the XCH4 background variability and the measurement noise. Note that, for simplicity, we did not consider correlations in Sϵ. The estimated background error ranges between 0.3 and 2.2 ppb for the individual case studies based on the differences of minimum and maximum average ΔXCH4 calculated under consideration of ±30 min time shifts of the simulated methane travel times. The measurement noise amounts to 0.6 ppb, calculated as the standard deviation of the averaged measurements of The Glade (E) and Za Miastem (N) from 07:00 to 10:00 UTC on 28 May 2018 (see top panel in Fig. ). W is a diagonal matrix with elements 1xa,j,j=1,…,m, which renders the second cost term dimensionless . Technically, we transform the Phillips–Tikhonov regularization problem into a plain least-squares fit using the definitions 2C=Sϵ-12KλW and d=Sϵ-12yλWxa, which transforms Eq. () to 3xλ=argmin‖Cx-d‖22, and is treatable by a standard least-squares solver (e.g., python module scipy.optimize.lsq_linear).

The a priori information xa for each ventilation shaft is taken from the annual E-PRTR emission inventory updated by . The a priori generally guides the minimization process towards physically reasonable solutions if the inverse problem tends to be ill-posed, e.g., when there is insufficient measurement information on some of the state vector elements. However, the solution is dependent on the regularization parameter λ, which has to be found by trading the propagation of measurement errors against influence of the a priori. Here, we use the L-curve criterion to determine the regularization parameter λ for each individual case study e.g.,. The L-curve is a graphical representation of the mismatch between measurements and simulations ‖Kxλ-y‖2 plotted against the norm of the state vector ‖xλ‖2 evaluated for a range of λ (see Fig. ). The plot typically looks like an L. For small λ, the measurement term dominates the cost function, and the estimate xλ becomes noisy and drives large deviations from the a priori. For large λ, the a priori term dominates the cost function, and the estimate xλ ignores the measurements and produces a large norm of the measurement term. The corner of the L indicates a reasonable regularization parameter for the given minimization problem and is graphically chosen. In addition, we found that the shape of the L-curve is sensitive to forward model errors, e.g., when errors in the FLEXPART trajectories and the driving wind fields suggest a spurious, erroneous link between emissions and methane enhancements. Obvious distortions of the L-curve shape are used as a criterion to filter out periods when the forward model does not represent the actual dispersion conditions.

Besides the L-curve, the regularized inversion approach holds another diagnostic measure: the emissions averaging kernel matrix Aλ with dimensions m×m. It is defined via the gain matrix Gλ . 4Aλ=GλK5Gλ=KTSϵ-1K+λ2⋅WTW-1KTSϵ-1 The averaging kernel matrix, for a given regularization strength λ, diagnoses how information propagates from the true and a priori states, xtrue and xa, into the emission estimate. 6xλ=Aλxtrue+(1-Aλ)xa The rows of Aλ are called the averaging kernels, quantifying how an estimated state vector element calculates from the other state elements and what portion comes from the prior. For our purposes, the averaging kernels quantify how the emission estimate for a ventilation shaft is affected by the neighboring shafts and whether there is sufficient measurement information. In the perfect case, the emissions averaging kernel is unity for the shaft under consideration and zero for all other shafts, indicating that the shaft can be perfectly resolved and discriminated from neighboring sources and that it is well constrained by measurement information. In reality, groups of neighboring sources and sources behind each other along the trajectory are not resolvable, and some shafts only marginally affect our measurements, implying broader and smaller emissions averaging kernels.

The errors due to measurement noise, background methane variability, and atmospheric transport incorporated in Sϵ are propagated into the a posteriori error covariance for the emission estimates via 7Sx,λ=GλSϵGλT, where we report the square root of the diagonal as the error bars of the shaft-wise emission estimates and the square root of the sum of the entire covariance matrix as the error of the total emissions aggregated over all shafts. For the case studies discussed in Sect. , the emission errors due to measurement noise range between 0.62 and 4.46 kt a-1, which is small compared to the errors introduced by the dispersion modeling ensemble that range between 27 and 143 kt a-1. Errors related to background methane variability introduced by a ±30 min time shift of the air mass travel time range between 0.83 and 8.5 kt a-1.

We report on six case studies on three different days of the CoMet campaign. For the days 28 May and 6 and 7 June 2018, Fig.  illustrates typical FLEXPART trajectories of air masses around midday dispersing out of the USCB coal mine ventilation shafts. For all cases, easterly winds led to the southern station Pustelnik being influenced by a few southern shafts (red trajectories) and the western station Raciborz being influenced by many shafts in various parts of the basin (blue trajectories). The eastern station The Glade provides the background measurements, and the northern station Za Miastem was not used here since The Glade (E) was the better background station given the prevailing easterly winds.

Figure  depicts the corresponding XCH4 measurements for all stations, indeed pointing at significantly elevated concentrations at the downwind sites typically amounting to ΔXCH4 on the order of 10 ppb with some diurnal and day-to-day variability. For 28 May, the maxima during the morning hours at Pustelnik (S) and Raciborz (W) are most likely connected to nighttime methane accumulation and subsequent transport with rising convection and mixing during the morning hours. When considering the Lagrangian travel time of air masses, these morning hours are excluded from the period of investigation since we have to wait for the air masses from the upwind site The Glade (E) to arrive downwind at Pustelnik (S) and Raciborz (W). Therefore, the period of investigation starts later than the Pustelnik (S) and Raciborz (W) measurement records. For Pustelnik (S), travel times ranged between 1.3 and 2 h and for Raciborz (W) between 3 and 5.5 h; 7 June had the longest travel times linked to the slow wind speeds on that day (see Fig. ). In particular, for 7 June, the consideration of the travel time implies that only a small fraction of the measurements at the end of the day is considered for the emission estimates. The stations The Glade (E) and Za Miastem (N) show roughly consistent background XCH4 for 28 May and 6 June, but, on 7 June, significant differences indicate that the background concentration field was not homogeneous. Nonetheless, the FLEXPART trajectories point to The Glade (E) being representative of the background conditions for the downwind stations Raciborz (W) and Pustelnik (S). Following the procedures described in Sects.  and , we calculate observed ΔXCH4 from the XCH4 observations by subtracting the background record of The Glade (E) from the Pustelnik (S) and Raciborz (W) records, shifting the time series by the calculated Lagrangian travel times. Then, we estimate the shaft-wise emissions by the Phillips–Tikhonov technique.

We estimated CH4 emissions from coal mine ventilation facilities in the USCB during the CoMet campaign in May–June 2018. To this end, we deployed four EM27/SUN spectrometers in a network configuration enclosing the USCB. Combining pairs of upwind–downwind XCH4 observations with trajectory simulations by the Lagrangian particle dispersion model FLEXPART, we attributed the observed ΔXCH4 enhancements to the emission rates of the facilities. The trajectory calculations were driven by wind fields simulated by WRF under assimilation of wind measurements by three wind lidars distributed throughout the region. The trajectory calculations also enabled us to take into account the travel time of air masses between the upwind and downwind stations. For emission estimation, we used a Phillips–Tikhonov regularization approach together with the L-curve criterion for selecting a well-suited regularization parameter. The regularization scheme comes with the emissions averaging kernel diagnostics that allow for quantifying which facilities or groups of facilities the measurements are sensitive to. For estimating errors, we constructed an ensemble of seven FLEXPART runs, each with slightly perturbed atmospheric parameters (wind speed, wind direction, PBL height).

Upscaling our emission estimates to annual emissions, we find higher emission rates than listed by E-PRTR. Other studies have shown better agreement between their instantaneous estimates and the E-PRTR inventory, while, in our study, only two out of six cases are compatible with the E-PRTR inventory within the error range (see Table ). The other four cases suggest 1.7 to 2.4 times higher emissions than reported by the E-PRTR. The comparisons with E-PRTR are only of an illustrative nature. Depending on the under-ground mining activities, the emissions from the mining process are highly variable in time, and thus our measurements are certainly not representative of the annual total reported by E-PRTR. In order to constrain the latter, a permanent observatory network would need to be operated with reasonably dense sampling throughout the year.

Our emissions estimates for the totals of all contributing facilities show errors in the range between 23% and 36%. Measurement errors (0.62 to 4.46 kt a-1) and background-variability-induced errors (0.83 to 8.5 kt a-1) are negligibly small compared to errors induced by uncertainties of the wind fields (27 to 143 kt a-1). As hinted at by the emissions averaging kernels, estimates for individual shafts are correlated, and these correlations were taken into account when calculating the aggregated total emissions. For all cases, these background concentrations were taken from the measurements conducted at the eastern station The Glade since the trajectory calculations showed that it was more representative for the background than the northern station Za Miastem. While for 28 May and 6 June, the two stations show similar concentrations (Fig. ), The Glade (E) records higher XCH4 than Za Miastem (N) on 7 June. Thus, the background concentration field has some spatial variability, which might be connected to remote sources such as the Krakow urban region affecting The Glade (E) but not Za Miastem (N) . In the future, we will aim at estimating errors due to spatial background variability by running a model that includes all known sources in a larger area around the target region or by deploying more spectrometers.

Our inverse method was set up such that the parameters to be estimated included all the individual CH4 ventilation shafts for which the trajectory calculations indicated contributions to the measurements. The problem requires regularization since CH4 plumes might mask each other (e.g., shafts located behind another shaft along the trajectory), since the detected contributions might have occurred only for a short period, and since, due to errors in the wind fields, the trajectories might indicate contributions when there were actually none or vice versa (e.g., for trajectories barely hitting the downwind station). The Phillips–Tikhonov regularization with L-curve criterion provides useful tools to diagnose the robustness and information content of the problem. The L-curve shows distortions for episodes when the FLEXPART trajectories cannot represent the true link between emissions and downwind concentrations. Thus, inspecting the L-curve allows for excluding episodes affected by these simulation errors. The emissions averaging kernels are useful to identify the shafts or groups of shafts for which the emissions can be reliably estimated from the observations. For our configurations, we found that we can resolve emissions of individual shafts for the Pustelnik (S) downwind station where only a few comparatively close facilities contribute to the ΔXCH4 enhancements. For the Raciborz (W) station with a much larger catchment area, we can typically resolve groups of shafts along the main wind direction, but disentangling individual shafts is not possible when they are close to each other or behind each other along the air mass trajectory. Nonetheless, we argue it is useful to set up the problem in terms of individual shafts instead of a priori aggregating shaft clusters since inspecting the emissions averaging kernels provides a tool to check which shafts can be resolved and since the aggregated total emissions and their errors can be calculated a posteriori.

CH4 emissions from sources other than coal mining are not considered in our FLEXPART simulations; i.e., the pairwise ΔXCH4 enhancements are assumed to be caused only by the ventilation shafts. have inspected EDGAR v4.3.2 for CH4 emissions from sources that are not related to coal mining activities such as landfills, wastewater treatment, and livestock in the USCB. They found that these other sources amount to roughly 14 % of the USCB total CH4 emissions and that the larger contributions stem form the northwest of the basin, which our measurements are not sensitive to. The CoMet inventory lists annual emission estimates for 4 of 16 landfills relevant for our case studies, which in total amount to 0.97 kt a-1. We expect similar emission estimates for the other 12 landfills reported with undefined emissions. Thus, we assume that contributions from sources other than coal mining are small compared to our error bars. We did not consider chemical reactions such as oxidation of methane with OH, since the timescales relevant for this study are too short for oxidation to have a significant influence on the emission estimations.

Overall, our study shows that deploying sun-viewing spectrometers in an ad hoc network configuration around the USCB allows for estimating CH4 emissions from coal mine ventilation facilities with some resolution for individual facilities and groups of them, depending on the deployment location. Given that the errors are dominated by uncertainties in the wind fields driving the trajectory calculations, it is essential to validate model winds by local wind data or, as in our case, to assimilate local wind lidar measurements. In the view of developing such networks toward a monitoring capacity, priority should be put on making the networks permanent for better temporal representativeness of the observations and on making the networks denser in order to gain sensitivity to more shafts and to better quantify spatial variability in the background concentrations. In addition to the monitoring aspect, permanent networks could also validate satellite missions, and the different ground-based and spaceborne emission estimation approaches could be consolidated.