Relative flux measurements of biogenic and natural gas-derived methane for seven U.S. cities

Using the Purdue University Airborne Laboratory for Atmospheric Research, we measured concentrations of methane and ethane emanating from seven U.S. cities (New York, NY, Philadelphia, PA, Washington, D.C./ Baltimore, MD, Boston, MA, Chicago, IL, Richmond, VA, and Indianapolis, IN), in order to determine (with a median 95% CI of roughly 7%) the fraction of methane emissions attributable to natural gas (Thermogenic Methane Emission Ratio [TMER]), for both summer and winter months. New methodology is introduced to compute inflow concentrations and to accurately define the spatial domain of the sampling region, using upwind measurements coupled with Lagrangian trajectory modeling. We show discrepancies in inventory-estimated TMER from cities when the sample domain is defined using political boundaries versus urban centers encircled by the flight track and highlight this as a potential source of error common to top-down studies. We found that methane emissions of natural gas were greater than winter biogenic emissions for all cities except Richmond, where multiple landfills dominate. Biogenic emissions increased in summer, but natural gas remained important or dominant (2 0 %–8 0 %). National inventories should be updated to reflect the dominance of natural gas emissions for urban environments and to account for seasonal increases in biogenic methane in summer.


Introduction
Methane (CH 4 ) is a potent greenhouse gas with contemporary concentrations today almost three times greater than in preindustrial times. Anthropogenic emissions of CH 4 have been studied from a wide range of sources, including agriculture, landfills, and oil and gas production, transportation, and processing (Börjesson and Svensson, 1997;Marchese et al., 2015;Roscioli et al., 2015;Subramanian et al., 2015;Eilerman et al., 2016). Emissions of CH 4 from cities has been a topic of increasing interest in recent literature Lamb et al., 2016;Plant et al., 2019). The underlying sources of urban emissions remain poorly understood (Alvarez et al., 2018) because they are spatially diffuse and arise from diverse source types including landfills, wastewater treatment street-level sewage leaks, natural gas leaks from distribution or within individual homes, appliances, and so on. Bottom-up inventories have been shown to underestimate the total magnitude, source distributions, and seasonal variability of CH 4 emissions within urban domains (Cui et al., 2015;McKain et al., 2015;Lamb et al., 2016).
Here we present aircraft measurements to determine a fundamental attribute of urban CH 4 emissions, the partitioning between biogenic (e.g., from landfills, wetlands, or sewers) and thermogenic CH 4 emissions (natural gas). This characterization provides a strong constraint for understanding the emission sources and designing mitigation pathways. We report airborne measurements of CH 4 and ethane (C 2 H 6 ; a component of natural gas) from seven urban areas representative of eastern and midwestern U.S. cities: Indianapolis, IN, Chicago, IL, Washington, DC, and Baltimore, MD, Philadelphia, PA, New York, NY, Richmond, VA, and Boston, MA. We use measurements of the C 2 H 6 : CH 4 ratio to estimate the fraction of urban CH 4 emissions that can be attributed to natural gas, with the rest (not associated with C 2 H 6 ) attributed to biogenic sources. Our data show how partitioning of CH 4 emissions changes by season and is dependent on the urban setting. Our analysis also contributes methodological developments to help precisely define the measurement domain sampled by the aircraft observations, as well as the background inflow concentrations entering the region. We also compare our results to those from an established network of tower measurements of CH 4 and carbon dioxide (CO 2 ) in Boston, MA, to test our methodology.
Measurements of C 2 H 6 and CH 4 in the atmosphere enable us to partition biogenic and thermogenic emissions because biogenic CH 4 is not co-emitted with C 2 H 6 . Thermogenic processing of organic carbon at extreme temperatures and pressures (Kidnay et al., 2011) produces CH 4 along with higher hydrocarbons (C2þ). Only a portion of the higher hydrocarbons is extracted as feedstock during the processing of natural gas before it enters the market. Thus, natural gas distributed throughout a city is composed of a mixture of hydrocarbons, the two most prevalent being CH 4 (% 95%) and C 2 H 6 (%3%). The C 2 H 6 : CH 4 ratios are somewhat variable, depending on market conditions and origin of the natural gas, but ratios at transmission stations are regularly monitored and reported to the public continuously as "gas quality" data. It is commonly accepted that natural gas is the only significant source of urban C 2 H 6 in most large cities across the United States, and other studies have leveraged these tracer-tracer ratios in a similar manner Lamb et al., 2016;Plant et al., 2019). Maasakkers et al. (2016) presented a spatially resolved version of the Environmental Protection Agency CH 4 inventory for the Continental United States (Gridded EPA inventory: GEPA), reporting anthropogenic CH 4 emissions from 22 source sectors of both biogenic and thermogenic origin. GEPA estimates the most significant biogenic sectors in the cities studied here are municipal and industrial landfills and wastewater treatment plants (WWTP). GEPA also estimates that the thermogenic (natural gas) emission sources in the study cities are primarily natural gas transportation and distribution infrastructure. End user emissions were excluded from the GEPA inventory because only a small number of case studies have been reported for "post-meter" sources such as appliances, leaks in houses, commercial equipment, and so on, and their aggregated contributions and urban spatial distributions are unknown (Merrin and Francisco, 2019;Saint-Vincent and Pekney, 2020).
An early study of C 2 H 6 : CH 4 ratios in eastern Massachusetts  showed that the "Thermogenic Methane Emissions Ratio" (TMER, FluxCH 4 ðThermogenicÞ FluxCH 4 ðTotalÞ ) exhibited significant seasonal variations, with more biogenic emissions in summer. There were no statistically significant seasonal changes detected in thermogenic emissions. Our objectives in this study are to quantify the thermogenic fraction of urban CH 4 emissions in seven cities, then use our results to assess the accuracy of the source attribution in available inventories. Our observations also allow us to assess whether summer increases in the fractional biogenic emission component are significant in other urban regions. We report here that TMER declines in summer in four of the six cities that were sampled in both seasons. Our observations, coupled to the results from McKain et al. (2015), suggest that higher biogenic emissions are typical in the summer season.

Sampling platform
Campaigns were flown in August/September 2017 and March 2018 on board the Purdue University Airborne Laboratory for Atmospheric Research, a fully instrumented Beechcraft 76 Duchess with a long history of making atmospheric trace gas measurements. The flight tracks are shown in Figure 1 for each season. The aircraft was outfitted with a Picarro Cavity Ring Down Spectrometer (model G2301-m) measuring CO 2 , CH 4 , and H 2 O, and a direct absorption C 2 H 6 analyzer designed by Aerodyne Research Inc. and reengineered at Harvard University to improve stability under flight conditions (Crosson, 2008;Yacovitch et al., 2014). Typical 1s precision in flight was roughly 100 ppb (ppb; 10 À9 mol mol air ), 1 ppb, and 50 ppt (ppt; 10 À12 mol mol air ) for CO 2 , CH 4 , and C 2 H 6 respectively. For these flights, the gas phase H 2 O measurement was not calibrated, though it is included in the data set for diagnostic purposes. A Best Air Turbulence Probe (BAT Probe) provided accurate and fast (50 Hz) 3-component wind speed and direction measurements (Crawford and Dobosy, 1992;Garman et al., 2006) on a subset of the flights. The CH 4 , CO 2 , and C 2 H 6 measurements were calibrated in flight by sampling from high pressure standard gases traceable to World Meteorological Organization/Global Atmosphere Watch calibration scales (CH 4 : X2004, CO 2 : X2007). The C 2 H 6 instrument was also corrected for instrument background drift with periodic in-flight injections of hydrocarbon free zero air (roughly 30s each); these zero injections are removed from the ambient data and filled by linear interpolation. More information about the instrument performance, calibration source gases, and calibration practices of the ALAR gas phase instruments can be found in Section 1 of the Supplemental Information (SI). Because the ALAR deployment did not sample Philadelphia, PA, in winter, we use data collected during the National Oceanic and Atmospheric Administration (NOAA) East Coast Outflow (ECO) Campaign on April 26, 2018, in our winter analysis for that city. ECO flights were deployed using a NOAA Twin Otter, with C 2 H 6 measurements using the same Harvard instrument and a comparable Picarro spectrometer was used to measure CH 4 (see Plant et al., 2019).

Experimental design
All flights (except one) carried out transects both upwind and downwind of the urban areas, sampling both the inflow and urban-influenced outflow. Flight days and sampling times were chosen based on forecast meteorology such that wind speed and direction was fairly constant throughout the flight, the Planetary Boundary Layer (PBL) was well developed to ensure steady transport across the sample domain, and that the aircraft was able to fly in the PBL in order to sample well mixed urban sources. Sampling transects usually occurred between 300 and 600 m above ground level.
Flights were designed to sample the outflow from the urban core of each city, as defined by the size and shape of the downwind plume. Downwind transects were selected for analysis from each flight based on the measured mixing ratio enhancements and the domain sampled by that Art. 9(1) page 2 of 15 Floerchinger et al: Urban methane source characterization from seven U.S. cities particular transect according to our analysis of transport such that cities that were sampled in both seasons, but for different meteorological conditions with downwind transects in multiple locations (Boston, MA, August 29, 2017), could be readily and effectively compared. In the case of the winter flight in Indianapolis where there were three identical transects flown, the transects were analyzed separately and the results were bootstrapped to obtain a single TMER for that flight (Section 6 of the SI). Figure 2 shows an example flight from Indianapolis, IN, on March 16, 2018, with prevailing winds from the east, with the upwind and downwind mixing ratio enhancements readily seen by the color scale.

Thermogenic methane emission ratio determination
In order to calculate the ratios of biogenic and thermogenic CH 4 flux for a particular city (TMER, FluxCH 4 ðThermogenicÞ FluxCH 4 ðTotalÞ ), downwind CH 4 and C 2 H 6 mixing ratio enhancements are computed by subtracting background values from the downwind measurements and integrating along the downwind flight track. Equation 1 is then used to solve for the TMER from each domain by computing the flux of CH 4 and C 2 H 6 through a plane perpendicular to the ground at the height of the aircraft taking into account the mole fraction enhancements observed at the aircraft and the associated wind speed and direction. Our method assumes that thermogenic emissions of CH 4 from an urban domain can be approximated using a single ethane to methane emission ratio (EMER, moles C 2 H 6 moles CH 4 ) published by pipeline companies in the mandated gas quality portion of their public informational postings Lamb et al., 2016;Plant et al., 2019). To account for error associated with the EMER from either onsite measurement uncertainty at the reporting stations or the variable residence time of natural gas within the network, we used the mean þ/-1 standard deviation (E EMER ¼+1s 10day ) for all gas quality measurements reported in the 10 days prior to the measurement date. A detailed description of the data sources and determination of the EMER for each city is included in Section 2 of the SI.  For 8 (of 13) flights with the most complex inflow patterns, we used an atmospheric transport model and measurements along the upwind transect measured during each flight to determine an MDI or effective inflow concentrations that can be subtracted from each mixing ratio observation in the downwind transect, to compute downwind enhancements due to urban emissions. To calculate the MDI for each flight, we use multi-particle back trajectories from the Stochastic Time Inverted Lagrangian Transport Model (STILT; Fasoli et al., 2018). The STILT model is a Lagrangian atmospheric transport model that can be run backward in time to statistically represent atmospheric dispersion and transport before an air mass reaches a particular point in time and space (the receptor). Ensembles of STILT runs were executed from receptor points distributed along each downwind flight track, spaced 10s apart. For each receptor, 500 particles were released and advected backward in time for 10 h, ensuring all particles were allowed sufficient time to exit the urban domain under study. Example STILT releases from three receptors along the flight track are shown in Figure 3. The inflow concentration values for each downwind receptor were determined from the measured values at each point where a STILT particle crossed the upwind transect. The STILT model was driven by the NAMS-12 km product as archived at the NOAA Air Resources Laboratory (ARL; Stein et al., 2015). For each receptor point, the inflow value was calculated as the mean of 500 upwind mole fraction estimates inferred from the back trajectories of the Lagrangian particles. The MDI was then smoothed along the downwind flight track with a penalized spline to account for the spatial resolution of the STILT receptors. The enhancements were then calculated by subtracting the smoothed MDI from the downwind measurements.
The errors in the transport simulations were taken into account when computing the overall uncertainty of the MDI (Section 3 of the SI). The STILT model can incorporate optional parameters to account for spatio-temporal error and autocorrelation in the horizontal and vertical advection parameters of the input meteorological model as well as error in the model estimate of the height of the planetary boundary layer . Lin and Gerbig (2005) describe how STILT increases the magnitude of the stochastic transport component applied to particle transport to statistically represent the impact of meteorological error on the resulting spatial distribution of the modeled particles (Lin and Gerbig, 2005). The STILT model then creates a second distribution of particles that statistically represents the transport error. The difference between total errors in MDI, calculated using the "erroradded" particle distributions, and the MDI calculated using the original particle distributions, approximates the effect of the meteorological error on the MDI (Equation 2).
Equation 2: Determination of transport error when computing the MDI Individual terms are defined in the list below as: Á E 2 transport : The actual variance of the transport error due to meteorological uncertainty Á s 2 w=error : The variance of the transport error of the MDI with added meteorological error Á s 2 : The variance of the transport error of the MDI without added meteorological error For 3 of the 13 flights presented (August 29, 2017, Boston, MA, June 6, 2017, Chicago, IL, September 2, 2017, New York, NY), we were able to measure the downwind enhancement with particularly stable upwind concentrations. These flights occurred in the presence of an onshore wind, and operational and aircraft safety constraints did not always allow the plane to fly over the water in order to observe upwind concentrations. Hence, a complete upwind fetch was not always flown. In these cases, the downwind enhancement was calculated using conventional methodology by subtracting a background that was computed by linearly interpolating the average background values observed on each side of the plume (Heimburger et al., 2017). For these flights in New York, NY, and Boston, MA, the wind vector was a consistent onshore fetch from the Atlantic Ocean. For the flight in Chicago, IL, there was a consistent onshore fetch from Lake Michigan. We are confident that for these three flights, there were no upwind sources of CH 4 or C 2 H 6 significantly contributing to the downwind enhancement.
For two flights (April 26, 2018, Philadelphia, PA, and June 19, 2017, Indianapolis, IN), the aircraft did not accomplish an upwind flight transect that was suitable to compute an MDI, and the dominant airflow was not from regions where we can definitively say there were no sources of CH 4 or C 2 H 6 upwind. The background was calculated using the interpolation method described above (Heimburger et al., 2017). In these cases, the errors associated with the TMER may be larger than included in our error estimates. We believe that the added uncertainty during these two flights is not large enough to affect our conclusions; these two flights are discussed in detail in Section 6 of the SI and are denoted with a "þ" in Figure  1.
The TMER is the ratio of CH 4 and C 2 H 6 fluxes across a hypothetical curtain traced by the flight track (Equation 1). To compute the ratio of the CH 4 and C 2 H 6 fluxes transported through this curtain, we correct for the nonorthogonality of the aircraft heading with respect to the mean wind direction along the flight transect. We calculate an angle ðYÞ at 10s intervals along the downwind transect, where Y is the angular deviation from normal of two vectors representing the direction of flight and the wind direction at the aircraft. The direction of flight is based on the direction of motion of the aircraft in time, and the mean wind direction is derived from the NAMS-12 km product at the point in time and space where the aircraft flew. The horizontal wind speed ðU Þ ( Figure 3D) was also determined from the NAMS-12 km model. The meteorological factor is then calculated ðcosðYÞ Ã U Þ and applied to each point along the downwind transect to obtain the flux through the curtain at that point (Figure 3C).
In order to assess the magnitude of the instantaneous error of the NAMS-12 km meteorology, a model-data comparison was done for three flights using the wind speed and direction measured by the onboard BAT Probe and values from NAMS-12 km. BAT Probe measurements were averaged to 45 s, and the temporally corresponding values were extracted from the NAMS-12 km meteorology. These analyses show a nominal average wind direction error of roughly 11 and an average wind speed error of roughly 1.5 m/s. This comparison is described in further detail in Section S3 of the SI.

Defining the emission domain influencing the downwind plume
The STILT model was originally developed to understand the influence of surface sources on enhancements observed at the point of measurement (Lin et al., 2003) by generating a sensitivity matrix (footprint) for a specific receptor to solve for the geospatial upstream surface influence (ppm Ã ð mmol m 2 s Þ À1 ) . For this study, the STILT model was run at 10s intervals along the downwind flight track and footprints were generated at a spatial resolution of 0.025 Â 0.025 (roughly 6.5 km 2 ). The footprint domains were defined so the target city and immediately outlying areas could be fully enclosed within the domain and are shown in Section 5 of the SI. The spatially resolved sensitivity of the ratio of the calculated flux at the curtain to the surface emissions can be calculated by Equation 3. We represent this flux sensitivity graphically by multiplying each downwind footprint by the meteorological variables in the flux calculation ðcosðYÞ Ã U Þ, then summing the set of footprints for the total downwind flight transect and normalizing them from 0 to 1. The result allows us to verify that the domains were sampled in a way that did not bias the calculated flux ratio to a small area of the urban domain due to either meteorological conditions or inconsistencies in the flight profile.
Equation 3: Sensitivity of measurement to a specific grid box within the domain. Individual terms are defined in the list below as: Á dFlux xy : The sensitivity of the receptor to the flux at grid box xy Á U : The NAMS-12 km wind speed Á cosðyÞ: nonorthogonality flight track correction factor Á Foot xy : The footprint value at grid box xy Á Emiss xy : The emissions at grid box xy 2.6. Calculation of regional inventories emission rates We compared to published inventories in order to contextualize our results and to evaluate the current understanding of greenhouse gas emissions from urban areas. For CH 4 emissions, we used the gridded EPA CH 4 inventory (Maasakkers et al., 2016). GEPA is a multi-sector CH 4 Art. 9(1) page 6 of 15 Floerchinger et al: Urban methane source characterization from seven U.S. cities inventory with 0.1 Â 0.1 spatial resolution. Of the 22 sectors reported in the inventory, we identified 12 as being of thermogenic origin and having the potential for C 2 H 6 co-emissions as shown in Section 5 of the SI. In order to calculate the inventory flux of CH 4 from each urban domain, GEPA was reprojected onto a Universal Transverse Mercator coordinate system so the total flux could be calculated using equal area grid boxes. After reprojection, the GEPA inventory was summed for each city. To investigate the sensitivity of our analysis to the prescribed domain boundaries, we summed the inventory in two ways (1) by subdividing the inventory based on the urbanized area boundaries defined by the U.S. Census Bureau in the Topologically Integrated Geographic Encoding and Referencing (TIGER) database and (2) by subdividing the inventory based on the flight tracks to compute the inventory emissions from the actual measured area (primarily the urban cores of each city). In order to understand how representative GEPA was to another large scale CH 4 inventory, the TMER for each city was also compared to the TMER calculated using EDGAR v 4.3.2. This comparison is shown in Section 6 of the SI. Because CO 2 and CH 4 measurements are much more common than C 2 H 6 measurements, we used the CO 2 : CH4 ratio to assess our methodology against existing data. We used the Anthropogenic Carbon Emission System (ACES) CO 2 emission inventory (Gately and Hutyra, 2017) for additional evaluation of our inventory framework. ACES is a 1 km Â 1 km anthropogenic CO 2 emissions inventory with hourly resolution compiled for 2013 and 2014. For this study, we used the average ACES emissions across all days in April 2014 from 18:00:00 to 22:00:00UTC and used that to calculate the CO 2 flux of each urban domain. Like GEPA, ACES was masked and summed based on the TIGER boundaries and the flight domains in order to determine the respective hourly emission rates of CO 2 from each urban domain sampled by the aircraft and to determine how susceptible total emission estimates are to the definition of the domain.

Comparison to ground network data
We compared the ratio of integrated CH 4 and CO 2 enhancements computed from our flights to data from the Harvard-Boston University Greenhouse Gas Network in the city of Boston, MA, as an additional evaluation of our methodology. The Harvard Copley site samples CH 4 and CO 2 at a height of 215 m and is located in the core city of Boston, MA (for a complete description of the site, refer to Sargent et al., 2018). Tower time series data for the month of April were subselected to include only daytime data between the hours of 12 p.m. and 5 p.m. local to ensure sampling when the tower inlet was within the daytime planetary boundary layer and to ensure that the observed enhancements would be comparable to the daytime aircraft flight. A standard major axis regression was then computed using the calibrated mixing ratios to determine a characteristic ratio between CO 2 and CH 4 for the Boston urban Core. Enhancement ratios using CO 2 from the Copley site were compared for winter, but not for summer, due to difficulty in resolving effects of CO 2 uptake by the summer biosphere (Briber et al., 2013;McKain et al., 2015;Sargent et al., 2018). We also present a comparison to tower measurements of TMER made in Indianapolis by the INFLUX project (Lamb et al., 2016). These comparisons further highlight the need for accurate representations of the sample domain, especially when attempting to compare multiple measurements of the same urban area. Figure 4B shows a typical MDI for a downwind plume, as calculated for the winter flight on April 9, 2018, over the urban core of Boston, MA. Structure in the MDI is a function of variable mixing ratios observed in the upwind transect and their transport across the domain into the downwind measurement, as simulated by the STILT model. Results from the comparison of horizontal winds from NAMS-12 km meteorology to the horizontal winds from the ALAR BAT probe measurement suggest that the error in the NAMS-12 km model was small and well accounted for in the parameters adapted from Lin and Gerbig (2005), and Gerbig et al. (2008). We computed a mean absolute direction error in the NAMS-12 km meteorology of only 11.2 (degrees) [10.6, 11.9] (+1s). The mean wind speed difference showed NAMS-12 km to be 1.5 (m/s) [1.33, 1.68] ((+1s) faster than the winds measured by the BAT probe with mean measured wind speeds averaging 7.56 (m/s). These results are further described in Section 4 of the SI. Subtraction of the MDI from the downwind measurement leaves the concentration enhancement due to emissions in the urban domain between upwind and downwind flight transects, enabling us to compute the TMER.

MDI and ground influence
Domain sensitivity maps illustrate the measurement domain sampled by each flight and depict the relative sensitivity of the TMER to emissions in each grid box within the domain. Figure 4C shows an influence map for the April 9, 2018, flight. As expected, the grid boxes closer to the aircraft more heavily influence the downwind enhancement used to compute the TMER. Domain sensitivity maps for other flights are shown in Section 5 of the SI (Figures S8-S21) and identify the domain sampled by the aircraft for all cities. The U.S. Census Bureau TIGER borders are overlaid on the influence maps in green and show that, in most cases, the aircraft sampled only the urban core of each city. Notably, the measurement domains are not well represented by political boundaries and must be further defined with tools such as meteorological models and footprint modeling as done here. Domain sensitivity maps for the remaining flights support the assertion that similar urban core domains were sampled by flights in various meteorological conditions and can be compared in our analysis (i.e., winter and summer).

Thermogenic methane emission fractions
We observed good agreement throughout this study between published EMERs and the slope of CH 4 and C 2 H 6 enhancements at those points in the track where we expect the sources to be predominantly natural gas, such as for the city gate sampling shown in Figure 2. Tracer-tracer plots comparing the downwind measurements of CH 4 and C 2 H 6 for each flight to the EMER obtained from the pipeline companies (e.g. Figure 2D) are shown in Section 9 of the SI ( Figure S26). Figure 2D shows an example tracer-tracer plot observed downwind of Indianapolis, IN, where biogenic sources are a significant fraction of the city's total CH 4 emissions. The CH 4 enhancements that we attributed to emissions of natural gas are clearly separated in the time series from the biological landfill point source, and the slope of the enhancements agrees well with the published EMER ( Figure 2D). The time series in Figure 2C shows three distinct sources that can be easily identified: the South Side Landfill (biogenic) and the City-Gate in Zionsville. Outside of those two easily distinguishable peaks in the time-series, our method is not able to attribute other enhancements to specific point sources, and thus, we refer to the rest of the urban plume as diffuse emission, likely from the natural gas distribution infrastructure, post-meter emissions, and other potential methane sources that may be collocated. Our estimate of the uncertainty in the EMER from the pipeline informational postings is discussed in Section 2 of the SI. The calculated TMER values for each urban domain (Equation 1) are shown in Figure 5. In winter, the TMERs ranged from 0.32 for Richmond, VA, to 1 for New York, NY. Uncertainties in the TMER vary from very tight, for example, 0.815 (þ0.004/-0.006) observed during a flight over New York, NY, on September 2, 2017, to significant uncertainty, for example, 0.384 (þ1.23/-0.13) observed during a flight over Philadelphia, PA, on August 28, 2017. The differences in the calculated relative uncertainties are a function of the complexity of upwind source emissions, which result in increased uncertainty in the calculated MDI, as described in detail in Section 3 of the SI.
The TMER values measured in four of six cities showed statistically significant seasonal differences. The Boston FluxCH 4 ðTotalÞ ) based on whether or not the inventory is subsampled using the domain bound by the sampling flight track or the U.S. Census Bureau's political boundaries. All of the inventory estimates of TMER were significantly lower than those measured by the aircraft in winter, and likewise three of the six cities measured in summer, regardless of inventory subset. GEPA estimated TMER from each city (except Boston, MA) to be less than 0.50, but values this low were observed by the aircraft on only 4 of 13 flights (winter: Richmond, VA, only; summer: Washington, DC/Baltimore, MD, Philadelphia, PA, Indianapolis, IN).

CO 2 : CH 4 comparison to ground data
Since CO 2 emission inventories are based on reliable proxies (e.g., traffic data, building maps, power plant locations, and reported emissions; Sargent et al., 2018) not available for CH 4 emission inventories, accurate determination of the CO 2 : CH 4 ratio can aid in the assessment of the urban CH 4 sources and source strengths (Plant et al., 2019). Figure  6 shows the ratio of CO 2 : CH 4 enhancement from each city measured during the winter flights compared to the ratio of ACES CO 2 emissions and the GEPA CH 4 emissions. Both inventories were subsampled using two domains for each flight: the U.S. Census Bureau TIGER boundaries and the urbanized core encircled by each flight. Every domain showed a larger CO 2 : CH 4 inventory estimate when the flight domains were used to subsample the inventories as opposed to the TIGER boundaries, with the average effect being a difference in the CO 2 : CH 4 ratio of 13.4%.
The ratio of CO 2 : CH 4 enhancements measured at the Copley site in the Boston Urban Greenhouse Gas Network was 287 (þ27/-22) mol CO 2 : CH 4 (r 2 ¼ 0.84, MA regression), in close agreement with the aircraft data (240 (þ26/-12) molCO 2 molCH 4 ), using data from the April 2018 ALAR flight (Figure 7). This comparison to independent determination of TMER tests our methodologies, and the good agreement supports our flux ratio sampling method.

Measurement and estimation of TMER
Determination of TMER, like inverse analysis of emissions, depends sensitively on the concentrations inferred in inflowing air Heimburger et al., 2017;Bares et al., 2018). A simple method used previously draws a straight line between plume edge concentrations, suitable in specific settings where the target region is isolated, with a clean upwind fetch. This approach does not account for inflow effects of inhomogeneous concentrations entering the target region from the upwind boundary, as commonly found along the East Coast Corridor of the United States. To address this issue, we have combined an atmospheric transport model with the upwind observations made from the aircraft to enable us to compute an MDI and subtract background values informed by both model meteorology and aircraft observations. We can propagate the uncertainty associated with our subtracted background values when we estimate the uncertainty of our final answer. As with any method of background estimation using upwind aircraft sampling, we make assumptions as to the applicability of upwind concentrations observed to the downwind transect. In these flights, we attempted to plan flights on days when the wind direction was expected to be relatively steady throughout the domain for the duration of the sampling, and, when operational constraints allowed, we sampled the upwind transect first. As shown in Figure 5, the relative uncertainty of our TMER estimates is variable and a function of the uncertainty estimated in the MDI (Equation 2 and Section 3 of the SI) and fluctuations in the pipeline EMER reported for each domain in the 10 days prior to the measurement. The uncertainty of the TMER is potentially underestimated on three flights, indicated by an "*" in Figure 1 (New York, NY [March 20, 2018], Philadelphia, PA [April 26, 2018], and Indianapolis, IN [June 19, 2017]). Further analysis of the flights with added uncertainty is described in detail in Section 6 of the SI. For the September 2, 2017, sampling flight of New York, NY, the prevailing wind direction was from the east, which justified a simple background approximation based upon the homogeneous upwind marine air mixing ratios. This flight presents the lowest uncertainty in the TMER (0.815 (þ0.004/-0.006; Flux CH 4 (Thermogenic))/(Flux CH 4 (Total))) as the pipeline EMER was the determining factor and was quite stable at 0.0213 (þ0.004/-0.003) molC 2 H 6 /molCH 4 . For the August 28, 2017, flight sampling Philadelphia, PA, there were significant CH 4 sources of biogenic origin upwind of the domain, which manifested as a larger uncertainty estimation in the bounds of the MDI and ultimately a larger uncertainty in the calculated TMER (0.384 (þ1.23/-0.13) (  tracer-tracer plots to determine similar relationships (Plant et al., 2019). We did the same for our data to compare our results to these methods. If the emissions are measured close to a city, such that the plume has not mixed homogeneously in the horizontal coordinate (e.g., if the correlation coefficient is not excellent), the slopes computed by this analysis can be significantly skewed by unmixed source plumes with high mixing ratios. This analysis is described in detail in Section 10 of the SI.

CO 2 : CH 4 ratios
As shown in Figure 6, the observed CO 2 : CH 4 ratios are all statistically significantly smaller than those from the emission model ratios. This largely reflects an underestimate of the CH 4 emissions in the GEPA inventory, consistent with the results here implying that the GEPA inventory underestimates the thermogenic CH 4 emissions, for all cities. This has been observed for other cities (Plant et al., 2019). The ACES CO 2 inventory has uncertain estimated to be <+10% (Gately and Hutyra, 2017), supported by the top-down analysis of CO 2 in Boston, MA (Sargent et al., 2018), and bias in ACES is unlikely to explain the large systematic differences between observed and inventory ratios.

Defining the domain
Unambiguously defining the domain sampled during an airborne study is another difficult task when analyzing regional scale airborne measurements. Because many of the domains sampled in this study are located in the densely populated East Coast of the United States, we employed the STILT model to better describe the relative sensitivity of our TMER calculation to emissions from ground sources throughout the domain. The ground source sensitivity maps shown in Figure 4C and in Section 5 of the SI show the normalized spatially resolved influence of the sampling domain on the flux through the downwind transect drawn by the aircraft. The flux sensitivity maps, in almost all cases, show that downwind concentrations are sensitive to emissions from grid boxes upwind of the domain, hence our focus on calculating a value for MDI that would enable the subtraction of the influence of those sources from the enhancement observed downwind of the urban core. The flux sensitivity maps help us to compare multiple measurement flights of the same geographic location. They graphically demonstrate that adjustments in the aircraft flight track enable us to sample a similar domain in both seasons regardless of the fact that the meteorology may be differing across flights.
Our summer flight over Indianapolis, IN, exemplifies the importance of defining the domain that influences the observed enhancements of CH 4 and C 2 H 6 . On June 19, 2017, the aircraft was able to obtain two downwind transects that were suitable for analysis (i.e., completely transiting through the urban plume). Of the two transects, one was composed of a much more urban fetch, sampling the core of the Indianapolis metro area, for which we computed a TMER of 0.42 (þ0.04/-0.01). In the second transect, we sampled a fetch that also included a large amount of semi-rural area in the suburbs north of the downtown metro area and computed a TMER of 0.26 (þ0.01/-0.01), representing relatively greater biogenic emissions. Using the flux sensitivity maps, we are able to see that the area measured by the transect with the more rural fetch measured a more analogous domain to that sampled during the winter time measurement of Indianapolis on March 16, 2018, (this is the reported value in Figure 5). A higher TMER value in the urban core appears typical of other cites (e.g., Boston, MA, see above). More information on this particular flight, along with the flux sensitivity maps for these transects, can be found in Section 6 of the SI.
The sampled domain must also be taken into account when comparing the results in this study to results in the literature. Lamb et al. (2016) used measurements of C 2 H 6 and CH 4 made from a tower in downtown Indianapolis (INFLUX network tower 11) during February and March 2015 to determine a TMER of approximately 0.43 (43% natural gas, 48% biogenic, and 9% other). Our summer TMER computed using the urban transect, mentioned above, compared well to theirs, but our winter TMER was significantly higher (0.71 (þ0.01/-0.02)). Further analysis of the flux sensitivity of the tower and sources within those footprints would be needed to more accurately compare to the Lamb et al. tower measurements.
Political boundaries typically do not define the areas that influence aircraft measurements, making it difficult to systematically compare to inventories or to studies of other cities. We have compared our results to inventories sampled using both political boundaries and the exact area encircled by the aircraft (Figures 5 and 6) and shown that the TMER of a "city" can vary significantly based on that definition.We suspect that some of this variance is driven by the presence of biogenic CH 4 point sources (landfills, WWTPs, active methanogenic wetland areas, etc.) near the upwind boundary of the urban domain. Evidently, the TMER of a city can be quite sensitive to whether these point sources influence the observations, or not. We conclude that defining the actual domain sampled in the study is crucial to interpreting top down studies of emissions and that a quantitative analysis of individual flight domains must be used when comparing measurements of a single urban area that may have been made under different meteorological conditions.We have presented here a straightforward method to make these comparisons.

Thermogenic fraction discussion
Local policy makers have shown a willingness to introduce legislation to spearhead greenhouse gas emission reductions at the city level. Local Law 97 (a component of the New York, NY, Climate Mobilization Act) is one example. It sets aggressive greenhouse gas emission reduction targets for buildings larger than 25,000 ft 2 in New York, NY, with a $268/ton fine for emissions above the target. As more cities begin to evaluate the prospect of CH 4 -specific emission reduction legislation, it will be more pressing for the scientific community to inform local policy makers of the emission sectors that dominate their local CH 4 emission profile so that emission reduction strategies can address the most effective approaches. In order to make such recommendations, we must be prepared with wellcharacterized CH 4 emission statistics for specific cities, which need to be supported by measurement campaigns, as current CH 4 inventories do not accurately reflect the distribution of sources and emission rates in the urban domain. New York, NY, is a good example, where we found that the overwhelming majority of CH 4 emissions are derived from natural gas sources, an observation that is not consistent with the distribution of sources in the GEPA inventory.
In this study, we have partitioned CH 4 emissions between biogenic and thermogenic sources for seven major urban areas. As shown in Figure 5, the GEPA CH 4 emission inventory currently underestimates the natural gas contribution to CH 4 emissions, in some cases (New York, NY, Boston, MA, Chicago, IL) by as much as 50%.
Our results showed statistically significant seasonality in the urban TMER in four of the six cities we were able to sample in both winter and summer. But CH 4 emission inventories still lack adequate seasonal resolution, making it impossible to accurately assess temporally varying emissions from data. We note that the significant biogenic sources in most urban environments are sewer systems, landfills, and wastewater treatment facilities and that there is likely some significant seasonality in those emissions not captured in the emission models (Cambaliza et al., 2014;Fries et al., 2018). Based on what is known about the seasonality of biogenic CH 4 sources and the seasonally invariant thermogenic emissions observed by Mckain et al., we suspect that biogenic emissions are the source of the seasonality in the urban TMER. Further research is needed to quantify the seasonal amplitude of the CH 4 flux from specific biogenic sectors and sources. Furthermore, recent studies have suggested that the total inventory flux estimates from many of the same urban areas measured in this analysis underestimate total emissions Plant et al., 2019).
The results from our study illustrate how dramatically different the CH 4 emission profiles can be from city to city. We find the TMER varying as much as a factor of 3 (0.32 for Richmond, VA, to 1.0 for New York, NY, in winter months). These differences can occur for multiple reasons. Cities with older natural gas infrastructure (e.g., with cast iron NG mains) such as New York, NY, and Boston, MA, can have greater natural gas emissions (Von Fischer et al., 2017). Some cities, such as Boston, MA, do not have landfills in the urban core where some, such as Richmond, have multiple. Future studies should aim to quantify both the TMER and total CH 4 flux from a larger distribution of cities to better quantify the emissions from cities with a wide array of potential source infrastructure.

Conclusion
Current emission inventories for the United States significantly underestimate the role of natural gas relative to biogenic CH 4 emissions in urban environments. Local policy makers must have knowledge of the emission profile of their city in order to best allocate resources and introduce and implement legislation to reduce greenhouse gas emissions. Our work suggests that urban areas with significant landfill infrastructure (e.g., Richmond, VA) may benefit from better landfill gas capture and recovery systems, whereas urban areas with dense and aging natural gas infrastructure (e.g., Boston, MA, and New York, NY) should devote their resources toward updating their natural gas distribution infrastructure and possibly controlling post-meter emissions. Our results also highlight the need for more urban scale observational CH 4 data in order to better parameterize the emission accounting used in national level CH 4 emission inventories. Currently, inventories are unable to provide the comprehensive bottom-up picture that they were designed to provide, and improvements require higher quality flux estimates from urban CH 4 sources, combining top-down and bottom-up methodologies.

Data accessibility statement
Flight data are available to the public and can be accessed from the Harvard Dataverse at https://doi.org/10.7910/ DVN/T7ANQD.

Supplemental files
The supplemental files for this article can be found as follows: See attached Supplementary Materials.