Abstract Abstract Emissions of methane (CH 4 ) and volatile organic compounds (VOCs) from oil and gas production may have large impacts on air quality and climate change. Methane and VOCs were measured over the Haynesville and Marcellus shale gas plays on board the National Center for Atmospheric Research C-130 and NOAA WP-3D research aircraft in June-July of 2013. We used an eddy covariance technique to measure in situ fluxes of CH 4 and benzene from both C-130 flights with high-resolution data (10 Hz) and WP-3D flights with low-resolution data (1 Hz). Correlation (R = 0.65) between CH 4 and benzene fluxes was observed when flying over shale gas operations, and the enhancement ratio of fluxes was consistent with the corresponding concentration observations. Fluxes calculated by the eddy covariance method show agreement with a mass balance approach within their combined uncertainties. In general, CH 4 fluxes in the shale gas regions follow a lognormal distribution, with some deviations for relatively large fluxes (>10 μg m À2 s Abstract ). Statistical analysis of the fluxes shows that a small number of facilities (i.e.,~10%) are responsible for up to~40% of the total CH 4 emissions in the two regions. We show that the airborne eddy covariance method can also be applied in some circumstances when meteorological conditions do not favor application of the mass balance method. We suggest that the airborne eddy covariance method is a reliable alternative and complementary analysis method to estimate emissions from oil and gas extraction. Introduction The advancement of horizontal drilling and hydraulic fracturing has promoted production of oil and natural gas in the United States (U.S.) significantly in recent years. Crude oil and natural gas production in the U.S. increased by 47.9% and 28.6%, respectively, from 2005 to 2013, making the U.S. the largest producer of oil and natural gas in the word [Energy Information Administration, 2013] . The processes associated with oil and natural gas extraction can lead to significant emissions of methane (CH 4 ), volatile organic compounds (VOCs), and nitrogen oxides (NO x = NO + NO 2 ) into the atmosphere. Based on the inventory of greenhouse gas (GHG) emissions by the U.S. Environmental Protection Agency (EPA), production and transportation of oil and natural gas contribute 28%, 21%, and 5% of the total emissions of CH 4 , nonmethane volatile organic compounds, and NO x in the U.S., respectively [U.S. Environmental Protection Agency, 2014]. These emissions have large impacts on both regional air quality [Edwards et al., 2014; Kemball-Cook et al., 2010; Schnell et al., 2009] and global climate change [Montzka et al., 2011] . Emissions of some air toxics (e.g., aromatic hydrocarbons) may also affect human health for people working at or living nearby the production sites [McKenzie et al., 2014] . total emissions of the species using the mass balance method [White et al., 1976] . Besides total emissions, emission patterns and emission strengths from different operation procedures, well types, and regions are possible but more difficult to obtain from aircraft observations [Caulton et al., 2014] . Ground investigations of individual wells using a downwind tracer ratio method [Allen et al., 2013] can help to address this issue, but this kind of research is both labor intensive and time consuming, resulting in large budgetary demands [Brandt et al., 2014] . Introduction Airborne flux measurements using the eddy covariance technique provide an approach that is independent of the mass balance method. The airborne eddy covariance technique has been applied to measure fluxes of CO 2 , ozone (O 3 ) [Mauder et al., 2007; Zulueta et al., 2013] , and isoprene Misztal et al., 2014] over vegetation, aromatics from urban emissions [Karl et al., 2009] , dust from the Sahara desert [Rosenberg et al., 2014] , and CH 4 from agricultural emissions [Hiller et al., 2014] . The utilization of the continuous wavelet transformation (CWT) approach to calculate airborne fluxes improves the spatial resolution of flux results significantly and makes comparisons between measurements and emission inventories possible on spatial scales of several kilometers [Karl et al., 2009; Metzger et al., 2013; Misztal et al., 2014] . Introduction In this study, airborne eddy covariance flux measurements were conducted for the first time over two shale gas production regions. We use the data sets to demonstrate the feasibility of the technique and present the results from airborne flux measurements over oil and natural gas production regions. Insights into the distributions of emission strengths from results of the eddy covariance flux measurements will also be presented. Measurements and Methods Measurements Two aircraft campaigns (Nitrogen, Oxidants, Mercury, and Aerosol Distributions, Sources, and Sinks (NOMADSS) and Studying the Interactions Between Natural and Anthropogenic Emissions at the Nexus of Climate Change and Air Quality (Southeast Nexus (SENEX))) were conducted using the National Center for Atmospheric Research (NCAR) C-130 and NOAA WP-3D aircraft, respectively, in June and July of 2013. The two campaigns were conducted under the broader research umbrella of the Southeast Atmosphere Study. While both missions had multiple scientific objectives, both the NCAR C-130 and NOAA WP-3D flew over shale gas production regions. Journal of Geophysical Research: Atmospheres 10.1002/2015JD023242 The Haynesville shale gas region was investigated in most detail by the two campaigns. Figure 1 shows flight tracks of the NCAR C-130 and NOAA WP-3D over the Haynesville shale gas region. The NOAA WP-3D conducted two flights (10 and 25 June) with rectangular flight tracks, aiming to derive total emissions of CH 4 in this region using the mass balance approach [Peischl et al., 2015] . The C-130 flew in this area on three different flights (5 June, 27 June, and 4 July). The C-130 also flew downwind of the Haynesville shale gas play on 22 June to sample outflow from the region. 10.1002/2015JD023242 In addition to the flights over the Haynesville shale gas play, observations from several other flights are also used in this study. On 5 July, the C-130 flew over the Atlantic Ocean to sample clear marine air. On 6 July, the NOAA WP-3D flew to the Marcellus shale gas play in northeastern Pennsylvania, and a similar rectangular flight pattern was conducted to estimate CH 4 emissions ( Figure S1 in the supporting information). This region accounts for over 70% of natural gas production in the Marcellus shale play in 2013 based on U.S. Energy Information Administration data (www.eia.gov). The WP-3D also flew to the Fayetteville shale play on 26 June and 8 July, and the data set on 8 July was used to calculate total CH 4 emissions in this region using the mass balance method [Peischl et al., 2015] , but the data will not be used in this study due to the mountainous terrain surrounding the Fayetteville shale play. Eddy covariance flux measurements over mountainous regions need additional corrections to vertical wind velocity to remove vertical motion that results from sloping topography and flow distortion [Reba et al., 2009] . 10.1002/2015JD023242 Payload and instrument layout of C-130 and WP-3D can be found on the NOMADSS website (https://www.eol. ucar.edu/content/c-130-layout) and SENEX website (http://www.esrl.noaa.gov/csd/projects/senex/p3payload. html), respectively. Methane (CH 4 ) and carbon dioxide (CO 2 ) were measured by wavelength-scanned cavity ring down spectroscopy on both the C-130 (Picarro G2311-f) and WP-3D (Picarro G1301-m) [Peischl et al., 2012] . On the C-130, volatile organic compounds (VOCs) were measured by a proton transfer reaction-mass spectrometer (PTR-MS) and a Trace Organic Gas Analyzer (one 30 s sample every 2 min) [Apel et al., 2010] . On the NOAA WP-3D, a PTR-MS measured a subset of VOCs online [Warneke et al., 2013] , and canister samples (72 canisters per flight) were also collected and analyzed after flights by a gas chromatography-mass spectrometry on ground (improved Whole Air Sampler With immediate Analysis System). During flights over oil and gas regions, the PTR-MS systems on board both the C-130 and WP-3D usually recorded 18-20 masses, each with a dwell time of 1 s, which are related to aromatics, alcohols, aldehydes, ketones, and organic acids. During the C-130 flights on 27 June and 4 July, the PTR-MS was run in flux mode, with measurements of masses attributed to benzene (m/z 79), toluene (m/z 93), isoprene (m/z 69), and methyl vinyl ketone + methacrolein (MVK + MACR) (m/z 71), each with a dwelling time of 0.1 s (Table S1 in the supporting information). Contributions of other nonbiogenic compounds (e.g., fragments from cyclohexanes) to signals of m/z 69 and m/z 71 are possible [Warneke et al., 2015; Yuan et al., 2014] , but they are expected to be small in the two oil and gas production regions in the daytime of summer. Only flux mode data from the PTR-MS on the C-130 are used to calculate eddy covariance fluxes of benzene in this study. For the two C-130 flights on 27 June and 4 July, high-frequency CH 4 data (10 Hz) were also (Figure 2b ) is the linear, equally weighted, bivariate orthogonal distance regression fit to the data points (same for other linear fits in this study). The dashed blue line is the 1:1 reference line. Journal of Geophysical Research: Atmospheres 10.1002/2015JD023242 acquired. Power spectral analysis of CH 4 and CO 2 signals from Picarro G2311-f instrument indicates that the instrument response may be limited to several hertz as a result of high-frequency attenuation. Winds were recorded by five-hole pressure sensors on the radome of the aircraft (Rosemount model 1221F1VL) at 25 Hz on the C-130 and at 1 Hz on the WP-3D [Khelif et al., 1999] . Good agreement of measured vertical wind speeds by C-130 and WP-3D (N = 3876, R = 0.61, and slope = 1.11 ± 0.02) was obtained during the coordinated aircraft intercomparison flight on 29 June 2013 (Figure 2 ). Eddy Covariance Methods An eddy covariance flux is defined as the averaged product of fluctuating terms of vertical wind speed and the concentration of a scalar. Two methods in the literature are generally used to calculate airborne eddy covariance fluxes: fast Fourier transformation (FFT) and continuous wavelet transformation (CWT). FFT can compute an average flux over a certain period or a certain flight leg for the case of aircraft measurements. CWT computes correlations with point-by-point flux outputs over a chosen bandwidth without the requirement of homogeneity or stationarity [Misztal et al., 2014] , which are defined as the conditions under which the statistical properties of airflow do not change with space and time [Reba et al., 2009] , respectively. In this study, we mainly use CWT; the FFT method is applied for the purpose of intercomparison and as a supplementary approach. Eddy Covariance Methods The wavelet transformation routine proposed by Torrence and Compo [1998] is used below. A continuous wavelet transform of a discrete sequence x(n) of N data points is defined as convolution of x(n) with a wavelet function [Mauder et al., 2007; Misztal et al., 2014] : Eddy Covariance Methods where a, b, and p are the scale parameter, space parameter, and normalized factor, respectively. Parameter ψ Ã p;a;b is the complex conjugate of the wavelet function, which is given by Eddy Covariance Methods The ψ nÀb a À Á is called the "mother wavelet," and for this study, we use the Morlet wavelet, which has been shown to be suitable for the analysis of atmospheric turbulence [Mauder et al., 2007] . The settings of scales for wavelet transformation are determined according to Torrence and Compo [1998] . The detailed procedures of the CWT method in previous studies [Karl et al., 2009 ] are adopted. CWT has several advantages for aircraft measurements compared to FFT method. (1) The effect of the lack of homogeneity or stationarity in aircraft measurements is minimized, as shown by measurements in an urban area [Karl et al., 2009] . Measurements over oil and gas production regions would have a similar inhomogeneity issue as urban areas. (2) CWT can produce time-resolved spectral contribution to the measured flux [Misztal et al., 2014] . Comparisons of CWT results with those from FFT show that flux estimates from CWT are quantitatively acceptable (usually better than 30%) [Karl et al., 2009; Mauder et al., 2007; Misztal et al., 2014] . Eddy Covariance Methods The segments for each calculation of CWT and FFT fluxes are selected based on minimal roll angle of the aircraft between turns and little altitude variations, following the suggestions in a recent study [Misztal et al., 2014] . The periods for vertical profiles or changing altitude for another flight leg are excluded for the flux analysis. No detrending is applied in this study, and the fluctuating terms are calculated from measurements subtracted by block average for each flight segment. The lag time between the signals from the gas analyzers and vertical wind speed, introduced from either different computer clocking or sampling time from inlet to detector, was determined before the implementation of eddy covariance flux calculation [Park et al., 2013] . The lag time for each flux segment is determined from the peak location of cross correlation between VOC signals and vertical wind speed by shifting VOC data points with steps according to their measurement frequency (0.1 s for C-130 and 1 s for WP-3D data). To improve the accuracy of the determined lag time, the lag time of benzene and toluene measured by PTR-MS is determined from comeasured isoprene, and the lag time of CH 4 measured by the Picarro instrument is determined from comeasured CO 2 , as the fluxes of isoprene and CO 2 due to emission and uptake by vegetation were much larger in this study. Eddy Covariance Methods The footprint of eddy covariance fluxes defines the source contribution area of the flux measurements. The footprint of each flux point depends on wind speed, flight altitude, boundary layer height, and convective velocity [Weil and Horst, 1992] , and it can be parameterized as Eddy Covariance Methods Journal of Geophysical Research: Atmospheres 10.1002/2015JD023242 where dx 0.5 is the half width of the horizontal footprint, u is the horizontal wind speed, z is the flight altitude, z i is the boundary layer height, and w* is the convective velocity scale which can be determined from the sensible heat flux (w′T′). The half width is defined as the horizontal distance where the flux footprint falls to half of its maximum value . For example, a typical half width of the horizontal footprint was 2.4 km for the triangle flight legs of the C-130 flight on 4 July over the Haynesville shale gas play (z i = 1.8 km, z = 570 m, u = 5.2 m/s, and w* = 1.6 m/s). Recently, Misztal et al. [2014] proposed that the source contribution area of a flux point from aircraft measurement can be approximated by upwind-pointed half dome with the dx 0.5 as the radius of the half dome. We derive that the source contribution area for each flux point is around 9 km 2 for the triangle flight legs of the C-130 flight on 27 June. We note that some newer methods are available for the calculation of flux footprint [e.g., Kljun et al., 2004] . Rough comparison between the method in Kljun et al. [2004] and equation (3) shows some differences up to a factor of~2 for z/z i > 0.5. However, these newer methods are more complicated than that in Weil and Horst [1992] and more difficult to use. Thus, we will use equation (3) for the estimation of flux footprint in this study. Results and Discussions Correlations and Enhancement Ratios of Different Species Enhancement ratios of different VOC species can be used to identify their emission sources. Figures 3a and 3b show scatterplots of excess CH 4 mixing ratio (measured mixing ratios minus background) versus benzene from all of the C-130 and NOAA WP-3D flights over and downwind from the Haynesville shale gas region. The data points in Figure 3b are grouped into two parts based on their respective slopes: the C-130 flight on 27 June and all of other flights over the Haynesville. Methane and benzene mixing ratios were correlated for both groups (R = 0.65 and R = 0.64), albeit with some scatter. The enhancement ratio of CH 4 to benzene in all flights, except the C-130 flight on 27 June, is determined to be 1053 ± 15 ppb/ppb. This enhancement ratio is consistent with the ratios from natural gas extraction obtained in other regions (200-1700 ppb/ppb) and much larger than those reported in urban areas (Table 1) . Emissions from landfills also have high enhancement ratios of CH 4 /benzene (>10 6 ppb/ppb) [Kim et al., 2006] , but landfill emissions are determined to be minor methane sources in the Haynesville shale gas play [Peischl et al., 2015] . Journal of Geophysical Research: Atmospheres 10.1002/2015JD023242 Data points on 27 June demonstrate a lower slope (275 ± 5 ppb/ppb) than those in other flights. During the flight on 27 June, winds were from the west, and the sampled air masses may have been affected by two nearby cities (Longview, TX and Tyler, TX) ( Figure 1 ). However, methane concentrations measured during this flight should still be mainly dominated by oil and gas emissions, considering the very low emission ratio of CH 4 to benzene (9.8 ppb/ppb) from vehicle exhaust [Kirchstetter et al., 1996] . 10.1002/2015JD023242 Scatterplots of toluene versus benzene are shown in Figure 3c . The enhancement ratio of toluene to benzene is 0.733 ± 0.007 ppb/ppb, which is similar to the ranges of reported emission ratios in several oil and gas production regions (0.89-2.0 ppb/ppb) ( Table 1 ) and significantly lower than that from urban emissions (2.55 ppb/ppb in Los Angeles) [Borbon et al., 2013] . The agreement of enhancement ratios with those from oil and gas production emissions indicates that the main sources of these species are from oil and gas extraction activities. Enhancement ratios of CH 4 and toluene to benzene determined from the WP-3D flight over the Marcellus shale play on 6 July are also consistent with signatures of oil and gas emissions (Table 1) . Continuous Wavelet Transformation Flux Results NCAR C-130 On 4 July, the C-130 flew over two different parts of the Haynesville shale play (flight track in Figure 1 ): (1) a triangle flight pattern at two different altitudes over the Louisiana part of the play and (2) a racetrack flight pattern at five different altitudes in Texas. The triangle flight pattern was conducted over areas with a larger well density centered in the middle of the play. The flight track and the CWT results from the triangle flight pattern are shown in Figure 4 . The data gaps in Figure 4 are due to either aircraft turning when performing the flight pattern or gaps in CH 4 data mainly as a result of routine background checks and calibrations. The C-130 entered this region from the northeast and flew in a counterclockwise pattern. During the first cycle, the C-130 flew at an altitude of 570 m above ground level (agl), and a maximum CH 4 flux was detected at the beginning of the second leg (leg #2) (32.140°N, 93.968°W). In this area, a hot spot is visible in the two-dimensional wavelet cross-spectrum between CH 4 and vertical wind speed, mainly at time scales of~32 s and~128 s (y axis of Figure S2 in the supporting information). A benzene flux was also observed at the beginning of leg #2. CWT fluxes of CH 4 and benzene show good correlation (R = 0.65) with a slope of 106 ± 9 g/g (or 514 ± 44 ppb/ppb) ( Figure 4c ). This emission ratio is somewhat smaller than the derived enhancement ratios in Figure 3 (860 ± 10 ppb/ppb), but still lies in the ranges of shale gas regions ( Table 1 ), indicating that fluxes of CH 4 and benzene detected at the beginning of leg #2 were from shale gas activities. NCAR C-130 After finishing the first cycle, the C-130 flew the same flight track again at 310 m agl about 25 min later. Again, fluxes of CH 4 and benzene were detected at the beginning of leg #2 (Figure 4b ), but the magnitudes of the fluxes were much smaller for both CH 4 and benzene. This variability may be attributed to (1) flux footprint was somewhat different at the two flight altitudes. The footprint widths (dx 0.5 ) were calculated to be 2.4 km and 1.8 km for the 570 m and 310 m flight legs, respectively. Wind directions Field et al. [2015] . NCAR C-130 f Gasoline vehicle exhausts [Kirchstetter et al., 1996] . g Urban emissions in Los Angeles [Borbon et al., 2013] . h Urban emissions in Boston/New York City [Warneke et al., 2007] . Journal of Geophysical Research: Atmospheres 10.1002/2015JD023242 (35°for 510 m leg and 54°for 310 m leg) were also slightly different when the aircraft flew over this hot spot. The difference in footprints may result in larger contribution from a point source to one flight leg than another leg, as implied in the distributions of flux footprint along the upwind distance [Kljun et al., 2004; Weil and Horst, 1992] . 10.1002/2015JD023242 (2) Random errors can contribute significantly to the calculated instantaneous fluxes (see discussion in section 3.3). (3) There might be some potential variability of the emission sources, such as short-term large emissions as a result of scheduled/unscheduled venting and unloading events of shale gas facilities [Allen et al., 2013] . This variability demonstrates the need for repeated measurements to obtain meaningful flux results for this small hot spot. The lower fluxes of both CH 4 and benzene from the second cycle of triangle pattern make it difficult to obtain an enhancement ratio as was obtained from the first triangle cycle. 10.1002/2015JD023242 We also observed concurrent enhancements of CWT fluxes of benzene and CH 4 during the C-130 flight on 27 June ( Figure S3 in the supporting information). The flux of benzene at this hot spot (32.386°N, 94.203°W) reached a maximum of 1.1 μg m À2 s À1 . The slope of CH 4 flux versus benzene flux was 6.2 g/g (or 30 ppb/ppb), which is significantly lower than the signature from oil and gas extraction and approaches that from urban emissions. However, we note that the two nearest cities (Tyler and Longview, TX) are both too far away (~50 and~100 km) to account for this flux hot spot, since half widths of the horizontal footprint of the flux measurements from aircraft are in the range of several kilometers (2.4 km for this flight) . Measurements of CO, a combustion tracer, also suggest that this plume was not from urban emissions. These elevated benzene and CH 4 fluxes may come from some other activities or point source in this area. NOAA WP-3D Both CH 4 concentration and vertical wind speed were recorded at 1 Hz on the NOAA WP-3D. To investigate the feasibility of using 1 Hz data for turbulent flux calculations, spectral analysis is performed to determine the length and time scales of eddies that contribute to the eddy covariance flux. Figure 5 shows FFT cross spectra of vertical wind speed and potential temperature (w′T′) from C-130 measurements on 27 June and 4 July. As shown in Figure 5a , cross spectra of w′T′ over different flight legs during the two flights are quite variable. Normalized cumulative cross spectra, commonly referred to as ogives, are calculated and plotted in Figure 5b . An averaged ogive is determined from individual curves to reduce variability. The flux of w′T′ is mainly contributed by eddies with frequencies in the range of 0.01 Hz-1 Hz. The energy flux of w′T′ carried by eddies with frequency greater than 1 Hz is only around 1% of the total flux. Eddy covariance fluxes of CH 4 and CO 2 calculated using 1 Hz aircraft data are 9% and 5%, respectively, lower than those determined from 10 Hz data during the first triangle pattern of the C-130 flight on 4 July, as shown in Figures 5c and 5d . Although the two different calculations obtain slightly different numbers (1% versus 5-9%), both calculations indicate that using 1 Hz data measured by aircraft at several hundred meter altitude to calculate eddy covariance flux should impose only small systematic errors (<10%). This result is consistent with the conclusions from aircraft measurements over the Sahara desert in the work of Rosenberg et al. [2014] and above California oak forests in the work of Karl et al. [2013] . From Figure 5b , we also conclude that a time scale of 1000 s will be enough to capture the largest eddies in the Haynesville shale gas play. This time scale corresponds to a flight leg of 100 km, at typical aircraft speeds of 100 m/s in the boundary layer for both the C-130 and the WP-3D. NOAA WP-3D The above analysis indicates that the CH 4 measurement data collected at 1 Hz on board the NOAA WP-3D can be used to calculate fluxes in the shale gas regions. Figure 6 shows CWT fluxes of CH 4 calculated from WP-3D flights on 10 and 25 June. From the plots, the locations of many hot spots of CH 4 fluxes are visible. For many of these flux hot spots, large facilities (e.g., gas processing plants and compressor stations) are identified close to the sampling locations (usually 0-3 km), based on visual inspections of Google Earth images. For example, Figure S4 in the supporting information). Figure 7 shows a time series of CWT CH 4 fluxes on 25 June. Hot spots in Figure 6 correspond to peak flux values in the time series plot (larger than 5 μg m À2 s À1 ) (see Figure 7 ). Besides these spikes, the CWT analysis suggests general upward fluxes of CH 4 (even though at lower magnitudes) from the region. Some periods associated with negative CH 4 fluxes are also obtained (as low as À2.5 μg m À2 s À1 ), which is due to geophysical variability of the instantaneous flux measurements. To understand the range of CH 4 fluxes, statistical analyses of CWT instantaneous fluxes are described in the next section. Statistical Analysis of CWT Instantaneous Fluxes 3.3.1. Cases With Zero Average Flux To investigate the distribution of random errors in calculation of CWT instantaneous fluxes and therefore the quality of the derived emission flux, we take two cases where no significant CH 4 flux is expected or observed: one is measurements in the boundary layer over the ocean, where methane is at its background and vertical fluxes are very small, and the other is a synthetic data set associated with Gaussian random errors for both concentration and vertical wind speed, resulting in a net eddy covariance flux of zero. Statistical Analysis of CWT Instantaneous Fluxes 3.3.1. Cases With Zero Average Flux On 5 July, the NCAR C-130 flew over the Atlantic Ocean, and measurements were made at different altitudes in the marine boundary layer ( Figure S5 in the supporting information). Measured CH 4 concentrations were 1822 ± 1 ppb, indicating a pristine environment without significant enhancement above the regional background of the western Atlantic Ocean (http://esrl.noaa.gov/gmd/dv/iadv/graph.php?code=BMW). The same method used to calculate CWT flux as for the other shale gas play flights is used for the marine CH 4 data. Even though the expected CH 4 flux over open ocean is very small (3.2-6.3 × 10 À5 μg m À2 s À1 ) [Rhee et al., 2009] , both positive and negative CH 4 fluxes were determined ( Figure S5 ). These positive and negative CH 4 fluxes are attributed to random errors in the CWT calculation and the measurement errors of the methane mixing ratios and the vertical wind speed. Figure 8a shows a histogram of the derived CH 4 fluxes. The distribution is centered on zero, reflecting the absence of a detectable methane flux by this method. Fitting using different functions to the histogram indicates that the Voigt function best describes the distribution of the CH 4 flux. We also tried a Gaussian function to fit the data points, but it did Journal of Geophysical Research: Atmospheres 10.1002/2015JD023242 not describe the long tails of the distributions (e.g., Figure 8) . The fitted Voigt curve shows a peak location (x 0 ) at 1.1 ± 0.3 × 10 À3 μg m À2 s À1 and a half width at half maximum (HWHM) of 2.2 × 10 À2 μg m À2 s À1 . 10.1002/2015JD023242 The ratio between x 0 and HWHM (x 0 /HWHM) is 5%, suggesting that this fitted Voigt curve follows a near-zero-centered distribution. 10.1002/2015JD023242 As a second test case, we created a synthetic data set following a Gaussian distribution. First, we created a time series of vertical wind speed (0 ± 1 m/s). Second, a series of CH 4 concentrations with the same average (1850 ppb) but different standard deviations (ranging from 0.05 ppb to 4 ppb) are prescribed. Random normally distributed noise was imposed on both synthetic time series. The histograms of the calculated CWT fluxes are shown in Figures 8b and 8c (also in Figure S6 in the supporting information). Similar to Figure 8a , a Voigt function describes the histogram structures of CWT fluxes from the synthetic data sets reasonably well. The x 0 /HWHM ratios for different fitted Voigt curves are between 0.4% and 4.4%. To avoid undesired correlation between vertical wind speed and concentration from single synthetic data set, an ensemble (N = 20) of synthetic data sets is constructed using different random seeds and similar results are obtained, as discussed above. 10.1002/2015JD023242 Based on investigations of pristine marine boundary layer data and synthetic data, we conclude that (1) in the case of a net zero flux, the distributions of instantaneous fluxes calculated by CWT is well described by a Voigt function, (2) the fitted Voigt curve represents the combined effect of geophysical variability and random noise in CWT calculations, and (3) the fitted Voigt curves center near zero for a net zero flux. Journal of Geophysical Research: Atmospheres 10.1002/2015JD023242 Random errors in CWT instantaneous fluxes may arise from several aspects: (1) concentration variability that is not due to turbulent mixing, e.g., spatial difference in the case of aircraft measurements and (2) random instrument noise for both gas concentration and wind measurements. The CWT method is a mathematical calculation procedure; thus, the combined effect of these random errors will eventually propagate in the final CWT results. Figure 9 shows histograms of CWT instantaneous fluxes of CH 4 inferred from the NOAA WP-3D measurements on 10 and 25 June over the Haynesville shale play and on 6 July over the Marcellus shale play. It is clear that the histograms in Figure 9 show a positive bias, indicative of a net upward flux. Based on the analysis in the previous section, random errors from CWT are represented by a zero-centered Voigt curve. Since a significant deposition flux of CH 4 is not expected [Born et al., 1990] , we apply Voigt fits to data points that correspond to CH 4 fluxes lower or equal to zero to represent random error from the CWT calculation. Residuals from the Voigt fits for CH 4 fluxes lower or equal to zero are fluctuating around zero, but positive residuals are clearly observed on the positive side of the x axis (especially larger than 1 μg m À2 s À1 in both plots). Since random errors in the CWT calculation are subtracted from the fitted Voigt curves, the residuals on the positive side of the x axis are interpreted as average emission fluxes from shale gas wells and facilities. Cases With Nonzero Flux Random errors in the CWT instantaneous fluxes affect not only the CH 4 flux from shale gas extraction activities but also all other CWT flux calculations. The histogram of CWT instantaneous fluxes of m/z 69 (isoprene + fragments from cyclohexanes) calculated from a C-130 flight over the Haynesville shale play on 4 July is shown in Figure 10 . We note that m/z 69 should mainly come from vegetation emissions of isoprene rather than oil and gas emissions (see section 2.1). Derived negative fluxes of isoprene are smaller but are still visible. A fit using the Voigt function is also conducted to isoprene fluxes that are lower or equal to zero. A much lower fitted random error from the CWT calculation of isoprene fluxes is obtained. Cases With Nonzero Flux The main difference between the case of isoprene and that of CH 4 is that CH 4 flux measurements are more affected by inherent random errors, due to the high atmospheric CH 4 background and variability of the background caused by a long lifetime compared to isoprene. Cases With Nonzero Flux Although the distribution of random errors in instantaneous fluxes is derived here, it is not possible to subtract random errors from each calculated data point of instantaneous flux. In spite of this, the confidence level to attribute each instantaneous flux to real emission could be derived from the fitting results in Figure 9 . Evidently, an instantaneous flux of CH kochellen@example.org μg m À2 s À1 determined on 25 June is more statistically significant than an instantaneous flux of kochellen@example.org μg m À2 s À1 (Figure 9b ), as the [Peischl et al., 2015] . The light blue error bars indicate the uncertainties of the estimates from the mass balance method. Journal of Geophysical Research: Atmospheres 10.1002/2015JD023242 fitted random errors (Voigt curve) account for 8% and 55% of the total measured data kochellen@example.org and 0.2 μg m À2 s À1 , respectively. À1 In summary, the statistical analysis on the distribution of calculated instantaneous CWT fluxes is a useful technique for small fluxes or when random errors contribute significantly to the derived instantaneous fluxes. The results from the analysis are used as an indicator of positive CH 4 fluxes and a quick evaluation on the statistical significance for a given flux level to be real emissions. In addition, the statistical analysis can separate the distribution of random errors from that of emission fluxes. The implication from the distribution of the derived emission fluxes will be discussed in section 3.4.3. Table 2 shows the CWT and FFT methane fluxes determined from different flights. Benzene fluxes will not be considered further, because the derived benzene fluxes are limited to only two C-130 flights. The values for CWT fluxes in Table 2 are the arithmetic means of instantaneous CWT fluxes for the respective periods over shale gas regions. The uncertainties of the averaged CWT and FFT fluxes in certain measured periods shown in Table 2 (usually <30%) are estimated from uncertainties in measured concentrations (<1%), systematic error (2-5%), and random error (around 20%) of airborne fluxes. The calculations of systematic error and random error for averaged fluxes in certain periods are shown in previous studies [Karl et al., 2009 Lenschow et al., 1994] . Using 1 Hz data of methane and vertical wind in WP-3D flights may contribute uncertainties of measured fluxes, and they are not accounted here. Methane Emissions and Its Distribution 3.4.1. Uncertainty Analysis of Airborne Eddy Covariance Fluxes The mass conservation equation of a scalar in the atmosphere is expressed as [Aubinet et al., 2012] Methane Emissions and Its Distribution 3.4.1. Uncertainty Analysis of Airborne Eddy Covariance Fluxes where C is the mean concentration of the scalar, U is the mean horizontal wind speed, F EC is the turbulent flux, and S is the source and sink term in the atmosphere, which is essentially zero for long-lived species (e.g., CH 4 ) at the time scales of convective mixing in the boundary layer. The three parts in the left-hand side of the equation are storage term (concentration change), horizontal advection, and eddy covariance flux divergence, respectively. After integrating equation (4) from ground to an altitude of z and rearranging it, the surface emission flux (F S ) can be described as Methane Emissions and Its Distribution 3.4.1. Uncertainty Analysis of Airborne Eddy Covariance Fluxes where F EC is the eddy covariance flux measured at an altitude of z, F HA is the horizontal advection flux, and z i is the boundary layer height. Specially, when z = z i , we get Journal of Geophysical Research: Atmospheres 10.1002/2015JD023242 where F Entrainment is the entrainment flux on the top of boundary layer. We note that the horizontal advection flux (and other flux terms) has a unit of μg m À2 s À1 in this study. As mentioned earlier, Peischl et al. [2015] used the mass balance method to determine the total emission fluxes and horizontal advection fluxes of CH 4 from both the Haynesville and Marcellus shale plays (Table 2) , based on measurements conducted by the WP-3D on 25 June and 6 July, respectively. To make the results in this study and those from the mass balance method in Peischl et al. 10.1002/2015JD023242 [2015] comparable, we divide the results in Peischl et al. [2015] by the targeted areas of the two shale gas plays enclosed by the upwind and downwind transects (2.2 × 10 4 km 2 in the Haynesville and 9.4 × 10 3 km 2 in the Marcellus) to transfer the unit to μg m À2 s À1 . 10.1002/2015JD023242 As shown by the equation (5), storage terms and horizontal advection flux need to be considered to connect the measured airborne eddy covariance fluxes with surface emissions (F S ). From equation (4), the underestimation of surface flux from measurements made at altitude can be derived from flux divergence by measuring eddy covariance flux at multiple altitudes . Flight legs at multiple altitudes to estimate flux divergence were not a focus of this study, especially for the WP-3D flights that only occurred at a single altitude. Instead, we use the horizontal advection flux from Peischl et al. [2015] and concentration drift to constrain the underestimation in this study (equation (5)). Here we use the WP-3D flight on 25 June as an example to discuss this issue. 10.1002/2015JD023242 1. The fraction of the underestimate of surface emissions due to horizontal advection flux (f HA ) could be derived from equations (5) and (6): 10.1002/2015JD023242 As horizontal advection flux is usually much larger than storage term and entrainment flux [Gordon et al., 2015] , f HA can be approximated to be z/z i for most of the cases. For z/z i = 0.35 ± 0.07 (25 June WP-3D flight) and F HA /F s = 0.8, using 0.35 as the correction fraction only introduces an error of 7% to the estimated surface emissions. Although the alternative is available, we derive the influence of horizontal advection from the estimates of total horizontal advection fluxes by the mass balance method in Peischl et al. [2015] (row 4 in Table 2 ), for the sake of more accurate estimation. Combining with the flight altitude (z) and boundary layer height (z i ), the difference between airborne eddy covariance flux and surface emission flux Peischl et al. [2015] and the targeted areas of the two shale gas plays (see texts). 10.1002/2015JD023242 d The values after plus-minus sign are the uncertainties of the calculated fluxes (see text in section 3.4.1). e The fraction of the area under the fitted Voigt curve to the total area under the measurements, which is an indicator for random errors in the CWT instantaneous fluxes. 10.1002/2015JD023242 f HER: high-emission regions (see section 3.4.3). g THP: ten highest peaks (see section 3.4.3). Journal of Geophysical Research: Atmospheres 10.1002/2015JD023242 is 0.28 ± 0.06 μg m À2 s À1 . Airborne flux measurements at lower altitude will be helpful to reduce the influence of horizontal advection. 10.1002/2015JD023242 2. We observed very little change of CH 4 concentration over time during the 25 June flight (À0.5 ppb/h). This concentration change is translated to a flux of À0.05 μg m À2 s À1 by integrating from the ground to the measurement altitude (500 m). 10.1002/2015JD023242 In summary, the airborne CH 4 eddy covariance fluxes measured during the WP-3D flight on 25 June are likely a lower limit of surface emissions. The underestimation is calculated to be 0.23 ± 0.06 μg m À2 s À1 , or the fluxes measured at altitude are 17-26% lower than the surface emissions. Using the same procedures as Haynesville, we determine that the airborne CH 4 fluxes derived from eddy covariance on 6 July over the Marcellus shale gas play are 43-62% (0.22 ± 0.04 μg m À2 s À1 ) lower than the surface emissions at our best estimate. The underestimation percentage in the flight of 6 July is higher than that on 25 June, since the WP-3D flew at higher altitudes relative to the boundary layer height on 6 July (z/z i = 0.5 ± 0.1). Methane Emission Strengths The CH 4 fluxes determined from different methods, which are tabulated in Table 2 , can be compared with each other. Fluxes calculated by FFT and CWT agree with each other within 30% for various flights, except for the triangle pattern during the C-130 flight on 4 July. The large difference between FFT and CWT during this period may be due to the effect of inhomogeneities on the FFT method [Misztal et al., 2014] , as a large peak of CH 4 fluxes were detected (see section 3.2.1). Thus, CWT flux may be considered more reliable for this period. Methane Emission Strengths The eddy covariance fluxes obtained in this study can be compared with the results from the mass balance method obtained by Peischl et al. [2015] . We note that the source contribution area of the mass balance and eddy covariance methods are different, although the same data sets are used: the mass balance method integrates the emissions in the areas enclosed by upwind and downwind flight legs, whereas the source contribution area of the eddy covariance method approximately comprises the projected upwind-pointed half domes with the radius as half widths of the horizontal footprint along the flight tracks [Misztal et al., 2014] . Based on footprint analysis, we roughly estimate that the total source contribution areas along the flight tracks for the eddy covariance method are in the range of 1-3 × 10 3 km 2 in the Haynesville flights and 0.7-2.2 × 10 3 km 2 in the Marcellus flight, both of which are small percentages (5-20%) of the targeted areas of the mass balance method in the two shale regions (2.2 × 10 4 km 2 in the Haynesville and 9.4 × 10 3 km 2 in the Marcellus). The small percentages of total areas sampled by eddy covariance fluxes in both regions may result in larger uncertainties when extrapolating the eddy covariance numbers to the entire region. As we did not selectively sample specific part of the regions or any large facilities during the aircraft measurements, we presume that the eddy covariance estimates from source contribution areas equivalent to 5-20% of each basin are representative of the whole shale gas extraction basins (Haynesville and northeastern Marcellus). Methane Emission Strengths As shown in previous section, the airborne eddy covariance fluxes measured at flight altitude may underestimate the surface methane emission fluxes. Surface emission fluxes inferred from eddy covariance measurements are calculated to be 1.23 ± 0.27 μg m À2 s À1 in the Haynesville and 0.64 ± 0.13 μg m À2 s À1 in the Marcellus after correction of the underestimation ( Table 2 ). The total emission fluxes estimated from the mass balance method for 25 June flight (Haynesville) and the 6 July flight (Marcellus) are 1.02 ± 0.29 μg m À2 s À1 and 0.44 ± 0.18 μg m À2 s À1 , respectively [Peischl et al., 2015] . Although the estimates from the eddy covariance method are somewhat higher than those from the mass balance method, the differences are both within the combined uncertainties of the eddy covariance method and the mass balance method. The reasonable agreement between the eddy covariance and mass balance methods indicates that the airborne eddy covariance method could be a reliable technique to estimate emissions from oil and gas extraction. The eddy covariance method also has several advantages that are described in the following paragraphs. À1 The flight patterns of the WP-3D on 10 and 25 June over the Haynesville shale play were quite similar (Figure 1) . Eddy covariance CH 4 fluxes for the two flights compared well with each other for both FFT and CWT calculations, implying that there was no large day-to-day variation of CH 4 emissions with regard to the sampled areas along the flight tracks. A comparison of estimates by the mass balance method from different Journal of Geophysical Research: Atmospheres 10.1002/2015JD023242 flights over the Haynesville is not available. The C-130 only flew over the middle of the extraction region, and no effective characterization of upwind and downwind regions was made. The NOAA WP-3D flight on 10 June was not used for the mass balance method either, due to the absence of a constant wind field [Peischl et al., 2015] . The inherent assumptions in the mass balance method allow this technique to be applied only when appropriate meteorological conditions are met [e.g., Trainer et al., 1995] . The restriction also affected other mass balance studies in the literature. For example, only one out of 12 flights conducted in the Uintah Basin, Utah, was suitable for emission estimates based on the mass balance method [Karion et al., 2013] . The successful implementation of eddy covariance method to the WP-3D flight on 10 June suggests that eddy covariance method can be applied (at least) sometimes when favorable meteorological conditions to use the mass balance method are either not met or difficult to obtain. The estimates from the eddy covariance method also provide an independent test of the mass balance method. Therefore, our results indicate that the airborne eddy covariance method could be a powerful alternative technique to estimate emissions from oil and gas extraction activities. The Distribution of Methane Emissions Besides absolute emissions, the results of eddy covariance flux over oil and gas production regions can provide additional information about the distribution of emission fluxes within an area. Distributions of residuals from Voigt fits for both the Haynesville flights (10 and 25 June) and the Marcellus flight (6 July) are shown in Figure 11 . It is clear that the distributions of residuals on 25 June and 6 July illustrate small variations as low as 0.15 μg m À2 s À1 and 0.1 μg m À2 s À1 , while the lowest on 10 June are 0.6 μg m À2 s À1 , owing to the higher random errors from CWT calculations on 10 June ( Table 2 ). As discussed above, the residuals from the Voigt fits are indicative of the actual emission fluxes of CH 4 from different sources in the shale gas region. Distributions of CH 4 emission fluxes for all three flights generally follow a lognormal distribution, as indicated by fitting performance in Figure 11 . However, an inability to describe data points with high fluxes (>10 μg m À2 s À1 ) based on the lognormal function is noticeable for the two Haynesville Figure S7 in the supporting information). This lognormal distribution is also in agreement with recent mobile measurements of CH 4 emissions in several shale basins in western U.S. [Brantley et al., 2014] . The longtailed structure of lognormal distribution implies that a small proportion of the facilities ("superemitters") make a disproportionate contribution to total CH 4 emissions. The Distribution of Methane Emissions High-emission regions (HERs) within a shale play are defined here as areas with a flux 3 times higher than the regional average. The averaged CWT fluxes determined in each basin are used as the surrogate of regional average. Figures 11b and 11d show cumulative fractions of the total CH 4 fluxes for flights on 25 June and 6 July, representing the Haynesville and Marcellus shale plays, respectively. The flight on 10 June is not used for this analysis, because the number of low-flux data points may be underestimated as a result of high random errors. The number of data points defined as HER accounts for 5% and 9% of the number of data points in Figures 11b and 11d , respectively. However, the contributions of these HERs to the determined CH 4 emission fluxes are determined to be 26% and 45% for the Haynesville flight (25 June) and the Marcellus flight (6 July), respectively. It is also notable that using the fitted lognormal curve to calculate the cumulative flux distribution underestimates the fraction contributed by HER for the flight on 25 June. The Distribution of Methane Emissions Another method to get more information on the distribution of CH 4 emissions within shale plays is peak analysis. The ten highest peaks (THPs) in the time series of CWT CH 4 fluxes are identified for all three WP-3D flights ( Figure S8 in the supporting information). As discussed above, these high-flux peaks are associated with large facilities or large-density wells with high emission rates. The 10 highest peaks contribute 28%-39% and 18% of the determined CH 4 fluxes in the Haynesville and
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