Mobile atmospheric measurements at the street level were conducted using two cavity ring-down spectroscopy (CRDS) analyzers (Picarro Inc. model G2301 and G4302), which were installed on the back seat of a 2012 Volkswagen Transporter (see Sect. S1.1 and Fig. S1 in the Supplement). The model G2301 instrument provides atmospheric mole fraction measurements of CO2, CH4, and H2O, each of them with an integration time of about 1 s, which results in a data frequency of ≈0.3 Hz for each species. The reproducibility for CH4 measurements was ≈1 ppb for 1 s integration time. The G2301 instrument was powered by a 12 V car battery via a DC-to-AC converter. The flow rate was ≈187 mL min-1. Given the volume and pressure of the measurement cell (volume 50 mL and pressure ≈190 mbar) the cell is flushed approximately every 3 s, so observed enhancements are considerably smoothed out. The factory settings for CH4 and CO2 were used for the water correction.

The G4302 instrument is a mobile analyzer that provides atmospheric mole fraction measurements of C2H6, CH4, and H2O. The flow rate is 2.2 L min-1 and the volume of the cell is 35 mL (operated at 600 mb, thus 21 mL at standard temperature and pressure – STP) so the cell is flushed in 0.01 s, which means that mixing is insignificant given the 1 s measurement frequency of the G4302. The additional measurement of C2H6 is useful for source attribution since natural gas almost always contains a significant fraction of C2H6, whereas microbial sources generally do not emit C2H6 (Yacovitch et al., 2014). The G4302 runs on a built-in battery that lasts for ≈6 h. The instrument can be operated in two modes at ≈1 Hz frequency for each species: the CH4-only mode and the CH4–C2H6 mode. In the CH4-only mode the instrument has a reproducibility of ≈10 ppb for CH4. The factory settings for CH4 and C2H6 were used for the water correction. In the CH4–C2H6 mode the reproducibility is about 100 ppb for CH4 and 15 ppb for C2H6. For Utrecht surveys (see Sect. S1.2, Fig. S2a), the G4302 was not yet available for the initial surveys in 2018, but it was added for the later revisits (see Sect. S1.2, Table S1 in the Supplement). For Hamburg (see Sect. S1.2, Fig. S2b), both instruments operated during the entire intensive 3-week measurement campaign in October–November 2018 (see Sect. S1.2, Table S2). The time delay from the inlet to the instruments was measured and accounted for in the data processing procedure. The Coordinated Universal Time (UTC) time shifts between the Global Positioning System (GPS) and the two Picarro instruments were corrected for each instrument in addition to the inlet delay (see Sect. S1.2, Tables S1 and S2). The clocks on the Picarro instruments were set to UTC but showed drift over the period of the campaigns. We recorded the drifts for each day's survey and corrected to UTC. The data were also corrected for the delay between air at the inlet and the signal in the CH4 analyzers. This delay was determined by exposing the inlet to three small CH4 pulses from exhaled breath, ranging from 5–30 s, depending on the instrument and tubing length. We averaged the three attempts to determine the delay for each instrument and used the delays for each instrument. Individual attempts were 1 to 2 s different from each other. For the G4302 the delay was generally about 5 s and for the G2301 it was about 30 s; the difference is mainly due to the different flow rates. The recorded CH4 mole fractions were projected back along the driving track according to this delay.

Teflon tubing (0.25 in.) was used to pull in air either from the front bumper (0.5 m a.g.l. – above ground level) to the G2301 or from the rooftop (2 m a.g.l.) to the G4302. To avoid dust in the inlets for both instruments, and Acrodisc^® syringe filter (0.2 µm) was used for G2301 and Parker Balston 9933-05-DQ was used for G4302. The G2301 was used for quantification and attribution purposes and the G4302 mainly for attribution. After a data quality check, a comparison between the two instruments during simultaneous measurements showed that all LIs were detectable by both instruments despite the difference in instrument characteristics and inlet height (see Sect. S1.3, Fig. S3). In the majority of cases CH4 enhancements for each LI from both instruments were similar to each other. We note that there is likely a compensation of differences from two opposing effects between the two measurement systems. The inlet of the G2301 was at the bumper and thus closer to the surface sources, but the rather low flow rate and measurement rate of the instrument led to some smoothing of the signal in the cavity. Because of the high gas flow rate, signal smoothing is greatly reduced for the G4302, but the inlet was on top of the car and thus further away from the surface sources (see Table S3, Sect. S1.3). The vehicle locations were registered using a GPS that recorded the precise driving track during each survey.

Utrecht is the fourth largest city in the Netherlands with a population of approximately 0.35 million within an area of roughly 100 km2. It is located close to the center of the Netherlands and is an important infrastructural hub in the country. The Utrecht city area that we target in this study is well constrained by a ring of highways around the city (A27, A12, A2, and N230) with approximately 0.28 million inhabitants living within this ring on roughly 45 km2 of land. Figure S2a (see Sect. S1.2) shows the streets that were driven in Utrecht and Fig. 1a shows the street coverage over four street categories (level 1, 2, 3, residential, and unclassified) obtained from the Open Street Map (OSM; https://www.openstreetmap.org/#map=6/51.330/10.453, last access: 22 April 2019). Table S4 (see Sect. S1.5) provides information on road coverage based on different street categories. The hierarchy of OSM road classes is based on the importance of roads in connecting parts of the national infrastructure. Level 1 roads are primarily larger roads connecting cities, level 2 roads are the second most important roads and part of a greater network to connect smaller towns, and level 3 roads have tertiary importance and connect smaller settlements and districts. Residential roads are roads that connect houses, and unclassified roads have the lowest importance of interconnecting infrastructure. Moreover, several transects were also made to measure the atmospheric mole fraction of CH4 from the road next to the waste water treatment plant (WWTP) in Utrecht – a potentially larger single source of CH4 emissions in the city (see Sect. S1.6, Table S5).

Hamburg is the second largest city in Germany (about 1.9 million inhabitants, 760 km2 area) and hosts one of the largest harbors in Europe. The study area in Hamburg is north of the Elbe river (Fig. 1b) with ≈1.4 million inhabitants on about 400 km2 land. Figure S2b (see Sect. S1.2) shows the streets that were covered in Hamburg and Fig. 1b shows the street coverage categorized in the four categories of OSM. More information on road coverage based on OSM street categories is provided in Table S4 (see Sect. S1.5). The local distribution companies (LDCs) in Utrecht (STEDIN; https://www.stedin.net/, last access: 30 September 2020) and Hamburg (GasNetz Hamburg; https://www.gasnetz-hamburg.de, last access: 20 October 2020) confirmed that full pipeline coverage is available beneath all streets. Therefore, the length of roads in the study areas of Utrecht and Hamburg are representative of NGDN length. The Hamburg harbor area hosts several large industrial facilities that are related to the midstream and downstream oil and gas sector, including refineries and storage tanks. An oil production site (oil well, separator, and storage tanks) at Allermöhe (in Hamburg-Bergedorf) was also visited. Information from the State Authority for Mining, Energy and Geology (LBEG, 2018) was used to locate facilities. Precise locations of the facilities surveyed are given in the Table S6 (see Sect. S1.6). In order to separate these industrial activities from the NGDN emissions in this study, CH4 emissions from these locations were estimated, but evaluated apart from the emissions found in each city. The reported in situ measurements, GPS data, and boundaries of study areas reported here are available on the Integrated Carbon Observation System (ICOS) portal (Maazallahi et al., 2020b).

The start and end points for each day's measurement surveys across Utrecht and Hamburg were the Institute for Marine and Atmospheric research Utrecht (IMAU; Utrecht University) and the Meteorological Institute (MI; Hamburg University), respectively. From these starting locations, each day's surveys targeted the different districts and neighborhoods of the cities (see Sect. S1.2, Tables S1 and S2). Measurement time periods and survey areas were chosen to select favorable traffic and weather conditions and to avoid large events (e.g., construction; see Sect. S1.5, Fig. S4), which normally took place between 10:00 and 18:00 LT. Average driving speeds on city streets were in the range of 17±7 km h-1 in Utrecht and 20±6 km h-1 in Hamburg.

As part of our driving strategy, we revisited locations where we had observed enhanced CH4 readings (see Sect. S1.7, Fig. S5). Not all recorded CH4 mole fraction enhancements are necessarily the result of a stationary CH4 source. For example, they could be related to emissions from vehicles that run on compressed natural gas or vehicles operated with traditional fuels but with faulty catalytic converter systems. Later we will discuss how to exclude or categorize these unintended signals (see Sect. 2.2.2 and 2.3.1). Therefore, we revisited a large number of locations – 65 in Utrecht (≈80 %) and 100 in Hamburg (≈70 % – where enhanced CH4 had been observed during the first survey in order to confirm the LIs. In contrast to the measurements carried out in many cities in the United States (US) (von Fischer et al., 2017), our measurements were not carried out using Google Street View cars, but with a vehicle from the Institute for Marine and Atmospheric research Utrecht (IMAU), Utrecht University (see Sect. S1.1, Fig. S1). Due to time and budget restrictions, it was not possible to cover each street at least twice, as done for the US cities. After evaluation of the untargeted first surveys that covered each street at least once, targeted surveys were carried out for verification of observed LIs and for collection of air samples at locations with high CH4 enhancements. The rationale behind this measurement strategy is that if an enhancement was not recorded during the first survey, it obviously cannot be verified in the second survey. The implications of the difference in the measurement strategy will be discussed in the Results and Discussion sections below.

In total, approximately 1300 km of roads were driven during Utrecht surveys and about 2500 km during the Hamburg campaign. In Utrecht, some revisits were carried out several months to a year after the initial surveys in order to check the persistence of the LIs. In Hamburg, revisits were also performed within the 4-week intensive measurement period. Further details about the driving logistics are provided in Sect. S1.6 and Tables S1 and S2. It is possible that pipeline leaks that were detected during the initial survey were repaired before the revisit, and the chance of this occurring increases as the time interval between visits gets longer.

In addition to the mobile measurement of C2H6 and CO2 for LI attribution purposes, samples for lab isotope analysis of δ13C–CH4 and δ2H–CH4 (hereinafter δ13C and δD, respectively) were collected during the revisits at locations that had displayed high CH4 enhancements during the first surveys. Depending on the accessibility and traffic, samples were either taken inside the car (see Sect. S1.8, Fig. S6a) using tubing from the bumper inlet or outside the car on foot using the readings from the G4302 to find the best location within the plume (see Sect. S1.8, Fig. S6b). All the samples taken in the north Elbe study area and from most of the facilities were collected when the car was parked, but the samples inside the new Elbe tunnel and close to some facilities where there was no possibility to park were taken in motion while we were within the plume. The sampling locations across the north Elbe study area in Hamburg were determined based on the untargeted surveys and the confirmation during revisits. The C2H6 information was not used in the selection of sampling locations in order to avoid biased sampling. Sampling locations from the facilities were determined based on wind direction, traffic, and types of activities. Samples for isotope analysis were collected in non-transparent aluminum-coated Tedlar Supelco SeupelTM Inert SCV gas sampling bags (2 L) and SKC standard FlexFoil^® air sample bags (3 L) using a 12 V pump and 1/4 in. Teflon tubing that pumps air with a flow rate of ≈0.25 L min-1. In total, 103 bag samples were collected at 24 locations in Hamburg, 14 of them in the city area north of the Elbe river and 10 at larger facilities. Usually, three individual samples were collected at each source location, plus several background air samples on each sampling day. This sampling scheme generally results in a range of mole fractions that allow source identification using a Keeling plot analysis (Keeling, 1958, 1961). Fossil CH4 sources in the study areas for this paper (inside the ring for Utrecht and north Elbe in Hamburg) refer to emissions originating from natural gas leaks.

Meteorological information reflecting the large-scale wind conditions during the campaigns was obtained from measurements at the Cabauw tower (51.970263∘ N, 4.926267∘ E) operated by the Koninklijk Nederlands Meteorologisch Instituut (KNMI) (Van Ulden and Wieringa, 1996) for Utrecht and the Billwerder tower (53.5192∘ N, 10.1029∘ E) operated by the MI at Hamburg University (Brümmer et al., 2012) for Hamburg. The wind direction and wind speed data from the masts were used for planning the surveys. Pressure and temperature measurements were used to convert volume to mass fluxes for CH4. We also used information from the towers for the GPDM calculations of the emission rates from larger facilities because the local wind measurements from the 2-D anemometer were not logged continuously due to failure in logging the setup of the measurements. In Utrecht, the Cabauw tower is located about 20 km from the WWTP. In Hamburg the Billwerder tower is about 18 km from the soil and compost company and about 8 km from oil production facilities. Uncertainties in the wind data will be described later.

The first step of the evaluation procedure is quality control of the data from both CH4 analyzers and the GPS records. Periods of instrument malfunction and unintended signals based on notes written during each day's measurements were removed from the raw data. Extraction of the LIs from in situ measurements requires estimation of the background levels (see Sect. S2.1, Fig. S7). We estimated the CH4 background as the median value of ±2.5 min of measurements around each individual point as suggested in Weller et al. (2019). For estimating the CO2 background level we used the 5th percentile of ±2.5 min of measurements around each individual point (Brantley et al., 2014; Bukowiecki et al., 2002). The background determination method for CH4 was selected from Weller et al. (2019) to follow the emission quantification algorithm for urban studies, and while this algorithm does not include background extraction for CO2, we chose the commonly adopted method of background determination for this component. These background signals were subtracted from the measurement time series to calculate the CH4 and CO2 enhancements. For C2H6, the background was considered zero as it is normally present at a very low mole fraction between ∼0.4 and 2.5 ppb (Helmig et al., 2016) and is lower than the G4302 detection limit.

We wrote an automated MATLAB^® script (available on GitHub from Maazallahi et al., 2020a) based on the approach initially introduced in von Fischer et al. (2017) and improved in Weller et al. (2019). This algorithm was designed to quantify CH4 emissions from ground-level emission release locations within 5–40 m from the measurement (von Fischer et al., 2017), such as pipeline leaks, and it has been demonstrated that the algorithm adequately estimates the majority of those emissions from a city (Weller et al., 2018). Using the same algorithm also ensures that results are comparable between European and US cities. The individual steps will be described below. Mapping and spatial analysis were conducted using Google Earth and ESRI ArcMap software. A flow diagram of the evaluation procedure is provided in Sect. S2.2 and Fig. S8.

Following the algorithm from von Fischer et al. (2017), measurements at speeds above 70 km h-1 were excluded, as the data from the controlled release experiments (von Fischer et al., 2017) were not reliable at high speed (Weller et al., 2019). We also excluded measurements during periods of zero speed (stationary vehicle) to avoid unintended signals coming from other cars running on compressed natural gas when the measurement car was stopped in traffic. In order to merge the sharp 1 Hz-frequency records of the GPS with the ≈0.3 Hz data from the G2301 analyzer, the CH4 mole fractions were linearly interpolated to the GPS times.

Weller et al. (2019) established an empirical equation to convert LIs observed with a Picarro G2301 in a moving vehicle in urban environments into emission rates based on a large number of controlled release experiments in various environments (Eq. 1). 1Ln(C)=-0.988+0.817⋅Ln(Q) In this equation, C represents CH4 enhancements above the background in parts per million (ppm) and Q is the emission rate in liters per minute (L min-1). Weller et al. (2019) used controlled releases to demonstrate that the magnitude of the observed methane enhancement is related to the emission rate and carefully characterized the limitations and associated errors of this equation. We used Eq. (1) to convert CH4 enhancements encountered during our measurements in Utrecht and Hamburg to emission rates, and we use these estimates to categorize LIs into three classes: high (emission rate > 40 L min-1), medium (emission rate 6–40 L min-1), and low (emission rate 0.5–6 L min-1), following the categories from von Fischer et al. (2017) (Table 1).

The spatial extent of individual LIs was estimated as the distance between the location where the CH4 mole fraction exceeded the background by more than 10 % (≈0.200 ppm; as used in von Fischer et al., 2017, and Weller et al., 2019) and the location where it fell below this threshold level again. LIs that stay above the threshold for more than 160 m were excluded in the automated evaluation because we suspect that such extended enhancements are most likely not related to leaks from the NGDN (von Fischer et al., 2017).

In a continuous measurement survey on a single day, consecutive CH4 enhancements above background observed within 5 s were aggregated and the location of the emission source was estimated based on the weighted averaging of coordinates (Eq. 2). Decimal degree coordinates were converted to Cartesian coordinates (see Sect. S2.3, Fig. S9) relative to local references (see Sect. S2.3, Table S7). In Utrecht, the Cathedral tower (Domtoren) and in Hamburg St. Nicholas' Church were selected as local geographic datums. LIs observed on different days at similar locations were clustered and interpreted as one point source when circles with a 30 m radius around the center locations overlapped, similar to Weller et al. (2019). The enhancement of the cluster was assigned the maximum observed mole fraction and located as the weighted average of the geographical coordinates of the LIs within that cluster (Eq. (2) from Weller et al., 2019), where wi is the CH4 enhancement of each LI. 2(lon,lat)=∑i=1nwi⋅loni,lati∑i=1nwi We compared the outputs of our software to the one developed by Colorado State University (CSU) for the surveys in US cities (von Fischer et al., 2017; Weller et al., 2019). A total of 30 LIs were detected and no significant differences were observed (linear fit equation y=1.00*x-0.00, R2=0.99) (see Sect. S2.4, Fig. S10). As mentioned above, in our campaign-type studies not all streets were visited twice, so this criterion was dropped from the CSU algorithm. Instead, we used explicit source attribution by co-emitted tracers.

The emission rate per kilometer of road covered during our measurements was then scaled up to the city scale using the ratio of total road length within the study area boundaries derived from OSM to the length of streets covered and converted to a per capita emission using the population in the study areas based on LandScan data (Bright et al., 2000). Note that in this upscaling practice, emissions quantified from facilities were excluded.

To account for the emission uncertainty, similar to Weller et al. (2018) for the US city studies, we used a bootstrap technique that was initially introduced in Efron (1979, 1982), as this technique is adequate in resampling of both parametric and non-parametric problems, even with a non-normal distribution of observed data. Tong et al. (2012) indicated that the bootstrap resampling technique is sufficiently capable of estimating the uncertainty of emissions with a sample size equal to or larger than nine. Efron and Tibshirani (1993) suggested that a minimum of 1000 iterations is adequate in the bootstrap technique. In this study, we used a non-parametric bootstrap technique to account for the uncertainty of total CH4 emissions from all LIs in each city with 30 000 replications. As mentioned above the algorithm is based on CH4 enhancements in measurements with 5–40 m of distance from a controlled release location and can produce large uncertainty for the emission quantification of individual LIs (Fig. 4 in Weller et al., 2019). However, with a sufficient sample size, the uncertainty associated with the total emissions quantified in an urban area is more precise.

Apart from the natural gas distribution network, there are larger facilities in both cities that are potential CH4 sources within the study area. Several facilities in or around the cities were visited during the mobile surveys to provide emission estimates. We applied a standard point source GPDM (Turner, 1969) to quantify methane emissions from these larger facilities. A flowchart describing the steps taken during quantification from facilities in given in Sect. S2.5. and Fig. S11. We note that emission quantification using GPDM with data from mobile measurements is prone to large errors (factor of 3 or more) (Yacovitch et al., 2018), especially when the measurements are carried out close to the source. In this study, we also report the data obtained from larger facilities, since rough emission estimates from facilities can be obtained in the city surveys. Caulton et al. (2018) discuss uncertainties of emission quantification with GPDM. Individual facilities were visited during the routine screening measurements and during revisits for LI confirmation and air sampling.

In Utrecht, the WWTP is located in the study area, and streets around this facility were passed several times during surveys. In Hamburg, we initially performed screening measurements in the harbor area (extensive industrial activities) and near an oil production site and then revisited these sites for further quantification and isotopic characterization. The data from the oil production site can be fit reasonably well with a GPDM and were therefore selected for quantification, similar to studies in a shale gas production basin in the USA (Yacovitch et al., 2015) and in the Netherlands (Yacovitch et al., 2018). 3C(x,y,z)=Q2⋅π⋅u⋅σy⋅σz⋅exp⁡-z-zsource22⋅σz2+exp⁡-z+zsource22⋅σz2⋅exp⁡-y22⋅σy2 In Eq. (3), C is the CH4 enhancement converted to grams per cubic meter (g m-3) at Cartesian coordinates x, y, and z relative to the source ([xyz]source=0 at ground-level source), x is the distance of the plume from the source aligned with the wind direction, y is the horizontal axis perpendicular to the wind direction, and z is the vertical axis. Q is the emission rate in grams per second (g s-1), u (m s-1) is the wind speed along the x axis, and σy and σz are the horizontal and vertical plume dispersion parameters (described below), respectively.

Determination of an effective release location is a challenge for the larger facilities. Effective emission locations for each facility were estimated based on wind direction measurements and the locations of maximum CH4 enhancements. The facilities were generally visited multiple times under different wind conditions. The locations of the maximum CH4 enhancements were then projected against the ambient wind, and the intersection point of these projections during different wind conditions was defined as the effective emission location of the facility. At least two measurement transects with different wind directions were used to estimate the effective location of the source. If wind directions, road accessibility, and the shape of plumes were not sufficient to indicate the effective source location, the geographical coordinates of centroids of the possible sources using Google Earth imageries and field observations were used to determine the effective emission location. For the WWTP in Utrecht we also contacted the operator and asked for the location of sludge treatment as it is the major source of CH4 emissions (Paredes et al., 2019; Schaum et al., 2015).

Neumann and Halbritter (1980) showed that the main parameters in a sensitivity analysis of GPDM are the wind speed and source emission height in close distance, and the influence of emission height becomes less further downwind compared to the mixing layer height. In this study, the heights of emission sources were low (<10 m) and estimated during surveys and/or using Google Earth imageries; considering such a larger measurement distance from the facilities, the main source of uncertainty of the emission estimates for the WWTP and compost and soil company is most likely the mean wind speed. For the upstream facilities in Hamburg the major sources of uncertainties can be the mean wind speed and emission height. We considered a 0–4 m source height for the WWTP in Utrecht, and for the upstream facilities in Hamburg we considered a 0–5 m emission height for the compost and soil site, 0–2 m for the separator, 0–10 m for the storage tank, and 0–1 m for the oil extraction wellhead. We used a 1 m interval for each of these height ranges to quantify emissions in GPDM.

Cross-wind horizontal dispersions σy were estimated from the measured plumes by fitting a Gaussian curve to the individual plumes from each set during each day's survey. A set of plumes is defined as back-to-back transects during a period of time downwind of each facility on different days. Later average emissions from all sets of plumes were used to report CH4 emissions for each of the facilities. A suitable Pasquill–Gifford stability class was then determined by selecting a pair of parameters (Table 1-1 in EPA, 1995) that matches best and giving the closest number the fitted value of σy. Vertical dispersions σz were then estimated with the identified Pasquill–Gifford stability class in the first step using the distances to the source locations (Table 1-2 in EPA, 1995). Uncertainties due to these estimates will be discussed below. Mass emission rates were calculated using the metric volume of CH4 at 1 bar of atmospheric pressure (0.715 kg m-3 at 0 ∘C and 0.666 kg m-3 at 20 ∘C, p. 1.124 in IPCC, 1996), and linear interpolation was used for temperatures in between.

Due to technical issues, local wind data were not logged continuously, and thus we used wind data from two towers, which are 8 to 20 km away from the facilities we focused on for emission quantifications. These distances introduce extra uncertainties in analyzing the emissions using GPDM, mainly in the wind speed. By comparing some of the local high-quality wind data to data from the towers, we estimated that the local wind speed is within the range of ±30 % of the collected tower data. This range was adopted to estimate the wind speed for emission quantifications for the set of plumes measured downwind of the facilities. The wind directions were aligned at the local scale of each facility based on the locations of sources and locations of maxima of average CH4 enhancements from a set of transects in each day's survey, and we considered ±5∘ uncertainty in the wind direction for the GPDM quantification.

During the Utrecht campaign, the overall mole fraction of CH4 and C2H6 in the NGDN was ≈80 % and ≈3.9 % (STEDIN, personal communication, 2020), and in Hamburg the mole fraction of CH4 and C2H6 in the NGDN was about ≈95 % and ≈3.4 % (GasNetz Hamburg, personal communication, 2020), respectively. This ratio can vary depending on the mixture of gas compositions from different suppliers, but should meet the standards for gas compositions in the Netherlands (65 mol %–96 mol % for CH4 and 0.2–11 mol % for C2H6; ACM, 2018) and in Germany (83.64–96.96 mol % for CH4 and 1.06–6.93 mol % for C2H6; DVGW, 2013). Compressed natural gas vehicles can be mobile CH4 emission sources (Nam et al., 2004; Curran et al., 2014; Naus et al., 2018; Popa et al., 2014), and in this study we also observed CH4 signals from vehicles. For example, the point-to-point C2H6:CH4 ratio (C2:C1) calculated from road measurements of a car exhaust shown in Fig. S12 (see Sect. S2.6) is 14.2±7.1 %. During the campaigns in Utrecht and Hamburg the C2:C1 of NGDNs was less than 10 %, and in our study, we removed all the locations where the C2:C1 ratio was greater than 10 %. CH4 emissions from combustion processes are always accompanied by large emissions of CO2 and can therefore be identified based on the low CH4:CO2 emission ratio. In this study, LIs with a CH4:CO2 ratio between 0.02 and 20 with R2 greater than 0.8 were attributed to combustion.

After sample collections, the bag samples were returned to the IMAU for analysis of both δ13C and δD (Brass and Röckmann, 2010), and some samples were analyzed at the Greenhouse Gas Laboratory (GGL) in the department of Earth Sciences, Royal Holloway University of London (RHUL), for δ13C (Fisher et al., 2006) (see Sect. S2.7, Fig. S13).

At the IMAU, we used a ThermoFinnigan MAT DeltaPlus XL (Thermo Fisher Scientific Inc., Germany) isotope ratio mass spectrometry (IRMS) instrument. We used a reference cylinder calibrated against Vienna Pee Dee Belemnite (VPDB) for δ13C and Vienna Standard Mean Ocean Water (VSMOW) for δD at the Max Planck Institute for Biogeochemistry (MPI-BGC), Jena, Germany (Sperlich et al., 2016). The cylinder contained CH4 mole fractions of 1975.5±6.3 ppb, δ13C=-48.14±0.07 ‰ vs. VPDB, and δD=-90.81±2.7 ‰ vs. VSMOW. The samples were pumped through a magnesium perchlorate (Mg(ClO4)2) dryer before the CH4 extraction steps.  Each sample was measured at least two times (up to four times) for each isotope. Every other sample, the reference gas was also measured three times for δ13C and δD. Each measurement, from the CH4 extraction to the mass spectrometer, took ≈30 min.

At the GGL, FlexFoil SKC bag samples were each analyzed for methane mole fractions and δ13C. Methane mole fractions were determined using a Picarro G1301 CRDS, which measured every 5 s for 2 min, resulting in a precision ±0.3 ppb (Lowry et al., 2020; France et al., 2016; Zazzeri et al., 2015). Each sample was then measured for stable isotopes (δ13C–CH4) using an Elementar Trace gas and continuous-flow gas chromatography isotope ratio mass spectrometry (CF-GC-IRMS) system (Fisher et al., 2006), which has an average repeatability of ±0.05 ‰. CH4 extraction was preceded by a drying process using Mg(ClO4)2. Each sample was measured three times for δ13C–CH4, and the duration of each analysis was ≈20 min. Both instruments are calibrated weekly to the WMO X2004A methane scale using air-filled cylinders that were measured by the National Oceanic and Atmospheric Administration (NOAA) and cylinders that were calibrated against the NOAA scale by the MPI-BGC (France et al., 2016; Lowry et al., 2020).

The analytical systems for isotope analysis have been described, used, and/or compared in several previous publications (Fisher et al., 2011; Röckmann et al., 2016; Umezawa et al., 2018; Zazzeri et al., 2015). Measurement uncertainties in δ13C and δD are 0.05 ‰–0.1 ‰ and 2 ‰–5 ‰, respectively.

After the LIs were analyzed and quantified, the measurements of C2H6, CO2, and isotopic composition from the air samples were used for source attribution. We characterize the observed LIs as of fossil origin when they had a concomitant C2H6 signal between 1 % and 10 % of the CH4 enhancements and when the isotopic composition was in the range -50 ‰ to -40 ‰ for δ13C and -150 ‰ to -200 ‰ for δD. An LI was characterized as microbial when there was no C2H6 signal (<1 % of the CH4 enhancements larger than 500 ppb), δ13C was between -55 ‰ and -70 ‰, and δD was between -260 ‰ and -360 ‰ (Fig. 7 in Röckmann et al., 2016). LIs with enhancements of CH4 lower than 500 ppb and no C2H6 signals were categorized as unclassified. LIs with no C2H6 signals, no significant CH4:CO2 ratio, and no information on δ13C and δD were also categorized as unclassified. The source signatures for each sampling location were determined by a Keeling plot analysis of the three samples collected in the plumes and a background sample taken on the same day.