During the CoMet 1.0 campaign several aircraft- and ground-based instruments were used to extensively sample greenhouse gas emissions of the USCB in early summer 2018. Here we present measurements taken aboard the DLR Cessna Grand Caravan 208B (Caravan). The Caravan was based in Katowice, Poland, from 29 May to 13 June 2018. Ten research flights were conducted in the USCB targeting different parts of the USCB. The flight paths were planned using a CH4 plume forecast provided by the online-coupled, 3 times nested global and regional MECO(n) model (Nickl et al., 2020). For our estimation of entire USCB emissions, we use airborne in situ observations from two flights on June 6, 2018, one in the morning (09:22–11:45 UTC, 11:22–13:45 CEST) and one in the afternoon (13:01–15:28 UTC, 15:01–17:28 CEST), in the following referred to as flights A and B, respectively. Figure 1 shows the flight track of flight B on a map with the CH4 emission sources. Both flights were designed in a box pattern with an upwind leg in the northeast approximately in the middle of the PBL and the downwind wall in the southwest with flight transects at several heights. CH4, CO2 and CO enhancements were clearly observed in the downwind wall. The flights were conducted in coordination with ground-based teams, which drove the instrumented vans below the upwind and downwind legs. Their tracks and sampled CH4 mole fractions for the afternoon flight are shown in Fig. 1. For the emission estimation, we selected ground-based data according to closeness in time. Sampling times for flight and ground-based data are listed in Table S1 in the Supplement.

Additionally, three Doppler wind lidar Leosphere Windcube 200S instruments were stationed at Rybnik, Wisła Mala and Krzykawka to measure vertical profiles of wind speed, wind direction and turbulence parameters (Fig. 1). Details on the CoMet lidar wind measurement setup and the planetary boundary layer height (PBLH) determination are given in Wildmann et al. (2020) and Luther et al. (2019).

A sophisticated suite of instruments aboard the Caravan gathered both meteorological parameters and trace gas concentrations. A five-hole probe, connected to a pressure transducer, is mounted on a nose boom under the left wing of the aircraft and measured the three-dimensional wind vectors. The temperature, pressure and humidity sensors and the calibration of the wind measurement system are described in detail by Mallaun et al. (2015). A flight-ready cavity ring-down spectroscopy (CRDS) analyzer (G1301-m, Picarro) was installed in the cabin of the aircraft. It measured CH4, CO2 and water vapor at a frequency of 0.5 Hz with cavity ring-down spectroscopy. Trace gas concentrations for water vapor were corrected according to Rella et al. (2013). The calibration and uncertainty assessment were conducted analogously to Klausner et al. (2020), who used the same instrument, aircraft and calibration technique. Details specific to the CoMet setup can be found in the Supplement (Table S2 and Sect. S1 in the Supplement). CO is measured with a modified quantum cascade laser spectrometer (QCLS) (Aerodyne) that also records CO2, CH4, ethane (C2H6) and nitrous oxide (N2O) (Kostinek et al., 2019). Furthermore, a dry-air sampler with 12 glass flasks (1 L) was installed aboard the Caravan, which were filled during the flight and later analyzed in the laboratory at the Max Planck Institute for Biogeochemistry for trace gas concentrations and isotopic signatures (CH4, CO2, CO, N2O, H2, SF6, δ13C-CO2, δ18O-CO2, δ13C-CH4, δ2H-CH4). However, in this study we focus only on the continuous in situ observations, while the results of ethane measurements and isotopic signatures will be published in a follow-up study.

Ground-based CH4 data were recorded by three teams using vans equipped with different CRDS analyzers (Picarro G2201-i, AGH University and University of Heidelberg; G2301, Utrecht University). The group from the AGH University measured below the upwind leg and groups from University of Heidelberg and Utrecht University sampled below the downwind tracks. For traceability between airborne and ground-based systems, an instrument intercomparison was conducted with the same four gas cylinders.

We use a mass balance method to calculate emission estimates for the USCB from two flights conducted on 6 June. This approach is subject to several assumptions. First, the wind speed, wind direction, emissions and PBLH should remain constant over the sampling time. Second, the trace gas plume has to be discernible from the atmospheric background. Third, there should not be any entrainment/detrainment into the free troposphere, and the lifetime of the species must be much longer than transport and sampling times. Finally, the trace gas plume should be well-mixed between the lowest flight track and the ground. These criteria are most likely to be met in the early afternoon, when the PBL has reached its maximum height and does not rise any further. The PBLH generally increases during the morning; hence afternoon flights are preferred over morning flights for mass balance studies. For our morning flight, we determine the temporal change of the PBLH during sampling to be 20 % of its final height. We apply a correction to the observed trace gas enhancements to account for this change (see Sect. 3.2).

In our approach we calculate the mass flux of each trace gas (CO2, CH4 and CO) through a vertical surface along the downwind flight tracks, here called “wall” (see Fig. 1). The wall stretches from the ground to the top of the PBL. Since the downwind measurements, ground-based and airborne, were not taken exactly on this wall, as a first step, all data used in the calculation are projected onto the closest point of the wall and then interpolated to fill the entire wall using the well-known kriging approach. The flux through the wall is defined by 1F=∫z=groundz=PBLH∫x=Sx=NΔcx,zvx,zdxdz, where Δcx,z is the concentration enhancement of the trace gas above the background at each grid point, while vx,z describes the wind speed component at each grid point perpendicular to the wall. The integration area is defined by the ground, the PBLH and the edges of the wall to the south S and north N (see bottom right panel of Fig. 2). The PBLH is determined from the vertical gradient of potential temperature, measured during profile flight sections, and the times when the top of the PBL was crossed in the wall. During the afternoon flight the PBL top was crossed three times in the wall and from this information the slanted boundary layer height could be well constrained.

The concentration enhancements Δc are calculated from observed, interpolated mole fractions m and the background mole fraction m0 of the trace gases using linear temperature and pressure profiles deduced from the airborne measurements: 2Δc=m-m0MpRT. Here, M is the gas molecular weight, p the pressure, R the universal gas constant, and T the temperature in kelvin.

To retrieve trace gas mole fractions m and wind speed v on the wall between the actual flight tracks, we use the kriging interpolation method with a stochastic Gaussian model. Kriging creates a grid of estimated values from data points with sparse spatial coverage and also gives standard errors for these values. We use a modified version of the EasyKrig software (© Dezhang Chu and Woods Hole Ocean Institution). For more details see Mays et al. (2009) and Pitt et al. (2019), who previously used this software in an aircraft mass balance study.

For CH4, not only the mole fraction measured along the flight transects but also the data of the ground-based measurements are included in the kriging. Although CO2 was also measured on the ground by the same instruments, the data cannot be used because they are heavily influenced by the surrounding car traffic. For ground-based CO2, neither large-scale enhancements nor background concentrations could be discerned. We chose the CH4 observations along the ground track closest in time to the airborne measurements. The data are projected onto the downwind wall, averaged over 20 s and then interpolated horizontally to regular distances before kriging. Airborne data are averaged over 10 s intervals in order to reach similar spatial resolution to the ground-based data. Only data below the PBLH are included in the kriging process. We then closely followed the approach described in Pitt et al. (2019). The kriging output fields of CH4, CO2, CO mole fractions and perpendicular wind speed are given at a grid resolution of 0.1∘ in latitudinal direction and 20 m in the vertical.

For an error estimate of the derived mass flux, we consider the statistical error of the input data and the systematic error of the method.

Several inventories of greenhouse gas and air pollutant emissions exist for the USCB. They vary in spatial and temporal resolution, as well as in the time for which they are available. Table 1 gives an overview of the six inventories we use in this study for comparison with top-down-derived CH4, CO2 and CO emissions in the USCB region.

The first point source inventory listed in Table 1 is the European Emission Release and Transfer Register (E-PRTR). It results from the regulation (EC) no. 166/2006, which implements the United Nations Economic Commission for Europe (UNECE) PRTR Protocol under which industrial facilities have to report their emissions to air if they exceed a threshold of 100 t a-1 for CH4, 100 kt a-1 for CO2 and 500 t a-1 for CO. Annual data can be downloaded from the European Environmental Agency's website (EEA, 2020). More information on the E-PRTR is given via its website: https://prtr.eea.europa.eu/ (last access: 24 February 2020).

The CoMet v2 inventory is a point source inventory based on the E-PRTR 2016 emissions created by the CoMet team especially for this campaign. It comprises anthropogenic sources of CH4 and CO2 in the USCB and its vicinity. The largest difference between the E-PRTR and the CoMet inventory is that E-PRTR considers each coal mine to be one single point source, often located at the mining operator headquarters, whereas in the CoMet inventory individual ventilation shafts were visually geo-localized using Google Earth. Then, the emission value of each mine was evenly distributed between all ventilation shafts belonging to that mine. Active Czech coal mines in the Ostrava region did not report any CH4 emissions to E-PRTR but were assumed to emit the same amount of CH4 per metric ton of extracted coal as Polish mines. We deduced a factor of 11.8±5.2 kg CH4 per metric ton of extracted coal for the USCB mines listed in Table S3 and applied this value to the Czech mines of Karviná, Karkov, CSM and Paskov. The locations of the 14 listed landfills and waste disposal sites were checked against satellite imagery. Their CH4 emission is assumed to be 3.3 kt a-1, which is less than 1 % of the total USCB emissions.

Scarpelli et al. (2020) published the newest gridded emission inventory available for comparison within this study. It only contains CH4 emissions from oil, natural gas and coal exploitation. But since these are the main sources (87 % according to CAMS) of CH4 emissions in the USCB, values are comparable to the total of other inventories. Scarpelli et al. (2020) use the national totals of emissions reported to the UNFCCC and distribute them according to the positions of relevant infrastructure. Uncertainties of the emissions are based on the emission factor uncertainties from the Intergovernmental Panel on Climate Change (IPCC) and are given as gridded information. Averaged over the USCB, the given relative error standard deviation for CH4 emissions is 60.9 %.

The Copernicus Atmospheric Monitoring System (CAMS) regional emission inventory (CAMS-REG-GHG/AP; Granier et al., 2019) is based on the TNO-MACC inventories (Kuenen et al., 2014). This inventory offers a resolution twice as high as the Scarpelli and EDGAR inventories. The inventory was also constructed by using the reported emission national totals by sector and spatially distributing them consistently across all countries by using proxy parameters.

The most widely used gridded emission inventory is probably the Emission Database for Global Atmospheric Research (EDGAR, https://data.europa.eu/doi/10.2904/JRC_DATASET_EDGAR, last access: 22 October 2020) global emission inventory. The most recent version 5.0 (https://edgar.jrc.ec.europa.eu/overview.php?v=50_GHG, last access: 22 October 2020) includes emissions of the three major greenhouse gases CO2, CH4 and N2O. It is based on the previous EDGAR version 4.3.2 (Janssens-Maenhout et al., 2019). We use the CO emissions from the air pollutant inventory (Crippa et al., 2018) from version 4.3.2. The most recent year of emission data is 2015 for CH4, 2018 for CO2 and 2012 for CO. In EDGAR, annual country-specific emissions are derived from international activity data and emission factors, which are then distributed in time and space using monthly shares and spatial proxy datasets. The data include uncertainty factors per species for three types of countries: OECD countries of 1990, countries with economies in transition in 1990 and the remaining countries in development. European emissions from EDGAR in 2012 have standard deviations of 16 % for CH4, 2.5 % for CO2 (Janssens-Maenhout et al., 2019) and 65  % for CO (Crippa et al., 2018).

The GESAPU inventory (Bun et al., 2019) has been created for Ukraine and Poland only for the reference year 2010. Originally, it is a point, line and area source inventory based on shapefiles. The advantage of this type of information is that it has a very high resolution but can also be gridded with any spatial resolution and orientation. The GESAPU inventory comprises all sectors of anthropogenic emissions. Here we use a gridded version of the emissions with a resolution of 15 arcsec (approximately 296m×463 m for the region).

Figure 2 shows the spatial distribution of CH4 emissions as given by the six inventories. Point sources from E-PRTR and the CoMet inventory are displayed as black markers while the background colors give the gridded inventory values. Although the inventories generally agree on the locations of CH4 emissions, there are several cases where sources seem to be missing. Regarding point sources, E-PRTR (top left) has fewer individual sources than the CoMet inventory (top right) due to the separation in single ventilation shafts. Additional mines in the CoMet inventory include the four Czech mines and the four ventilation shafts of the Brzeszcze mine around 19.15∘ E and 49.95∘ N. The gridded Scarpelli (top left) emission distribution for CH4 does not represent the point sources well. There are no emissions north of 50.2∘ N although several mines are located in this northern area. Generally the CAMS (top right) emission maxima seem to represent the point source locations better than the Scarpelli or EDGAR (bottom left) emission distribution, with the exception of the Czech mines, which are included in Scarpelli and EDGAR, but not in CAMS. In the GESAPU inventory, the high CH4 emissions associated with mining activities were visualized by overlaying a marker for sources above 1 kt a-1 on the gridded emission map. These are fewer high-emitting sources than in the E-PRTR inventory. This could be caused by consolidation and separation of mines between 2010 and 2017, the respective years for the data. Two flights (on 6 June 2018), which are shown as blue tracks in Fig. 2, were designed to capture the emissions of the region during northeasterly wind conditions.

The CO2 and CO emission distribution in the inventories is displayed in Fig. 3. CO2 point sources (from E-PRTR and CoMet) agree well with EDGAR and CAMS, except for the strong CO2 and CO emissions associated with the Łagisza power plant and ArcelorMittal steel factory at 50.34∘ N and 19.28∘ E, which are correctly placed in the northeast corner of the flight track in E-PRTR, CoMet and GESAPU. Instead, EDGAR and CAMS include an emission hot spot to the southeast and east, respectively, of this location that is not associated with a point source. The Rybnik power plant, located in the central western USCB, is the strongest point source emitter of CO2 in all inventories. CO has one emission hot spot in the USCB, namely the ArcelorMittal steel factory next to the Łagisza power plant with 137 kt a-1 in E-PRTR 2017. This source is not represented in EDGAR and shifted to the east in CAMS. GESAPU includes this source, but with much lower emissions of 63 kt a-1.

To compare the emission inventories with our mass balance flights, the emissions of each inventory are summed up within an area representative of the flight track and wind direction (more details see Sect. 3.3), which is marked by the black boxes in Figs. 2 and 3. Since some of the CO2 and CO sources are obviously misplaced in the gridded inventories, but really lie within our mass balance area, we enlarged the mass balance area toward the east in order to include these sources into the USCB sum. These enlargements are marked by red lines in Fig. 3. Although missing sources influence the comparison between inventories and the emission estimate via aircraft, the misplacements might not, since misplaced emissions are now within the enlarged mass balance area.

For each inventory, the total annual emission from the enlarged area including the reported uncertainty is given in Table 2. These values include emissions from all sectors available in the inventories (see also discussion in Sect. 4). Scarpelli assumes the highest emissions for CH4, followed by CAMS and CoMet. GESAPU features the lowest CH4 emissions, which might partly arise from the sources in the Czech Republic, which are not covered in the inventory. The highest CO2 emissions are assumed by the EDGAR inventory. CO emissions are highest in CAMS, closely followed by GESAPU.

The meteorological conditions have to fulfill certain criteria for a feasible mass balance calculation. On 6 June 2018, the weather conditions for an airborne mass balance experiment in the USCB were advantageous due to relatively constant wind speed and wind direction over the sampling time. The PBLH changed considerably during flight A in the morning, but was rather constant during flight B in the afternoon.

The wind lidar measurements at Rybnik airport were located close to the center of our in situ wall (Fig. 2) and can be used to assess the wind history over the entire measurement day. Vertical profiles of wind speed and wind direction show that during the previous night a low-level jet blew over the area with wind speeds of more than 10 m s-1; in the morning the wind slowed down to around 5 m s-1 and then accelerated to 6–7 m s-1 around 13:00 UTC (Fig. 4, Table 3). The boundary layer wind direction was between 50 and 70∘ over the entire day. The nightly low-level jet prevented accumulation of emissions, and the slowing down around 06:00 UTC provided relatively constant wind speeds for 4 h before we started our downwind sampling at 10:00 UTC. This steady wind history prior to the flight is crucial for the mass balance approach, because of the assumptions stated in Sect. 2.2. During this time emissions from the farthest shafts (75 km from downwind wall) were able to travel from emission to observation location at constant wind speed and direction. A comparison of aircraft observations in the downwind wall and wind lidar averages during the observation times is given in Table 3. Observed wind speeds with the lidar are within the range of aircraft-observed wind speeds. Generally wind speeds in the southern USCB were about 1 m s-1 higher than in the northern part of the USCB.

The diurnal development of the PBLH, with a maximum of 1.7 km above sea level (a.s.l.), is discernible from the wind lidar observations. The PBLH measured by the wind lidar increased from 1.1 to 1.5 km during the sampling of flight A but remained relatively constant at 1.7 km during flight B. We also determined the PBLH from two vertical aircraft profiles of potential temperature, observed before and after the sampling of the downwind wall (Fig. S3). Before flying the wall pattern, we obtained a vertical profile in the southern part of the USCB area (around 49.8∘ N, 18.2∘ E). After finishing the wall pattern a northern profile was sampled on the way back to Katowice airport (50.3∘ N, 18.2∘ E). During both flights, the PBLH was about 400 m lower in the southern part than in the northern part of the USCB. Thus, the PBLH data in Table 3 describe a latitudinal gradient for the aircraft and temporal changes from the wind lidar.

Furthermore, for the mass balance, we assumed no entrainment from the free troposphere during sampling time. This assumption is supported by a strong capping inversion at the PBLH observed in the aircraft profiles (Fig. S3). Still, since the PBLH was increasing during the sampling for flight A, there was considerable entrainment of free-tropospheric air into the mixed layer. The correction we applied for this temporal change of the PBLH is described in the following section. The uncertainty related to this correction is assessed in the sensitivity test (Sect. 3.4) concerning the temporal PBLH variability.

For our mass balance, we use airborne in situ observations from two flights on 6 June 2018. CH4, CO2 and CO enhancements were clearly observed in the downwind wall. The ground-based teams drove below the upwind and downwind legs using the closest highways and national roads. Halfway through the southern track we ascended and descended to derive the height of the PBL based on meteorological measurements. Above the PBL, observed CH4 and CO concentrations were lower than within the PBL, while CO2 concentrations were higher.

In a first step of emission estimation for the entire USCB (as described in Sect. 2.2) the observed data in the downwind wall are inter- and extrapolated using the kriging algorithm (Fig. 5). Details of the kriging parameters can be found in the Supplement (Sect. S2). Mole fractions in the wall are cut off below the ground, above the PBL, and to the south and north of the flight legs (points S and N).

For the morning flight A, the trace gas plumes reach from the ground to the top of the PBL. The transects on the ground and at 800 m show the highest CH4 maxima (Fig. S4). At 1000 and 1100 m the maximum enhancements are lower. The same is true for the CO2 and CO enhancements. This is probably caused by the growing PBLH during the flight. During the downwind measurement of the morning flight A, the height of the PBL increased from 1.2 k a.s.l. (0.9 km above ground level, a.g.l.) to 1.5 km a.s.l. (1.2 km a.g.l.), which is an increase of 20 %. The lowest transect (800 m) was sampled first in the shallowest PBL. The two upper transects were sampled about half an hour later, when the PBLH had increased by about 20 %. Thus the emissions from the USCB were mixed within a much smaller volume during the lowest transect than during the following two. The ground-based sampling of the morning flight took place between 09:00 and 10:40 UTC. Two cars started in the center of the downward projected flight track and moved away from each other to the south and north. Thus, the central part was sampled first, during low-PBLH conditions. To account for the low PBLH during the first flight transect and the ground-based sampling, we apply a correction factor of -20 % to the ground observations and the lowest flight transect. Figure S4 shows the original, uncorrected observational data, while Fig. 5 shows the corrected values. Corrected enhancements are on the order of 0.16 ppm CH4, 7 ppm CO2 and 130 ppb CO.

During the afternoon flight B, the CH4 plume is evenly distributed between the ground observations and the lowest flight track at 800 m (Fig. 6). Thus, we assume good vertical mixing within the PBL and use the same CO2 and CO mole fractions at the ground as in the lowest flight transect. Trace gas enhancements are on the order of 0.12 ppm CH4, 6 ppm CO2 and 120 ppb CO, thus lower than during the morning flight. The main CH4 plume is located at 50.0∘ N with a secondary plume around 49.8∘ N. There are two CO2 plumes at 50.0 and 50.1∘ N. The CO plume is located at 50.0∘ N.

The horizontal wind speed shows a latitudinal gradient with higher wind speeds in the south than in the north for both flights. This gradient is preserved when using a kriged wind field for flux calculation instead of an average wind speed for the whole downwind wall (as discussed in Sect. 3.4).

Error estimates from the interpolation and extrapolation are retrieved from the kriging software as gridded fields (see Fig. S5). The KSE generally increases with distance to the measurement locations and is highest at the ground for CO2, CO and wind speed because no ground-based measurements were available for these parameters.

We applied both the downwind and the upwind methods (see Sect. 2.2.1) to determine atmospheric background mole fractions of trace gases. Average background mole fractions and standard deviations for both methods are summarized in Table 4. Figure 6 shows the observed PBL mole fractions of CH4, CO2 and CO at different heights for flight B. The highest transect (light blue), originally planned in the free troposphere above the PBL turned out to partially be within the PBL, but the southern and northern ends were sampled in the free troposphere. The background mole fractions according to the downwind method are displayed as dotted lines. For flight A, the background could not be reached to the south of the downwind wall, and only background values from the north were used for CH4 and CO2 (Fig. S4).

The upwind mole fractions (black lines) were shifted to the corresponding latitudes of the downwind wall based on the wind direction. The CH4 upwind mole fractions follow the same north–south gradient as the downwind background (Fig. 6, top). Around 49.94∘ N the CH4 mole fraction is slightly enhanced in the upwind. There is a similar enhancement around 50.13∘ N in flight A (Fig. S4). Due to the projection, these would be between 50.2 and 50.3∘ N on the inflow track. The only source upwind of the inflow track in the inventories is the Trzebinia mine and power plant at 19.44∘ E and 50.16∘ N. We use the ground-based observations below the upwind track (grey line) to confirm our aircraft observations. They show similar absolute values and a similar north–south trend to the airborne track. Additionally, there are three spikes between 49.73 and 49.78∘ N. These locations correspond to an inflow latitude of around 50.0∘ N and probably originate from sources close by, since they do not appear in the airborne observations. The largest peak most likely originates from the coal processing and waste water treatment facilities right upwind of the measurement route at 50.027∘ N and 19.438∘ E.

The CO2 upwind background is higher than downwind mole fractions at both ends of the measurement transects but lower in the center, where the downwind plume was observed. The average upwind background of CO2 is 2 and 1 ppm higher than the downwind background for flights A and B, respectively. This discrepancy is caused by the biogenic uptake of CO2 between the upwind and downwind transects. The impact of the biogenic sink is discussed below.

Upwind CO observations during flight B do not cover the complete transect due to a start delay of the QCLS. Thus, we did not use the CO upwind background for this flight. The CO upwind observations for flight A show small variations resulting in a background standard deviation of about 9 ppb. Here, the upwind CO measurements are smaller than downwind background values.

The upwind background method calls for an estimate of the biogenic uptake of CO2. We estimate this uptake from the STILT trajectories and the VPRM model (see Sect. 2.3.2). Figure S2 exemplary shows the truncated trajectories for the 800 m altitude transect of flight B. Trajectories for other transects and flight A are very similar. The biogenic uptake for each trajectory is determined from the last hour of transport. By subtracting the VPRM uptake from the corresponding downwind measurement (as the uptake is negative), one can obtain a downwind CO2 concentration without biospheric influence. This uptake is on average 1.00 ppm for flight A and 0.95 ppm for flight B.

From the two mass balance flights on 6 June 2018, we determined the total USCB emissions of CH4, CO2 and CO. Figure 7 summarizes the best-estimate emissions and the sensitivity calculations (see Sect. 2.3). The uncertainty of the best-estimate includes the statistical error, calculated from the uncertainties of the input parameters and the systematic error calculated from the sensitivity tests. The CH4 emission estimates for the entire USCB on 6 June are 13.8±4.3 and 15.1±4.0 kg s-1 for flights A and B, respectively. This is a difference of 9 % between the two flights. The CO2 emission estimates are 1.21±0.75 and 1.12±0.38 t s-1 for the two flights, also with a difference of 9 %, but with the morning flight results being higher. Finally, CO emissions from the USCB were calculated to be 10.1±3.6 and 10.7±4.4 kg s-1 for flights A and B, respectively. The discrepancy between them is 6 %.

We determined the systematic errors with several sensitivity tests applied to the treatment of different variables during the mass balance calculation (Fig. 7). Systematic errors are calculated as the emission difference between the best estimate mass balance using downwind background as described in Sect. 2.3 and the sensitivity studies.

Upwind background method

This background method leads to almost the same CH4 emission estimate for flight A. The flight B estimate is 18 % larger than the best estimate, showing that the assumption of a linear background gradient is not true for this case. The CO2 emission estimate using an upwind background is 50 % and 16 % smaller than the best estimate for flights A and B, respectively. Especially for flight A, the upwind CO2 mole fractions in the PBL might be enhanced due to a shallower PBLH. Also, the experiment was not conducted in a Lagrangian way, meaning that the sampling time difference between upwind and downwind does not match the travel time of the air. With potentially inhomogeneous biosphere–atmosphere fluxes, this could cause a problem. For CO the upwind background method yields an emission estimate difference of 3 % for flight A. For flight B we did not calculate a CO emission estimate because of an incomplete upwind measurement (Fig. 6). In general, CO upwind and downwind background data are quite similar.

This detailed emission estimate, as described above, can help to understand uncertainties of a mass balance study in cases where less information is available. We ensured the validity of the mass balance technique by performing multiple vertical transects and even driving underneath the flight path to capture the signal at the surface layer. Many mass balance studies do not put in this level of effort, hence we can estimate how necessary these extra precautions are with regard to calculating the true emissions. Furthermore, when using mass balance techniques at any point to verify emissions from a policy enactment standpoint, resources should be used as efficiently as possible. By using the information from single transects within the boundary layer of each flight, we calculated the emissions under the simple assumption of a perfectly mixed boundary layer. The PBLH was kept constant for all transects. Figure 8 shows the results of the single-transect mass balance calculations for the two flights on 6 June 2018. The average of the single transects (blue) is always well within the uncertainty range of the kriging mass balance results (red). Nevertheless, by assuming that one individual transect is representative for the entire PBL, transect emission estimates deviate up to 40 % in both directions from the kriging estimate for CH4. This deviation is much larger than the kriging estimate uncertainty. Deviations are largest for transects close to the PBLH when the concentration gradient between the boundary layer and free troposphere is also large, e.g. the highest CH4 transects. Thus, when calculating emissions from single transects the flight altitude should be well below the PBLH to avoid sampling free-tropospheric air masses. On the other hand, these results discourage using single-transect mass balance estimates anyway.