All flight measurements analysed in this work were made using the UK's Facility for Airborne Atmospheric Measurement (FAAM) BAe-146 atmospheric research aircraft. A description of the full aircraft scientific payload can be found in Palmer et al. (2018). Here, we summarise the instrumentation relevant to this study.

Meteorological and thermodynamic parameters were measured using the core instrument suite on board the FAAM aircraft. A Rosemount 102 total air temperature probe measured air temperature with an estimated uncertainty of ±0.1 K. Static pressure was measured using a series of pitot tubes (uncertainty ±0.5 hPa), and three-dimensional wind components were measured using a nose-mounted five-port turbulence probe (uncertainty ±0.5 ms-1).

Dry mole fractions of CO2 and CH4 were measured using a cavity-enhanced absorption spectrometer (Fast Greenhouse Gas Analyzer (FGGA); Los Gatos Research Inc., USA), sampling air through a window-mounted rear-facing chemistry inlet. A full description of the FGGA for measurements on board the FAAM aircraft was reported by O'Shea et al. (2013), with a modified instrumental setup (used after January 2019) described by Shaw et al. (2022). Raw CO2 and CH4 mole fraction data were corrected for small effects associated with water vapour dilution and spectroscopic error. Calibration was performed approximately hourly during flights, using two reference calibration gas cylinders (encapsulating a representative range of background and in-plume mole fractions) traceable to the WMO-X2007 scale for CO2 (Tans et al., 2009) and the WMO-X2004A scale for CH4 (Dlugokencky et al., 2005). A target reference gas cylinder was also sampled hourly to quantify small sources of instrumental drift and non-linearity and to define measurement error. For a full description of data correction, calibration, and validation, refer to O'Shea et al. (2013) and Pitt et al. (2019). CH4 and CO2 data were measured at 1 Hz for flights conducted in 2018 and at 10 Hz for flights conducted in 2019 (Foulds et al., 2022; Shaw et al., 2022). 10 Hz measurements were time-averaged onto a 1 Hz grid for consistency between datasets. The representative 1 standard deviation (1σ) measurement uncertainties were ±2.86 ppb CH4 and ±0.46 ppm CO2 at a sampling rate of 1 Hz and ±3.23 ppb CH4 and ±0.72 ppm CO2 at 10 Hz.

Ethane (C2H6) mole fractions were measured using a tunable infrared laser direct absorption spectrometer (TILDAS, Aerodyne Research Inc.), operating at 1 Hz in the mid-infrared region (λ=3.3 µm). Raw C2H6 mole fraction data were corrected for spectroscopic effects associated with water vapour using the method described by Pitt et al. (2016). Calibration was performed using two gas standards (encapsulating a range of mole fractions) certified by the Swiss Federal Laboratories for Materials Science and Technology (EMPA). The TILDAS instrument has a reported precision of ±50 ppt over a 10 s averaging period. Two levels of data quality were provided for the C2H6 dataset. The “high quality” data included data that were calibrated at a stable altitude to account for systematic biases from optical effects induced by pressure (see Pitt et al., 2016). The “reduced quality” data included regular linear calibration (at ∼45 min intervals) but included data where calibration was not possible at a stable altitude. However, as we use enhanced C2H6 mole fractions (background subtracted) in this work, the systematic altitude-dependent biases were effectively removed, and the reduced quality C2H6 data were considered acceptable.

Nitrogen monoxide (NO) and nitrogen dioxide (NO2) were measured using a custom-built chemiluminescence instrument (Air Quality Design Inc.; see Graham et al., 2020, and Lee et al., 2009, for detail). NO2 was measured on a secondary channel following photolytic conversion to NO using a blue light converter (395 nm) and subsequent detection via chemiluminescence. In-flight calibrations were performed frequently using a small flow of NO calibration gas (5 ppm NO in N2). Estimated accuracies were ±4 % for NO and ±5 % for NO2, with precisions of 31 and 45 pptv for NO and NO2 respectively at 1 Hz. NO and NO2 mole fractions below the instrument detection limit of 30 pptv were removed.

All instrumentation on board the FAAM aircraft were synchronised with respect to time at the beginning of each day. However, instrument-specific temporal drift led to small temporal discrepancies (<10 s) between instruments during some flights. In cases where identified plumes were misaligned in time, data were manually corrected to align the peaks where possible.

Data availability from some instruments for some flights was limited (see Table A1). The NOx instrument suffered from large data gaps in three Assessing Atmospheric Emissions from the Oil and Gas Industry (AEOG) flights. This may have been because local NOx background mole fractions were below the instrument limit-of-detection (30 pptv). However, data availability within plumes was also affected for these, and other, flights.

This work used data collected as part of two field measurement campaigns: the Assessing Atmospheric Emissions from the Oil and Gas Industry (AEOG) programme and the Methane Observations and Yearly Assessments (MOYA) project. The AEOG flights targeted two key production regions on the UK continental shelf (UKCS). A total of 14 flights over the North Sea in the northern UK and West Shetland region were conducted in April 2018, September 2018, or March 2019. The MOYA campaign involved three flights in July and August 2019, surveying two regions on the Norwegian continental shelf (one in the North Sea and one in the Norwegian Sea). Figure 1 shows flight tracks for the AEOG and MOYA campaigns, as well as the offshore hydrocarbon fields and corresponding field types.

Emissions from oil and gas facilities were identified in flight time-series data using the method described in Foulds et al. (2022). Briefly, plumes were both manually and statistically identified. Manual identification relied on visual inspection of the time-series data for enhancements. Statistical identification involved the determination of a background (and associated standard deviation) for each flight survey, manifested as a mode in the data of approximately 2 ppm CH4 (equivalent to the Northern Hemisphere CH4 background). Emission plumes were defined as enhancements that exceeded 2 standard deviations above the flight-specific background value. Manually and statistically identified plumes were compared to confirm likely emissions and not just singular, extreme data points in the time series. There is the potential that extremely small emission sources (with peak concentration enhancements within 2 standard deviations of the flight-specific background value) were not captured by this analysis. Such sources are indistinguishable from natural background variability and therefore cannot be accounted for.

Gas flaring could not be confirmed visually during the flight campaigns due to distance to targeted facilities. In the absence of visual flare confirmation, plumes associated with gas flaring were identified by correlated enhancements in the expected gas-phase components of flared hydrocarbon gas (i.e. CO2, CH4, C2H6, and NOx) above their respective background mole fractions. Plumes which did not contain correlated enhancements of all four of these components were discarded. For example, plumes containing enhancements in only CO2, CH4, and C2H6, and which therefore lacked enhancements in NOx, were discarded as they were assumed to result from gas venting without flaring. Similarly, plumes containing only enhancements in CO2 and NOx, and therefore lacking enhancements in either CH4 or C2H6, were assumed to result from emissions from power generation, such as diesel generators. Unfortunately, this approach does not preclude the possibility of including emissions from multiple mixed sources of CO2, CH4, C2H6, or NOx, such as co-located venting and power generation emissions.

Representative median-average background CO2, CH4, C2H6, and NOx mole fractions were determined for each plume using the 50 neighbouring 1 Hz measurements to either side of the plume. Plumes for which this was not possible due to missing background data for one or more components (i.e. fewer than 10 background data points) were discarded. Plumes were additionally discarded if one or more components lacked sufficient data within the plume (i.e. fewer than three data points). The NOx data generally suffered from data unavailability (see Table A1), with large proportions of missing 1 Hz data. During background measurement, missing data could be attributed largely to NOx mixing ratios below the instrument limit-of-detection (30 pptv), but missing data within plumes were also common. If enough data were present, missing NOx data were interpolated using normalised values of the CO2 and CH4 plume data. Figure 2 shows an example in which three missing data points within a single plume were interpolated and reconstructed using the mean-average normalised CO2 and CH4 data. Using this method relies on the assumption that each gas has an identical plume morphology, which may not always be the case if there are multiple co-located sources upwind (France et al., 2021). However, Fig. 2 clearly demonstrates that all four gas components showed consistent plume morphologies in this example. Finally, plumes were discarded if the maximum within-plume enhancement was within 2 standard deviations (2σ) of the local background mole fraction.

Background mole fractions were subtracted from within-plume mole fractions to calculate enhancements. The resultant plume enhancements were then integrated (with respect to time) to determine the amount of each component within the emission plume. Integrating the data, rather than performing linear regression of co-located components, allows for slight temporal discrepancies in measured plumes to be ignored. Temporal discrepancies which lead to misaligned plumes could affect linear correlations between plume components.

Many emission inventories group emissions from the oil and gas sector into a single category, representing intentional venting, flaring, and leakage. The two emission inventories used here provide separate categories for flaring emissions.

The Global Fuel Exploitation Inventory (GFEI) is a globally gridded inventory of CH4 emissions from oil, gas, and coal exploitation, available at 0.1∘×0.1∘ for 2019 (Scarpelli et al., 2020). The GFEI provides gridded emissions from different sectors (e.g. exploration, production, transport, transmission, and refining) and from specific processes such as venting and flaring, based on country reports submitted in accordance with the United Nations Framework Convention on Climate Change (UNFCCC). CH4 emissions from flaring during gas production, gas processing, and oil production were examined here. In the GFEI, CH4 emissions from flaring during oil exploration, gas exploration, and oil refining are grouped together with emissions from leakage and venting, and hence these emissions were not analysed. Comparisons between the GFEI and CH4 emission fluxes measured in the North Sea have already been made by Foulds et al. (2022) and Pühl et al. (2023).

The anthropogenic emission dataset Evaluating the Climate and Air Quality Impacts of Short-lived Pollutants (ECLIPSE) v5 provides global CH4 and NOx emissions (amongst other pollutants) for flaring as a separate sub-sector, at 0.5∘×0.5∘ resolution for 2020 (Stohl et al., 2015). The ECLIPSE emission dataset was created using the Greenhouse gas - Air Pollution Interactions and Synergies (GAINS) model and international and national activity data for energy usage, industrial production, and agricultural activities. ECLIPSE products used GAINS emissions data up until 2010, after which emissions were projected into the future using current legislation and representative concentration pathways (Klimont et al., 2017).

Figure 4a shows the distribution of combustion efficiencies calculated without C2H6 (Eq. 2; Nara et al., 2014) and with C2H6 included (Eq. 3). Combustion efficiencies were marginally greater when C2H6 was not included in the calculation. However, even when including C2H6 in the calculation, efficiencies were high, with some plumes approaching 100 % efficiency and all efficiencies greater than 94 %. The median combustion efficiency across all sampled plumes without C2H6 included was 98.7 % (mean=98.3 % ± 1.4 %, 1σ), and the median efficiency with C2H6 included was 98.4 % (mean=97.9 % ± 1.7 %, 1σ) (see also Fig. C1). These values are exceptionally close to the 98 % combustion efficiency assumed by many emission inventories. However, Fig. 4a shows a strongly skewed distribution, indicating that assumptions of 98 % combustion efficiency is likely to be an overestimate in some cases. A summary of all results can be found in Table 1.

Figure 4b shows the linear relationship between combustion efficiencies calculated with and without C2H6. The linear relationship was estimated using reduced major axis regression. Combustion efficiencies calculated including C2H6 (Eq. 3) were marginally smaller than those calculated without C2H6 (Eq. 2). This relationship provides an approximation for estimating combustion efficiencies accounting for C2H6 in the absence of direct C2H6 observations. The R2 value for the linear regression was 0.996, indicating a high degree of model fit.

There was a small difference in combustion efficiencies (calculated including C2H6) measured during the AEOG and MOYA campaigns. The median combustion efficiency measured during AEOG (n=46 plumes) was 97.6 % (mean=97.5 % ± 1.6 %, 1σ), whilst the median combustion efficiency measured during MOYA (n=12) was 99.6 % (mean=99.4 % ± 0.6 %, 1σ). We cannot provide a conclusive explanation for this small difference in combustion efficiencies between the two campaigns but propose two explanations. AEOG sampled primarily UK-based platforms, whilst MOYA sampled Norwegian platforms. It may therefore be possible that differences in facility type, age, or operational practices in the two regions were responsible for the observed distinction in combustion efficiency. Alternatively, the measurements could be explained by differences in emissions from different hydrocarbon field types (see Fig. 1) with different gas compositions. Wilde et al. (2021) measured different VOC compositions in emissions from different field types in the North Sea region, and this may align with differences in the combustion efficiency observed here. However, Plant et al. (2022) found no correlation between combustion efficiency and factors such as well age, or gas-to-oil ratio, for onshore facilities in the USA.

Whilst combustion efficiency is expected to decrease with increasing wind speed (Jatale et al., 2016), recent studies have found little to no impact on flaring efficiency at wind speeds of up to 15 ms-1 (Caulton et al., 2014; Plant et al., 2022). Figure 5 shows an extremely weak but positive correlation (p=0.04; R2=0.08) between combustion efficiency and wind speed across the 58 identified plumes, although there was much scatter in the data. The observed trend was likely skewed by the greater number of plumes sampled under wind speeds of approximately 15 ms-1, several of which were measured during the MOYA campaign. Plumes sampled during the MOYA campaign had typically higher combustion efficiencies and therefore may be influencing the observed trend. The only plume measured in wind speeds of approximately 20 ms-1 (19.6 ms-1) showed a lower combustion efficiency (∼95.0 %) relative to many of those measured at wind speeds of 15 ms-1. Unfortunately, this was an isolated measurement, and a larger sample size of plumes sampled under higher wind speeds (>15 ms-1) would be required to draw meaningful conclusions on combustion efficiencies at such wind speeds. Our results were therefore in agreement with the conclusions of both Caulton et al. (2014) and Plant et al. (2022), which both showed no statistical relationship between combustion efficiency and wind speed.

Figure 6a shows the distribution of DREs calculated for both CH4 and C2H6 using Eq. (4) and fuel composition data provided by BEIS. The efficiency of CH4 destruction was marginally greater than that for C2H6, with median values of 98.5 % (mean=97.9 % ± 1.7 %, 1σ) and 97.9 % (mean=97.6 % ± 1.7 %, 1σ) for CH4 and C2H6 respectively (Table 1; see also Fig. C2). Gvakharia et al. (2017) reported marginally lower median DRE values of 97.1 % (±0.4 %) for CH4 and of 97.3 % (±0.3 %) for C2H6, from 37 flare plumes in the Bakken formation, United States. Plant et al. (2022) reported mean DRE values for CH4 of 97.3 %, 96.5 %, and 91.7 % from the Eagle Ford, Bakken, and Permian basins (United States) respectively. These results are in excellent agreement with our own. Figure 6b shows the relationship between DREs for the two fuel components, with a strong correlation between the two, even for DREs calculated for plumes from platforms for which flare gas composition was not available (see Sect. 2.3.2).

Figure 7 shows the distribution of NOx emission ratios calculated using both CO2 and CH4 as reference gases (ΔNOx:ΔCO2 and ΔNOx:ΔCH4 respectively). Mean NOx emission ratios were 0.004 ± 0.004 (1σ; median=0.003) ppmppm-1 when using CO2 as the reference gas and 0.48 ± 0.65 (1σ; median=0.26) ppmppm-1 when using CH4 as the reference gas (Table 1). There was substantial variability in the amount of NOx produced relative to both CO2 and CH4, as indicated by the large standard deviations about the mean ratios and the skewed long-tail distributions in both Fig. 7a and b. This may be a consequence of the inclusion of mixed emission sources within our dataset; it is difficult to distinguish between plumes containing pure flaring emissions and those potentially containing mixed emissions from co-located sources.

Four of the five greatest ΔNOx:ΔCH4 ratios (>1.1 ppmppm-1) were measured over deep-water oilfields west of the Shetland Isles, where oil production is typically performed by floating production storage and offloading (FPSO) vessels. An additional high ΔNOx:ΔCH4 ratio (of 1.5 ppmppm-1) was measured in a shallow water field, east of Scotland, also operated by an FPSO. FPSO vessels have been reported to contribute to 21 % of all offshore flaring volume (Charles and Davis, 2021), and the high ΔNOx:ΔCH4 ratios measured in the vicinity of their operation here could indicate a difference in operational practice (e.g. diesel generators on board FPSO vessels contributing to NOx emissions) compared with fixed platforms. The same five FPSO plumes also had the five greatest ΔNOx:ΔCO2 ratios.

Typically, NOx emissions from flares are estimated using emission factors and activity rates and often use flare heat as a proxy for NOx emission rates. Torres et al. (2012c) reported a mean NOx:CO2 ratio of 0.00020 (±0.00014) ppbppb-1 from 24 test flares operated under a range of conditions (fuel gas composition, fuel gas flow, lower heating value, and steam or air assisted flow). In comparison, the smallest ΔNOx:ΔCO2 ratio measured in this study was 0.0005 ppbppb-1. The reason for the order of magnitude difference between the NOx:CO2 ratios measured in this work and those reported by Torres et al. (2012c) is unknown but is perhaps due to the specific flaring conditions measured in each case (Torres et al. measured emissions from manual test flares with targeted gas compositions and heating values and not real-world flares operating in the North Sea).

Figure 8a shows the relationships between combustion efficiency (calculated with C2H6) and ΔNOx:ΔCH4. Higher combustion efficiencies were typically associated with higher relative amounts of NOx, consistent with higher temperature flaring. Figure 8a appears to show an exponential relationship between combustion efficiency and ΔNOx:ΔCH4, but a linear regression is also shown for comparison (p=9.3×10-5; R2=0.24). NOx only appeared to be produced in substantial amounts (relative to CH4) at combustion efficiencies greater than ∼96 %, with a general increase in NOx ratios with increasing combustion efficiency beyond this point. However, plumes measured during the MOYA campaign appeared to have reduced NOx ratios relative to many of those measured in AEOG, despite having greater combustion efficiencies, implying possible differences in flare operation. Torres et al. (2012c) found a similar result, with minimal NOx produced below a combustion efficiency threshold of roughly 80 %, above which NOx production increased roughly linearly. Wind speed appeared to have very little influence on NOx emission ratios (p=0.2; R2=0.03) (Fig. 8b).

The mean ΔC2H6:ΔCH4 ratio across all gas flaring plumes was 0.13 ± 0.06 (1σ) ppmppm-1, with ratios ranging between 0.04 and 0.33 (median=0.11) ppmppm-1 (Table 1 and Fig. C3). These results were in excellent agreement with measurements reported by Wilde et al. (2021), in which ΔC2H6:ΔCH4 ratios ranged between 0.03 and 0.18 ppmppm-1. Ratios of between 0.03 and 0.08 ppmppm-1 were also measured for oil and gas emissions in the southern North Sea (Pühl et al., 2023). It should be noted that the ratios measured by Wilde et al. (2021) and Pühl et al. (2023) were not specifically attributed to flared emissions and were likely to be representative of total emissions from oil and gas infrastructure, including any vented emissions or fugitive natural gas leaks. Their ratios therefore cannot be compared directly against our own results but may serve as an indication of the relative impacts of flaring on ΔC2H6:ΔCH4 ratios. ΔC2H6:ΔCH4 ratios greater than 0.1 ppmppm-1 are typically associated with emissions from oil wells, whilst ratios below 0.1 ppmppm-1 are usually associated with emissions from gas wells (Xiao et al., 2008; Wilde, 2021).

The ECLIPSE inventory contains flaring emission products for both CH4 and NOx, and hence the NOx:CH4 ratio for this dataset was calculated. Figure 9 shows the ECLIPSE NOx:CH4 emission ratio in the North Sea (for flared emissions), in units of mass per unit mass. Conversion of the ΔNOx:ΔCH4 ratio measured in this work (in units of mole fraction per unit mole fraction) yields a median ΔNOx:ΔCH4 of 0.70 gg-1 (mean=1.30 (±1.77) gg-1). The measured values were roughly 30 times greater than the highest ECLIPSE ratios in the North Sea, although NOx:CH4 ratios in the ECLIPSE inventory globally reached values greater than 2.0 GgGg-1. Our study finds that the ECLIPSE inventory may underestimate the NOx:CH4 ratio by more than an order of magnitude in the North Sea region.

There are a few possible reasons for this disparity in NOx:CH4 ratios between datasets. Firstly, inventories are typically representative of annual emissions, whereas our ratios are snapshots calculated for emissions at the time of sampling. If flaring emissions can be expected to vary throughout the year, either as a result of changes to operation or to local meteorology, this may lead to differences. Secondly, our measurements are only comparable to inventory grid cells if a representative population of flaring emissions were sampled. Thirdly, the ECLIPSE inventory for 2020 was calculated by projecting activity data for 2010 forwards in time using legislative and representative concentration pathways (Klimont et al., 2017), and these may not be valid for current emission scenarios.