Local to regional methane emissions from the Upper Silesia Coal Basin (USCB) quantified using UAV-based atmospheric measurements

Coal mining accounts for ~ 12 % of the total anthropogenic methane emissions worldwide. The Upper Silesian Coal Basin, Poland, where large quantities of CH4 are emitted to the atmosphere via ventilation shafts of underground hard coal (anthracite) mines, is one of the hot spots of methane emissions in Europe. However, coalbed CH4 emissions into the atmosphere are poorly characterized. As part of the Carbon Dioxide and CH4 mission 1.0 (CoMet 1.0) that took place in May – June 2018, we flew a recently developed active AirCore system aboard an unmanned aerial vehicle (UAV) to obtain 20 CH4 and CO2 mole fractions 150-300 m downwind of five individual ventilation shafts in the USCB. In addition, we also measured δ13C-CH4, δ2H-CH4, ambient temperature, pressure, relative humidity, surface wind speeds and directions. We have used 34 UAV flights and two different approaches (inverse Gaussian approach and mass balance approach) to quantify the emissions from individual shafts. The quantified emissions were compared to both annual and hourly inventory data, and were used to derive the estimates of CH4 emissions in the USCB. We found a high correlation (R2 = 0.7 – 0.9) between the 25 quantified and hourly inventory data-based shaft-averaged CH4 emissions, which in principle would allow regional estimates of CH4 emissions to be derived by upscaling individual hourly inventory data of all shafts. Currently, such inventory data is available only for the five shafts we quantified though. As an alternative, we have developed three upscaling approaches, i.e., by scaling the E-PRTR annual inventory, the quantified shaft-averaged emission rate, and the shaft-averaged emission rate that are derived from the hourly emission inventory. These estimates are in the range of 325 – 447 kt CH4/year for the 30 https://doi.org/10.5194/acp-2021-1061 Preprint. Discussion started: 3 January 2022 c © Author(s) 2022. CC BY 4.0 License.

quantified CH4 emissions and comparisons with annual and hourly inventories, quantified CO2 emissions, and regional USCB emission estimates that are scaled up from quantified shaft ventilation emissions of CH4 and CO2. A conclusion is given in Sect. 4.

Methodology 100
2.1 UAV-based Active AirCore system The active AirCore system was introduced in Andersen et al. (2018), and further refined in Andersen et al. (2021). The active AirCore system is an air sampling tool which collects air along the trajectory of a UAV flight by pulling air through a long coiled-up stainless-steel tube. The pump is a small KNF020L micropump, which provides a vacuum downstream of a 45 µm pinhole orifice in order to create conditions for critical flow. Thus, the sampling flow rate of the AirCore only 105 depends on the upstream pressure (ambient pressure), which is measured through the datalogger, along with ambient temperature, ambient relative humidity, temperature within the carbon fibre box housing, and GPS coordinates. This study used three different active AirCore systems, all having 1/8 in. tubing. The lengths of the AirCore were 48.2 m, 46.9 m, and 48.5 m, with estimated volumes of 323 cc, 315 cc, and 325 cc, respectively. The UAV that the active AirCore system is attached to is a DJI Inspire Pro 1. Once an air sample has been obtained, the air is analyzed by a cavity ringdown 110 spectrometer (CRDS, model no. G2401-m, Picarro Inc.) for CO2, CH4, and CO mole fractions. The CRDS used a high-CH4 analysis mode due to the large range of observed CH4 mole fractions (up to 200 ppm). A two-point calibration was used using a known WMO-scale gas mixture around ambient CH4 mole fractions (WMO X2007, X2004A, and X2014A scales for CO2, CH4, and CO, respectively), and a certified mole-fraction gas mixture from the Dutch National Metrology Institute (VSL) containing a high mole-fraction of CH4 (301.1 ppm). 115 Directly after the CRDS analysis, the AirCore samples were collected in Tedlar bags for further analysis of isotopic signatures of δ 13 C-CH4 and δ 2 H-CH4. The isotopic composition was determined by analyzing the samples stored in the Tedlar bags using a continuous flow isotope ratio mass spectrometer system. More details about the analytical system and the calibration are provided in Brass and Röckmann, 2011;Röckmann et al, 2016;Menoud et al., 2021. Out of the 59 flights 120 performed during this study, the air samples from 34 flights were stored in Tedlar bags for further analysis of isotopic composition. Borynia VI, Pniowek IV, and Pniowek V had two separate days where isotopic compositions were measured, while Brzeszcze IX and Zofiowka IV had 1 day. Each day collected between 4 and 5 samples which were used to determine the isotopic signature using a keeling plot.

Meteorological data 125
tethered through a fishing pole for easier retrieval and reuse, but was lost during the fourth flight due to getting too close to power lines. Four flights had radiosonde profiles to estimate the wind speeds and directions. Flights #5 to #33 were obtained from a nearby meteorological station operated by the Polish meteorological office (IMGW). This was the 130 Katowice Synoptic meteorological station, located at coordinates 50.240556N, 19.032778E. The use of this meteorological data, located a few tens of kilometers away from the measurement sites, may add significant uncertainty to the wind speed and direction for those flights, which was not quantified. For the second half of the campaign, from flight #34 to #59, a mobile onsite meteorological station was used. The surface wind speed and wind direction were measured using a Campbell CSAT3 3-D Sonic Anemometer. The CSAT3 has an operating temperature range of -30 • C to 50 • C. 135 A comparison study of two anemometers, Campbell CSAT3 and Gill R3-50, conducted by Grare et al. (2016) showed that the Campbell CSAT3 measurements are sensitive to small changes in wind direction. The mean differences wind speed and wind direction between the Katowice Synoptic meteorological station and the mobile meteorological stations for flights #34 and onward were 1.7 ± 0.7m/s and 38.8 ± 29.6 • , respectively.

Flight information 140
From an internal CoMet inventory based on E-PRTR 2017 emission data, there are 59 ventilation shafts related to hard coal mining operations located within the USCB. Fig. 1 indicates the size of this region. We sampled air from 5 of these ventilation shafts based on their accessibility, and performed a total of 59 flights during the period from May 18 to June 1, 2018. 36 of the 59 flights fulfilled the sampling criteria presented in Andersen et al. (2021). The flights were performed downwind of a specific ventilation shaft while flying perpendicular tracks transecting the plume at incremental 145 heights. This effectively creates a vertical curtain transecting the ventilation shaft plume. The curtain is spaced out into gridded boxes in horizontal(y)-and vertical (z)-direction of size equal to the largest distance between two data point coordinates in the flight, and the largest altitude difference between two point coordinates throughout the flight. The criteria states that the mean wind speed during the flight is larger than 2 m/s and that the flights are performed perpendicular to the wind direction (within 15 degrees). Table (1) shows the number of flights per shaft that fulfilled these 150 criteria, along with the number of measurement days present for each shaft. The flight pattern for the flights was a 'curtain' shape downwind the plume, attempting to intersect the plume at different altitude levels. Fig. 2a shows an example of this pattern. The flight duration varied between 8 and 12 minutes, and distances downwind the plume ranged between 100 to 350 m downwind the ventilation shafts.  for flights #5 to #33 was obtained. The red border indicates the total size of the Silesia Coal Basin where the majority of coal mining shafts were located. We have primarily performed measurements in the south-western part of the region (© Google Maps).

Emission determination
The emitted CH4 emanating from the ventilation shafts is quantified using the methodology derived in Andersen et al. (2021). At each ventilation shaft, CH4 is vented to the atmosphere through one or more diffusers. Given the distance of 100 170 -300 m between the UAV measurements and the ventilation shaft, the emission source can be regarded as a point source.
The gridded plane is then used to quantify the emitted emission by applying an inverse Gaussian approach and a mass balance approach. The Gaussian model is given as: where ! is the dry mole fraction at a given position x, y, and z, which are the projected positional coordinates downwind the plume, across the plume horizontally, and across the plume vertically. The units of ! (x, y, z) in mol/mol, and the units of x, y, and z are given in m. The emission rate Q is given in kg/s, the wind speed u in m/s, and the stack height h is given in m. The parameters σy and σz describe the dispersion of the pollutants in the horizontal-and vertical direction, respectively, and have units of m. V is the dry molar volume in m 3 /mol, and %& ! is the 180 molar mass of CH4, 0.016 kg/mol.
For the mass balance approach, the gridded flight pattern is extrapolated into a full 2D plane using a kriging method, to which the mass balance equation is applied. Fig. 2 shows a measured UAV-based active AirCore profile of CH4 mole fractions along with the 2D extrapolated kriged CH4 plane, and the inverse Gaussian's estimate plane of CH4 mole 185 fractions. The mass balance equation is given as: where the output of the emission rate Q is in kg/s, v is the wind speed in m/s and assumed to be constant throughout the duration of the flights, ki is the number of horizontal grid boxes in the kriged plane, kj is the number of vertical grid boxes in the kriged plane, MCH4 is the molecular mass of CH4 in kg/mol, Ci, j is the CH4 mole fraction in grid box i, j in mol/mol, ∆X is the area of each grid box in m 2 , R is the universal gas constant, 8.3145 kg m 2 /s 2 K mol, T is the temperature in K, and Pi, 190 j is the pressure at each grid box in Pa.

Inventory emissions 195
The E-PRTR inventory gives the annual emission for each coal mine in the Silesia region. An internal CoMet inventory, which is based on reported 2018 E-PRTR inventories (Gałkowski et al., 2021), lists 59 facilities related to coal mining operations in the USCB, and divides the annual coal mine inventory by geo-localized (via Google Earth) active ventilation shafts for each coal mine. For the comparison used in this study, the active ventilation shafts are assumed to be the same as the ones stated in the internal CoMet inventory, but the E-PRTR values that are being divided equally among active 200 shafts have been updated to the reported E-PRTR 2018 inventories. Pniowek, with a reported emission rate of 54.8 kt CH4/year and three active shafts thus yields an average emission rate of 18.3 kt CH4/year for ventilation shafts Pniowek III, IV, and V. The inventory value for Borynia VI is 7.4 kt CH4/year, for Zofiowka IV 12.7 kt CH4/year, and for Brzeszcze IX 6.9 kt CH4/year.

205
A second set of inventory data for May to June 2018 is also used for comparison during this study. This is hourly data calculated from raw CH4 concentration measurements and air flow rate measurements obtained within each specific ventilation shaft. Fig. 3 shows a schematic design of a ventilation shaft. The concentration of CH4 is measured with an EMAG-Serwis type DCH methane sensor placed 10 to 15 m down into the exhaust shaft. This sensor has a measurement range of 0 -100 % with measurement errors of 5 % of the reading value. The conditions are often rough and the relative 210 humidity is high, and the readings of relative humidity could exceed 100% when the filter is wet. The air flow rate is measured using a Prandtl's tube located between the main valve and the fan. According to Swolkień (2020), the relative uncertainty for the air flow rate is 10 %. According to the statements of ventilation engineers, about 5% of the vented air to the atmosphere is from air inflow via the ventilation shaft closure, and we have taken that into account during the calculation of the hourly emission rates, i.e., CH4 concentrations multiplied by 95% of the measured air flow rates. 215 The conversion into CH4 emissions rate is done as follows: Where P is the atmospheric pressure in Pa, R is the universal gas constant in J mol -1 K -1 , T is the ambient temperature in K, 2304 is the volumetric flow rate of CH4 in m 3 s -1 , given by the air flow rate multiplied by the CH4 concentration.
Lastly, ρ is the molar density of CH4 in g mol -1 (16.043 g mol -1 ). A temperature of 20 • C and a pressure of 101325 Pa 220 was used for the calculation.

Up-scaling
As mentioned in Sect. 2.3, more than 70 facilities related to coal mining operations are located in the USCB. According to the internal CoMet inventory, 59 are active ventilation shafts. After obtaining CO2 and CH4 emissions from 5 of the 59 shafts in the USCB, three distinct approaches are used to obtain an estimate of the regional emission rate. The first method uses the linear correlation of shaft-averaged emissions between our UAV quantified and high frequency 230 (hourly) reported emissions to scale the annual E-PRTR emissions. To avoid the large influence of the intercept, the linear curve has been forced through zero, making the slope the only factor to scale the emissions. The second approach uses the mean quantified shaft emissions, multiplied with the number of ventilation shafts in the region. The third approach scales the mean hourly inventory emission rate to derive the mean quantified emission rate based on the linear correlation of shaft-averaged emissions between our UAV quantified and high frequency (hourly) reported 235 emissions, which is then multiplied by the number of active ventilation shafts in the region. Fig. 4 shows the sampled isotopic signatures of δ 13 C-CH4 and δ 2 H-CH4 from the flights during the study, separated into different shafts and different days. For the five sampled ventilation shafts, the δ 13 C-CH4 values ranged between -53.4 and -240 41.3 % and the δ 2 H-CH4 values ranged between -175.0 and -151.2 %. According to Sherwood et al., 2021, isotopic signature values from coal mining vary from country to country and the source signature in Poland was found to be -48 ± 15 (± 1σ) % for δ 13 C-CH4 and -194 ± 37 for δ 2 H-CH4, respectively. All the isotopic signatures found from the UAV active AirCore respectively (Stanisavljevic, 2021). Overall, the addition of δ 13 C-CH4 and δ 2 H-CH4 measurements, and the good agreement between the found source signatures with those of other groups during the same campaign, indicate that we have clearly sampled the coal mine ventilation shafts using the UAV-based active AirCore system. Based on what is shown in Fig. 4 it is unlikely that other regional CH4 sources (such as biomass burning, landfills, and ruminants) have influenced the active AirCore measurements. 250  (Sherwood et al., 2021;Lan et al., 2021). The grayshaded area indicates the isotopic signatures found from other groups during the CoMet 1.0 campaign, and represents the calculated 255 weighted average for the coal in the USCB (Stanisavljevic, 2021;Menoud et al., 2020)

Quantified CH4 emissions
Fig . 5&6 show the estimated CH4 emission rates from individual ventilation shafts, for each day. Averages range between 2.7 ± 2.0 and 15.0 ± 2.3 kt/year for the inverse Gaussian approach, and between 0.8 ± 1.0 and 14.4 ± 3.7 kt/year for the mass balance approach. Large variations are seen from day-to-day for the same coal mine ventilation 260 shafts. The inverse Gaussian approach and mass balance approach have a mean difference of 2.5 kt/year, with a maximum difference of 8.9 kt/year on May 31. This is likely due to the majority of the plume being located outside of the gridded curtain, which causes the inverse Gaussian to move the center line of the plume off the grid to obtain the best fit between model and data, while the mass balance is constrained to only include what is included in the kriged plane. The same is seen in the first flight on May 25 for Pniowek IV (see Fig. 6 outside the measured grid. Three of the days were either weekend days or holidays. May 19 was a Saturday, while May 20 and May 28 were public holidays in Poland. The emission rates of CH4 could have been affected by irregular mining activity on these particular days. If mining operation were reduced on those days, less coal would have been cracked from the bedrock, and would 270 lead to less CH4 venting to the atmosphere, which will be further discussed in Sect. 3.3. Pniowek V was sampled on two of these days and can be compared to normal days. The holidays have an average estimate of 7.6 ± 3.6 kt/year for the inverse Gaussian, whereas the average during the sampled weekdays is 12.1 ± 2.7 kt/year. For the mass balance approach the mean weekend/holiday emissions are 8.3 ± 2.7 kt/year, while the weekday emissions have an average of 9.2 ± 7.4 kt/year, so here the difference is not significant. May 31 only has one successful flight, and only has mole 275 fraction enhancement along the edge of the flight (see supplement Fig. 15 flight #56), which leads to underestimation of the emission rate using the mass balance approach. Comparatively, the inverse Gaussian finds the plume center outside of the sampled plane, and estimates a much larger emission rate. Excluding the flight on May 31, the weekly mean becomes 13.3 ± 2.5 kt/year for the inverse Gaussian and 13.5 ± 1.4 kt/year for the mass balance approach. The weekend/holiday emissions are for the inverse Gaussian within the range of the error, while the mass balance does not overlap. The ratio 280 of weekend/holiday emissions to weekday emissions is 0.63 for the inverse Gaussian approach and 0.90 for the mass balance approach. This may indicate that there is an influence on the emitted CH4 during weekends/holidays. This means that the quantified emissions of the one day of measuring Brzeszcze IX may also be lower than on normal weekdays.     Fig. 7 shows the hourly inventory emissions for each ventilation shaft. The inventory reported to the E-PRTR is based on 295 this data. Note that inventory measurement for Borynia VI is missing for the period between May 19 and May 30 (Fig.   7a). We assume this was due to a malfunctioning CH4 sensor inside the ventilation shaft. The listed inventory data for Borynia VI in Table (2) was therefore calculated with data from May 30 to June 02. The Borynia VI inventory may therefore not represent the actual inventory of the days of measurements. The same can be concluded for Brzeszcze IX (Fig. 7b), which only has one given measurement point. The variability in the emitted emission is clearly seen in the 300 data from Pniowek IV, Pniowek V, and Zofiowka IV (Fig. 7c, The gray-shaded areas in Fig. 7 indicate days that were either weekend days or public holidays, and the highlighted red areas indicate flight days. As seen in Fig. 7e, some of the largest emissions occur during weekend/holidays, while some of the lowest emissions occur during the weekdays. There does not seem to be a consistent difference in emitted CH4 305 between weekdays and weekend days/holidays, as previously postulated in Sect. 3.2. The CH4 emissions of individual ventilation shafts show large variations, both hour-to-hour and day-to-day. In comparing the quantified CH4 emission rate on an individual flight basis with the annual emission rate reported to the E-PRTR, we found that the correlation is very low (R 2 < 0.05). Fig. 8a shows the correlation between the E-PRTR annual emissions that has been divided by the number of active ventilation shafts for a particular coal mine, and the UAV-based 315 active AirCore inverse Gaussian quantified CH4 emissions averaged by shaft emissions. Also, here the correlation is low (R 2 < 0.07, N = 5). When the total reported mine emissions for a specific mine from the E-PRTR inventory are divided equally by the number of active shafts, shaft-specific emission info is lost. The non-existing correlation indicates that the agreement between the snapshot flight quantified emissions with the E-PRTR inventory is poor. The hourly inventory data shown in Fig. 8b is therefore required for a direct comparison with the quantified emissions.

Comparison with inventory
Comparing this data on a daily-averaged basis with daily-averaged flight data sees a slight improvement in the obtained 325 correlation (R 2 = 0.23, N = 9), although the correlation is still weak. Due to the lack of hourly data for Brzeszcze IX, it has been omitted for the comparison. There can still be large variations on hourly basis, and thus a direct comparison between the hourly inventory over a day with snapshot flight profiles during the same day may not always align. Therefore, we have averaged the days together and compare shaft-specific averaged hourly data with shaft-specific averaged UAV quantified emissions from the same days. This is shown in Fig. 8c, which obtains a stronger correlation than the 330 two previous comparisons, with an R 2 = 0.86 (N = 4). When the linear fit is forced through zero, a higher R 2 value (0.95) is obtained. The quantified emissions are roughly 40 % lower than those of the hourly inventory; however, this is not significantly when considering the large standard deviation of the measurements.
The much-improved correlation from comparing hourly inventory data from individual shafts as opposed to a total mine 335 emission divided equally over active shafts (i.e., based on the E-PRTR 2018 inventory), indicates that translating shaft-quantified snapshot emissions to annual inventories is difficult. The hourly inventory data is not always available, but our evaluation indicate that they are required to make meaningful comparisons between quantified emissions and inventories. Due to the good correlation between the hourly inventory and the quantified emissions per shaft, we can use the hourly inventory data to scale up the quantified emissions. We use the slope of 1.1 and the intercept of -4.0 of 340 the linear fit to scale up our quantified emissions. This will be discussed in Sect. 4. For the mass balance approach (data not shown), the correlations are also much improved when hourly inventory data is used for comparison, although the R 2 values are slightly lower than those for the inverse Gaussian approach. Annual E-PRTR (2017)  has been forced through origin. All panels display only the data from the inverse Gaussian approach; however, the title lists the curve fit from the mass balance approach as well. The E-PRTR inventory has been divided by the number of active ventilation shafts, and the 350 number of active shafts is taken from the internal CoMet inventory, which had emission profiles based on 2018 Fig. 9 shows the boxplot comparison between estimated emissions from both the inverse Gaussian approach and the mass balance approach, against the hourly inventory for each ventilation shaft. The inventory data includes data for the same days as the flights, except for Borynia VI and Brzeszcze XI. As previously mentioned, Brzeszcze XI contains only an annual estimate, while for Borynia VI inventory data are missing for the specific days when this shaft was sampled. 355 Pniowek V, the shaft with the best statistics (N = 13 for the inverse Gaussian and N = 14 for the mass balance approach over 5 different days), has largely overlapping distributions with the hourly inventory data, although leaning towards the lower end of the hourly inventory distribution. This indicates that this statistical pool is sufficient to accurately quantify comparable emissions. Pniowek IV and Zofiowka IV both have N = 5 for the inverse Gaussian, and N = 7 and N = 5 for the mass balance, respectively. Zofiowka IV has overlapping distributions with the hourly inventory, but the quantified 360 emissions largely span the lower hourly inventory distribution. This is seen with all other shafts as well. Pniowek IV has only a small overlap with the hourly inventory distribution for both the inverse Gaussian and mass balance approach. This could be due to variable winds making quantification difficult flights, or perhaps that the flights were performed at times of low emission that the hourly inventory did not pick up. Brzeszcze IX is difficult to compare, due to the lack of hourly inventory data, and the only hour inventory data matches the upper end of the inverse Gaussian estimates. Finally, Borynia 365 VI has the lowest statistics with N = 2 for the inverse Gaussian and N = 3 for the mass balance approach over two different days. There is no overlap between the distributions. Borynia VI, as well as Brzeszcze IX, are difficult to compare, due the lack of direct hourly inventory data around the days of flying.
Thus, the measured distributions for Pniowek V, Pniowek IV, and Zofiowka IV all over with the hourly inventory 370 distributions for the same day, with a minimum of N > 5 flights. The largest overlap is as mentioned found in Pniowek V, containing several days of sampling and N > 13. These distribution comparisons suggest that although single flight estimates may not be correlated well with the hourly inventory, the averaged estimates of multiple flights show a strong correlation with those of the inventory, which suggests that more than one flights are required to obtain a good estimate. Note that for all shafts, the UAV estimated emission distribution is located on the lower end of the inventory distribution.

Carbon dioxide emission
Similar to the coal mining shaft sampled in Andersen et al. (2021), a strong correlation is found between the emitted 380 CO2 and CH4. The way of obtaining the emitted CO2 emission using the correlation between CO2 and CH4 mole fractions, the emitted CH4 emissions, and the molar mass constants of CO2 and CH4 is given as: where QCH4 is the quantified CH4 emission, the slope is the slope of the linear fit between CO2 and CH4, and MCO 2 and MCH4 are the molar masses of CO2 and CH4, respectively. There were some flights that had no, or low correlation, and were thus omitted from the CO2 emission calculation. These were flights with R 2 < 0.5. Of the 36 flights that fulfilled 385 the criteria list, the number of flights above an R 2 value of 0.5 was 25, with an average R 2 of 0.8. The average CH4/CO2 slope was 4.6 ± 2.9 ppmCH4 /ppmCO 2 .

Upscaling to regional estimates
As shown in Table (2), the mean quantified CH4 emission of the five sampled coal mine ventilation shafts is 5.5 ± 2.6 kt 400 CH4/year for the inverse Gaussian approach and 5.4 ± 3.2 kt CH4/year for the mass balance approach, respectively. For CO2, the mean emission is 4.2 ± 2.2 kt CO2/year for the inverse Gaussian approach and 3.8 ± 2.3 kt CO2/year for the mass balance, respectively. As much as 59 active ventilation shafts are located across the entire USCB. According to the 2018 E- PRTR inventory, the regional CH4 emissions adds up to 447.9 kt CH4/year, while the regional CO2 emissions are stated to be

[Mt CO2/year]. 405
Three distinct approaches have been used to obtain an estimate of the regional emission rate. The first method uses the linear correlation of shaft-averaged emissions between our UAV quantified and high frequency (hourly) reported emissions shown in Fig. 8d to scale the annual E-PRTR emissions. To avoid the large influence of the intercept, the linear curve has been forced through zero, making the slope the only factor to scale the emissions. For the inverse Gaussian approach, the slope is 410 0.744, which multiplied with the 447.9 kt CH4/year inventory results in 332.6 kt CH4/year. For the mass balance, with a slope of 0.6, the resulting emissions are 268.2 kt CH4/year. These results are shown in Fig. 11a as yellow bars.
The second approach uses the mean quantified shaft emissions of 5.5 ± 2.6 kt CH4/year for the inverse Gaussian approach and 5.4 ± 3.2 kt CH4/year for the mass balance approach, multiplied with the number of ventilation shafts in the region. This 415 amounts to a regional emission of 324.5 ± 147.5 kt CH4/year for the inverse Gaussian approach and 318.6 ± 188.8 kt CH4/year for the mass balance approach, respectively. These emission estimates compare well with the ones from the previous approach, but are lower than the emissions estimated by Fiehn et al. (2020) and Kostinek et al. (2021). These are shown in Fig. 11a as blue bars.

420
The third approach uses the linear curve from Fig. 8c to scale the mean hourly emission rate calculated from hourly inventory data, to derive the mean quantified emission rate, which is then multiplied by the number of active ventilation shafts in the region. Here, both the slope and intercept are used for the scaling. The mean hourly inventory emission rate is 10.4 ± 3.1 kt CH4/year. The linear curve using the inverse Gaussian approach has a slope of 1.113 and an intercept of -4.0, resulting in a derived mean quantified emission rate of 7.6 ± 2.3 kt CH4/year. For the mass balance, a slope of 0.873 and an 425 intercept of -3.2 results in a derived mean quantified emission rate of 5.9 ± 1.8 kt CH4/year. Multiplying these numbers with the number of active ventilation shafts results in regional emission rates of 446.9 ± 133.2 kt CH4/year for the inverse Gaussian and 346.9 ± 103.4 kt CH4/year for the mass balance approach, respectively. The regional estimates for the inverse Gaussian approach and mass balance approach resulting from the third upscaling approach are shown in Fig. 11a as purple bars. Figure 11. A comparison of regional inventory emissions for CH4. The first bar (red) represents the E-PRTR inventory. The second bar (yellow) represents the E-PRTR inventory scaled by the linear fit. Bars three and four (teal) represent the estimated regional emissions from Fiehn et al. (2020) from their two flights. Bars five and six (green) represent the estimated regional emissions from the two flights of Kostinek et al. (2021). Bars number seven (blue) and eight (light blue) represent the regional emission using the quantified 435 inverse Gaussian and mass balance estimates, respectively. The last two bars, ten (purple) and eleven (light purple), represent the scaled regional emission using the inverse Gaussian approach and the mass balance approach, respectively.
Comparing the inverse Gaussian-derived regional emission with both the annual E-PRTR inventory and the regional estimates from Fiehn et al. (2020), the results are close to one another, and are not statistically different when their 440 uncertainties are considered. Fiehn et al. (2020) estimated the regional emissions over two separate flights during the same CoMet campaign to be 437.6 ± 114.2 kt CH4/year and 478.8 ± 95.1 kt CH4/year, similar to the 447.9 kt CH4/year E-PRTR inventory. Kostink et al. (2021) also estimated the regional emissions over two separate flights, and found emissions rates of 451 ± 77 kt CH4/year and 423 ± 79 kt CH4/year. Our estimated emissions appear to be lower, except for the inverse Gaussian-derived scaled hourly rate. Since we have only quantified 5 individual shafts out of 59 active shafts in the region, 445 the small number of quantified shafts could be one of the main causes of the difference.
The upscaling process for CO2 cannot be explored by the same approaches as for CH4, since the linear curves from Fig. 8 are only valid for CH4. Therefore, only the second approach can be used, where the mean quantified CO2 emission will be multiplied with the number of active ventilation shafts in the region. The mean CO2 emission is 4.2 ± 2.2 kt CO2/year for the 450 inverse Gaussian approach and 3.8 ± 2.3 kt CO2/year for the mass balance, which yields a regional emission estimate of 0.3 ± 0.1 Mt CO2/year for the inverse Gaussian approach and 0.2 ± 0.1 Mt CO2/year for the mass balance approach, respectively. This is significantly less than the E-PRTR inventory of 35.3 Mt CO2/year and the estimated regional emissions rates from Fiehn et al. (2020) of 38.2 ± 22.7 Mt CO2/year and 35.3 ± 11.7 Mt CO2/year. Comparatively, these estimates are ~ 1 % or less of the listed E-PRTR inventory. According to the E-PRTR (2018) inventory, 98.2 % of emitted CH4 in the 455 USCB originates from underground and related operations, 1.5 % coming from opencast mining and quarrying, and 0.3% from waste and waste water management. For CO2, the major contributors are thermal power stations and other combustion installations and production and processing of metals. These account for 78.9 % and 16.3 %, respectively. Residential heating accounts for 2.6 %, while other industrial manufacturing accounts for 2.2 %. However, CO2 emissions from coal mining activities are not included in the E-PRTR inventory. 460 The upscaling uses daily snapshots to estimate an annual emission by multiplying the annual average of the five sampled shafts by the number of ventilation shafts in the region. As shown in Sect. 3.3, each ventilation shaft can have significant variations in its daily emissions, thus this adds uncertainty to the daily snapshots extrapolated to an annual emission. Ventilation shafts can have significantly different emission rates, thus grouping the 5 shafts together to obtain the average 465 does not accurately represent the emission distribution in the whole region. This adds additional uncertainty to the upscaled regional emission. Despite this, we see a good agreement with the two flights from Fiehn et al. (2020), Kostinek et al. (2021) and the E-PRTR inventory for CH4 within the error bars (see Fig. 11a), especially using the third approach of deriving the quantified emissions from hourly inventory data and scaling this to a regional emission rate. This indicates that the upscaling of the ventilation shafts emission estimated from the UAV-based active AirCore can be a useful tool for 470 relatively cheap and easy-to-obtain regional emission estimates. Estimated regional CO2 emissions are vastly smaller than the suggested regional inventory and also the regional emissions found by Fiehn et al. (2020). The estimated regional CO2 emissions account for ∼ 1 % of inventory, confirming that the coal mine ventilation shafts are not a major source of CO2 in the USCB. This is also reflected in the E-PRTR inventory, which does not list coal mining as a CO2 source at all. Due to t he omission of CO2 emitted from underground coal mining in the E-PRTR inventory, we conclude that the CO2 475 inventory is missing a source of roughly 1 %.

Conclusions
It is important to obtain independent estimates of the emission magnitudes from coal mining shafts and verify reported emission inventories to be able to reduce the overall emissions. Using the UAV-based active AirCore system, we have made atmospheric measurements of CH4 and CO2 mole fractions downwind of five different coal mine ventilation shafts in the 480 USCB. We apply an inverse Gaussian approach as well as a mass balance approach to quantify the CH4 and CO2 pointsource emissions for the five sampled ventilation shafts, and compare these estimates with reported inventory data. The estimated point sources are used to extrapolate a total USCB regional CH4 and CO2 estimate.
The CH4 emission estimates indicate that the coal mine ventilation shafts have highly variable emission rates. Over the five 485 quantified shafts, the quantified emissions using the inverse Gaussian approach range between 1.2 and 15.0 kt CH4/year, with a mean of 5.5 ± 2.6 kt CH4/year. For the mass balance approach, the quantified emissions range between 0.3 and 19.3 kt CH4/year with a mean value of 5.4 ± 3.2 kt CH4/year. This large variability is reflected in the hourly inventory data for the same coal mine ventilation shafts, and it is therefore clear that comparisons of the UAV-based active AirCore quantified emissions and annually averaged inventories show very low (R 2 = 0.06). Day-by-day comparisons of the 490 quantified emissions with hourly inventory during the same days yields a better correlation (R 2 = 0.23), but the best correlation is found on shaft-by-shaft comparisons, obtaining an R 2 of 0.85 for the inverse Gaussian approach and 0.67 for the mass balance approach. Distribution comparisons between the hourly inventory and the quantified emissions show that more flights are beneficial to accurately estimate the shaft emissions. Due to the large variability of the shaft emissions, single flights may sample at times of small or large emission. Correlation between CH4 and CO2 495 mole fractions is large for all flights (average R 2 = 0.8) and has an average slope value of 4.6 ppmCH4 /ppmCO 2 .
Quantified CO2 emissions for the combined five ventilation shafts yield an average of 4.4 ± 2.2 kt CO2/year for the inverse Gaussian and 3.8 ± 2.3 kt CO2/year for the mass balance approach. To obtain regional estimates, we have used three upscaling approaches by scaling the E-PRTR annual inventory, the 500 quantified shaft-averaged emission rate, and the shaft-averaged emission rate that are derived from the hourly emission inventory. The first approach obtains emission rates of 333 kt CH4/year from the inverted Gaussian approach and 268 kt CH4/year from the mass balance approach, respectively, which compares well with the second approach of 325 ± 148 kt CH4/year (Gaussian) and 318.6 ± 189 kt CH4/year (mass balance). These estimates are slightly lower than the previous results from Fiehn et al. (2020), Kostinek et al. (2021) and the E-PRTR inventory of 448 kt CH4/year. The third approach 505 results in regional emission estimates of 447 ± 133 kt CH4/year (Gaussian) and 347 ± 103 kt CH4/year (mass balance), providing a good comparison with both the E-PRTR inventory and previous results from Fiehn et al. (2020) and Kostinek et al. (2021). However, the differences are not significant when the relatively large uncertainties are considered. Upscaled regional emissions for CO2 amount to 0.2 -0.3 Mt CO2/year for both quantification approaches, and represent only ~ 1 % of the reported inventory and regional CO2 estimates from Fiehn et al. (2020), confirming that the coal mine ventilation shafts 510 are not a minor contributor to the regional CO2 emissions.
The uncertainty in the emissions quantified by UAV-based AirCore measurements is linked to the stability of the wind, as discussed in Andersen et al. (2021). The 10-12 minute snapshots are not instantaneously sampled, and an unstable wind may cause the emission plume to meander across the plane. Although a single flight may not accurately represent the ventilation shaft emissions, this study shows that with multiple flight quantifications for a single shaft a good estimate of the shaft's emission rate can be made. Short-term flights over the span of two weeks are used to estimate an annual average, where emission rates may vary week-to-week. The regional emission estimates assume that all shafts of a single coal mine emit an equal amount, which clearly is not true. A more accurate up-scaling model taking into account the individual emission size of different shafts would help improve this estimate. 520 The use of UAV-based active AirCore measurements in combination with the inverse Gaussian approach and the mass balance approach has been demonstrated to be able to quantify the emissions from individual ventilation shafts, which can then be used to estimate regional emissions of both CH4 and CO2. The uncertainty of the regional estimates can be reduced by increasing the number of quantified shafts. The UAV system is flexible and versatile, and opens up opportunities to 525 quickly obtain regional estimates in regions that are otherwise hard to access. Be it the determination of a single emitting point source or a regional estimate, the UAV-based active AirCore system can be a valuable tool to help understand the CH4 budget, and verify and constrain uncertainties of single strong CH4 point source emitters or regions.