Inference of Global Methane Emissions from Oil and Gas Production Citation Tribby, Ariana Linnae (2023) Inference of Global Methane Emissions from Oil and Gas Production. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/pjn3-az83. https://resolver.caltech.edu/CaltechTHESIS:06022023-045855497 Abstract Atmospheric methane plays a significant role in warming the climate. Characterizing its sources and sinks is important for future climate and air quality impacts. Global methane background trends suggest a sustained increase in emissions since 2007. There is no debate that reducing anthropogenic (human-driven) emissions can lead to short-term decreases in atmospheric methane, posing an attractive avenue towards mitigating climate change. Yet, effective policy to limit emissions from energy-related activities relies on accurate emission estimates, and historically, it has been challenging to diagnose both the magnitude and origin of methane leaks from a wide range of facilities and components across production, transmission, storage, and distribution systems. We present a novel Bayesian hierarchical model to improve methane emission estimates on global and regional scales from oil and gas processes. We also present methods to optimize time and cost of model simulations of certain trace gases, including several of which have important climate implications. Finally, we present our efforts in characterizing fossil methane from burgeoning oil production in Oklahoma and Texas using long term ground-based remote-sensing observations combined with Stochastic Time-Inverted Larangian Transport modeling. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: Ethane, propane, methane, natural gas, energy Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Wennberg, Paul O. Group: Resnick Sustainability Institute Thesis Committee: Seinfeld, John H. (chair) Wennberg, Paul O. Blake, Geoffrey A. Flagan, Richard C. Defense Date: 1 June 2023 Funders: Funding Agency Grant Number NSF Graduate Research Fellowship DGE-1745301 Resnick Sustainability Institute UNSPECIFIED NASA 80NSSC22K1066 Record Number: CaltechTHESIS:06022023-045855497 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:06022023-045855497 DOI: 10.7907/pjn3-az83 Related URLs: URL URL Type Description https://pubs.acs.org/doi/10.1021/acs.est.2c00927 DOI Article adapted for Chapter 2 ORCID: Author ORCID Tribby, Ariana Linnae 0000-0002-6435-4575 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 15276 Collection: CaltechTHESIS Deposited By: Ariana Tribby Deposited On: 09 Jun 2023 22:05 Last Modified: 18 Nov 2025 19:21 Thesis Files PDF - Final Version See Usage Policy. 66MB Repository Staff Only: item control page

Inference of global methane emissions from oil and gas production Thesis by Ariana Linnae Tribby In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2023 Defended June 1, 2023 ii Ó 2023 Ariana L. Tribby ORCID: 0000-0002-6435-4575 All rights reserved iii ABSTRACT Atmospheric methane plays a significant role in warming the climate. Characterizing its sources and sinks is important for future climate and air quality impacts. Global methane background trends suggest a sustained increase in emissions since 2007. There is no debate that reducing anthropogenic (human-driven) emissions can lead to short-term decreases in atmospheric methane, posing an attractive avenue towards mitigating climate change. Yet, effective policy to limit emissions from energy-related activities relies on accurate emission estimates, and historically, it has been challenging to diagnose both the magnitude and origin of methane leaks from a wide range of facilities and components across production, transmission, storage, and distribution systems. We present a novel Bayesian hierarchical model to improve methane emission estimates on global and regional scales from oil and gas processes. We also present methods to optimize time and cost of model simulations of certain trace gases, including several of which have important climate implications. Finally, we present our efforts in characterizing fossil methane from burgeoning oil production in Oklahoma and Texas using long term ground-based remotesensing observations combined with Stochastic Time-Inverted Larangian Transport modeling. iv PUBLISHED CONTENT AND CONTRIBUTIONS Tribby, A. L.; Bois, J. S.; Montzka, S. A.; Atlas, E. L.; Vimont, I.; Lan, X.; Tans, P. P.; Elkins, J. W.; Blake, D. R.; Wennberg, P. O. Hydrocarbon Tracers Suggest Methane Emissions from Fossil Sources Occur Predominately Before Gas Processing and That Petroleum Plays Are a Significant Source. Environ. Sci. Technol. 2022, acs.est.2c00927. https://doi.org/10.1021/acs.est.2c00927. A.L.T. performed research, analyzed data, and wrote the manuscript. Tribby, A.L.; Wennberg, P.O. An analysis coordinate transform to facilitate use of in-situ aircraft observations for flux estimation. In preparation for submission to Atmospheric Measurement Techniques. A.L.T. performed research, analyzed data, and wrote the manuscript. Tribby, A.L.; Wu, Dien; Laughner, J.L.; Parker, H.A; Wennberg, P.O. Towards constraining methane emissions in southern Oklahoma using STILT analysis of remote sensing and flask observations of hydrocarbon tracers. In preparation for submission to Atmospheric Chemistry & Physics. A.L.T. performed research, analyzed data, and wrote the manuscript. v TABLE OF CONTENTS Abstract……………………………………………………………………………………….…..iii Published Content and Contributions……………………………………………………………..iv Table of Contents ……………………………………………………………………………….…v List of Figures ....………………………………………………………………………………...vii List of Tables …………………………………………………………………………………….xx Chapter 1: Introduction ……………………………………………………………………….…...1 1.1 Recent trends in atmospheric methane ………………………………………………..1 1.2 Methane emissions from fossil energy ………………………………………………..2 1.3 Fossil methane emission monitoring ……………………………………………….....2 1.4 Thesis overview ….…………………………………………………………………....3 Chapter 2: Hydrocarbon tracers suggest methane emissions from fossil sources occur predominately pre-gas processing and that petroleum plays are a significant source……………..6 2.1 Introduction …………………………………………………………………………...6 2.2 Materials and methods ……………………….……………………………………….7 2.3 Results and discussion …….…………………………………………………………10 Chapter 3: An analysis coordinate transform to facilitate use of in-situ aircraft observations for flux estimation …….……………………………………………………………………………..24 3.1 Introduction ………………………………………………………………………….24 3.2 Methods ……………………………………………………………………………...25 3.2.1 ATom observations ……….………………………………………………..25 3.2.2 GEOS-Chem simulations ………………………………………………….26 3.3 Results ……………………………………………………………………………….27 Chapter 4: Towards constraining methane emissions in southern Oklahoma using STILT analysis of remote sensing and flask observations of hydrocarbon tracers …….………………………….33 4.1 Introduction ………………………………………………………………………….33 4.2 Methods ……………………………………………………………………………...33 4.2.1 TCCON measurements of ethane and propane ………….…………………33 4.2.2 GEOS-Chem simulations ………………………………………………….35 4.2.3 NOAA flask observations ……….…………………………………………35 4.2.4 STILT modeling …………………………………………………………...36 4.2.5 Emissions prior …………………………………………………………….36 4.2.6 Bayesian modeling ………………………………………………………...37 4.3 Results and analysis …………..……………………………………………………...38 4.4 Future work ……..…………………………………………………………………....43 Appendix S: Supplementary information for hydrocarbon tracers suggest methane emissions from fossil sources occur predominately pre-gas processing and that petroleum plays are a significant source ……………………………………………………………………………………………46 S.1 Economics & production of oil and natural gas ……………………………………..46 S.2 NOAA & FRAPPE observations ……………………………………………………49 S.2.1 Processing and statistical methods ………………………………………...49 S.2.2 Chemical aging approach to determining methane background …………..51 S.2.3 Methane anomaly plots for NOAA and FRAPPE campaigns …….……….56 S.2.4 Maps of FRAPPE and NOAA SGP observations compared to oil and gas sites …………………………………………………………………………………....60 vi S.2.5 Comparison to Lan et al. 2019 study ………………………………………63 S.3 ATom & HIPPO aircraft observations ………………………………………………65 S.4 GEOS-Chem simulations ……………………………………………………………71 S.5 Bayesian inference …………………………………………………………………..82 S.5.1 Background and priors …………………………………………………….82 S.5.2 Simulation-based calibration ………………….…………………………...89 S.5.3 Posterior samples – ATom observations ……….………………………….90 S.5.4 Posterior predictive check – ATom observations …………………………94 S.5.5 Posterior samples – HIPPO observations ………………………………....98 S.5.6 Posterior predictive check – HIPPO observations ……………………….102 S.5.7 Sigma parameter sensitivity analysis …………………………………….107 S.5.8 Estimating an overall emissions scalar …………………………………..109 S.5.9 Estimating C2H6 and C3H8 emissions ……………………………………109 S.6 Oil and Gas emission ratios ………………………………………………………..112 S.6.1 Hydrocarbon wellhead composition ……………………………………..112 S.6.2 Impact of reallocation of CH4 emissions on the transportation sector footprint ………………………………………………………………………………..…115 Appendix A: Supplementary information for an analysis coordinate transform to facilitate use of in-situ aircraft observations for flux estimation …………..…………………………………….123 Appendix B: Supplementary information for towards constraining methane emission in southern Oklahoma using STILT analysis of remote sensing and flask observations of hydrocarbon tracers …………………………………………………………………………………………………..135 vii LIST OF FIGURES Number a. 1 2. 3. 4. 5. Page Methane atmospheric “background” mole fraction rising worldwide. Data provided by NOAA. ………………...……………………………………………………….…………1 Measurements of C2H6 and C3H8 from ongoing NOAA GML tower and aircraft sites (Table S1) from 2005-2018. The data follow the photochemical aging distribution described in Parrish et al. 2018, where the data below 1 ppb C3H8 are affected by photochemically aged emissions and mixing processes. As such, we only study the ratio of these gases in the 50th highest percentile (everything above 1 ppb C3H8) that would indicate fresh emissions. After this filtering, two sites, Northwestern CO and Western UT (site codes NWR and UTA), did not have any data in the fresh emission regime and are not included in further analysis (more detail in Figure S8)……..........................................................................................10 Yearly correlation between NOAA hydrocarbon vs CH4 anomaly in Oklahoma. We show the percent change of anomalies/year with respect to the mean hydrocarbon and methane anomalies. The trend for C3H8/CH4 is 7.13 ± 1.44 % with an R2 of 0.71. The trend for C2H6/CH4 is 5.87 ± 1.26 % with an R2=0.69. The variability in the trend comes from the standard error of a linear regression. The variability in the individual points comes from the 95% confidence interval of a pairs bootstrap of the alkanes and CH4 anomalies. (We ran a pairs bootstrap for co-measurements of C3H8 and ∆CH4 and compute the slope of the correlation for each bootstrap sample and repeated this for every year in the data; please see the methods section). This trend in units of ppt/ppb/year is shown in Figure S21……………………………………………..……………………………………...…12 Comparison of C3H8 vs C2H6 for NOAA, ATom aircraft, and GEOS-Chem simulations during fall/winter seasons. NOAA photochemically-aged measurements (all sites, 20052018), as explained in the text, are shown on the heat map (colored by the number density of data). The spring/summer seasons are included in Figure S29-30, S33. HIPPO is shown in Figure S34..…………………….…………………………………………………..….13 Impact of revised C3H8 emissions on GEOS-Chem simulation. Combined Pacific and Atlantic transects for ATom 4 aircraft campaign, which took place during Spring 2018, are shown in gold. The GEOS-Chem simulation using default C3H8 emissions are shown in blue and orange, referring to the Pacific and Atlantic transects, respectively. The GEOSChem simulation after implementing the revised C3H8 emissions is shown in green. The rest of the ATom campaigns are shown in Figure S36…….……………..………………14 Global revised ethane anthropogenic fossil emissions compared to other studies. Our emissions estimate in 2016-2018 (during ATom) and 2009-2011 (during HIPPO) includes our revised emissions for winter, fall and spring seasons that we determined with our Bayesian model during each season. As discussed in the text, fewer samples were obtained during HIPPO, resulting in a sampling bias that we test by restricting observations and simulations to +/- 300 K potential temperature (Figure S56-S57). This test affects the estimate about +/- 1Tg during 2010-2011, but affects our estimate by up to 12 Tg in 2009. We compare our revised emissions to the default emissions from GEOS-Chem v13.0.0. The studies included here (23,25-27) represent anthropogenic fossil emissions except viii 6. 7. 8. 9. 10. Dalsoren et al. 2018 which also includes biofuel, agriculture, and waste. We obtained the CEDS CMIP6 estimate from Dalsoren et al. 2018. Our emissions estimates do not include biomass burning or biofuels. Propane emissions are included in Figure S62………..……16 Global Literature and Observationally Informed Emission ratios (OIER) C3H8/CH4 and C2H6/CH4. The “weighted raw gas ratio” in the figure represents the “literature ratio” described in the text, calculated using Equation 2. OIER, ratios between our revised C2H6 and C3H8 emissions and literature CH4 emission estimates, are shown for several literature CH4 estimates, including IEA 2021 (76.4 Tg/yr)34, Scarpelli et al. 2020 (65.7 Tg/yr)33, and Global Carbon Project 2020 bottom-up estimate (128 Tg/yr, 2008-2017 average)32. The variability in the literature ratio is attributed to the 95% CI of pairs bootstrap samples of hydrocarbon composition measurements (see text for more detail). The variability in the OIER is attributed to the 95% CI of our revised C3H8 and C2H6 emission estimates. We also compare C3H8/CH4 and C2H6/CH4 correlations from in-situ observations, including NOAA observations from Northern Oklahoma (2017 average from Figure S21, units of kg/kg) and FRAPPE observations from Northern Colorado (2014 from Figure S9, units of kg/kg). The variability in the NOAA ratio is relatively low because it is calculated from a multi-year average slope, and the error in the slope is low (see Figure S21, left). The variability in the FRAPPE ratio is relatively high because we use the 95% CI derived directly from our bootstrap samples, as described in the methods section………………………………….17 Flight paths during ATom flight campaign. We use summer 2016 and winter 2017 campaigns over the Atlantic ocean in our analysis. We only consider observations above 20 degrees North, as explained in the methods…...………………………………………26 GEOS-Chem-simulated C3H8 “curtain” during ATom 2 winter 2017 campaign, along pressure and latitude. All GEOS-Chem simulations were sampled along aircraft latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 shows simulations sampled 5 days after the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the median aircraft time. FIRST row: 4x5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. SECOND row: 2x2.5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black. C2H6 is included in the SI…………..…………….28 GEOS-Chem-simulated C3H8 “curtain” during ATom 2 winter 2017 campaign, along potential temperature and latitude. All GEOS-Chem simulations were sampled along aircraft latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 shows simulations sampled 5 days after the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the median aircraft time. FIRST row: 4x5 resolution. SECOND row: 2x2.5 resolution. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black. C2H6 is included in the SI. ………………………………………………..……….29 GEOS-Chem simulations and ATom aircraft C3H8 vs potential temperature. Left: Includes aircraft observations and simulations sampled 5 days after the aircraft flight path. Middle: Includes aircraft observations and simulations sampled during the aircraft flight path. ix 11. 12. 13. 14. 15. 16. 17. 18. 19. S1. S2. S3. S4. S5. Right: Includes aircraft observations and simulations 5 days before the aircraft flight path. C2H6 included in the SI…………………………………………………………...………30 Bayesian inference results, 97.5% confidence interval. Top: C3H8. Bottom: C2H6.………31 Updated ethane and propane volume mixing ratios (VMR) for TCCON retrievals. Updated VMR are derived using the new ginput-devel algorithm (see Methods) and GEOS-Chem profiles made using revised hydrocarbon emissions from Tribby et al. 2022. Index is a proxy for the hybrid pressure level. Shown in blue are the standard a priori profiles used in ggg………………………………………………………………………………………..34 CH4 emissions constructed using wellhead density, used for computing STILT contribution. C2H6 and C3H8 are included in the SI…...…………………………..………37 TCCON dry mole fractions of C2H6 and C3H8……………………….…………………..39 C2H6 and C3H8 NOAA flask data. Data filtered for fresh emission chemical regime. Not yet background corrected. Marker size correlates to relative wind magnitude….……………39 Example of mole fraction contribution to the NOAA tower flask receptor over the 3-day back trajectory. …………………………………………………………………………..40 STILT-modeled receptor anomaly mole fraction compared to NOAA flask backgroundcorrected anomaly. Only including tower observations here. Background described in the methods…...……………………………………………………………………………...41 Posterior samples for x scalar parameter and s for C2H6………………………………...42 Posterior predictive check of C2H6 and C3H8 NOAA flask anomalies. Posterior predictive checks are explained in the text above. The pseudo data are shown in blue with 30, 50, 70, and 99th percentiles…………………………………...…………………………………..42 Economic trends of natural gas and natural gas liquids. Left: Trends in natural gas and hydrocarbon production (EIA) and total ethane summed with rejected ethane modeled by OPIS, Point Logic, provided by IHS Markit. Right: The value of ethane compared to natural gas represented by fractionation spread (frac spread) on the left axis. Ethane rejection in the U.S. and major U.S. refining areas is plotted on the right axis. (Data by OPIS, Point Logic, provided by IHS Markit.)..…………………………………………..46 Global Oil production. Data provided by IEA (https://www.iea.org/fuels-andtechnologies/oil)..............................……………………………………………………...47 Top Natural Gas-Producing US basins/Countries and their corresponding oil production. Top: Oil and gas production for the top 7 natural gas producing basins that account for 86% of total U.S. natural gas production.8,9 Bottom: Global oil and gas production for the top 5 natural gas producing countries that account for 50% of global natural gas production.10,11……………………………………………………………...…………….48 Observed pipeline composition in Playa del Rey and ethane rejection trends. Left: The ratio of propane/methane and ethane/methane measured in natural gas withdrawn from Playa del Rey in Southern California,12 compared to U.S. ethane rejection (see Figure S1 for more information on rejection; data provided by IHS Markit). Right: The ratio of U.S. propane production and total ethane production (including rejection, ER). The production data is provided by EIA13,14s and the rejection data is provided by IHS Markit. The in-situ observed ratio is calculated from NOAA-ongoing observations, see Figure S9……………………………………………..………………………………………….48 Major Oil/Natural Gas Shale Plays in the U.S. & NOAA ongoing measurement locations. Approximate geographical locations of NOAA ongoing measurement locations are shown in the blue stars on the map. Not pictured is East Trout Lake (ETL) site, located in x S6. S7. S8. S9. S10. S11. Saskatchewan, Canada (54.3541N, 104.9868W). Well and basin layers provided by https://atlas.eia.gov/apps/all-energy-infrastructure-andresources/explore...............................................................................................................49 FRAPPE observations. The outline of Colorado state is shown in blue. We show data already pre-processed and filtered for fresh emissions, as discussed in this section……………………………………………………………………………………51 Identifying fresh emission chemical regime in NOAA and FRAPPE campaigns. Left: Varying C3H8 percentiles at the NOAA SGP site. The inflection point between aged and fresh emission regime is visually contained within varying the C3H8 percentile cutoff by ± 10%. We chose the 50th percentile of C3H8 as the demarcation between these regimes (about 103 ppt). Right: C3H8 vs C2H6 using FRAPPE data (already pre-processed, as described in the methods in the main text). FRAPPE observations are quite consistent with NOAA, hence we use the same C3H8 demarcation between the aged and fresh chemical regime…………………………………………………...……………………………….52 NOAA C3H8 vs C2H6 after filtering for fresh emissions. We used C3H8 50th percentile as a marker for fresh emissions (please see details in text above). Sites NWR and UTA only had C3H8 mole fractions below this demarcation and were assumed to be affected only by aged emissions, and as such, were excluded from further analysis……………………….52 C3H8 vs C2H6 after filtering for fresh oil and gas emissions. Left: The filtering method is described in Section 3.1. We show observations for all NOAA sites (2005-2018, see Table S1), NOAA for SGP site only (2006-2018 Oklahoma tower and aircraft observations), and FRAPPE campaign (2014 aircraft observations around Colorado). Top: FRAPPE linear least squares slope 95% CI is [0.76, 0.87] (ppb/ppb, R2 = 0.97) compared to [0.63, 0.70] (ppb/ppb, R2 = 0.98) for all NOAA sites. Variability in the slope for both FRAPPE and NOAA is given by a pairs bootstrap analysis, described in Section 2.1. Right: Slope before 2012 (2005-2011): [0.62, 0.67] (95% CI), R2 = 0.98. Slope after 2012 (2012-2018): [0.63, 0.71] (95% CI), R2 = 0.98. We use data from SGP, TGC, ETL, HIL, DND, BAO, and WKT sites (see Table S1) before filtering for air influenced by fresh oil/gas emissions, which is shown here. We use both tower and aircraft data. We use pairs bootstrapping to arrive at confidence intervals, described in detail in Section 2.1…………………………….…….53 Background estimate for CH4 at NOAA SGP site. Left: Background estimate for CH4 at NOAA SGP site. Left: Using 50% ±10% percentile cutoff of C3H8 has a minimal effect on the background CH4 estimation. Right: C3H8 vs CH4 Anomaly at NOAA SGP site. A CH4 anomaly is calculated by linearly interpolating the estimated CH4 background to the raw CH4 measurement timescale. The interpolated background is then subtracted from the raw CH4 measurements. Using 50% ±10% percentile cutoff of C3H8 has a minimal effect on CH4 anomaly cross plots. Using a pairs bootstrap approach (see Section S2.1), we generate thousands of slope replicates and calculate the following 95% CIs for the slope using the following C3H8 percentile cutoffs: [0.0458, 0.0526] (30th percentile); [0.0460, 0.0534] (40th percentile); [0.0481, 0.0563] (50th percentile)……………… ……………………………54 Methane vs time for NOAA sites. The estimated background is shown in red. Raw CH4 data is shown in blue. The background was calculated using 50% C3H8 percentile cutoff method…………………………………………………………………………………....56 xi S12. S13. S14. S15. S16. S17. S18. S19. C2H6 vs CH4 anomaly for NOAA sites. The data for each site were filtered using the chemical aging regime to filter for fresh emissions and to construct CH4 anomalies (Section 2.2). See Table S1 for a description of site location/observation type. We also ran a bootstrap for each individual site (bootstrapping methods, main text). The 95% CI slopes (ppb/ppb) are as follows: BAO: [0.0833, 0.1449], R2 = 0.91; DND: [0.0289, 0.1205], R2 = 0.63; ETL: [0.0030, 0.0176], R2 = 0.46; HIL: [0.0116, 0.0313], R2 = 0.56; TGC: [0.0400, 0.0730], R2 = 0.74; WKT: [0.0324, 0.0510], R2 = 0.75; SGP: [0.0645, 0.0749], R2 = 0.86…………………………………………………………...…………………………..57 C3H8 vs CH4 anomaly for NOAA sites. The data for each site were filtered using the chemical aging regime to filter for fresh emissions and to construct CH4 anomalies (Section 2.2). See Table S1 for a description of site location/observation type. We also ran a bootstrap for each individual site (bootstrapping methods, main text). The 95% CI slopes (ppb/ppb) are as follows: BAO: [0.0587, 0.0922], R2 = 0.91; DND: [0.0221, 0.1003], R2 = 0.61; ETL: [0.0013, 0.0136], R2 = 0.41; HIL: [0.0078, 0.0216], R2 = 0.54; TGC: [0.0228, 0.0506], R2 = 0.68; WKT: [0.0195, 0.0321], R2 = 0.71; SGP: [0.0426, 0.0499], R2 = 0.83………………………………………………………………...……………………..59 C2H6 vs CH4 anomaly for NOAA SGP site and FRAPPE study. We use the chemical aging approach defined in Section 3.1 to identify C3H8 and CH4 observations within a fresh oil and gas emissions chemical regime. We construct CH4 background-corrected anomalies as described in SI Section S2. Results with C2H6 are similar and shown in Figure S9. NOAA observations for SGP site (Oklahoma, Table S1) are shown here. We show correlations between 2006-2011, labeled as “NOAA SGP < 2012” (HIPPO takes place between 20092011), 2013-2015 (FRAPPE takes place in 2014), and 2016-2018 (ATom time period). Left: The slope of the correlation between C3H8 and CH4 anomaly for NOAA observations before 2012 is [0.031, 0.040] ppb/ppb, R2 = 0.85; between 2013-2015 is [0.045, 0.084], R2 = 0.82; and between 2016-2018 is [0.039, 0.059], R2 = 0.86. FRAPPE is [0.063, 0.085] ppb/ppb, R2 = 0.83. The slope of the correlation for all years of NOAA is [0.043, 0.050] ppb/ppb, R2 = 0.83. C3H8 vs CH4. Right: C2H6 vs CH4 The FRAPPE slope (95% CI, ppb/ppb) is [0.0763, 0.1047], R2 = 0.85. C2H6 vs CH4 NOAA slope for all years is [0.0647, 0.0749], R2 = 0.86. The C2H6 vs CH4 slope before 2012 is [0.047, 0.060], R2= 0.85; from 2013-2015 is [0.066, 0.143], R2 = 0.85; and from 2016-2018 is [0.058, 0.084], R2 = 0.88. …………………………………………………………………………………………....60 NOAA observations at SGP site (Oklahoma). The observations shown here are preprocessed and filtered for fresh emissions as discussed in the methods section in the main body………………………………………………………………………………………61 Oklahoma oil and gas wells. Plot adapted from Oklahoma Geological Survey16: http://www.ogs.ou.edu/fossilfuels/MAPS/GM-36.pdf......................................................61 Oklahoma oil and gas production by county. Plot was created by Joe Wertz of StateImpact Oklahoma17………….……………………………………………………………………62 Oil and gas production value by county in Colorado. The plot was obtained from Water Education Colorado (founded by Colorado State Legislature).18…………………………62 C3H8 and C2H6 correlation at NOAA SGP site– yearly and tower observations. Left: C3H8 vs C2H6 colored by all years for the NOAA SGP site. Slope: [0.63, 0.70] (95% CI), R2=0.98. Right: Slope of C3H8 vs C2H6 for ground- and tower-based measurements NOAA SGP site. (The highest tower sampling is 374m sampling at SGP.) The slope is [0.66, 0.70], and R2=0.99, comparable to [0.63, 0.70] 95% CI slope of the correlation that includes both xii S20. S21. S22. S23. S24. S25. S26. aircraft and tower observations (this Figure, left side). We bootstrapped the samples to obtain a 95% CI (see methods, main text). …………………………………………………………………………………………....63 NOAA C3H8 and C2H6 vs CH4 anomaly colored by year. Data is for SGP site only. C3H8/∆CH4 slope: [0.43, 0.50] ppb/ppb, R2= 0.83. C2H6/∆CH4 slope: [0.65, 0.75] ppb/ppb, R2= 0.86. We use data within the fresh emission regime (see Section 2.2). Our methods for determining CH4 anomalies are described in detail in section 2.3, and our methods for determining the 95% CI via bootstrapping is described in the methods section of the main text………………………………………………………………………………..………64 Yearly correlation between NOAA hydrocarbon vs CH4 anomaly. Left: Average hydrocarbon vs CH4 anomaly for each year for NOAA SGP site. C3H8/CH4 anomaly slope: 3.12 ± 0.63 ppt/ppb/year (R2=0.71), and C2H6/CH4 anomaly trend is 3.89 ± 0.84 ppt/ppb/year (R2=0.69). The variability in the trend (ppt/ppb/year) comes from the standard error of a linear regression. The variability in the yearly slope (ppt/ppb) comes from the 95% confidence interval of a pairs bootstrap (we ran a pairs bootstrap for co-measurements of C3H8 and ∆CH4 and compute the slope of the correlation for each bootstrap sample and repeated this for every year in the data; please see the methods section of the main text for more information about pairs bootstrapping). Right: Same as left, but in units of percent change with respect to the mean hydrocarbon and methane anomalies. The resulting trend for C3H8/CH4 is 7.13 ± 1.44 % with an R2 of 0.71. The trend for C2H6/CH4 is 5.87 ± 1.26 % with an R2=0.69. Both trends are calculated in the same way as the left figure……………………………………………………………………………………..65 Truncated ATom and HIPPO flight paths. Flight paths used in this analysis are shown above (Top: ATom, Bottom: HIPPO). We split the data into Pacific (left column) and Atlantic (right column) “curtains” shown above for ATom, but HIPPO only offered Pacific curtains over remote ocean. The flight paths shown above do not encompass the entire dataset due to filtering out measurements south of 20 latitude north, those obtained over land, and those associated with very recent emissions. A summary of the filtering parameters we use in the main text are shown in Table S2………………………………………………………………………………………...66 Stratospheric filter using N2O. Left: ATom. Right: HIPPO. In both figures, GEOS-Chem simulations were interpolated to aircraft latitude, longitude, time, and potential temperature in order to compare N2O. However, for all subsequent analysis, GEOS-Chem was filtered by N2O before interpolating simulations to aircraft potential temperature. We use these figures to arbitrarily choose 0.327 and 0.320 N2O mole fractions as a filter cutoff for ATom and HIPPO, respectively, as described in the main text………………………………….68 ATom HCN Pacific transects. HCN (left column), Ethane (middle column), and tropopause height (right column)………………………. ……………………………………………69 ATom HCN Atlantic transects. HCN (left column), Ethane (middle column), and tropopause height (right column)…………. …………………………………………….70 ATom HCN vs C2H6. This data includes all four ATom campaigns and ocean transects and has been filtered using the specifications outlined in the methods section in the main text. The few points with very high HCN and C2H6 are associated with biomass burning. We assigned a weak percentile score for each datapoint, and the values greater than or equal to equal to the 87th percentile are highlighted in black. Those points were replaced with NaN and then interpolated using the “backfill” method for C3H8 and C2H6………….………..70 xiii S27. S28. S29. S30. S31. S32. S33. GEOS-Chem simulated C2H6 vs potential temperature and latitude during 2017. These data are analyzed for Pacific and Atlantic transects during January-Feburary 2017. Aircraft observations are shown in black. GEOS-Chem simulations are colored by the sampling time, in days beyond the flight path. (We found the median time of in-situ sampling of the aircraft, and then sampled the GEOS-Chem model for several days before and after the median to generate what we call “synoptic replicates” here. Each of the synoptic replicates were sampled along the flight path latitude, longitude, time and potential temperature using nearest neighbor interpolation.) In this figure we include ± 5 days to demonstrate the variance, but we use up to ± 2 days of the GEOS-Chem replicates in the Bayesian model. All remaining simulations of ATom and HIPPO C2H6 and C3H8 are included in the SI………………………………………………………………………...……………….72 GEOS-Chem v13.0.0 default and revised emissions. Top: Default C3H8 emissions. Upper middle: Default C2H6 emissions. Bottom middle: Revised C3H8 emissions scaled by the observed NOAA C3H8/C2H6 ratio (0.67 mol/mol, Figure S9). Bottom: Difference between revised and default C3H8 emissions used by GEOS-Chem v13.0.0…….……..…………73 GEOS-Chem simulated C2H6 vs potential temperature during ATom campaign. Each plot is specific to the ocean transect. GEOS-Chem simulations are colored by the sampling time, in the number of days from the day of the flight. (We found the median time of in-situ sampling of the aircraft, and then sampled the GEOS-Chem model for several days before and after the median to generate “synoptic replicates.” Each of the synoptic replicates were sampled along the flight path latitude, longitude, time of day and potential temperature using nearest neighbor interpolation.)…………………………….……………………...74 GEOS-Chem simulated C3H8 vs potential temperature during ATom campaign. Each plot is specific to the ocean transect. GEOS-Chem simulations are colored by the sampling time, in the number of days from the day of the flight. (We found the median time of in-situ sampling of the aircraft, and then sampled the GEOS-Chem model for several days before and after the median to generate “synoptic replicates.” Each of the synoptic replicates were sampled along the flight path latitude, longitude, time of day and potential temperature using nearest neighbor interpolation.)………………………….………………………...76 GEOS-Chem simulated C2H6 vs potential temperature during HIPPO aircraft campaign. Each plot is specific to the ocean transect. GEOS-Chem simulations are colored by the sampling time, in the number of days from the day of the flight. (We found the median time of in-situ sampling of the aircraft, and then sampled the GEOS-Chem model for several days before and after the median to generate “synoptic replicates.” Each of the synoptic replicates were sampled along the flight path latitude, longitude, time of day and potential temperature using nearest neighbor interpolation.)………...…………………...77 GEOS-Chem simulated C3H8 vs potential temperature during HIPPO aircraft campaign. Each plot is specific to the ocean transect. GEOS-Chem simulations are colored by the sampling time, in the number of days from the day of the flight. (We found the median time of in-situ sampling of the aircraft, and then sampled the GEOS-Chem model for several days before and after the median to generate “synoptic replicates.” Each of the synoptic replicates were sampled along the flight path latitude, longitude, time of day and potential temperature using nearest neighbor interpolation.)………………...…………...78 Comparison of C3H8 vs C2H6 for NOAA, ATom aircraft, and GEOS-Chem (GC) simulations. NOAA photochemically-aged measurements (all sites, 2005-2018), as explained in the text, are shown on the heat map (colored by density of data). Note the xiv S34. S35. S36. S37. S38. S39. S40. S41. S42. S43. S44. S45. S46. S47. distinction between winter/fall and spring/summer seasons. HIPPO is included in the SI, Section 3……………………………………………………………………………….…79 C3H8 vs C2H6 for HIPPO aircraft and GEOS-Chem simulations. Please see section 3.2 in the main text for a discussion……………………………………..………………………80 GEOS-Chem simulations using the default and revised C3H8 emissions during all four ATom campaigns. Please see section 3.2 in the main text for more discussion……….…81 GEOS-Chem simulations using the default and revised C3H8 emissions during all 5 HIPPO campaigns. Please see section 3.2 in the main text for more discussion…………………81 Schematic of hierarchical Bayesian model. Level 0 contains the hyperparameter β, the parameter we ultimately wish to get estimates for. Level 1 corresponds to the day the GEOS-Chem model was sampled (there are 5 days because we sampled 2 days before and after the mean flight path). There will be variability from day to day, and the location and scale parameters for a given day are conditioned on the hyperparameters.……………….83 Prior for 𝜏!" parameter for the GEOS-Chem simulations in the Bayesian hierarchical model. The x-axis corresponds to the GEOS-Chem sample replicate, in units of days above or below the aircraft path (day 0)……………... ……………………………………………86 Prior for the 𝜎!" parameter for ATom 2 observations in the Bayesian hierarchical model…….……………………………………………………………………………….87 Prior distribution for 𝛽! parameter in the Bayesian hierarchical model………………….87 Prior predictive checks during ATom 2, Atlantic curtain. Top: Empirical cumulative distribution function of pseudo data of GEOS-Chem simulations given our priors. Bottom: Empirical cumulative distribution function of pseudo data of the 𝛽#,!" parameter given our priors…………………………………………………………………………………..…88 Z-score and shrinkage. Top: C2H6 during ATom 2 Atlantic curtain. Bottom: C3H8 during ATom 4 Atlantic curtain. Satisfactory z-score is symmetric about zero with a magnitude less than 5, while shrinkage should be around 1…………….…………………………….90 HMC Posterior samples for 𝛽#,!" and 𝛽! parameters using C2H6 ATom 4 aircraft and GEOSChem simulations. Beta_1 parameter is a vector of length 5, corresponding to the synoptic replicates of GEOS-Chem. Beta_1[0] and beta_1[1] correspond to 2 days before the aircraft, beta_1[2] is the plane path, and beta_1[3] and beta_1[4] correspond to 2 days after the aircraft. The hyperparameter 𝛽! is represented by beta_..……………………………91 HMC Posterior samples for 𝛽#,!" and 𝛽! parameters using C3H8 ATom 4 aircraft and GEOSChem simulations. Beta_1 parameter is a vector of length 5, corresponding to the synoptic replicates of GEOS-Chem. Beta_1[0] and beta_1[1] correspond to 2 days before the aircraft, beta_1[2] is the plane path, and beta_1[3] and beta_1[4] correspond to 2 days after the aircraft. The hyperparameter, 𝛽! , is represented by beta_.…………………………….92 Posterior samples of 𝛼#,!" vs 𝛼! during ATom 4. Top: C2H6 observations. Bottom: C3H8 observations….……………………….………………………………………………….93 𝛼! hyperparameter estimate for each season during the ATom campaign. We do not include the summer values to calculate an overall 𝛼 estimate as discussed in the methods in the main text. Top: C2H6, Bottom: C3H8. ……………………………………………………94 Posterior predictive check of C2H6 using ATom data. Posterior predictive checks are explained in the text above. The pseudo data are shown in blue with 30, 50, 70, 99th percentiles. Please see Figure S46 for the estimated values of 𝛼! that were used to scale the GCS data in each season/transect. …………………………………….………………….95 xv S48. S49. S50. S51. S52. S53. S54. S55. S56. S57. S58. S59. S60. S61. Posterior predictive check of C3H8 using ATom data. (Posterior predictive checks are explained in the text above.) The pseudo data are shown in blue with 30, 50, 70, 99th percentiles. Please see Figure S46 for the estimated values of 𝛼! that were used to scale the GCS data in each season/transect..………………...…………………………………….97 Difference between aircraft and GEOS-Chem C3H8 simulations. Simulations and aircraft observations during ATom 2, Atlantic transect, are shown. Points are colored by altitude (left) and potential temperature (right).………………. ………………………………....98 HMC Posterior samples for 𝛽#,!" and 𝛽! parameters using C2H6 HIPPO 5 aircraft and GEOS-Chem simulations. Beta_1 parameter is a vector of length 5, corresponding to the synoptic replicates of GEOS-Chem. Beta_1[0] and beta_1[1] correspond to 2 days before the aircraft, beta_1[2] is the plane path, and beta_1[3] and beta_1[4] correspond to 2 days after the aircraft. The hyperparameter, 𝛽! , is represented by beta_...................................99 HMC Posterior samples for 𝛽#,!" and 𝛽! parameters using C3H8 HIPPO 5 aircraft and GEOS-Chem simulations. Beta_1 parameter is a vector of length 5, corresponding to the synoptic replicates of GEOS-Chem. Beta_1[0] and beta_1[1] correspond to 2 days before the aircraft, beta_1[2] is the plane path, and beta_1[3] and beta_1[4] correspond to 2 days after the aircraft. The hyperparameter, 𝛽! , is represented by beta_...................................100 Posterior samples of 𝛼#,!" vs 𝛼! during HIPPO 5. Top: C2H6 observations. Bottom: C3H8 observations. ß..................................................................................................................101 𝛼! hyperparameter estimate for each season during the HIPPO campaign. We do not include the summer values to calculate an overall 𝛼 estimate as discussed in the methods in the main text. Top: C2H6, Bottom: C3H8. There are many fewer observations during HIPPO than ATom resulting in a much larger spread and bigger uncertainty in defining 𝛼! ………………………………………………………………………………………..101 Posterior predictive check of C2H6 using HIPPO data. (Posterior predictive check method is described in the text above.) The pseudo data are shown in blue with 30, 50, 70, 99th percentiles. Please see Figure S53 for the estimated values of 𝛼! that were used to scale the GCS data in each season/transect. ……………………………………………………...103 Posterior predictive check of C3H8 using HIPPO data. (Posterior predictive check method is described in the text above.) The pseudo data are shown in blue with 30, 50, 70, 99th percentiles. Please see Figure S53 for the estimated values of 𝛼! that were used to scale the GCS data in each season/transect.……… ………………………………………………104 Bayesian 𝛼! hyperparameter estimate and posterior predictive checks using HIPPO aircraft observations > 300 K.……… …………………………………………………………..105 Bayesian 𝜶𝒊 hyperparameter estimate and posterior predictive checks using HIPPO aircraft observations < 300 K…….……………………………………………………………...106 Posterior samples of 𝛼#,!" vs 𝛼! using a scalar 𝜎!" parameter. We use 𝜎!" = 3.5 instead of the usual distribution in the lognormal likelihood during ATom 4 time period.………..107 Estimate of 𝛼 hyperparameter after using a scalar 𝜎!" parameter. We use 𝜎!" = 3.5 in the lognormal likelihood during ATom 4 time period……..……………………………….107 Posterior predictive check for C3H8 using a scalar 𝜎!" parameter. We use 𝜎!" = 3.5 in the lognormal likelihood…...……………………………………………………………….109 Global ethane and propane emissions during 2009-2018. “Unscaled” represent integrated default emissions from GEOS-Chem v13.0.0. “Revised C3” represent the revised C3H8 xvi emissions after implementing the default v13.0.0 C2H6 proxy. “Scaled+Revised C3” represents the revised C3H8 emissions after scaling with our mean Bayesian estimate (Section 5.8). “Scaled C2” represent the revised emissions after scaling with our mean Bayesian estimate (Section 5.8). ∗: Note that our mean scaled C3 estimate shown here are skewed, as the 2009 winter HIPPO observations are latitudinally biased. We show that C3 emissions increase by 65% from 2010 to 2017 when excluding the bias below in Figure S62……………………………………………………...………………………………110 S62. Global revised ethane and propane anthropogenic fossil emissions compared to other studies. Our emissions estimate in 2016-2018 (during ATom) and 2009-2011 (during HIPPO) includes GEOS-Chem v13.0.0 emissions for winter, fall and spring seasons scaled by 𝛼, that we determined with our Bayesian model during each season. As discussed in the text, fewer samples were obtained during HIPPO, resulting in a sampling bias that we test by restricting observations and simulations to ± 300K potential temperature (Figure S51S52). This test affects the estimate about ± 1 Tg during 2010-2011 but affects our estimate by up to 12 Tg in 2009. ∗∶ This 2009 estimate is highly biased, as the latitudinal coverage of aircraft observations is not representative of the global spatial distribution of methane emissions from oil and gas processes and the confidence interval stretches to nearly 40 Tg (please see Section 3.3 text and Figure S51-52). We compare our revised ethane and propane emissions to the default emissions from GEOS-Chem v13.0.0 (relevant anthropogenic inventories include Tzompa-Sosa et al. 201725 for C2H6, and Xiao et al. 20084 for C3H8). ‡∶ The studies included here38–41 represent anthropogenic fossil emissions, except Dalsøren et al. 2018 which also includes biofuel, agriculture, and waste. We obtained the CEDS CMIP6 estimate from Dalsøren et al. 2018. Our emissions estimates do not include biomass burning or biofuels. Please see Section 5 in the SI for more information on estimating these emissions…..………………………………………….111 S63. Literature and Observationally-Informed Emission ratios. Top: U.S. basins; Bottom: Global basins. The weighted raw gas ratio represents the “literature ratio” described in the main text. OIER, ratios between our revised C2H6 and C3H8 emissions and literature CH4 emission estimates, are shown for several literature CH4 estimates, including Alvarez et al. 2018 (13 Tg/yr)64 and EPA 2017 estimate (7.8 Tg/yr, 2021 report)63 for U.S. basins, and IEA 2021 (76.4 Tg/yr),65 Scarpelli et al. 2020 (65.7 Tg/yr),66 and Global Carbon Project 2020 bottom-up estimate67 (128 Tg/yr, 2008-2017 average) for global basins. The variability in the literature ratio is attributed to the 95% CI of pairs bootstrap samples of hydrocarbon composition measurements (see main text for more detail). The variability in the OIER is attributed to the 95% CI of our revised C3H8 and C2H6 emission estimates. We also compare C3H8/CH4 and C2H6/CH4 correlations from in-situ observations, including NOAA observations from Northern Oklahoma (2017 average from Figure S21, units of kg/kg) and FRAPPE observations from Northern Colorado (2014 from Figure S9, units of kg/kg). The variability in the NOAA ratio is relatively low because it is calculated from a multi-year average slope, and the error in the slope is low (see Figure S21, left). The xvii variability in the FRAPPE ratio is relatively high because we use the 95% CI derived directly from our bootstrap samples described in the main text..………………………..115 A1. A2. A3. A4. GEOS-Chem-simulated C2H6 “curtain” during ATom 2 winter 2017 campaign, along pressure and latitude. All GEOS-Chem simulations were sampled along aircraft latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 shows simulations sampled 5 days after the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the median aircraft time. FIRST row: 4x5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. SECOND row: 2x2.5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black. C3H8 is included in the main body……………….123 GEOS-Chem-simulated C3H8 “curtain” during ATom 1 summer 2016 campaign, along pressure and latitude. All GEOS-Chem simulations were sampled along aircraft latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 shows simulations sampled 5 days after the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the median aircraft time. FIRST row: 4x5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. SECOND row: 2x2.5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black………………………………….………………..124 GEOS-Chem-simulated C2H6 “curtain” during ATom 1 summer 2016 campaign, along pressure and latitude. All GEOS-Chem simulations were sampled along aircraft latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 shows simulations sampled 5 days after the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the median aircraft time. FIRST row: 4x5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. SECOND row: 2x2.5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black……………………………….…………………..125 GEOS-Chem-simulated C2H6 “curtain” during ATom 2 winter 2017 campaign, along potential temperature and latitude. All GEOS-Chem simulations were sampled along aircraft latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 shows simulations sampled 5 days after the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the median aircraft time. FIRST row: 4x5 resolution. SECOND row: 2x2.5 resolution. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black. C3H8 is included in the main body…………………………………...…………...127 xviii A5. A6. A7. A8. A9. A10. A11. B1. B2. B3. B4. B5. B6. GEOS-Chem-simulated C3H8 “curtain” during ATom 1 summer 2016 campaign, along potential temperature and latitude. All GEOS-Chem simulations were sampled along aircraft latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 shows simulations sampled 5 days after the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the median aircraft time. FIRST row: 4x5 resolution. SECOND row: 2x2.5 resolution. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black………………………………………………………………………...…………..128 GEOS-Chem-simulated C2H6 “curtain” during ATom 1 summer 2016 campaign, along potential temperature and latitude. All GEOS-Chem simulations were sampled along aircraft latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 shows simulations sampled 5 days after the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the median aircraft time. FIRST row: 4x5 resolution. SECOND row: 2x2.5 resolution. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black…………………………………………………………………………...………..130 GEOS-Chem simulations and ATom aircraft C2H6 vs potential temperature. Left: Includes aircraft observations and simulations sampled 5 days after the aircraft flight path. Middle: Includes aircraft observations and simulations sampled during the aircraft flight path. Right: Includes aircraft observations and simulations 5 days before the aircraft flight path. C3H8 included in the main body.… ……….…………………………………………….130 C3H8 posterior samples for the conditional parameter and the hyperparameter during ATom 2 winter 2017. Top: 4x5. Middle: 2x2.5. Bottom: 0.5x0.625……………….…………..131 C2H6 posterior samples for the conditional parameter and the hyperparameter during ATom 2 winter 2017. Top: 4x5. Middle: 2x2.5. Bottom: 0.5x0.625……...…………………….132 Posterior predictive check of C3H8 using ATom data. Left: 4x5. Middle: 2x2.5. Right: 0.5x0.625. Samples are during ATom 2 winter 2017. Pseudo data are shown in blue with 30, 50, 70, 99th percentiles. Please see Table 1 for values used to scale GCS data….……133 Posterior predictive check of C2H6 using ATom data. Left: 4x5. Middle: 2x2.5. Right: 0.5x0.625. Samples are during ATom 2 winter 2017. Pseudo data are shown in blue with 30, 50, 70, 99th percentiles. Please see Table 1 for values used to scale GCS data.………133 Temporal intersection between NOAA flask (aircraft + tower) and TCCON observations. …………………………………………………………………………………………..135 Oil and gas well geospatial data from FrackTracker.org……………………….………..135 Density of oil and gas wells per .1x.1 degree grid…………………..………………….136 Well density (zoom in). The blue circles are the footprint lat/lon, and the squares are the 0.1x0.1 degree bins in which the density was calculated. The colorbar is in units of wells/cell………………………………………………………………………………..136 Emissions of methane, ethane, and propane used as a prior for the STILT analysis. These emissions were computed as described in the main text………………………………..137 Priors for key parameters in our Bayesian analysis. Our methodology for choosing these priors is explained in the main text……...………………………………………………138 xix xx LIST OF TABLES Number S1. S2. S3. S4. S5. A1. Page Sites for NOAA Ongoing Observations in the U.S……………………………………….50 Filters for Aircraft Measurements………….…………………………………………….66 Boundary estimates for emissions grid…………………………………………………110 Statistical summaries of hydrocarbon wellhead composition for the globe. Units are in mole % for the US,42–49 Russia,50–56 Qatar,57 Iran,58 and Canada 59–62. Top: C1; Middle: C2; Bottom: C3………………………………………………………………………………………..112 Statistical summaries of hydrocarbon wellhead composition in the U.S. Units are in mole %.42–49 Top: C1; Middle: C2; Bottom: C3……….………………………………………..113 Bayesian inference 97.5% confidence interval………….………………………………134 1 Chapter1 INTRODUCTION 1.1 Recent trends in atmospheric methane The atmospheric surface concentration of methane (CH4) is almost 3 times greater than its preindustrial value.1,2 CH4 has a stronger global warming potential compared to CO2, and despite having a shorter lifetime, has played a significant role in warming the climate: CH4 has contributed about 23% to the additional radiative forcing that has accumulated in the lower atmosphere since 1750.3 In addition to its radiative effects, CH4 impacts background tropospheric ozone levels and the amount of stratospheric water vapor. As such, characterizing the sources and sinks of CH4 is critical for future climate and air quality impacts. While in situ measurements of atmospheric CH4 are highly accurate (Figure 1), processes behind these global trends remains uncertain. There is no debate that humans have caused of the bulk of the rise in atmospheric CH4 from preindustrial times. However, characterization of the reason for the stabilization from 1998 to 2007 and the acceleration in global CH4 since has proved difficult. Indeed, it has been suggested that the change in observed growth rate may, in part, reflect changes in changes in the CH4 atmospheric lifetime rather than simply changes in emissions.4 Figure a. Methane atmospheric “background” mole fraction rising worldwide. Data provided by NOAA.2 Nonetheless, the acceleration since 2007 unambiguously suggests a sustained increase in emissions. 2 Global sources of CH4 include both natural and human-caused sources, including wetlands, fossil fuels (production, storage, transport, and incomplete combustion of oil/gas and coal), agriculture (livestock and rice cultivation), landfills and fires.1 Globally, estimates of total CH4 emissions are relatively certain at 572 Tg/year, of which 50-65% are attributed to anthropogenic sources.1 Relative to the anthropogenic sector, fossil fuels are thought to make up about 35% of CH4 emissions, while agriculture and waste are estimated at about 60%, and biomass burning at 10% from a bottom-up perspective.1 While regional and sector emissions remain very uncertain, there is no debate that reducing anthropogenic (human-driven) emissions can lead to short-term decreases in atmospheric CH4. 1.2 Methane Emissions from Fossil Energy Not only do fossil fuels constitute a significant fraction of human-influenced CH4 emissions, but a wide variety of technologies already exist to reduce such emissions from oil and gas operations; IEA estimates that almost 50% of these emissions could be avoided at zero net cost.5 Thus, reducing uncertainty in CH4 emission inventories to effectively reduce CH4 emissions surrounding the energy sector presents an attractive avenue to mitigate climate change. Yet, effective policy to limit emissions from oil and gas activities relies on accurate emission estimates. Historically, it has been challenging to diagnose both the magnitude and location of emissions from a wide range of facilities and components across production, transmission, storage, and distribution systems. Past studies have generated conflicting claims about the magnitude or origin of emissions, such that top-down estimates (estimates derived from large-scale atmospheric observations) often exceed bottom-up estimates (totals based on facility-scale emission inventories). Recent work has found that divergent estimates can be largely attributed to a skewed distribution of emissions,6 where a small number of extreme leaks account for the majority of emissions.7–10 Recently, bottom-up11,12 and top-down13,14 studies have found that the majority of fossil CH4 leaks occur mainly during the production process through planned venting/flaring and unintended leakage, with a smaller fraction originating from downstream processes such as separation, storage, and transportation. Venting and flaring of natural gas depends on many factors, including lack of proximity to a commercial market and lack of infrastructure.15 The latter is often a challenge in burgeoning oil production sites where the value of oil can outweigh the associated natural gas byproduct, resulting in low prices for natural gas and increased venting or flaring of excess gas. 1.3 Fossil Methane Emission Monitoring Space-based monitoring has come a long way over the years and will be invaluable for quickly identifying super-emitter leaks and increase transparency of facility-wide processes.16 However, at this point in time, space-based monitoring is best-suited for diagnosing super-emitters rather than small-moderate leaks. Generally, this method cannot resolve point sources smaller than facility- 3 wide scale.17 For this reason, ground-based monitoring is still important. There are many types of low-cost instrumentation (near infrared laser absorption spectroscopy, direct absorption mid-IR spectroscopy, metal oxide sensors) that can be mounted on stationary towers or drones that effectively capture small to moderate CH4 emissions.18 A widely-used method to apportion CH4 flux is to measure atmospheric molecules that are co-emitted with CH4 from source processes. For example, ethane (C2H6) is the second most abundant component of natural gas besides CH4, but unlike CH4, it does not have a biogenic origin, singling out CH4 from fossil activities. Despite being a widely used tracer for fossil activities, interpreting changes in C2H6 is complicated,19,20 discussed in more detail in Chapter 2. In Chapter 2, I provide compelling evidence that propane (C3H8), another abundant component of natural gas, can serve as an effective tracer for production emissions from the oil and gas sector. There are few studies that characterize atmospheric trends of C3H8, and even fewer that attempt to quantify its emissions. Therefore, the focus of this thesis is diagnosing CH4 emissions from oil and gas production using C3H8 as a tracer in addition to C2H6. 1.4 Thesis Overview The work included in this thesis details my efforts to estimate global and regional fossil CH4 emissions. In Chapter 2 (published in ES&T), I develop a novel Bayesian hierarchical model to improve global C3H8, C2H6, and CH4 emission estimates from energy production. Chapter 3 (in preparation for submission to AMT) expands on the methods used in Chapter 2 to illustrate how using potential temperature as a diagnostic coordinate is useful for comparing observations with chemical transport models, enabling use of much lower spatial resolution, and therefore, much less costly simulations. Chapter 4 (in preparation for submission to ACP) details my initial effort to characterize fossil CH4 emissions in Oklahoma and Texas using long term ground-based remotesensing observations combined with Stochastic Time-Inverted Lagrangian Transport modeling. References (1) Saunois, M.; Stavert, A. R.; Poulter, B.; Bousquet, P.; Canadell, J. G.; Jackson, R. B.; Raymond, P. A.; Dlugokencky, E. J.; Houweling, S.; Patra, P. K.; Ciais, P.; Arora, V. K.; Bastviken, D.; Bergamaschi, P.; Blake, D. R.; Brailsford, G.; Bruhwiler, L.; Carlson, K. M.; Carrol, M.; Castaldi, S.; Chandra, N.; Crevoisier, C.; Crill, P. M.; Covey, K.; Curry, C. L.; Etiope, G.; Frankenberg, C.; Gedney, N.; Hegglin, M. I.; Höglund-Isaksson, L.; Hugelius, G.; Ishizawa, M.; Ito, A.; Janssens-Maenhout, G.; Jensen, K. M.; Joos, F.; Kleinen, T.; Krummel, P. B.; Langenfelds, R. L.; Laruelle, G. G.; Liu, L.; Machida, T.; Maksyutov, S.; McDonald, K. C.; McNorton, J.; Miller, P. A.; Melton, J. R.; Morino, I.; Müller, J.; Murguia-Flores, F.; Naik, V.; Niwa, Y.; Noce, S.; O’Doherty, S.; Parker, R. J.; Peng, C.; Peng, S.; Peters, G. P.; Prigent, C.; Prinn, R.; Ramonet, M.; Regnier, P.; Riley, W. J.; Rosentreter, J. A.; Segers, A.; Simpson, I. J.; Shi, H.; Smith, S. J.; Steele, L. P.; Thornton, B. F.; Tian, H.; Tohjima, Y.; Tubiello, F. N.; Tsuruta, A.; Viovy, N.; Voulgarakis, A.; Weber, T. S.; van Weele, M.; van der Werf, G. R.; Weiss, R. F.; Worthy, D.; Wunch, D.; Yin, Y.; Yoshida, Y.; Zhang, W.; Zhang, Z.; Zhao, Y.; Zheng, B.; Zhu, Q.; Zhu, Q.; 4 Zhuang, Q. The Global Methane Budget 2000–2017. Earth Syst. Sci. Data 2020, 12 (3), 1561– 1623. https://doi.org/10.5194/essd-12-1561-2020. (2) Dlugokencky, E. J.; Lang, P. M.; Crotwell, A. M.; Mund, J. W.; Crotwell, M. J.; Thoning, K. W. Atmospheric Methane Dry Air Mole Fractions from the NOAA ESRL Carbon Cycle Cooperative Global Air Sampling Network, 1983-2017, Version: 2018-08-01, 2018. ftp://aftp.cmdl.noaa.gov/data/trace_gases/ch4/flask/surface/. (3) Etminan, M.; Myhre, G.; Highwood, E. J.; Shine, K. P. Radiative Forcing of Carbon Dioxide, Methane, and Nitrous Oxide: A Significant Revision of the Methane Radiative Forcing: Greenhouse Gas Radiative Forcing. Geophys. Res. Lett. 2016, 43 (24), 12,614-12,623. https://doi.org/10.1002/2016GL071930. (4) Turner, A. J.; Frankenberg, C.; Kort, E. A. Interpreting Contemporary Trends in Atmospheric Methane. Proc. Natl. Acad. Sci. 2019, 201814297. https://doi.org/10.1073/pnas.1814297116. (5) IEA. Methane Tracker Database: Interactive Database of Country and Regional Estimates for Methane Emissions and Abatement Options, 2021. https://www.iea.org/articles/methanetracker-database#sources. (6) Zavala-Araiza, D.; Lyon, D. R.; Alvarez, R. A.; Davis, K. J.; Harriss, R.; Herndon, S. C.; Karion, A.; Kort, E. A.; Lamb, B. K.; Lan, X.; Marchese, A. J.; Pacala, S. W.; Robinson, A. L.; Shepson, P. B.; Sweeney, C.; Talbot, R.; Townsend-Small, A.; Yacovitch, T. I.; Zimmerle, D. J.; Hamburg, S. P. Reconciling Divergent Estimates of Oil and Gas Methane Emissions. Proc. Natl. Acad. Sci. 2015, 201522126. https://doi.org/10.1073/pnas.1522126112. (7) Zavala-Araiza, D.; Alvarez, R. A.; Lyon, D. R.; Allen, D. T.; Marchese, A. J.; Zimmerle, D. J.; Hamburg, S. P. Super-Emitters in Natural Gas Infrastructure Are Caused by Abnormal Process Conditions. Nat. Commun. 2017, 8, 14012. https://doi.org/10.1038/ncomms14012. (8) Caulton, D. R.; Lu, J. M.; Lane, H. M.; Buchholz, B.; Fitts, J. P.; Golston, L. M.; Guo, X.; Li, Q.; McSpiritt, J.; Pan, D.; Wendt, L.; Bou-Zeid, E.; Zondlo, M. A. Importance of Superemitter Natural Gas Well Pads in the Marcellus Shale. Environ. Sci. Technol. 2019, 53 (9), 4747–4754. https://doi.org/10.1021/acs.est.8b06965. (9) Omara, M.; Zimmerman, N.; Sullivan, M. R.; Li, X.; Ellis, A.; Cesa, R.; Subramanian, R.; Presto, A. A.; Robinson, A. L. Methane Emissions from Natural Gas Production Sites in the United States: Data Synthesis and National Estimate. Environ. Sci. Technol. 2018, 52 (21), 12915–12925. https://doi.org/10.1021/acs.est.8b03535. (10) Brandt, A. R.; Heath, G. A.; Cooley, D. Methane Leaks from Natural Gas Systems Follow Extreme Distributions. Environ. Sci. Technol. 2016, 50 (22), 12512–12520. https://doi.org/10.1021/acs.est.6b04303. (11) IPCC. 2006 IPCC Guidelines for National Greenhouse Gas Inventories; Report; Prepared by the National Greenhouse Gas Inventories Programme, 2006. (12) Höglund-Isaksson, L. Bottom-up Simulations of Methane and Ethane Emissions from Global Oil and Gas Systems 1980 to 2012. Environ. Res. Lett. 2017, 12 (2), 024007. https://doi.org/10.1088/1748-9326/aa583e. (13) Alvarez, R. A.; Zavala-Araiza, D.; Lyon, D. R.; Allen, D. T.; Barkley, Z. R.; Brandt, A. R.; Davis, K. J.; Herndon, S. C.; Jacob, D. J.; Karion, A.; Kort, E. A.; Lamb, B. K.; Lauvaux, T.; Maasakkers, J. D.; Marchese, A. J.; Omara, M.; Pacala, S. W.; Peischl, J.; Robinson, A. L.; Shepson, P. B.; Sweeney, C.; Townsend-Small, A.; Wofsy, S. C.; Hamburg, S. P. Assessment of Methane Emissions from the U.S. Oil and Gas Supply Chain. Science 2018, eaar7204. https://doi.org/10.1126/science.aar7204. 5 (14) Tribby, A. L.; Bois, J. S.; Montzka, S. A.; Atlas, E. L.; Vimont, I.; Lan, X.; Tans, P. P.; Elkins, J. W.; Blake, D. R.; Wennberg, P. O. Hydrocarbon Tracers Suggest Methane Emissions from Fossil Sources Occur Predominately Before Gas Processing and That Petroleum Plays Are a Significant Source. Environ. Sci. Technol. 2022, acs.est.2c00927. https://doi.org/10.1021/acs.est.2c00927. (15) International Energy Agency, (IEA). Flaring Emissions, 2020. https://www.iea.org/reports/flaring-emissions. (16) Irakulis-Loitxate, I.; Guanter, L.; Liu, Y.-N.; Varon, D. J.; Maasakkers, J. D.; Zhang, Y.; Chulakadabba, A.; Wofsy, S. C.; Thorpe, A. K.; Duren, R. M.; Frankenberg, C.; Lyon, D. R.; Hmiel, B.; Cusworth, D. H.; Zhang, Y.; Segl, K.; Gorroño, J.; Sánchez-García, E.; Sulprizio, M. P.; Cao, K.; Zhu, H.; Liang, J.; Li, X.; Aben, I.; Jacob, D. J. Satellite-Based Survey of Extreme Methane Emissions in the Permian Basin. Sci. Adv. 2021, 7 (27), eabf4507. https://doi.org/10.1126/sciadv.abf4507. (17) Cusworth, D. H.; Jacob, D. J.; Varon, D. J.; Chan Miller, C.; Liu, X.; Chance, K.; Thorpe, A. K.; Duren, R. M.; Miller, C. E.; Thompson, D. R.; Frankenberg, C.; Guanter, L.; Randles, C. A. Potential of Next-Generation Imaging Spectrometers to Detect and Quantify Methane Point Sources from Space. Atmospheric Meas. Tech. 2019, 12 (10), 5655–5668. https://doi.org/10.5194/amt-12-5655-2019. (18) Torres, V. M.; Sullivan, D. W.; He’Bert, E.; Spinhirne, J.; Modi, M.; Allen, D. T. Field Inter-Comparison of Low-Cost Sensors for Monitoring Methane Emissions from Oil and Gas Production Operations; preprint; Gases/In Situ Measurement/Validation and Intercomparisons, 2022. https://doi.org/10.5194/amt-2022-24. (19) Turner, A. J.; Frankenberg, C.; Wennberg, P. O.; Jacob, D. J. Ambiguity in the Causes for Decadal Trends in Atmospheric Methane and Hydroxyl. Proc. Natl. Acad. Sci. 2017, 114 (21), 5367–5372. https://doi.org/10.1073/pnas.1616020114. (20) Kort, E. A.; Smith, M. L.; Murray, L. T.; Gvakharia, A.; Brandt, A. R.; Peischl, J.; Ryerson, T. B.; Sweeney, C.; Travis, K. Fugitive Emissions from the Bakken Shale Illustrate Role of Shale Production in Global Ethane Shift: Ethane Emissions From the Bakken Shale. Geophys. Res. Lett. 2016, 43 (9), 4617–4623. https://doi.org/10.1002/2016GL068703. (21) Xiao, Y.; Logan, J. A.; Jacob, D. J.; Hudman, R. C.; Yantosca, R.; Blake, D. R. Global Budget of Ethane and Regional Constraints on U.S. Sources. J. Geophys. Res. 2008, 113 (D21). https://doi.org/10.1029/2007JD009415. (22) Frankenberg, C.; Kulawik, S. S.; Wofsy, S. C.; Chevallier, F.; Daube, B.; Kort, E. A.; O&amp;apos;Dell, C.; Olsen, E. T.; Osterman, G. Using Airborne HIAPER Pole-to-Pole Observations (HIPPO) to Evaluate Model and Remote Sensing Estimates of Atmospheric Carbon Dioxide. Atmospheric Chem. Phys. 2016, 16 (12), 7867–7878. https://doi.org/10.5194/acp-167867-2016. (23) Wofsy, S. C.; the HIPPO Science Team and Cooperating Modellers and Satellite Teams. HIAPER Pole-to-Pole Observations (HIPPO): Fine-Grained, Global-Scale Measurements of Climatically Important Atmospheric Gases and Aerosols. Philos. Trans. R. Soc. Math. Phys. Eng. Sci. 2011, 369 (1943), 2073–2086. https://doi.org/10.1098/rsta.2010.0313. 6 Chapter2 Hydrocarbon tracers suggest methane emissions from fossil sources occur predominately pre-gas processing and that petroleum plays are a significant source Tribby, A. L.; Bois, J. S.; Montzka, S. A.; Atlas, E. L.; Vimont, I.; Lan, X.; Tans, P. P.; Elkins, J. W.; Blake, D. R.; Wennberg, P. O. Hydrocarbon Tracers Suggest Methane Emissions from Fossil Sources Occur Predominately Before Gas Processing and That Petroleum Plays Are a Significant Source. Environ. Sci. Technol. 2022, acs.est.2c00927. https://doi.org/10.1021/acs.est.2c00927. Abstract We use global airborne observations of propane (C3H8) and ethane (C2H6) from the Atmospheric Tomography (ATom) and HIAPER Pole-to-Pole Observations (HIPPO), as well as US-based aircraft and tower observations by NOAA and from the NCAR FRAPPE campaign as tracers for emissions from oil and gas operations. To simulate global mole fraction fields for these gases, we update the default emissions configuration of C3H8 used by the global chemical transport model, GEOS-Chem v13.0.0, using a scaled C2H6 spatial proxy. With the updated emissions, simulations of both C3H8 and C2H6 using GEOS-Chem are in reasonable agreement with ATom and HIPPO observations, though the updated emissions fields underestimate C3H8 accumulation in the arctic wintertime pointing to additional sources of this gas in the high latitudes (e.g., Europe). Using a Bayesian hierarchical model, we estimate global emissions of C2H6 and C3H8 from fossil fuel production in 2016-2018 to be 13.3 ± 0.7 (95% CI) and 14.7 ± 0.8 (95% CI) Tg/year, respectively. We calculate bottom-up hydrocarbon emission ratios using basin composition measurements weighted by gas production, and find their magnitude is higher than expected and is similar to ratios informed by our revised alkane emissions. This suggests emissions are dominated by pregas processing activities in oil-producing basins. 2.1 Introduction Many studies have diagnosed recent methane (CH4) trends (both global and regional) using ethane (C2H6) atmospheric ratio signatures. However, the rejection of C2H6 by oil and gas producers (in the US, and presumably in countries following similar economic trends, Figure S1) results in an increase in the mole fraction of C2H6 in the natural gas pipelines. Thus, to the extent that losses occur in the pipelines and at the end users of natural gas, emissions of C2H6 may not necessarily directly reflect CH4 emissions, adding additional uncertainty in CH4 emission estimates from natural gas operations. In addition, a global uptick in hydraulic fracturing has shifted production 7 from dry to wet fields resulting in an increase in the ratios of both C2H6 and C3H8 to CH4,1 further complicating the use of the alkanes to diagnose the underlying CH4 emission sources.2–4 Given the uncertainty in using C2H6 alone as a tracer for CH4 emissions, we use both C2H6 and propane (C3H8) to diagnose whether significant CH4 emissions from natural gas and petroleum occur pre-gas processing. Unlike C2H6, C3H8 has a much higher market value and therefore does not undergo “rejection.”5 Provided downstream losses are minimal and the raw gas ratio of C3H8 to CH4 is known, C3H8 can provide a constraint for raw natural gas pre-gas processing CH4 emissions. In this study, we employ global observations from aircraft, including the 2009-2011 HighPerformance Instrumented Airborne Platform for Environmental Research (HIAPER) Pole-toPole Observations (HIPPO)6 and the 2016-2018 Atmospheric Tomography (ATom)7 missions, which provide vertical profiles of a variety of constituents, including C2H6 and C3H8, around the remote atmospheres of the globe. Together with the large-scale chemical transport model GEOSChem, we estimate global fossil emissions of C2H6 and C3H8. 2.2 Materials and methods Observations from the National Oceanic and Atmospheric Administration (NOAA) Global Monitoring Laboratory (GML) Measurements of CH4,8–10 C2H6 and C3H811 from flask air collected by the NOAA GML tower12 and aircraft13 near oil/natural gas basins were used as pre-gas processing references. We refer to site locations using state abbreviations. More information on data processing/spatial coverage in included in Section S2, Table S1 and Figure S5. To better quantify geophysical variability and generate a confidence interval in the correlation between C2H6 and C3H8 mole fractions, we implement a pairs bootstrap to generate replicates of C2H6 and C3H8 observations. The CIs calculated from the bootstrapped samples are much broader than those calculated assuming the noise in the measurements is dominated by analytical errors. This suggests that geophysical noise induced by differences in transport and chemistry dominates the statistics. See Section S2.1 for more details. FRAPPE Observations FRAPPE C130 flight data were taken within the Colorado Front Range between July 26-August 19 2014. We accessed the data on October 6, 2021 from www-air.larc.nasa.gov from the WAS C130 merge file. Our data processing for FRAPPE is similar to our methods for the NOAA in situ samples. A spatial illustration of FRAPPE observations is shown in Figure S6. 8 HIAPER POLE-TO-POLE OBSERVATIONS (HIPPO) & ATMOSPHERIC TOMOGRAPHY (ATom) data The HIPPO campaign was a sequence of five global measurement campaigns which sampled from near the North Pole to the coastal waters of Antarctica, covering different seasons between 2009 and 2011. Similarly, ATom took place from 2016 and 2018. Flight paths of HIPPO and ATom campaigns are illustrated in Figure S22 and specific details about the data sources are included in Section 3, SI. Only data observed at > 20 degrees north was used since the majority of emissions of these shortlived gases of interest lie in the northern hemisphere. The lifetime of C3H8 and C2H6 are on the order of a few months or shorter during the summer, and the time it takes for mixing between the northern to southern hemispheres is on the order of a year,14 so the mole fraction of these gases of interest is very low in the southern hemisphere. Because C2H6 and C3H8 are relatively short-lived gases, their abundance in the stratosphere is low and poorly connected to the underlying fluxes. To exclude stratospheric observations, we use N2O (Panther/UCATS instrument) which is inert and generally well-mixed in the troposphere, but is destroyed in the stratosphere by photolysis and reaction with O1D.15 Thus, we exclude from our analysis data with low N2O mole fraction (Figure S23). As our focus in this analysis is quantifying the global emissions of these gases, we exclude from our analysis data where local fluxes substantially influence the mole fraction of these alkanes. We use a simple land and altitude constraint, and HCN as a tracer to remove plumes from highly local sources (including both energy infrastructure and wildfires, Figure S24-26). We also exclude regions and times where the lifetime of the alkanes is very short and thus regional / local sources dominate the variance. Thus, we do not analyze the aircraft summer data (but results for the summer are shown in the SI) or data in the subtropics, where the alkane distribution is very sensitive to transport from the extratropics where most emissions of C2H6 and C3H8 originate. To exclude subtropical air, we only analyze measurements with tropopause pressure above 100 hPa (about 5% of the data was excluded under this constraint) for both ATom and HIPPO, which was sufficient to reduce the influence of tropical intrusions. See Table S1 for a comprehensive outline of the filters we use. As in other studies,16,17 we use potential temperature (𝜃, in units of Kelvin) in our analysis as a zonal coordinate. Potential temperature is conserved following adiabatic flow, and in the extratropics, variability within large-scale circulation can be well captured using this coordinate system. As a result, trace gases that have long lifetimes compared to synoptic-scale meteorology, which has a horizontal length scale of an order of 1000 kilometers or more and a timescale of about 10 days,14,18 will be well correlated with 𝜃. Using 𝜃 as a dynamical coordinate allows us to more accurately compare low spatial resolution GEOS-Chem simulations with the aircraft in situ measurements (compared with simply using altitude and latitude coordinates, Figure S27). 9 Potential temperature is not well-correlated with trace gases in the tropics or boundary layer, where moist convection and surface drag-driven turbulence can result in non-unique pairs, or when the photochemical lifetimes are short (summer). GEOS-Chem Simulations We simulated HIPPO and ATom measurements using the GEOS-Chem “classic” global 3-D chemical transport model with default settings (details about the simulations and emissions are provided in the SI, Section 4). We use the same constraints as the aircraft observations except we use a boundary layer height parameter. As described below, we use a Bayesian model to provide a best estimate for global emissions of C2H6 and C3H8 and their uncertainty. One contribution to the error estimate is transport errors in GEOS-Chem. To capture some of the uncertainty in the transport field, we sample the GEOS-Chem model several days before and after the in-situ sampling time along the aircraft flight path, which we refer to as “synoptic replicates.” Finally, all GEOS-Chem simulations of C3H8 and C2H6 were interpolated on the vertical coordinate using 𝜃 to the aircraft measurements. As expected, GEOS-Chem synoptic replicates show less consistency in latitude (Figure S27), providing support for using 𝜃 as an analysis coordinate. Bayesian Inference We wish to quantify the global emissions of C3H8 and C2H6 using the observed mole fraction of these alkanes during ATom and HIPPO. The ambient mole fraction of C3H8 and C2H6 is most sensitive to their total northern hemisphere emissions during the winter/fall/spring when there is decreased sunlight/oxidation. As such, we assume differences between the GEOS-Chem simulations and the aircraft observations can be largely attributed to the underlying emissions grid, such that, 𝑎 = gcs ⋅ 𝛼 (1) where 𝑎 is the aircraft C2H6 or C3H8 mole fraction, gcs is the GEOS-Chem simulation of C2H6 or C3H8 mole fraction, and 𝛼 is a scalar that represents the missing emissions of C3H8 and C2H6 from default emissions. We developed a Bayesian hierarchical model to estimate the missing emissions, where equation (1) forms the basis of our model. Our model only uses the GEOS-Chem simulated alkane mole fraction data (synoptic replicates), the alkane mole fractions observed by the aircraft, tropopause height, and UTC time. Our complete statistical model and its development, priors (Figure S37-41), as well as the software used, are included in the SI, section 5. Hydrocarbon Percent Composition literature compilation and bootstrapping We gather literature measurements of hydrocarbon composition from unprocessed gas from oiland gas- producing basins in the U.S. and around globe to calculate emission ratios. Summary 10 statistics of the percent composition by region and the corresponding literature source is included in Table S4-5 (SI). Gas composition varies significantly across basins, so we perform bootstrap calculations for data samples within each basin separately. For each basin, we draw random pairs of hydrocarbon composition measurements (CH4, C2H6, and C3H8) the size of the dataset, then take the mean and repeat this 10,000 times. We use these bootstrap samples in subsequent calculations (Equation 2), to arrive at emission ratios (Figure 6). 2.3 Results and discussion CH4 leaks from U.S. energy activities are dominated by pre-gas processing emissions C3H8 and C2H6 are highly correlated at the NOAA sites (Figure 1). The data shown were obtained across 2-11 years and include tower and aircraft data (Table S1). The cross plot of C3H8 and C2H6 illustrate two distinct chemical regimes, similar to those described by Parrish et al. 2018.19 Above 1 ppb C3H8, the distribution is nearly linear, consistent with the mixing of fresh nonphotochemically aged emissions into the background atmosphere. At mole fractions below 1 ppb, a second regime is defined by mixing of the aged emissions (the lifetime of C3H8 is much less than that of C2H6). To explore the characteristics of pre-gas processing emissions, we study the ratio of these gases within the 50th highest percentile of C3H8 for the combined sites. Varying this demarcation ± 10% negligibly affects the linear fit (Figure S10). We find that the ratio of C3H8 to C2H6 in the linear regime to be [0.63, 0.70] (ppb/ppb, 95% CI), and FRAPPE observations show a similar trend at [0.76, 0.87] (Figure S9). Figure 1. Measurements of C2H6 and C3H8 from ongoing NOAA GML tower and aircraft sites (Table S1) from 2005-2018. The data follow the photochemical aging distribution described in Parrish et al. 2018, where the data below 1 ppb C3H8 are affected by photochemically aged emissions and mixing processes. As such, we only study the ratio of these gases in the 50th highest percentile (everything above 1 ppb C3H8) that would indicate fresh emissions. After this filtering, 11 two sites, Northwestern CO and Western UT (site codes NWR and UTA), did not have any data in the fresh emission regime and are not included in further analysis (more detail in Figure S8). Within the fresh emission chemical regime, the NOAA C3H8/C2H6 ratio changes minimally before and after 2012 ([0.62, 0.67] and [0.63, 0.71], respectively, ppb/ppb 95% CI, Figure S9) and over the entire timeseries (Figure S19). An unchanging C3H8/C2H6 ratio over time across the U.S. despite large changes in the C3H8/C2H6 ratio in processed gas during the same years (Figure S1), suggests that the majority of the alkane (and likely CH4) emissions occur pre-gas processing when all the C3H8 and sometimes much of the C2H6 are separated from the raw gas. Conversely, postgas processing (pipeline) composition of C2H6 at Playa del Rey in Southern California follows rejection trends, where the C3H8/C2H6 ratio has decreased by 8% from 2008 to 2018, and in recent years is about 18% lower in magnitude compared to the NOAA ratio (Figure S4). (Processed gas in California is a good representation of typical gas composition of domestic and globally-imported consumer-grade gas.20) Our results are in agreement with Rutherford et al. 2021’s US-based model for CH4 emissions, which finds that unintentional emissions from the production segment (namely, liquid storage tanks and other equipment leaks) are the largest contributors to divergence with the EPA’s GHGI.21 We use the same chemical aging approach to construct a background for NOAA and FRAPPE CH4 observations (Figure S7, S11). Since we only focus on the linear part of the chemical aging distribution, our analysis is not terribly sensitive to how the CH4 anomaly is determined (it simply produces varying intercepts, Figure S10). Consistent with the analysis of Lan et al. 20192 (see Figure S20-21), the ratio of C3H8 and C2H6 to CH4 has increased with time, reflecting a growing importance of oil exploration on CH4 emissions in the US. C3H8 demonstrates to be a useful tracer that constrains oil and gas related CH4 emissions. Given that the fit of C3H8 vs CH4 (and C2H6 vs CH4) have similar precision over the whole record, using C3H8 as a tracer likely separated nearby competing non-oil and gas CH4 emissions. However, if there were to be non-oil and gas CH4 emissions that were spatially coherent to the NOAA observation sites, our C3H8 vs CH4 and C2H6 vs CH4 emission ratios would be impacted. Investigating and potentially separating spatially coherent emissions of non-fossil origins would be the topic of future studies. NOAA observations at Oklahoma ARM site are especially impacted by nearby unprocessed gas emissions, as C2H6 and C3H8 correlations with CH4 have less noise compared to other sites (Figure S12-13). While the ratios of C3H8 and C2H6 vs CH4 have increased by 50% at NOAA Oklahoma site since 2010, we find that both C2H6 and C3H8 vs CH4 ratios are fractionally increasing at the same rate (Figure 2). That the atmospheric C2H6 and C3H8 increase fractionally the same suggests that the ratio of the alkanes in the reservoirs producing these emissions do not change significantly over the time of this record. Below, we use the 2017 average C3H8/CH4 and C2H6/CH4 from NOAA Oklahoma site ([0.060, 0.061] ppb/ppb (C2H6/CH4 is [0.086, 0.088], Figure S21) to compare our 12 emissions estimates for C3H8 and C2H6 to published estimates of CH4 emissions from oil and gas exploration. Figure 2. Yearly correlation between NOAA hydrocarbon vs CH4 anomaly in Oklahoma. We show the percent change of anomalies/year with respect to the mean hydrocarbon and methane anomalies. The trend for C3H8/CH4 is 7.13 ± 1.44 % with an R2 of 0.71. The trend for C2H6/CH4 is 5.87 ± 1.26 % with an R2=0.69. The variability in the trend comes from the standard error of a linear regression. The variability in the individual points comes from the 95% confidence interval of a pairs bootstrap of the alkanes and CH4 anomalies. (We ran a pairs bootstrap for comeasurements of C3H8 and ∆CH4 and compute the slope of the correlation for each bootstrap sample and repeated this for every year in the data; please see the methods section). This trend in units of ppt/ppb/year is shown in Figure S21. Default GEOS-Chem simulations underestimate C3H8 compared to aircraft observations We compare the cross plot of C3H8 to C2H6 from the HIPPO and ATom aircraft measurements and GEOS-Chem simulations to the NOAA measurements (Figure 3). As expected, both the aircraft observations and GEOS-Chem simulations fall under the photochemically aged emissions part of the NOAA distribution. While the aircraft data overlay the NOAA measurements almost perfectly (especially in the winter when the lifetimes of both gases are longest), GEOS-Chem underestimates C3H8, particularly over the Atlantic curtain (Figure 3,4). The same conclusion is drawn for HIPPO time periods (Figure S31-32, S34). Because the atmospheric lifetimes of C3H8 13 and C2H6 are different and vary seasonally due to the much higher concentrations of OH in the summer, our estimate of global C2H6 and C3H8 emissions from GEOS-Chem comparisons are sensitive to the a priori spatial distribution of these emissions. Figure 3. Comparison of C3H8 vs C2H6 for NOAA, ATom aircraft, and GEOS-Chem simulations during fall/winter seasons. NOAA photochemically-aged measurements (all sites, 2005-2018), as explained in the text, are shown on the heat map (colored by the number density of data). The spring/summer seasons are included in Figure S29-30, S33. HIPPO is shown in Figure S34. Relative to C2H6, the default GEOS-Chem v13.0.0 C3H8 emissions result in a much larger underestimate of C3H8 mole fractions over the Atlantic transect compared to the Pacific (Figure 3,4) implying an underestimate over North America. This pattern is most clearly visible in the summer when the C3H8 lifetime is short. In contrast, the default C2H6 emissions produce a good simulation of the ATom data (within 5%) over both ocean basins (Figure 3,4). As such, we use the mean ratio observed in the linear regime of the NOAA data (0.67 C3H8/C2H6, ppb/ppb Figure S9) as the default global ratio of their emissions to update GEOS-Chem. In mass units (as used in the GEOS-Chem emissions), this is ≈ 0.99 kg C3H8 / kg C2H6. Given the remarkable coherence in both the large-scale fields from the aircraft over both the Atlantic and Pacific transects and in the NOAA data, the spatial distribution of the emissions ratios for both gases must be very similar upwind of the Pacific (e.g., Asia) and the Atlantic (North America). As such, in our revised emissions fields for C3H8, we simply used the default C2H6 emissions configuration used by GEOS-Chem v13.0.0. This scaling substantially altered the spatial distribution of C3H8 emissions (Figure S28). The effect on the C3H8 simulation is shown in Figure 4 using ATom 4 as an example, where updating the emissions resulted in a much better agreement between GEOS-Chem C3H8 and aircraft measurements (other campaigns are included in Figure S35-36). Although simulations are greatly improved using the revised emissions, it appears there is a missing high latitude source of C3H8 and C2H6 (Figure S47-48, S54-55). 14 Figure 4. Impact of revised C3H8 emissions on GEOS-Chem simulation. Combined Pacific and Atlantic transects for ATom 4 aircraft campaign, which took place during Spring 2018, are shown in gold. The GEOS-Chem simulation using default C3H8 emissions are shown in blue and orange, referring to the Pacific and Atlantic transects, respectively. The GEOS-Chem simulation after implementing the revised C3H8 emissions is shown in green. The rest of the ATom campaigns are shown in Figure S36. Bayesian model suggests decadal increase in global C2H6 and C3H8 anthropogenic fossil emissions The results of our Bayesian inference were satisfactory. We had good sampling of our posterior and the sampling diagnostics were excellent (Figure S43-44, S50-51). We performed tests that verified our inference procedure could capture the ground truth (using simulated data for which the ground truth is known), and that our posterior was more concentrated around the ground truth than the prior (Figure S42). Furthermore, our model could generate the measured data reasonably well; the majority of the measured aircraft data fell into the 30th and 50th percentile of the simulated Bayesian model data (Figure S47-48, 54-55). The exception to this was the summer season, where the Bayesian model does not capture the measured aircraft data. This is expected, since during the summer we do not observe a robust relationship between potential temperature and C3H8 or C2H6. The model remained robust even when varying the sensitivity to low mole fractions of alkanes with tropical origin (Figure S58-60). During ATom 2 (winter) Atlantic curtain, the GEOS-Chem simulations poorly capture the observed C2H6 and C3H8 at low potential temperature compared to the aircraft. These measurements are samples obtained at low altitude, high latitude, and cold temperatures (Figure S49). During the winter, these arctic airmasses are often characterized by stagnant conditions, with less mixing with the mid-latitudes.22 As a result, emissions that occur at high latitudes during the winter can be trapped there unless the zonal flow is disrupted. Additionally, emissions of C2H6 and C3H8 near the arctic during the winter will oxidize more slowly relative to mid-latitudes due to the cold temperature and minimal sunlight. These conditions result in high C2H6 and C3H8 mole fraction over the arctic relative to remote mid-latitude chemical regimes. The measurements subject to arctic conditions during ATom were too few to make a substantial impact on the overall 15 Bayesian emissions estimate, but during HIPPO winter flights, few samples were obtained resulting in a large bias towards arctic data. We place much more weight on the ATom winter C3H8 analysis estimate of global C3H8 emissions since the arctic represents only a small fraction of the atmosphere. It is likely that GEOS-Chem v13.0.0 is missing a high latitude emissions source (Figure S47-49, S54-55). Underestimation of C3H8 and C2H6 at high latitudes is consistent with other studies, which found fossil fuel emissions from Eurasia accounted for the largest underestimation.23 It is possible that emissions from northern Europe may account for this discrepancy, as fossil emissions were found to be underestimated23 and our revised C3H8 emissions decreased in that region after implementing the emission C2H6 proxy (Figure S28). This, combined with a relatively lower number of HIPPO aircraft observations at lower latitudes, results in a substantial positive bias on the overall Bayesian emissions estimate for C3H8 during winter 2009 (Figure S62). We report our Bayesian estimates for each seasonal campaign and ocean transect during 20092011 and 2016-2018, and what the GEOS-Chem v13.0.0 default emissions grids should be scaled by, according to our analysis (Figure S45-46, S52-53, and SI section 5.8). We estimate global emissions of C2H6 and C3H8 from fossil fuel production from 2016-2018 to be 13.3 ± 0.7 (95% CI) and 14.7 ± 0.8 (95% CI) Tg/year, respectively. Our results compare well to other studies (Figure 5, Figure S62). Our estimates suggest emissions of C2H6 have increased by about 15% from 2010-2017 when comparing the mean revised C2H6 emissions during those time periods (Figure S61). Emissions of C3H8 are calculated to have increased more (65%, Figure S62), but this estimate is highly uncertain due to the few samples obtained during HIPPO and the impact of the Arctic winter pooling in both campaigns. Nevertheless, these increases are consistent with greater oil production emissions contribution. Similarly, Helmig et al. 2016, which used data from a global surface network and atmospheric column observations, found about a 22% increase in C2H6 emissions between 2009 and 2014.24 16 Figure 5. Global revised ethane anthropogenic fossil emissions compared to other studies. Our emissions estimate in 2016-2018 (during ATom) and 2009-2011 (during HIPPO) includes our revised emissions for winter, fall and spring seasons that we determined with our Bayesian model during each season. As discussed in the text, fewer samples were obtained during HIPPO, resulting in a sampling bias that we test by restricting observations and simulations to ± 300K potential temperature (Figure S56-S57). This test affects the estimate about ± 1 Tg during 2010-2011, but affects our estimate by up to 12 Tg in 2009. We compare our revised emissions to the default emissions from GEOS-Chem v13.0.0. The studies included here23,25–27 represent anthropogenic fossil emissions, except Dalsøren et al. 2018 which also includes biofuel, agriculture, and waste. We obtained the CEDS CMIP6 estimate from Dalsøren et al. 2018. Our emissions estimates do not include biomass burning or biofuels. Propane emissions are included in Figure S62. Oil exploration plays a more significant role in global CH4 compared to dry gas We calculate an emission ratio of C3H8/CH4 for n basins or countries using the following equation, ! ! "#$% & ∗ " &'%&% ! & ) " !& #* ! !"& "#$% ∗ "(%&% 𝐸 " !# = ∑)*+, '( !" (2) where 𝑃&'( is the dry natural gas production (in million tonnes), 𝐶# and 𝐶) are the bootstrapped samples of measured hydrocarbon fractions in raw natural gas samples (in mass %, details on the bootstrapping in the methods section), and 𝑡𝑜𝑡 is the sum of the bootstrapped samples of measured * hydrocarbon fractions for CH4, C2H6, and C3H8. (Note that our 𝐸 9*!: emission ratios are inherently " 17 * weighted by natural gas production by basin, 𝑃&'( .) 𝐸 9*#: is calculated similarly. We refer to the " emission ratio in Equation 2 as the “literature” emission ratio, since we combine a variety of natural gas composition measurements for wet and dry basins. We calculate a global literature emission ratio using hydrocarbon and dry natural gas production data from the top 5 producing natural gas basins around the world that made up 50% of the total natural gas production in 2019.28,29 We also calculate a U.S. literature emission ratio using the top 7 natural gas producing basins that account for 86% of total U.S. natural gas production.30,31 We show the relative production of the top global and U.S. basins used in our analysis in Figure S3. Additional summary statistics and sources for the composition measurements are included in Table S4-S5. Separately, we calculate an “observationally informed emission ratio (OIER)” by taking the ratio between our revised C3H8 emissions with literature estimates of CH4 emissions from oil and natural gas processes. The OIER for C2H6/CH4 is calculated similarly. Previous studies have constrained global CH4 emissions from Natural Gas/Petroleum systems to range from 63 – 91 Tg/yr.25,32–37 Given our estimate for revised C2H6 and C3H8 emissions, this implies a mean alkane ratio of 100:[8.0, 10.0]:[6.5, 7.3] molar % (CH4:C2H6:C3H8) in 2016-2018. We compare our literature ratio with several OIER using global estimates in Figure 6 and with U.S. estimates in Figure S63. The small abundance of spatial and temporal literature measurements of raw gas composition throughout basins most affect the final uncertainty in the emission ratio comparison. Figure 6. Global Literature and Observationally Informed Emission ratios (OIER) C3H8/CH4 and C2H6/CH4. The “weighted raw gas ratio” in the figure represents the “literature ratio” described in 18 the text, calculated using Equation 2. OIER, ratios between our revised C2H6 and C3H8 emissions and literature CH4 emission estimates, are shown for several literature CH4 estimates, including IEA 2021 (76.4 Tg/yr)34, Scarpelli et al. 2020 (65.7 Tg/yr)33, and Global Carbon Project 2020 bottom-up estimate (128 Tg/yr, 2008-2017 average)32. The variability in the literature ratio is attributed to the 95% CI of pairs bootstrap samples of hydrocarbon composition measurements (see text for more detail). The variability in the OIER is attributed to the 95% CI of our revised C3H8 and C2H6 emission estimates. We also compare C3H8/CH4 and C2H6/CH4 correlations from in-situ observations, including NOAA observations from Northern Oklahoma (2017 average from Figure S21, units of kg/kg) and FRAPPE observations from Northern Colorado (2014 from Figure S9, units of kg/kg). The variability in the NOAA ratio is relatively low because it is calculated from a multi-year average slope, and the error in the slope is low (see Figure S21, left). The variability in the FRAPPE ratio is relatively high because we use the 95% CI derived directly from our bootstrap samples, as described in the methods section. Unprocessed dry gas has a smaller C3H8/CH4 and C2H6/CH4 ratio compared to unprocessed associated gas from oil-producing basins (“wet” gas). A greater contribution of emissions from dry basins would decrease the magnitude of the overall literature ratio, assuming minimal C3H8 leakage after separation from raw gas, given the high market value of C3H8. In the U.S., the basin with the highest gas production is the Appalachian (East Coast) (Figure S3). If CH4 leaks were proportional to production, we would expect a “dry” (small) emission ratio that resembles the composition of the Appalachian region (6% mass/mass, calculated from Table S3). However, we find the production-weighted ratio to be much larger than expected (15%, Figure S63). The second-largest gas producing region, the Permian (Southwestern US), is also the largest oil producer in the U.S. and vastly overpowers the Appalachian in terms of oil production (Figure S3). The magnitude of our production-weighted raw gas “literature” emission ratios suggest a significant contribution from wet gas and emissions that are biased towards oil-producing basins. We find similar results for global emission ratios (Figure 6). The Global Carbon Project CH4 emissions estimate implies an OIER that is dry relative to the production-weighted raw gas ratio (literature ratio), Figure 6. Instead, the IEA (76 Tg/yr) and Scarpelli et al. 2016 (66 Tg/yr) CH4 emissions estimates yield an OIER that is within a few percent of the production-weighted raw gas literature ratio, given our revised C3H8 and C2H6 emissions. Both of those studies estimate oil production emissions to have a relatively higher contribution to the global footprint compared to dry gas production. The FRAPPE and NOAA Oklahoma observed emission ratios compare well to the global OIER (Figure 6) and U.S. OIER (Figure S63), suggesting high emissions from oil production. Indeed, there are substantial oil production activities (Figure S15-18) surrounding the NOAA Oklahoma and FRAPPE observation sites. Increasing tends in the Oklahoma emission ratios are consistent with production trends: oil production in Oklahoma tripled from 2010 to 201738,39 (compared to doubling of gas production) and in 2020, Oklahoma was the fourth-largest oil producer in the U.S.40 (Note that Oklahoma was not included in calculations for the literature ratio, since 19 Oklahoma natural gas production does not rank in the top 7.) Several factors may reduce incentive or ability for oil producers to capture associated natural gas byproducts, including low market prices and lagging pipeline infrastructure.41 Since our findings suggest that CH4 losses are likely greater and biased towards oil-producing sites, a significant fraction of bottom-up estimates of CH4 emissions may be misallocated to dry CH4 production, when they should instead be included with the oil production sector. Correctly attributing CH4 emissions to oil production would increase the greenhouse gas footprint of petroleum-based transportation, while decreasing the greenhouse gas emissions ascribed to natural gas-powered power plants. At a minimum, the CO2 equivalent footprint of the global transportation sector would increase by roughly 5%, using IEA’s estimate of 76 Tg/year CH4 emissions from oil and natural gas and recent transportation CO2 emission estimates (Section 6.4, SI).36,42 This estimate will only increase when accounting for vented and flared losses of associated natural gas that is not accounted for in marketed associated gas (which we use to calculate these numbers). ACKNOWLEDGMENTS This work was supported by the Resnick Sustainability Institute, including computations conducted in the Resnick High Performance Computing Center. A.L.T. received funding from NSF award No. DGE-1745301. NOAA support was provided for HIPPO by NSF award no. AGS-0628452; California Institute of Technology support for ATom was provided by NASA grant award No. NNX15AG61A. NOAA support for ATom was provided by NASA EVS2 award No. NNH17AE26I; additional support was provided by NASA Upper Atmosphere Research Program award No. NNH13AV69I. NOAA laboratory and salary support is from NOAA Climate Change Program. S.A.M. acknowledges funding in part from NOAA Climate Program Office’s AC4 Program. NOAA flask sampling and technical support was provided by Dr. Fred Moore of NOAA/CIRES. Additional technical support was provided by C. Siso, B. Miller, M. Crotwell, C. Sweeney, A. Andrews, J. Higgs, D. Neff, J. Kofler, K. McKain, M. Madronich, P. Handley, and S. Wolter. We thank IHS Markit for providing PointLogic economic data. REFERENCES (1) U.S. Energy Information Administration. 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Data 2020, 12 (1), 563–575. https://doi.org/10.5194/essd-12-563-2020. (34) IEA. Methane Tracker Database: Interactive Database of Country and Regional Estimates for Methane Emissions and Abatement Options, 2021. https://www.iea.org/articles/methanetracker-database#sources. (35) Maasakkers, J. D.; Jacob, D. J.; Sulprizio, M. P.; Turner, A. J.; Weitz, M.; Wirth, T.; Hight, C.; DeFigueiredo, M.; Desai, M.; Schmeltz, R.; Hockstad, L.; Bloom, A. A.; Bowman, K. W.; Jeong, S.; Fischer, M. L. Gridded National Inventory of U.S. Methane Emissions. Environ. Sci. Technol. 2016, 50 (23), 13123–13133. https://doi.org/10.1021/acs.est.6b02878. 23 (36) EPA (Environmental Protection Agency). Global Anthropogenic Non-CO2 Greenhouse Gas Emissions: 1990-2030., 2012. (37) Turner, A. J.; Jacob, D. J.; Wecht, K. J.; Maasakkers, J. D.; Lundgren, E.; Andrews, A. E.; Biraud, S. C.; Boesch, H.; Bowman, K. W.; Deutscher, N. M.; Dubey, M. K.; Griffith, D. W. T.; Hase, F.; Kuze, A.; Notholt, J.; Ohyama, H.; Parker, R.; Payne, V. H.; Sussmann, R.; Sweeney, C.; Velazco, V. A.; Warneke, T.; Wennberg, P. O.; Wunch, D. Estimating Global and North American Methane Emissions with High Spatial Resolution Using GOSAT Satellite Data. Atmospheric Chem. Phys. 2015, 15 (12), 7049–7069. https://doi.org/10.5194/acp-15-7049-2015. (38) U.S. Energy Information Administration. Petroleum & Other Liquids: Oklahoma Field Production of Crude Oil, 2021. https://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?f=M&n=PET&s=MCRFPOK1. (39) U.S. Energy Information Administration. Natural Gas: Oklahoma Natural Gas Marketed Production, 2021. https://www.eia.gov/dnav/ng/hist/n9050ok2a.htm. (40) U.S. Energy Information Administration. Oklahoma State Profile Analysis, 2021. https://www.eia.gov/state/analysis.php?sid=OK. (41) Kevin Crowley; Collins, R. Oil Producers Are Burning Enough “Waste” Gas to Power Every Home in Texas. Bloomberg. April 10, 2019. https://www.bloomberg.com/news/articles/2019-04-10/permian-basin-is-flaring-more-gas-thantexas-residents-use-daily. (42) Liu, Z.; Ciais, P.; Deng, Z.; Lei, R.; Davis, S. J.; Feng, S.; Zheng, B.; Cui, D.; Dou, X.; Zhu, B.; Guo, R.; Ke, P.; Sun, T.; Lu, C.; He, P.; Wang, Y.; Yue, X.; Wang, Y.; Lei, Y.; Zhou, H.; Cai, Z.; Wu, Y.; Guo, R.; Han, T.; Xue, J.; Boucher, O.; Boucher, E.; Chevallier, F.; Tanaka, K.; Wei, Y.; Zhong, H.; Kang, C.; Zhang, N.; Chen, B.; Xi, F.; Liu, M.; Bréon, F.-M.; Lu, Y.; Zhang, Q.; Guan, D.; Gong, P.; Kammen, D. M.; He, K.; Schellnhuber, H. J. Near-Real-Time Monitoring of Global CO2 Emissions Reveals the Effects of the COVID-19 Pandemic. Nat. Commun. 2020, 11 (1), 5172. https://doi.org/10.1038/s41467-020-18922-7. 24 Chapter3 An analysis coordinate transform to facilitate use of in-situ aircraft observations for flux estimation Ariana L. Tribby, Paul O. Wennberg In preparation for submission to Atmospheric Measurement Techniques. Abstract Analysis of aircraft observations of atmospheric trace gases is key towards improving fundamental chemical processes and quantifying anthropogenic emissions. A common approach for such analysis is use of chemical transport models to produce 4-D fields for comparison with these observations together with various inversion techniques to constrain the underlying fluxes. Yet, time and monetary constraints of expensive computational jobs for chemical transport modeling can be a significant hindrance. Here, we show the advantages of using potential temperature as a dynamical coordinate to compare such simulations to aircraft observations of trace gases whose concentration fields are strongly influenced by synoptic-scale gradients. We use global observations of ethane and propane from the Atmospheric Tomography (ATom) aircraft mission and simulate globe mole fractions for these gases using GEOS-Chem High Performance v13.4.1. We show that Bayesian estimates of the fluxes of these gases to the Northern Hemisphere are invariant (± 10%) even as the simulation spatial and temporal resolution are increased 100-fold. Our approach can have broad applications for the modeling of trace gases in the extratropics, particularly those with longer lifetimes compared to synoptic timescales. 3.1 Introduction A common approach for estimating fluxes of trace gases to the atmosphere involve comparing atmospheric simulations with in-situ observations. Such studies enable the use of sparse observations made by aircraft, for example.1–3 However, computational load can limit the feasibility of these comparisons. Often, efforts are focused on increasing the temporal and spatial resolution of the simulations as a means of capturing the fine scale structure that adds variance to the 4-D chemical fields. This significantly increases the computational load and analysis time. Motivated by previous analyses of column CO2 observations,4,5 we illustrate here how potential temperature (𝜃, in units of Kelvin) can be useful in model-observation comparisons, particularly when the trace gases under analysis have fluxes that are largely dependent on synoptic-scale dynamics. Variability in the extra-tropics within large-scale circulation can be well-captured since 𝜃 is conserved following adiabatic flow. Trace gases that have longer lifetimes compared to 25 synoptic-scale meteorology (about 10 days),6 will be well correlated with 𝜃. (The correlation does not hold in the tropics or boundary layer, or when the photochemical lifetimes are short, i.e., during the summer months.) In this study, we use global aircraft observations of ethane (C2H6) and propane (C3H8) from Atmospheric Tomography (ATom) mission during 2016-2017 and simulate those global fields using the chemical transport model, GEOS-Chem High Performance v13.4.1. We show that when used a zonal coordinate, 𝜃 improves model/observation correlation compared with using classical latitude, longitude, altitude and time coordinates. We use the Bayesian hierarchical model from Tribby et al. 2022 to evaluate flux estimates from simulations performed at 4x5, 2x2.5, and 0.5x0.625 resolutions, and find that when using 𝜃, the comparisons have negligible difference. As such, 𝜃 offers an opportunity to optimize time and cost of model simulations for certain trace gases, including several of which have important climate implications. 3.2 Methods 3.2.1 ATom observations The Atmospheric Tomography (ATom) aircraft campaign comprised of four sequential global flights. We use two flight campaigns during July-August 2016 and January-February 2017. As in Tribby et al. 2022, we exclude from our analysis stratospheric observations (using N2O) and data influenced by highly local emission sources (boundary layer and biomass burning).7 When using 𝜃 as a vertical interpolation coordinate, we exclude the summer months from our analysis, since the lifetime of C2H6 and C3H8 are reduced, and regional/local sources dominate the variance. Further, we exclude subtropical transport by limiting observations with tropopause pressure above 100 hPa (only about 5% of data was affected by this constraint), which sufficiently reduced subtropical influence. We show flight paths for the data above 20 degrees north in Figure 7, as we only consider northern fluxes since most emissions of short-lived C2H6 and C3H8 originate in the northern hemisphere, and their lifetimes are shorter than northern-southern hemispheric exchange rate. 26 Figure 7. Flight paths during ATom flight campaign. We use summer 2016 and winter 2017 campaigns over the Atlantic Ocean in our analysis. We only consider observations above 20 degrees north, as explained in the methods. 3.2.2 GEOS-Chem simulations We simulated ATom aircraft observations using the GEOS-Chem classic global3-D chemical transport model in v13.4.1 (doi:10.5281/zenodo.6564702) on Amazon Web Services (AWS) using a public GEOS-Chem Amazon Machine Image (ami-0491da4eeba0fe986).8 We used the standard full-chemistry option and 3 horizontal resolutions to simulate ATom1 & 2, including 4x5, 2x2.5, and 0.5x0.625, all with the native 72 hybrid sigma/pressure levels using MERRA-2 reanalysis meteorology products by the Global Modeling and Assimilation Office (GMAO) at NASA Goddard Space Flight Center,9 available on the AMI. For all 3 horizontal resolution simulations, we output hourly simulations over the ATom 1 and 2 flight campaign periods. We conducted a global simulation for 4x5 and 2x2.5 horizontal resolutions before sampling to the aircraft path, except for 0.5x0.625, detailed below. Default chemistry and configurations were used for 2x2.5 and 4x5, except for custom C2H6 and C3H8 emissions, described below. We used a 1year spin-up at 4x5 horizontal resolution, followed by a 10-day spin-up with the 2x2.5 or 0.5x0.625 meteorological files. The 0.5x0.625 simulations were conducted using a nested-grid over a custom box that encompassed the ATom Atlantic curtain transect. The vertices of our custom grid included a minimum/maximum latitude of (18.0, 88.0) and a minimum/maximum longitude of (-90.0, -15.0) with 3-grid buffer for all sides. We generated global boundary condition tri-hourly daily files for our custom grid using a 4x5 simulation and custom emissions for C2H6 and C3H8, described below. In addition, we re-used the 4x5 spin-up restart files when generating boundary condition files. During the nested run, several species were flagged as having negative values during PBL mixing in GEOS-Chem, including HNO3, NH3, NO, NO2, O3, and halogen chemistry sea salt alkalinity variables, SALAAL and SALCAL, causing the simulations to end. Manually increasing the background concentrations or reducing the transport/convection timestep to 150 seconds and the chemistry/emission timestep to 300 seconds did not prevent these issues. We kept the timesteps at 27 those reduced values and edited the wrapper module, mixing_mod.F90, to replace negative values with zero to allow the model to run. No other species were flagged as having negative values. Emissions for C2H6 and C3H8 were computed using the Harmonized Emissions Component (HEMCO)10 Standalone version 3.5.0-rc.1 and GEOS-Chem 14.0.0-rc.1 on AWS using a public Amazon Machine Image (ami-0491da4eeba0fe986). We revised the default emissions using the same methods from Tribby et al. 2022: we scaled all sectors of default C2H6 by 1.1, and we substituted C3H8 with default C2H6 before scaling by 1.2. 3.3 Results In Figure 8, we show curtain plots for C3H8 for 4x5, 2x2.5, and 0.5x0.625 horizontal resolution GEOS-Chem simulations. We interpolate 4x5 and 2x2.5 along pressure and latitude to the 0.5x0.625 scale. As expected, 0.5x0.625 show more defined structures. However, if we instead create the same curtain plots but using 𝜃 as the vertical coordinate (without interpolation), the three simulations look very similar (SI). This holds true for the winter 2017 observations, but not for the summer 2016 observations, since the increased sunlight/oxidation reduces the chemical lifetime of C2H6 and C3H8, resulting in a poor relationship with 𝜃 (Figures A5, A6). 28 Day 0 Day + 5 0.5x0.625 2x2.5 4x5 Day -5 Figure 2. GEOS-Chem-simulated C H “curtain” during ATom 2 winter 2017 campaign, along pressure and latitude. Figure 8. GEOS-Chem-simulated C3H8latitude “curtain” during ATom 2 winter All GEOS-Chem simulations were sampled along aircraft and a single median time/longitude during the 2017 campaign, along flight overand the Atlantic ocean. Column 1 shows simulations sampled 5 days afterwere the median aircraft time; Columnaircraft 2 pressure latitude. All GEOS-Chem simulations sampled along latitude and a shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the single during theto 0.5x0.625 flight grid over median median aircraft time. time/longitude FIRST row: 4x5 resolution, interpolated using the latitudeAtlantic and pressure ocean. Column 1 shows coordinates. SECOND row: 2x2.5 resolution, interpolated to 0.5x0.625 grid usingtime; latitudeColumn and pressure 2 coordinates. simulations sampled 5 days before the median aircraft shows simulations sampled THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft on the median aircraft time; Column 3 shows simulations sampled 5 days after the median aircraft time. FIRST row: 4x5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. SECOND row: 2x2.5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black. C2H6 is included in the SI. 3 8 flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black. C2H6 is included in the SI. Day 0 Day + 5 0.5x0.625 2x2.5 4x5 Day -5 29 Figure 3. GEOS-Chem-simulated C H “curtain” during ATom 2 winter 2017 campaign, along potential temperature Figure 9. GEOS-Chem-simulated C3Halong during ATom winter 2017 campaign, along 8 “curtain” and latitude. All GEOS-Chem simulations were sampled aircraft latitude and a single median2 time/longitude during the flight over the Atlanticand ocean.latitude. Column 1 shows sampled 5 days after the median were aircraft time; potential temperature Allsimulations GEOS-Chem simulations sampled along aircraft Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 before the median aircraft time. FIRST row: 4x5 resolution. SECOND row: 2x2.5 resolution. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shows simulations sampled 5 days before the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days after the median aircraft time. FIRST row: 4x5 resolution. SECOND row: 2x2.5 resolution. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black. C2H6 is included in the SI. 3 8 When we interpolate the GEOS-Chem simulations along aircraft latitude, longitude, time, and 𝜃, we see excellent agreement between simulations and the aircraft observations, consistent across all 3 horizontal resolutions (Figure 10). Furthermore, there is generally good agreement between the aircraft observations and simulations 5 days before and after the flight path, which is expected during the winter months when C3H8 and C2H6 have longer lifetimes and higher abundance. 30 Figure 10. GEOS-Chem simulations and ATom aircraft C3H8 vs potential temperature. Left: Includes aircraft observations and simulations sampled 5 days after the aircraft flight path. Middle: Includes aircraft observations and simulations sampled during the aircraft flight path. Right: Includes aircraft observations and simulations 5 days before the aircraft flight path. C2H6 included in the SI. We compare the aircraft observations with the GEOS-Chem simulations using the same Bayesian hierarchical model from Tribby et al. 2022 to capture the contribution of uncertainty due to transport in GEOS-Chem. In summary, Tribby et al. 2022 assumed differences between the GEOSChem simulations and aircraft observations are largely dependent on the underlying emissions grid during the winter when there is decreased sunlight/oxidation, such that 𝑎 = gcs ⋅ 𝛼 (1) where 𝑎 is the aircraft mole fraction, gcs is the GEOS-Chem simulation, and 𝛼 is a scalar that quantifies the difference between the simulations and the aircraft observations (that directly attributes the missing emissions). Since in our simulations here, we updated the fluxes to those estimated in Tribby et al. 2022, we expect 𝛼 to be close to 1. We follow all methods of the previous study, including sampling the GEOS-Chem simulations several days before and after the aircraft flight latitude, longitude, and time before interpolating on the vertical level using 𝜃. Please refer to Tribby et al. 2022 for the complete statistical model and its derivation, the software, and the development of the priors. 31 With 𝜃 as the interpolation coordinate, the Bayesian results are similar regardless of the simulation grid scale (Figure 11): the mean posterior varies 10% or less between all horizontal resolutions for both C3H8 and C2H6. Furthermore, the confidence interval spread was about the same for the finest and coarsest resolutions, illustrating the value of using 𝜃 as the analysis coordinate. Figure 11. Bayesian inference results, 97.5% confidence interval. Top: C3H8. Bottom: C2H6. References (1) Xiao, Y.; Logan, J. A.; Jacob, D. J.; Hudman, R. C.; Yantosca, R.; Blake, D. R. Global Budget of Ethane and Regional Constraints on U.S. Sources. J. Geophys. Res. 2008, 113 (D21). https://doi.org/10.1029/2007JD009415. (2) Zhou, M.; Langerock, B.; Wells, K. C.; Millet, D. B.; Vigouroux, C.; Sha, M. K.; Hermans, C.; Metzger, J.-M.; Kivi, R.; Heikkinen, P.; Smale, D.; Pollard, D. F.; Jones, N.; Deutscher, N. M.; Blumenstock, T.; Schneider, M.; Palm, M.; Notholt, J.; Hannigan, J. W.; De Mazière, M. An Intercomparison of Total Column-Averaged Nitrous Oxide between Ground-Based FTIR TCCON and NDACC Measurements at Seven Sites and Comparisons with the GEOS-Chem Model. Atmospheric Meas. Tech. 2019, 12 (2), 1393–1408. https://doi.org/10.5194/amt-12-1393-2019. (3) Frankenberg, C.; Kulawik, S. S.; Wofsy, S. C.; Chevallier, F.; Daube, B.; Kort, E. A.; O&amp;apos;Dell, C.; Olsen, E. T.; Osterman, G. Using Airborne HIAPER Pole-toPole Observations (HIPPO) to Evaluate Model and Remote Sensing Estimates of Atmospheric Carbon Dioxide. Atmospheric Chem. Phys. 2016, 16 (12), 7867–7878. https://doi.org/10.5194/acp-16-7867-2016. (4) Keppel-Aleks, G.; Wennberg, P. O.; Schneider, T. Sources of Variations in Total Column Carbon Dioxide. Atmospheric Chem. Phys. 2011, 11 (8), 3581–3593. https://doi.org/10.5194/acp-11-3581-2011. 32 (5) Keppel-Aleks, G.; Wennberg, P. O.; Washenfelder, R. A.; Wunch, D.; Schneider, T.; Toon, G. C.; Andres, R. J.; Blavier, J.-F.; Connor, B.; Davis, K. J.; Desai, A. R.; Messerschmidt, J.; Notholt, J.; Roehl, C. M.; Sherlock, V.; Stephens, B. B.; Vay, S. A.; Wofsy, S. C. The Imprint of Surface Fluxes and Transport on Variations in Total Column Carbon Dioxide. Biogeosciences 2012, 9 (3), 875–891. https://doi.org/10.5194/bg-9875-2012. (6) Wohltmann, I. Integrated Equivalent Latitude as a Proxy for Dynamical Changes in Ozone Column. Geophys. Res. Lett. 2005, 32 (9), L09811. https://doi.org/10.1029/2005GL022497. (7) Tribby, A. L.; Bois, J. S.; Montzka, S. A.; Atlas, E. L.; Vimont, I.; Lan, X.; Tans, P. P.; Elkins, J. W.; Blake, D. R.; Wennberg, P. O. Hydrocarbon Tracers Suggest Methane Emissions from Fossil Sources Occur Predominately Before Gas Processing and That Petroleum Plays Are a Significant Source. Environ. Sci. Technol. 2022, acs.est.2c00927. https://doi.org/10.1021/acs.est.2c00927. (8) Zhuang, J.; Jacob, D. J.; Gaya, J. F.; Yantosca, R. M.; Lundgren, E. W.; Sulprizio, M. P.; Eastham, S. D. Enabling Immediate Access to Earth Science Models through Cloud Computing: Application to the GEOS-Chem Model. Bull. Am. Meteorol. Soc. 2019, 100 (10), 1943–1960. https://doi.org/10.1175/BAMS-D-18-0243.1. (9) Gelaro, R.; McCarty, W.; Suárez, M. J.; Todling, R.; Molod, A.; Takacs, L.; Randles, C. A.; Darmenov, A.; Bosilovich, M. G.; Reichle, R.; Wargan, K.; Coy, L.; Cullather, R.; Draper, C.; Akella, S.; Buchard, V.; Conaty, A.; da Silva, A. M.; Gu, W.; Kim, G.-K.; Koster, R.; Lucchesi, R.; Merkova, D.; Nielsen, J. E.; Partyka, G.; Pawson, S.; Putman, W.; Rienecker, M.; Schubert, S. D.; Sienkiewicz, M.; Zhao, B. The Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2). J. Clim. 2017, 30 (14), 5419–5454. https://doi.org/10.1175/JCLI-D-16-0758.1. (10) Lin, H.; Jacob, D. J.; Lundgren, E. W.; Sulprizio, M. P.; Keller, C. A.; Fritz, T. M.; Eastham, S. D.; Emmons, L. K.; Campbell, P. C.; Baker, B.; Saylor, R. D.; Montuoro, R. Harmonized Emissions Component (HEMCO) 3.0 as a Versatile Emissions Component for Atmospheric Models: Application in the GEOS-Chem, NASA GEOS, WRF-GC, CESM2, NOAA GEFS-Aerosol, and NOAA UFS Models. Geosci. Model Dev. 2021, 14 (9), 5487–5506. https://doi.org/10.5194/gmd-14-5487-2021. 33 Chapter4 Towards constraining methane emissions in southern Oklahoma using STILT analysis of remote sensing and flask observations of hydrocarbon tracers Ariana L. Tribby, Dien Wu, Josh L. Laughner, Harrison A. Parker, Paul O. Wennberg In preparation for submission to Atmospheric Chemistry and Physics. 4.1 Introduction Previous studies have seen evidence for significant, nearby oil and gas production hydrocarbon emissions using ethane and propane flask observations from the NOAA station in Lamont, Oklahoma (Tribby et al. 2022). Their reported decadal trend is consistent with Oklahoma oil and gas production activities that tripled during the same time.1,2 We develop a methodology to quantify emissions of methane from this region using long-term measurements of ethane and propane tracers, in conjunction with NOAA flask. Finally, we will quantify regional emissions using STILT. This analysis is in preparation for submission to ACP. 4.2. Methods 4.2.1 TCCON measurements of ethane and propane Remote sensing observations from ground-based Fourier transform spectrometer located in Lamont, Oklahoma are part of the Total Carbon Colomn Observing Network (TCCON), which includes 29 active sites located around the world.3 The TCCON instruments are solar-viewing Bruker 125HR (high-resolution) FT-IR spectrometers (near-infrared) that record an interferogram every few minutes that are converted to spectra. The volume mixing ratio (VMR) of numerous trace gases are derived from the measured spectra using a nonlinear least-squares algorithm that minimizes the residuals between a measured spectrum and one that is the product of the a priori profile and a uniform scalar.4 Column abundances of atmospheric gases are computed by integrating the optimally-scaled prior profiles.5 The column abundances are converted to column dry mole fractions (DMF) by dividing by the column of O2. In this analysis, we take advantage of new retrievals of ethane and propane together with standard retrievals of methane. The a priori profiles are constructed using correlations between meteorological variables and observations (i.e., balloon) of trace gas DMFs in the atmosphere. While these a priori are satisfactory for remote observations typical of TCCON sites, in the context of intense oil and gas emissions, they are not appropriate for regions such as Oklahoma. Here, we use GEOS-Chem simulations of C2H6 and C3H8 (see configurations for GEOS-Chem below) at Oklahoma to update 34 the a priori profiles for the TCCON retrievals using the newly-developed ginput-devel algorithm (https://github.com/WennbergLab/py-ginput-devel.git), Figure 12. This product was developed for TCCON users to derive a priori profiles using custom trace gas column profiles. The algorithm samples custom trace gas profiles (at a frequency of every 3 hours) and interpolates along geopotential height to arrive at the same vertical coordinates as the meteorology used in TCCON GGG2020, which uses the Goddard Earth Observing System Forward Product for Instrument Teams (GEOS FP-IT) reanalysis product. The geopotential height is computed by normalizing the geometric height by gravity and linearly interpolated in log(pressure) from the model’s level edge pressures. The edge heights are calculated using the hydrostatic equation, # + <𝑃𝐻𝐼𝑆 + , 2 𝑐, ∑./ 01. 𝜃- ∆𝑃 C, where ∆𝑃 is the difference in 9, : at the lower and upper edges of layer l, PHIS $ is the surface geopotential, 𝑐, is the specific heat, and 𝜃- is the virtual potential temperature in the layer (https://gmao.gsfc.nasa.gov/GMAO_products/documents/GEOS-5_Filespec_Glossary.pdf). We calculate 𝜃- using the virtual temperature (“TV”) and water profile. All profiles of interfering species in the spectra of C2H6 and C3H8 are taken from the default a priori profiles used in GGG2020. Below is a comparison of an example of the updated VMR for C2H6 and C3H8. Figure 12. Updated ethane and propane volume mixing ratios (VMR) for TCCON retrievals. Updated VMR are derived using the new ginput-devel algorithm (see Methods) and GEOS-Chem profiles made using revised hydrocarbon emissions from Tribby et al. 2022. Index is a proxy for the hybrid pressure level. Shown in blue are the standard a priori profiles used in ggg. 35 We obtain column average dry mole fractions (DMF) with high temporal frequency for ethane and propane at the Lamont site from 2017-2020 (see Results). We also filter for scaling factor (VSF) error less than 10 to reduce solar zenith angle dependence. 4.2.2 GEOS-Chem simulations We use GEOS-Chem simulations to develop custom priors for our TCCON retrievals of C2H6 and C3H8. We ran GEOS-Chem classic global3-D chemical transport model in v13.4.1 (doi:10.5281/zenodo.6564702) on Amazon Web Services (AWS) using a public GEOS-Chem Amazon Machine Image (ami-0491da4eeba0fe986). We used the standard full-chemistry option at 4x5 degree horizontal resolution at the native 72 hybrid sigma/pressure levels using GEOS-FP meteorology products available on AWS to simulate C2H6 and C3H8 from June 1 – October 1 20172020, with output frequency of every 3 hours. Default chemistry and configurations were used except for custom C2H6 and C3H8 emissions, described below. We used a 1-year spin up at 4x5 horizontal resolution. Emissions for C2H6 and C3H8 were computed using the Harmonized Emissions Component (HEMCO) Standalone version 3.5.0-rc.1 and GEOS-Chem 14.0.0-rc.1 on AWS using a public Amazon Machine Image (ami-0491da4eeba0fe986). We revised the default emissions using the same methods from Tribby et al. 2022: we scaled all sectors of default C2H6 by 1.1 and substituted C3H8 with default C2H6 before scaling by 1.2. 4.2.3 NOAA flask observations We use observations from the NOAA Oceanic and Atmospheric Administration (NOAA) Global monitoring Laboratory (GML) measurements of C3H8, C2H6 and CH4 from flask air samples collected by the NOAA GML tower and aircraft at the Southern Great Plains (SGP) location in Lamont, Oklahoma from 2017-2020. The C3H8 and C2H6 were accessed from https://gml.noaa.gov/aftp/data/trace_gases/, while CH4 was accessed from https://gml.noaa.gov/aftp/data/trace_gases/ch4/pfp/. We use measurement quality flags labeled as either preliminary or good sampling analysis only. There were unequal number of quality measurements for all 3 alkane species, so we matched UTC time stamps that were shared between all 3 to avoid sampling bias. As in Tribby et al. 2022 we use 1 ppb C3H8 as a threshold for photochemically aged samples. We restrict our analysis to samples associated with fresh emissions (unaged). We only use summer data between June 1-October 1 2017-2020. Wind speed and direction for Lamont NOAA flasks was obtained from the nearby Blackwell station at https://mesonet.agron.iastate.edu/sites/windrose.phtml?station=WDG&network=OK_ASOS. We interpolated the speed and direction using the nearest neighbor UTC time. 36 4.2.4 STILT modeling We use the Stochastic Time-Inverted Lagrangian Transport (STILT) model,6 which simulates atmospheric transport backward in time by releasing an ensemble of representative air parcels at a receptor location, and simulating their stochastic transport by extracting parameters from assimilated meteorological fields. Only flask NOAA observations are modeled at this time, and plans for using TCCON retrievals with STILT are described in future directions. 1000 air parcels are released per tower receptor longitude/latitude/time/altitude. Our model area is defined as 2050N latitude, 90-110W longitude. To transport the air parcels, we use the North American Mesoscale Forecast System (NAM) (12 km resolution) run by the National Centers for Environmental Prediction (NCEP). The impact on wind error is a topic of future work, but we utilize a generous uncertainty of 50% in modeled mole fractions for preliminary Bayesian estimates below.7 STILT generates a footprint, which describes the influence of potential upwind source regions to downwind receptor mole fraction anomaly, in units of ppm/(µmolm-2). Each footprint has a horizontal resolution of 0.1x0.1 degrees. The footprints, multiplied by emissions, describes the contribution to the mole fraction anomaly at the receptor, in units of ppb. 4.2.5 Emissions prior Oil and gas wells shapefiles were downloaded from https://www.fractracker.org/map/us/ in April 2023 for the following regions: Oklahoma, Colorado, Kansas, Missouri, new Mexico, Oklahoma and Texas (see SI for visualization). We use geopandas (v 0.12.2) for processing and analysis. After converting all coordinates to WGS 84, we compute well density for every 0.1x0.1 cell (figure, SI). We then use Zhang et al. 2020’s8 CH4 emission estimates in the Permian basin to derive a CH4 emission rate for our entire footprint area using our computed well density, Figure 13. We use the mean C3H8/CH4 and C2H6/CH4 emission ratios from 2017 at Lamont Oklahoma (Tribby et al. 2022) to estimate C3H8 and C2H6 emissions at 0.1x0.1 degrees (Figures in SI). Integrated emissions over our footprint area are as follows: CH4 at 7.6 ± 1.4 Tg/yr, C3H8 at 1.3 ± 0.5 Tg/yr, and C2H6 at 1.2 ± 0.5 Tg/yr, where uncertainty is the propagated error between Zhang et al. 2020 CH4 emission rate uncertainty and the variability in the hydrocarbon emission ratio from Tribby et al. 2022. We compare our area totals with other studies in the SI. 37 Figure 13. CH4 emissions constructed using wellhead density, used for computing STILT contribution. C2H6 and C3H8 are included in the SI. We convert from latitude/longitude coordinates to units of meters using pyproj Geod package (v3.5.0). Finally, we filled any zero values in the emissions grid with 1e-15 to avoid issues with log(0) before scaling by the STILT footprint in the Bayesian modeling below. 4.2.6 Bayesian modeling We assume a linear relationship between the STILT-modeled mole fraction (𝑦3 ) and the observed mole fractions (𝑦4 ) such that 𝑦4 = 𝑥𝑦3 , where x is the state vector representing the emissions scaling factor. This assumption holds because the lifetime of ethane and propane are on the order of weeks during the summertime and longer at other times of year. This is sufficiently long with respect to transport over a 3-day footprint period that we can assume these gases are passive tracers. We can reasonably approximate ethane and propane as lognormally distributed: 𝜎 ~ 𝑁𝑜𝑟𝑚(0.9, 0.15) 𝑙𝑜𝑔#4 𝑥 ~ 𝑁𝑜𝑟𝑚(0,1) ∆𝑦4% ~ LogNorm 9𝑥∆𝑦3% , 𝜎: where ∆𝑦4& is the jth observed enhancement hydrocarbon mole fraction, and ∆𝑦3& is the jth modeled enhancement mole fraction, which are the STILT footprintsj,k (of k spatial grid cells) 38 scaled by the emissions priork. We define xk on a log scale for its prior for two reasons. First, it is well documented that emissions from oil and gas follow a heavy-tail distribution, 9–12 so this will generate scaling factors on an appropriate scale. Second, the emissions priork is likely an underestimate since we use well density to linearly scale our derived emission rate and do not account for super emitters. The prior for 𝜎 is sufficiently broad to allow for an error estimate of 50% in ppb enhancement (the generated samples are in log scale). Figures for our priors are shown in the SI. We run our statistical model using Stan software13 (version 2.26) with CmdStanPy Python interface (version 0.9.67).14 Stan is a probabilistic programming language that uses Hamiltonian Monte Carlo (HMC),15 which allows for more efficient sampling of the posterior. We parse Markov chain sampling using ArviZ (version 0.11.1).16 We use bebi103 package (version 0.1.0)17 to prepare data for Stan sampling, parse MCMC samples, plot posteriors and plot posterior predictive checks. Finally, other software we use in our analysis includes Holoviews version 1.14.5,18 Bokeh version 2.3.3,19 Pandas version 1.3.1,20 SciPy version 1.6.2,21 and NumPy version 1.20.3.22 We set the warmup iterations to 2000 and conducted 1000 samples. 4.3. Results & analysis The TCCON dry mole fractions (DMF) of C3H8 and C2H6 are very well correlated (Figure 14). In anticipation of performing a STILT run using TCCON columns, we have prepared a TCCON dataset in which TCCON and NOAA flask observations overlap in day of measurement (SI). We have not yet completed the algorithm for executing STILT for TCCON column receptors at the time of this thesis preparation, and this task is left for future work prior to submission of this study for peer review. 39 Figure 14. TCCON dry mole fractions of C2H6 and C3H8. We show NOAA flask tower and plane C3H8 and C2H6 for Lamont in the ‘fresh emission’ regime (Figure 15). Most samples with highly elevated C3H8 and C2H6 are associated with wind direction vector originating from a south/south-westerly direction. Figure 15. C3H8 and C2H6 NOAA flask data. Data filtered for fresh emission chemical regime. Not yet background corrected. Marker size correlates to relative wind magnitude. 40 Below we show an example of our modeled mole fraction anomaly (ym) contribution to the NOAA tower flask receptor (STILT footprint scaled by our emissions prior), over the 3 day back-trajectory (Figure 16). At first glance though all the receptor days, there seem to be a significant number of footprints from North, South-East origin contributing to the receptor mole fraction. However, more analysis is needed, as some footprints show a spread-out influence compared to others. Figure 16. Example of mole fraction contribution to the NOAA tower flask receptor over the 3day back trajectory. The ym summed across the entire footprint area represents the total modeled mole fraction anomaly at the receptor location after influence from neighboring regions. We show this estimate for every receptor day and compare this to NOAA tower flask background-corrected anomalies (Figure 17). STILT underestimates NOAA flask observations significantly. More analysis is needed to determine the validity of these estimates, as we cannot unambiguously determine whether the emission estimates are significantly underestimated or there are other factors contributing to these low anomalies. Incorporating the aircraft data and the TCCON retrievals in our STILT analysis will be helpful in determining whether the high C3H8 and C2H6 we see in the tower data is due to the presence of highly local emissions (as this will result in highly elevated mole fractions at the surface) or whether our emissions prior is underestimated. 41 Figure 17. STILT-modeled receptor anomaly mole fraction compared to NOAA flask backgroundcorrected anomaly. Only including tower observations here. Background described in the methods. We estimate a scaling factor directly related to the missing emissions using our Bayesian model. We start by estimating a scaling factor for the entire footprint region (all oil and gas basins included in the emissions grid, Figure 13). We simply use the receptor anomalies (Figure 17) to do this. Our HMC sampling was successful; using bebi103’s stan.check_all_diagnostics function, our sampling had effective sample size for all parameters (based on the suggestion of 50 effective samples per split chain)23 and 0 out of 4000 iterations ended with a divergence or saturated the maximum tree depth with no other indication of pathological behavior. The 95% credible interval of the scaling factor parameter samples is [2.9, 5.8] for C2H6 and [3.2, 6.2] for C3H8 (Figure 18). Using the 50th percentile of the samples, this corresponds to 5-6 Tg/yr of C3H8 and C2H6 for the entire footprint area. Based on previous studies, this is likely an overestimate. Incorporating additional datasets in our STILT analysis such as aircraft and TCCON will be invaluable in determining the magnitude of these regional emissions. 42 Figure 18. Posterior samples for x scalar parameter and s for C2H6. We performed posterior predictive checks, which involve drawing parameter values out of the posterior, using those parameters in the likelihood to generate a pseudo dataset, and repeat. This allows us to see whether our Bayesian model can produce the observed data. Below, we show the posterior predictive checks for our analysis (Figure 19). The majority of the measured C3H8 and C2H6 NOAA data fell into the 30th and 50th percentile of the simulated Bayesian model data. Figure 19. Posterior predictive check of C3H8 and C2H6 NOAA flask anomalies. Posterior predictive checks are explained in the text above. The pseudo data are shown in blue with 30, 50, 70, and 99th percentiles. 43 4.4. Future work We plan to extend the STILT-modeled framework to the column and aircraft measured C2H6 and C3H8 to diagnose why STILT produces very low mole fraction anomalies compared with the tower observations. One hypothesis, is that a large emission is occurring in close proximity to the site that is not captured in our emissions prior. If this is the case, we anticipate that the column observations and those obtained in situ at higher altitudes will show much less of a divergence from these observaitons. We also plan to expand our Bayesian analysis to find independent emissions scalars for each basin (ie, which basin has the most impact on the observations and what emissions lead to the observations). We will further constrain our prior by including TCCON in the inversion, and need to finish STILT modeling for TCCON columns. This is more computationally intense as we need to advect air from multiple altitude levels. Author Contributions J.L.L. created ginput-devel to incorporate chemical profiles into VMR. H.A.P. employed GGG2020 to create TCCON retrievals and conducted additional post-processing. D.W. provided guidance in running STILT for NOAA flasks, and working on code to run STILT using DMF columns from TCCON. A.L.T. ran GEOS-Chem simulations for TCCON priors, processed NOAA flask and TCCON data, ran STILT, prepared ym, created Bayesian model and ran HMC calculations. References (1) U.S. Energy Information Administration. Petroleum & Other Liquids: Oklahoma Field Production of Crude Oil, 2021. https://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?f=M&n=PET&s=MCRFPOK1 (accessed 2021-12-17). (2) U.S. Energy Information Administration. Natural Gas: Oklahoma Natural Gas Marketed Production, 2021. https://www.eia.gov/dnav/ng/hist/n9050ok2a.htm. (3) Wunch, D.; Toon, G. C.; Blavier, J.-F. L.; Washenfelder, R. A.; Notholt, J.; Connor, B. J.; Griffith, D. W. T.; Sherlock, V.; Wennberg, P. O. The Total Carbon Column Observing Network. Philos. Trans. R. Soc. Math. Phys. Eng. Sci. 2011, 369 (1943), 2087–2112. https://doi.org/10.1098/rsta.2010.0240. (4) Laughner, J. 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Methane Emissions from US Low Production Oil and Natural Gas Well Sites. Nat. Commun. 2022, 13 (1), 2085. https://doi.org/10.1038/s41467-022-29709-3. (13) Stan Development Team. Stan Modeling Language Users Guide and Reference Manual, 2021. https://mc-stan.org. (14) Stan Dev Team. CmdStanPy (0.9.76), 2021. https://pypi.org/project/cmdstanpy. (15) Gelman, A. Bayesian Data Analysis, Third edition.; Chapman & Hall/CRC texts in statistical science; CRC Press: Boca Raton, 2014. 45 (16) Kumar, R.; Carroll, C.; Hartikainen, A.; Martin, O. ArviZ a Unified Library for Exploratory Analysis of Bayesian Models in Python. J. Open Source Softw. 2019, 4 (33), 1143. https://doi.org/10.21105/joss.01143. (17) Bois, J. Justinbois/Bebi103: 0.1.0, 2020. https://doi.org/10.22002/D1.1615. (18) Rudiger, P.; Stevens, J.-L.; Bednar, J. 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Validating Bayesian Inference Algorithms with Simulation-Based Calibration. ArXiv180406788 Stat 2020. 46 Appendix S Supplementary Information for “Hydrocarbon Tracers Suggest Methane Emissions from Fossil Sources Occur Predominately Before Gas Processing and that Petroleum Plays Are a Significant Source” S1. Economics and Production of Oil & Natural Gas The development of the hydraulic fracturing (fracking) technique has led to a widespread increase in the production of associated and non-associated natural gas,1 as well as natural gas liquids, or NGLs (Figure S1, left and Figure S2). NGLs are extracted with raw gas and are, just after extraction, often separated from the stream to yield consumer-grade natural gas and the more valuable alkane liquids.2 Basins with petroleum typically have a larger composition of ethane and propane and other NGLs, whereas “dry” basins, such as Fayetteville and Appalachian in the U.S., tend to provide mostly dry natural gas with low fractions of NGLs.3 By volume, ethane, C2H6, is the second most abundant component of natural gas after CH4, while propane (C3H8) is the third most abundant.4 The fraction of C2H6 (but not C3H8) removed during gas processing changes significantly over time. Over the last 10 years, the dramatic increase of C2H6 production (Figure S1, left) has exceeded domestic demand or ability to export it abroad,5 resulting in C2H6 prices generally at or below natural gas since 2012 (Figure S1, right).6,7 As a result, it is often more economical to sell C2H6 as natural gas rather than separate it from the raw stream. Producers can increase the amount of C2H6 they sell as natural gas by “rejecting” it (not recovering it). Rejection of C2H6 has continued to grow almost continuously over the past decade (Figure S1, right) resulting in increasing abundance of C2H6 in the natural gas distribution system. Figure S1. Economic trends of natural gas and natural gas liquids. Left: Trends in natural gas and hydrocarbon production (EIA) and total ethane summed with rejected ethane modeled by OPIS, Point Logic, provided by IHS Markit. Right: The value of ethane compared to natural gas 47 4500 4000 3500 3000 2500 2000 1500 1000 500 0 500 450 400 350 300 250 200 150 100 50 0 1990 1995 Crude Oil 2000 2005 2010 Natural Gas Liquids 2015 Natural Gas Liquids & Other primary Oil (Mt) Crude Oil Production (Mt) represented by fractionation spread (frac spread) on the left axis. Ethane rejection in the U.S. and major U.S. refining areas is plotted on the right axis. (Data by OPIS, Point Logic, provided by IHS Markit.) 2019 Other primary oil Figure S2. Global oil production. Data provided by IEA (https://www.iea.org/fuels-andtechnologies/oil). 48 Figure S3. Top Natural Gas-Producing US basins/Countries and their corresponding oil production. Top: Oil and gas production for the top 7 natural gas producing basins that account for 86% of total U.S. natural gas production.8,9 Bottom: Global oil and gas production for the top 5 natural gas producing countries that account for 50% of global natural gas production.10,11 Figure S4. Observed pipeline composition in Playa del Rey and ethane rejection trends. Left: The ratio of propane/methane and ethane/methane measured in natural gas withdrawn from Playa del Rey in Southern California,12 compared to U.S. ethane rejection (see Figure S1 for more 49 information on rejection; data provided by IHS Markit). Right: The ratio of U.S. propane production and total ethane production (including rejection, ER). The production data is provided by EIA13,14s and the rejection data is provided by IHS Markit. The in-situ observed ratio is calculated from NOAA-ongoing observations, see Figure S9. S2. NOAA & FRAPPE Observations S2.1 Processing and statistical methods Ethane and propane mole fraction data from aircraft measurements, tall tower, and surface flasks are publicly available at https://gml.noaa.gov/ccgg/arc/?id=155. Methane mole fraction data is publicly available at https://gml.noaa.gov/ccgg/obspack/data.php?Id=obspack_multispecies_1_CCGGAircraftFlask_v2.0_2021-02-09 , https://gml.noaa.gov/ccgg/obspack/data.php?Id=obspack_multispecies_1_CCGGSurfaceFlask_v2.0_2021-02-09, and https://gml.noaa.gov/ccgg/obspack/data.php?Id=obspack_multispecies_1_CCGGTowerInsitu_v1.0_2018-02-08. We first discuss NOAA ongoing observations. We use measurement quality flags labeled as either preliminary or good sampling and analysis only. Some sites had an unequal number of quality measurements between alkane species, so we match UTC time stamps that are shared between each species to avoid sampling bias. We drop any corresponding paired measurements of CH4, C2H6 and C3H8 that are labeled as NaN (all three pairs are dropped). Figure S5 shows the spatial location of the NOAA ongoing observation sites used in this analysis, and Table S1 lists the temporal and spatial coverage offered at each site. Most sites offered a few measurements each week for the years indicated. State Boundary Oil Wells Gas Wells Tight Oil & Shale Gas Plays Sedimentary Basins Figure S5. Major Oil/Natural Gas Shale Plays in the U.S. & NOAA ongoing measurement locations. Approximate geographical locations of NOAA ongoing measurement locations are shown in the blue stars on the map. Not pictured is East Trout Lake (ETL) site, located in 50 Saskatchewan, Canada (54.3541N, 104.9868W). Well and basin layers provided by https://atlas.eia.gov/apps/all-energy-infrastructure-and-resources/explore . Table S1. Sites for NOAA Ongoing Observations in the U.S. Site Site Years Measurement Processing Location Abbreviation Method lab Homer, IL HIL 2015 Aircraft/Tower CCGG, HATS 2018 Lamont, SGP 2006 Aircraft/Tower CCGG OK 2017 Dahlen, DND 2014 Aircraft/Tower CCGG, ND HATS 2016 East Trout ETL 2014 Aircraft/Tower CCGG, Lake, HATS Canada 2018 Wendover, UTA 2006 Tower CCGG, UT ARL 2016 Boulder, BAO 2014 Tower CCGG, CO HATS 2016 Moody, WKT 2015 Tower CCGG, TX HATS 2018 Sinton, TGC 2015 Aircraft/Tower CCGG, TX HATS 2018 Niwot NWR 2005- Tower CCGG, Ridge, CO 2014 ARL For FRAPPE, we also use 1000 meters as a marker for the boundary layer, and analyze measurements taken above it. We also drop any corresponding paired measurements of CH4, C2H6 and C3H8 that are labeled as NaN (all three pairs are dropped). Figure S6 shows the spatial location of the FRAPPE observations (after filtering) in Colorado. 51 Figure S6. FRAPPE observations. The outline of Colorado state is shown in blue. We show data already pre-processed and filtered for fresh emissions, as discussed in this section. To better quantify geophysical variability and generate a confidence interval in the correlation in measured mole fractions between C2H6 and C3H8, we implement a pairs bootstrap to generate replicates of C2H6 and C3H8 observations for NOAA and FRAPPE observations. We draw random samples of pairs of C2H6 and C3H8, where instead of drawing two random samples of each array, we draw the same indices from both arrays so we end up with paired samples, since C2H6 and C3H8 were measured together and we want to compute the correlation. We draw samples the size of the dataset, then compute the slope of the correlation. We repeat this 10,000 times. As shown for different scenarios below, we perform this bootstrap for individual sites separately, as well as all sites combined. The confidence interval reported for correlations between C2H6, C3H8, and CH4 anomalies is the 95% CI of the 10,000 samples. The CIs calculated from the bootstrapped samples are much broader than those calculated assuming the noise in the measurements is dominated by analytical errors. This suggests that geophysical noise induced by differences in transport and chemistry dominates the statistics. S2.2 Chemical aging approach to determining methane background We take a chemical aging approach to defining the threshold between samples associated with fresh emissions (unaged) and photochemically aged emissions. As in Parrish et al 2018,15 we observe both fresh and aged regimes (Figure S7 below). We chose the 50th percentile of C3H8 as the demarcation between these regimes (about 103 ppt) and show in Figure S10 that our analysis of the ethane and propane ratio to methane is not terribly sensitive to the choice. This threshold will clearly depend on the fraction of samples obtained in the two regimes. 52 Figure S7. Identifying fresh emission chemical regime in NOAA and FRAPPE campaigns. Left: Varying C3H8 percentiles at the NOAA SGP site. The inflection point between aged and fresh emission regime is visually contained within varying the C3H8 percentile cutoff by ± 10%. We chose the 50th percentile of C3H8 as the demarcation between these regimes (about 103 ppt). Right: C3H8 vs C2H6 using FRAPPE data (already pre-processed, as described in the methods in the main text). FRAPPE observations are quite consistent with NOAA, hence we use the same C3H8 demarcation between the aged and fresh chemical regime. After filtering for fresh emissions using C3H8 percentile method, two NOAA observation sites (NWR and UTA) only showed aged emissions (Figure S8). Consequently, these sites were not used in the subsequent analysis. Figure S8. NOAA C3H8 vs C2H6 after filtering for fresh emissions. We used C3H8 50th percentile as a marker for fresh emissions (please see details in text above). Sites NWR and UTA only had C3H8 mole fractions below this demarcation and were assumed to be affected only by aged emissions, and as such, were excluded from further analysis. 53 After filtering for fresh emissions using C3H8 percentile method, the cross plot of C3H8 vs C2H6 is similar for all NOAA sites, NOAA SGP only, and FRAPPE observations (Figure S9). Figure S9. C3H8 vs C2H6 after filtering for fresh oil and gas emissions. Left: The filtering method is described in Section 3.1. We show observations for all NOAA sites (2005-2018, see Table S1), NOAA for SGP site only (2006-2018 Oklahoma tower and aircraft observations), and FRAPPE campaign (2014 aircraft observations around Colorado). Top: FRAPPE linear least squares slope 95% CI is [0.76, 0.87] (ppb/ppb, R2 = 0.97) compared to [0.63, 0.70] (ppb/ppb, R2 = 0.98) for all NOAA sites. Variability in the slope for both FRAPPE and NOAA is given by a pairs bootstrap analysis, described in Section 2.1. Right: Slope before 2012 (2005-2011): [0.62, 0.67] (95% CI), R2 = 0.98. Slope after 2012 (2012-2018): [0.63, 0.71] (95% CI), R2 = 0.98. We use data from SGP, TGC, ETL, HIL, DND, BAO, and WKT sites (see Table S1) before filtering for air influenced by fresh oil/gas emissions, which is shown here. We use both tower and aircraft data. We use pairs bootstrapping to arrive at confidence intervals, described in detail in Section 2.1. After identifying the fresh emissions, we defined a background for CH4 observations and constructed CH4 anomalies by doing the following: - Find corresponding co-CH4 measurements in the aged air regime as identified by C3H8 mole fraction (below 103 ppt C3H8). Interpolate this CH4 array to the full timeseries using time to obtain a CH4 background. Subtract this interpolated background from the full CH4 array to obtain a CH4 anomaly. Note that because the CH4 lifetime is much longer than either C2H6 or C3H8, the differences are much smaller. Since we only focus on the linear part of the curve, our analysis is not terribly sensitive to how the CH4 anomaly is determined (it simply produces varying intercepts, see our quantitative analysis on the impact on the slope in Figure S10). Again, to get C3H8/ C2H6, we only consider the fresh emission 54 regime (beyond 103 ppt C3H8). Figure S10 shows our calculated CH4 background and CH4 anomalies for the NOAA SGP site (near Lamont, OK). Figure S10. Background estimate for CH4 at NOAA SGP site. Left: Using 50% ±10% percentile cutoff of C3H8 has a minimal effect on the background CH4 estimation. Right: C3H8 vs CH4 Anomaly at NOAA SGP site. A CH4 anomaly is calculated by linearly interpolating the estimated CH4 background to the raw CH4 measurement timescale. The interpolated background is then subtracted from the raw CH4 measurements. Using 50% ±10% percentile cutoff of C3H8 has a minimal effect on CH4 anomaly cross plots. Using a pairs bootstrap approach (see Section S2.1), we generate thousands of slope replicates and calculate the following 95% CIs for the slope using the following C3H8 percentile cutoffs: [0.0458, 0.0526] (30th percentile); [0.0460, 0.0534] (40th percentile); [0.0481, 0.0563] (50th percentile). Below in Figure S11, we show the result of our CH4 background calculations for each NOAA site. 55 56 Figure S11. Methane vs time for NOAA sites. The estimated background is shown in red. Raw CH4 data is shown in blue. The background was calculated using 50% C3H8 percentile cutoff method. S2.3 Methane anomaly plots for NOAA and FRAPPE campaigns Below, we show the results of our CH4 anomaly calculations for NOAA and FRAPPE observations using the methods described in Section 2.2 (above). First, we show correlations for individual NOAA sites (Figures S12, S13), followed by a comparison between NOAA SGP site (Oklahoma site) and FRAPPE observations (Figure S14). 57 Figure S12. C2H6 vs CH4 anomaly for NOAA sites. The data for each site were filtered using the chemical aging regime to filter for fresh emissions and to construct CH4 anomalies (Section 2.2). See Table S1 for a description of site location/observation type. We also ran a bootstrap for each individual site (bootstrapping methods, main text). The 95% CI slopes (ppb/ppb) are as follows: BAO: [0.0833, 0.1449], R2 = 0.91; DND: [0.0289, 0.1205], R2 = 0.63; ETL: [0.0030, 0.0176], R2 58 = 0.46; HIL: [0.0116, 0.0313], R2 = 0.56; TGC: [0.0400, 0.0730], R2 = 0.74; WKT: [0.0324, 0.0510], R2 = 0.75; SGP: [0.0645, 0.0749], R2 = 0.86. 59 Figure S13. C3H8 vs CH4 anomaly for NOAA sites. The data for each site were filtered using the chemical aging regime to filter for fresh emissions and to construct CH4 anomalies (Section 2.2). See Table S1 for a description of site location/observation type. We also ran a bootstrap for each individual site (bootstrapping methods, main text). The 95% CI slopes (ppb/ppb) are as follows: BAO: [0.0587, 0.0922], R2 = 0.91; DND: [0.0221, 0.1003], R2 = 0.61; ETL: [0.0013, 0.0136], R2 = 0.41; HIL: [0.0078, 0.0216], R2 = 0.54; TGC: [0.0228, 0.0506], R2 = 0.68; WKT: [0.0195, 0.0321], R2 = 0.71; SGP: [0.0426, 0.0499], R2 = 0.83. 60 Figure S14. C2H6 vs CH4 anomaly for NOAA SGP site and FRAPPE study. We use the chemical aging approach defined in Section 3.1 to identify C3H8 and CH4 observations within a fresh oil and gas emissions chemical regime. We construct CH4 background-corrected anomalies as described in SI Section S2. Results with C2H6 are similar and shown in Figure S9. NOAA observations for SGP site (Oklahoma, Table S1) are shown here. We show correlations between 2006-2011, labeled as “NOAA SGP < 2012” (HIPPO takes place between 2009-2011), 2013-2015 (FRAPPE takes place in 2014), and 2016-2018 (ATom time period). Left: The slope of the correlation between C3H8 and CH4 anomaly for NOAA observations before 2012 is [0.031, 0.040] ppb/ppb, R2 = 0.85; between 2013-2015 is [0.045, 0.084], R2 = 0.82; and between 2016-2018 is [0.039, 0.059], R2 = 0.86. FRAPPE is [0.063, 0.085] ppb/ppb, R2 = 0.83. The slope of the correlation for all years of NOAA is [0.043, 0.050] ppb/ppb, R2 = 0.83. C3H8 vs CH4. Right: C2H6 vs CH4 The FRAPPE slope (95% CI, ppb/ppb) is [0.0763, 0.1047], R2 = 0.85. C2H6 vs CH4 NOAA slope for all years is [0.0647, 0.0749], R2 = 0.86. The C2H6 vs CH4 slope before 2012 is [0.047, 0.060], R2= 0.85; from 2013-2015 is [0.066, 0.143], R2 = 0.85; and from 2016-2018 is [0.058, 0.084], R2 = 0.88. S2.4 Maps of FRAPPE and NOAA SGP observations compared to oil and gas sites Below, we show the location of the NOAA samples taken at the SGP site in Oklahoma, which include a combination of aircraft and tower measurements (Figure S15). We add the approximate location on top of a USGS map of oil and gas sites in Oklahoma, using coordinates for Lamont and Billings for reference (Figure S16), where we see that the SGP measurements are taken around a mix of oil and gas sites. We include a figure of Oklahoma oil and gas production by county (Figure S17), where we see widespread surrounding oil and gas production. 61 Figure S15. NOAA observations at SGP site (Oklahoma). The observations shown here are preprocessed and filtered for fresh emissions as discussed in the methods section in the main body. OKLAHOMA GEOLOGICAL SURVEY Charles J. Mankin, Director 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 Abell N Abell W Ada District Ada District East Ada N Ada S Ada SW Adair Adams District Adamson NE Agra Agra N Agra NW Agra S Agra W Alabama Alabama E Alabama Middle Alabama SE Alabama S Alabama SW Alabama W Alamo Alamo E Alamo NW Alamo SE Alamo S Alamo SW Alamo W Alden Alden NE Alden N Aledo Aledo SE Aledo S Aledo SW Aledo W Alex NW Alko Allen District Allen NW Alluwe Almeda Alpha Alpha SE Alsuma District Altona Altus Altus E Altus NE Altus W Alva Alva E Alva NE Alva N Alva S Amber Amber NE Amber N Amorita Amorita NE Amorita N Amorita S Anadarko W Antelope Antelope NW Anthon Anthon NE Anthon NW Anthon SE Anthon SW Antioch Antioch District East Antioch NE Antioch N Antioch S Apache Apache E Apache N Apache SE Apache S Apache SW Apache Townsite Apperson SW Arapaho Arapaho NE Arcadia Arcadia E Arcadia NW Arcadia SE Arcadia S Arcadia SW Ardmore Ardmore E Ardmore SW Ardmore W Arlington NW Arlington SE Arlington S Arlington W Arnett Arnett Airport NE Arnett E Arnett NE Arnett SE Arnett S Arnett SW Arnoldview Arnoldview E Arnoldview NW Arnoldview SE Arpelar N Asher Asher N Asher SE Asher S Asher W Ashland Ashland N Ashland S Ashley SE Asp NW Asp SE Asp W Asphaltum Atlantic Atlantic N Atlee Atlee NW Atoka Townsite E Atoka Townsite N Atoka Townsite SE Atoka Townsite S Atwood E Atwood N Atwood NW Atwood SE Atwood SW Atwood Townsite Atwood W Autwine Autwine E Autwine SE Autwine SW Autwine W Avant Avant W Avard E Avard NW Avery Avery NE Avery N Avery SW Avoca E Avoca SW Aydelotte Aydelotte W Aylesworth Aylesworth District SE 18N 3W 18N 3W 3N 6E 3N 7E 4N 6E 3N 6E 3N 6E 26N 15E 8N 9E 17E 16N 5E 17N 5E 17N 4E 16N 4E 17N 3E 9N 11E 9N 11E 9N 11E 9N 11E 9N 11E 9N 11E 10N 11E 7N 1W 7N 1W 7N 1W 7N 1W 7N 1W 7N 1W 7N 2W 6N 13W 6N 13W 13W 16N 18W 15N 18W 15N 18W 15N 19W 16N 19W 5N 6W 23N 9E 5N 7E 8E 25N 17E 26N 11E 16N 8W 15N 8W 19N 14E 16N 9W 1N 20W 1N 19W 1N 19W 2N 21W 27N 14W 26N 13W 27N 13W 28N 14W 26N 13W 8N 7W 8N 6W 9N 7W 28N 10W 28N 10W 29N 10W 28N 11W 7N 11W 23N 2W 23N 2W 14N 17W 15N 17W 15N 17W 14N 16W 14N 18W 3N 2W 3N 1W 4N 2W 3N 2W 3N 5N 12W 5N 11W 5N 11W 5N 11W 4N 11W 4N 11W 5N 11W 26N 5E 13N 17W 13N 16W 14N 1W 14N 1W 14N 1W 13N 1W 13N 1W 13N 2W 5S 1E 5S 2E 5S 1E 4S 1E 13N 5E 13N 6E 13N 6E 13N 5E 19N 24W 19N 24W 20N 23W 20N 24W 19N 23W 19N 24W 19N 25W 5N 2W 5N 2W 5N 2W 5N 2W 6N 13E 6N 4E 6N 4E 6N 4E 6N 4E 6N 3E 4N 12E 4N 12E 3N 12E 27N 12W 20N 20N 1W 20N 2W 3S 4W 25N 8E 25N 8E 5S 4W 5S 5W 2S 12E 2S 11E 2S 12E 3S 11E 5N 9E 6N 9E 6N 9E 5N 10E 5N 9E 6N 9E 9E 26N 1E 26N 1E 25N 1E 26N 1W 26N 1E 23N 12E 23N 11E 26N 14W 26N 16W 17N 6E 18N 6E 17N 6E 16N 5E 4E 6N 3E 11N 4E 11N 3E 6S 6E 6S 7E 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 Bado E Bado N Bado SE Bado S Bakersburg W Bald Bald Hill Bald S Balko NE Balko N Balko S Balko SW Balko W Bandwheel Bandwheel E Banner NE Banner School NE Banzet NW Barker Barnes Barnes E Barnes N Barnes NW Barnes SE Barnes W Barnsdall Barnsdall S Barnsdall W Bartlesville-Dewey Baum Baum N Bearden Bearden E Bearden NE Bearden N Bearden NW Beaver E Beaver Island Beaver Island NE Beaver Island SW Beaver NE Beaver N Beaver S Beaver W Bebee E Bebee NE Bebee SE Bebee-Konawa SW Beggs District Beidleman Beidleman W Beland Belford NW Belle Isle Belleview Bellmont Bellmont N Bellmont W Bellvue S Bengal NE Benjamin Benmartin Berlin SE Berwyn Berwyn SW Bessie E Bethany Bethany SE Bethany S Bethel Bethel E Bethel NE Bethel N Bethel SE Big Bend Big Bend E Big Bend N Big Bend W Big Pond Big Pond District East Big Pond S Big Pond SW Bigham Bigham S Bigham SW Bighorse NE Bilby District Billings Billings E Billings NE Billings NW Billings Townsite Billings W Binger Binger NE Binger S Birch Creek Birch Creek S Birch Creek W Bird Creek Bishop Bixby-Jenks District Black Dog Black Dog District South Black Dog W Blackburn Blackburn E Blackburn NE Blackburn N Blackburn SE Blackburn S Blackland Blackland NE Blackland SW Blackwell Blackwell District East Blackwell NE Blackwell NW Blackwell SE Blackwell W Blackwell-Newkirk Gas Area Blakely Blakely E Blakely N Blakely SE Blanchard NE Blanchard N Blanchard NW Blanco Blanco S Bloomington Bloomington E Bloomington N Bloomington S Blucher Blue Jacket N Blue Jacket W Bluff Creek Blumenshine Blumenshine E Blumenshine W 20N 14W 21N 14W 20N 14W 20N 14W 5N 18C 2N 15E 14N 14E 1N 15E 2N 23C 2N 22C 1N 22C 1N 21C 2N 22C 24N 8E 24N 9E 27N 4W 15N 4E 28N 19E 23N 7E 23N 3W 23N 3W 24N 3W 24N 3W 23N 3W 23N 3W 24N 11E 23N 11E 24N 10E 27N 13E 3S 3S 3E 10N 9E 10N 9E 10N 9E 10N 9E 10N 8E 4N 24C 23N 3E 23N 4E 23N 3E 5N 24C 5N 23C 4N 24C 4N 22C 5N 5E 5N 5E 4N 5E 5E 15N 12E 13N 10E 13N 10E 14N 17E 24N 4E 12N 3W 7S 3W 11N 5E 12N 5E 11N 5E 17N 8E 5N 21E 8N 16N 18E 11N 23W 3S 2E 3S 2E 11N 16W 12N 4W 12N 4W 12N 4W 9N 7E 9N 8E 10N 7E 10N 7E 9N 8E 25N 3E 25N 3E 25N 3E 25N 2E 15N 7E 15N 8E 14N 8E 14N 7E 11N 10E 10N 10E 10N 10E 27N 12E 19N 15E 23N 2W 24N 2W 24N 2W 24N 2W 24N 2W 23N 2W 10N 10W 10N 9W 9N 11W 24N 10E 23N 10E 24N 10E 21N 13E 17N 26W 18N 13E 22N 8E 22N 8E 22N 8E 22N 7E 22N 7E 22N 7E 22N 7E 22N 7E 22N 7E 27N 7E 27N 8E 27N 7E 27N 1W 27N 1E 27N 1E 28N 2W 26N 1E 27N 2W 28N 1E 11N 10E 12N 11E 12N 10E 11N 11E 8N 3W 8N 4W 8N 5W 3N 14E 3N 14E 6N 23W 6N 23W 7N 23W 6N 23W 14N 27N 21E 27N 21E 29N 2W 2N 10W 2N 9W 2N 10W 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 Boar Creek Boar Creek E Boggy Depot E Boggy Depot SE Boiling Springs N Bokoshe SE Bokoshe S Bolen Spring Boley Boley E Boley NW Boley S Boomer Lake NE Boomer Lake NW Boone SE Boston Boston E Boston N Boston W Boulanger NW Bowlegs Bowlegs District SW Bowring E Bowring SE Boyd E Boyd S Boynton Boynton NW Boynton W Brady Brady SW Braman Braman District SE Braman NE Braman N Braman NW Braman SW Braman W Branstetter District Bray SE Bray S Bray SW Breathwaite Brent Brewer S Brick Bridgeport Brinkman S Brinton Bristow Bristow District South Bristow E Bristow NE Bristow N Bristow NW Bristow Townsite Bristow W Britton Britton NE Britton S Britton W Brock Brock E Brock N Brock NW Brock SE Broken Arrow District Brooken Brooksville Brooksville E Brooksville N Brooksville SE Brooksville S Brooksville SW Brookville NW Brown Brown E Brown Middle Brown S Brown SW Broxton N Broxton NW Broxton S Broxton SW Broxton W Broyles Bruce Bruce District East Brushy Mountain Bryan Bryan NE Bryan N Bryan NW Bryan SE Bryan SW Bryan W Bryant Bryant E Bryant SE Bryant S Buell Buena Vista NE Buena Vista N Buena Vista S Buffalo Buffalo E Buffalo Mountain Buffalo Mountain S Buffalo N Buffalo NW Buffalo SE Buffalo SW Buffalohead (abd.) Buffalohead W Bulldog Bulldog District North Burbank Burbank SW Burbank Townsite Burlington NE Burlington N Burlington NW Burlington S Burlington SW Burlington W Burmah N Burnett Burnett NW Burnett S Burnett W Burney E Burneyville NE Burneyville W Burns Flat Burt SW Burton SE Butler-Custer Butler-Custer W Butner Butterly Butterly NE Butterly N Butterly NW Butterly S Butterly SW Byars E Byars NE Byars NW Byars S Byars SW Byng W Byron SE Byron S 22N 22N 3S 3S 25N 8N 8N 25N 12N 12N 12N 12N 20N 20N 5N 21N 22N 22N 22N 29N 8N 28N 27N 3N 2N 14N 14N 14N 2N 2N 28N 28N 29N 29N 29N 28N 28N 22N 2N 2N 11N 10N 4N 17N 12N 6N 13N 16N 15N 16N 16N 16N 16N 16N 16N 13N 13N 12N 13N 5S 5S 5S 5S 6S 18N 9N 8N 9N 8N 8N 8N 9N 20N 20N 20N 20N 20N 7N 6N 6N 6N 6N 18N 17N 17N 13N 20N 20N 21N 20N 20N 20N 20N 11N 11N 10N 10N 23N 22N 22N 21N 27N 27N 4N 3N 28N 28N 27N 27N 24N 24N 24N 24N 26N 25N 26N 29N 28N 29N 28N 27N 28N 16N 8N 8N 8N 8N 11N 7S 7S 10N 1S 14N 13N 9N 1N 1N 1N 1N 1N 1N 5N 5N 5N 4N 5N 4N 28N 28N 9E 9E 10E 10E 20W 25E 24E 18E 8E 7E 8E 2E 2E 12W 7E 8E 7E 7E 10E 6E 6E 11E 12E 21C 20C 16E 15E 15E 1W 1W 1W 1W 1W 1W 2W 1W 2W 11E 5W 6W 6W 18W 24E 14E 18E 12W 22W 12E 9E 9E 10E 9E 9E 8E 9E 8E 3W 3W 3W 4W 1E 1E 1E 1W 1E 14E 18E 3E 3E 3E 3E 3E 3E 3E 4W 4W 4W 4W 4W 12W 12W 11W 12W 12W 4E 9E 9E 18E 5E 6E 5E 5E 5E 5E 5E 12E 12E 12E 12E 9E 5E 5E 5E 22W 22W 20E 21E 22W 23W 22W 23W 3E 3E 9E 9E 6E 5E 5E 11W 12W 12W 12W 12W 11W 18W 2E 2E 2E 2E 14E 1W 1W 18W 18W 9C 18W 18W 8E 1E 1E 1E 1E 1E 1E 3E 3E 2E 2E 2E 5E 10W 10W 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 Chilocco E 29N Chilocco SE 29N Chimney Mountain 10N Chisney S 8N Chisum S 5N Chitwood 4N Chitwood NW 5N Chitwood S 4N Choate Prairie 8N Choctaw 12N Choctaw NE 12N Choctaw N 12N Choctaw S 11N Choska 16N Choska NW 16N Cimarron City E 16N Citra 4N 4N Citra NE 4N Civit 4N Civit E 4N Civit NE 4N Civit N 4N Civit NW 3N Civit SE 3N Civit S 3N Civit SW 4N Civit W 21N Claremore 21N Claremore E 1S Clarita 1N Clarita District 29N Clark Creek 29N Clark Creek E 29N Clark Creek W 10N Clay City SE 14N Clayton NW 8N Clear Brook 8N Clear Brook SW 8N Clear Brook W 2N Clear Lake District 2N Clear Lake District West 3N Clear Lake N 10N Clearview District 11N Clearview N 11N Clearview W 21N Cleveland 21N Cleveland E 12N Clinton 12N Clinton E 12N Clinton N 11N Clinton S 9N Cloudchief NW 27N Clyde E 27N Clyde S 1N Coalgate 1N Coalgate E 1N Coalgate NE 1N Coalgate N 1N Coalgate SW Coalgate W 11N Coalton 12N Coalton N 21N Cody 21N Cody SW 29N Coffeyville S 14N Cole District 22N Collinsville 11N Colony NW 10N Colony W 2S Comanche Lake Comanche Lake District South 2S 2S Comanche Lake N 2N Como 2N Como NW 1N Como SE 1N Como SW 16N Concharty Hills 13N Concho 13N Concho NE 14N Concho N Conway NW 3N Conway S 26N Coodys Bluff 14N Coon Creek 15N Coon Creek NE 15N Coon Creek N 15N Coon Creek NW 14N Coon Creek W 17N Cooper 6N Corbett NE 6N Corbett NW 6N Corbett SE 6N Corbett S 6N Corbett W 9N Cordell S 16N Corine District 11N Corn 9N Corn District 5S Cornish SE 5S Cornish SW 4S Cornish W 17N Cottingham E 17N Cottingham NE 4S Cottonwood Creek 19N Council Creek 20N Council Creek N 19N Council Creek SE 19N Council Creek SW 13N Council Hill District 12N Council Hill S 12N Council Hill Townsite 6S Courtney NE 7S Courtney SE 21N Covington S 21N Covington W 9N Cowden S 17N Coweta District 17N Coyle 17N Coyle Middle 18N Coyle N 18N Coyle NW 17N Coyle SE 17N Coyle S 17N Coyle W 15N Crane SE 16N Crawford NW 17N Crescent E 23N Crescent Star 23N Crescent Star S 25N Crescent Valley W 18N Crescent-Lovell 6N Criner SW 6N Criner W 10N Cromwell 10N Cromwell E 10N Cromwell S 6N Cross Roads NE 6N Cross Roads N 1N Cruce N 1N Cruce NW 1N Cruce W 5S Cumberland 9N Cummings 26N Curl Creek Curty 5N Curty SE 5N Curty SW 18N Cushing 17N Cushing Townsite 14N Custer City E 14N Custer City N 13N Custer City SE 13N Custer City S 5N Cyril NW 5N Cyril W 3E 3E 7E 3E 3E 6W 7W 6W 14E 1W 1W 1W 1W 16E 16E 3W 9E 9E 2E 2E 2E 2E 1E 2E 2E 1E 1E 15E 17E 8E 8E 23W 22W 24W 1W 1E 1W 1W 1W 26C 25C 26C 10E 10E 10E 8E 8E 17W 16W 17W 17W 16W 5W 6W 10E 11E 11E 10E 10E 9E 14E 13E 6E 15E 15E 14E 15W 15W 7W 6W 7W 25C 24C 25C 24C 14E 8W 7W 7W 7E 7E 17E 1W 1W 1W 1W 1W 10W 1E 1E 1E 1E 1W 17W 16E 15W 3W 4W 5W 4W 4E 3E 1W 4E 4E 4E 3E 16E 16E 16E 2W 3W 4W 4W 15W 16E 1E 1E 2E 1E 1E 1E 1E 14W 25W 3W 5E 5E 5W 4W 4W 4W 8E 8E 8E 2E 2E 6W 6W 6W 7E 14E 15E 4W 4W 5W 7E 5E 15W 16W 15W 16W 10W 10W 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 Cabaniss NW Cache Creek Cache Creek N Cache Creek NW Cache Creek S Cache Creek W Caddo Caldwell California Creek Calumet E Calvin Calvin E Calvin N Calvin NW Calvin SE Calvin S Calvin W Camargo NW Camargo SW Cameron Campbell Camrick District Camrick Gas Area Canadian Canary Candy Creek Caney Caney NW Canton NW Canute N Canyon Creek Canyon Creek SE Canyon Creek S Capitol Hill S Caple N Caple S Capron Capron E Capron NE Capron N Capron NW Capron W Captain Creek N Captain Creek S Captain Creek W Carlton Lake W Carmel Carnegie NE Carnegie N Carnegie S Carnegie SW Carnegie W Carney SE Carney-Lincoln Carpenter Carpenter NE Carr City Carrier Carrier NW Carson Carson E Carson SE Carson W Carter Carter E Carter N Carter SE Carter SW Carter W Carthage Carthage District NE Carthage E Carthage Gas Area Carthage NW Casey Casey E Casey NE Casey N Castaneda Castaneda E Castaneda NW Castaneda S Castle Castle E Castle NW Castle SW Caston E Cat Tail Springs Cat Tail Springs E Catale District Catale E Catesby N Catoosa District Catoosa E Cedardale NE Cedardale NW Cedars Cement Cement SE Center Center NE Center NW Center S Center W Centerpoint Centerpoint SW Centerpoint W Centrahoma Centrahoma NE Central School NW Centralia E Centralia NE Ceres NE Ceres S Cestos Cestos SE Cestos S Cestos SW Chandler Chandler E Chandler NE Chandler NW Chandler S Chaney N Checotah Checotah District NW Checotah E Checotah SE Cheek Cheek NW Chelsea Cherokee S Cherokee SW Cherokee W Cherokita Trend Chester W Cheyenne Cheyenne Valley Cheyenne Valley S Cheyenne Valley W Cheyenne W Chickasha Chigley W Chiles Dome Chiles Dome SE Chiles Dome SW Chilocco 6N 3S 3S 3S 4S 3S 3S 29N 28N 13N 6N 6N 6N 6N 5N 5N 6N 18N 18N 7N 23N 1N 2N 8N 29N 24N 29N 29N 19N 11N 23N 23N 23N 11N 1N 28N 28N 29N 29N 29N 28N 14N 13N 13N 18N 1S 9N 8N 7N 6N 7N 15N 16N 12N 13N 8N 23N 24N 8N 8N 8N 8N 9N 8N 9N 8N 8N 8N 5N 6N 5N 5N 6N 21N 21N 21N 21N 5N 5N 6N 5N 11N 12N 12N 11N 6N 7N 7N 24N 24N 24N 20N 20N 24N 22N 9N 6N 5N 4N 4N 4N 4N 4N 9N 9N 9N 1N 2N 17N 27N 27N 24N 23N 19N 19N 19N 19N 14N 14N 14N 15N 14N 24N 11N 12N 11N 11N 5S 5S 24N 26N 26N 26N 27N 21N 13N 22N 21N 21N 12N 4N 1N 3N 3N 2N 29N 12E 10W 11W 11W 10W 11W 1E 4W 15E 8W 10E 10E 10E 10E 10E 10E 10E 21W 20W 26E 15W 20C 19C 16E 13E 12E 12E 12E 14W 20W 10E 10E 10E 3W 17C 17C 13W 12W 12W 13W 13W 13W 2E 2E 2E 24W 22W 13W 13W 14W 14W 14W 3E 3E 22W 20W 5E 8W 8W 12E 12E 12E 11E 22W 21W 22W 21W 22W 22W 10C 11C 11C 12C 10C 6E 6E 6E 6E 5C 6C 4C 5C 9E 9E 9E 9E 24E 2E 2E 18E 18E 26W 14E 15E 18W 18W 27E 9W 8W 5E 5E 4E 5E 4E 2E 2E 2E 10E 10E 1E 19E 19E 1W 1W 18W 17W 18W 19W 3E 4E 4E 4E 4E 25W 17E 16E 18E 17E 1W 1W 17E 11W 11W 13W 10W 17W 23W 14W 14W 15W 23W 8W 2E 9E 10E 9E 2E 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 Dacoma E Dague Dague NE Dague SE Dague S Daisy SE Daisy W Dale Dale NE Dale N Dale SW Dale W Dalton Dalton NE Dalton W Davenport N Davenport NW Davenport West District Davidson Davis Davis NE Davis N Davis S Davis SW Davis W Dawson District Deaner N Decherds Bend Decherds Bend N Decherds Bend NW Deer Creek Deer Creek S Deer Creek SW Deese NW Del City Delaware-Childers Dempsey Dempsey W Denver NE Denver SE Depew Depew E Depew N Depew NW Depew SE Depew Townsite Depew W Devol SE Dewar Dibble NE Dibble SE Dibble SW Dill Dill City Dill NE Dill S Dilworth District Dixie Dixie NW Doby Springs SE Doe Creek NW Dog Creek Dog Creek NE Dog Creek N Dog Creek SE Dog Creek S Dog Creek SW Dog Creek W Doga E Doga N Doga NW Doga SE Doga S Doga SW Dolberg District Dombey Dombey NW Dombey W Domes SW Domes-Pond Creek Donnelly N Donnelly W Douglas N Douglas SE Douglas S Douglas W Dougout Creek Dower E Dower N Dower SE Doyle E Driftwood SW Drum Creek Drum Creek N Drum Creek NW Drummond Ranch Drummond Ranch N Drumright W Duff E Duke NE Duke SW Duncan NE Duncan SW Duncan W Dundee NW Dunlap W Duquesne Durant E Durant N Durant NW Durant W Durham SE Dustin Dustin NE Dustin N Dustin SE Dustin W 25N 6N 6N 5N 5N 1N 11N 11N 11N 11N 11N 24N 25N 24N 15N 15N 14N 3S 1N 1N 1N 1S 1S 1S 20N 11N 8S 8S 8S 27N 27N 27N 3S 11N 27N 12N 12N 9N 8N 15N 15N 16N 16N 15N 15N 15N 5S 11N 7N 6N 6N 11N 9N 12N 11N 28N 3S 3S 27N 28N 28N 28N 28N 27N 28N 28N 28N 24N 24N 24N 24N 24N 24N 2N 4N 5N 4N 26N 27N 14N 14N 21N 20N 20N 21N 4N 1N 1N 1N 1N 27N 25N 25N 25N 26N 26N 17N 22N 3N 1N 1N 1S 1N 3S 17N 21N 6S 6S 6S 6S 15N 9N 10N 9N 9N 9N 12W 16C 16C 16C 16C 15E 14E 2E 3E 3E 2E 2E 8E 8E 7E 5E 5E 4E 18W 2E 2E 2E 2E 1E 1E 14E 11E 2E 2E 2E 3W 3W 3W 1E 2W 15E 24W 25W 1W 1E 8E 8E 7E 7E 8E 7E 7E 13W 13E 4W 4W 5W 8E 19W 8E 8E 1E 4W 24W 2W 8E 8E 8E 8E 8E 7E 8E 5E 5E 5E 5E 5E 4E 4E 20C 19C 19C 10E 11E 10E 9E 4W 4W 4W 5W 22C 21C 21C 21C 4W 11W 4E 4E 4E 8E 8E 6E 3W 22W 23W 7W 8W 8W 4W 8W 6E 9E 8E 8E 8E 25W 12E 12E 12E 12E 11E 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 E-B Ranch N E-B Ranch SE Eagle City Eagle City S Eagle City W Eakly S Eakly-Weatherford Trend Earlsboro Earlsboro N Earlsboro NW Eason Eason N Eason NW Eastman NE Eastman N Echo E Eddy N Eddy NW Edgewood Edgewood S Edgewood-Garfield SW Edith N Edith S Edmond NE Edmond S Edmond SW Edmond Townsite Edmond W 6W 3S 5W 4S 17N 13W 16N 13W 17N 14W 9N 13W 10N 12W 5E 9N 5E 10N 4E 9N 2E 6N 3E 7N 2E 7N 1E 6S 1W 6S 2W 23N 3W 27N 3W 26N 21N 11E 21N 11E 3W 24N 28N 19W 27N 19W 2W 14N 2W 13N 3W 13N 3W 14N 4W 14N 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 Edna District Edna S Eight Mile Mountain El Dorado District El Dorado S El Reno El Reno SE Eldorado SE Eldorado SW Elgin S Elgin SW Elk City Elk City E Elk City S Elk Horn Elk Horn NE Elk Horn N Elk Horn NW Elk Horn SE Elk Horn S Elm Grove Elmwood Elmwood S Emma SW Empire-Comanche Enfisco Enfisco W Enid NE Enterprise Enterprise N Enville NE Enville NW Enville S Enville SW Enville W Eola-Robberson Erick Erick Gas Area South Erick Townsite NW Essaquanahdale Essaquanahdale W Eufaula NE Eufaula NW Eva E Eva N Eva NW Eva SE Eva S Eva SW Evansville E Evansville NW Exendine NE 14N 14N 2S 2S 12N 11N 1S 2S 29N 29N 10N 10N 19N 19N 20N 20N 18N 18N 13N 2N 1N 7N 2S 26N 27N 23N 23N 23N 6S 6S 7S 7S 6S 1N 9N 8N 9N 3S 3S 10N 10N 4N 4N 4N 3N 3N 3N 15N 15N 11N 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 Fair Oak Fair Oak N Fair Oak NW Fair Oak SW Fairfax NW Falkner E Falkner NE Falkner SE Falkner W Fallis Fallis NE Fallis N Falls E Falls NE Falls NW Falls SW Falls W Farris S Farry NE Farry NW Farry SW Fay E Fish E Fitts Fitts E Fitts N Fitts W Flagg SW Flat Rock Flat Rock W Flats NW Flats W Flesher Flesher E Fletcher NE Flint Creek N Flint Creek W Florence Chapel Florence Chapel N Florence Chapel NW Florence SW Florence W Floris Floris SE Floris S Fonda Fonda NE Fonda SE Fonda SW Fonda W Foraker Foraker NE Foraker N Foraker S Foraker SW Forgan Forgan E Forgan NE Forgan N Forgan NW Forgan S Forgan SW Fort Cobb Fort Cobb NW Fort Sill Fort Sill E Fort Sill N Fort Sill NW Fort Sill SE Fort Supply E Fort Supply NE Fort Supply N Fort Supply NW Fort Supply SE Fort Supply S Forty Five Fortyfour Fortyfour NE Foster Fourdee E Fourdee NE Fourdee NW Fourdee SE Foyil Francis S Frankfort Frankfort E Frankfort S Franklin E Franklin NE Franklin N Frederick SE Frederick S Frederick W Freedom N Freeny Freeny N French French E Fritzlen Fritzlen E Fuhrman Fuhrman SE 1W 16N 1W 16N 1W 16N 1W 15N 5E 24N 28N 16W 29N 16W 28N 16W 28N 16W 2E 15N 2E 15N 2E 15N 1W 9N 1W 9N 2W 9N 1W 9N 2W 9N 4S 14E 28N 17W 28N 18W 27N 18W 15N 13W 8E 7N 7E 2N 7E 2N 7E 2N 6E 2N 27N 16W 20N 12E 20N 11E 6N 11C 6N 11C 9E 22N 22N 10E 9W 4N 2W 6N 3W 6N 1W 4N 1W 4N 1W 4N 9W 27N 9W 27N 5N 22C 4N 22C 4N 22C 19N 14W 19N 14W 19N 14W 19N 15W 19N 15W 7E 28N 7E 29N 7E 28N 7E 27N 7E 27N 6N 24C 5N 24C 6N 24C 6N 23C 6N 23C 4N 23C 4N 23C 7N 12W 8N 12W 3N 10W 3N 10W 4N 11W 3N 11W 3N 10W 24N 22W 25N 21W 25N 22W 25N 22W 24N 22W 24N 22W 25N 12E 9E 16N 9E 17N 3W 1W 22N 1W 23N 2W 22N 1W 22N 22N 17E 4N 6E 29N 6E 29N 6E 29N 1W 1W 10N 1W 10N 2S 17W 2S 18W 2S 18W 27N 17W 4W 8N 4W 8N 3W 5N 5N 2W 29N 14W 29N 13W 9E 9N 9E 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 Gage Gage N Gage SE Gaines Gaines NW Gano NW Gano S Gans Gans NE Gans SE Gans SW Gansel S Gansel SW Garber Garber E Garber NW Garber SE Garber SW Garber W Garcreek Garden Grove S Garden Grove SW Garden S Garr Garr N Garr NW Garr W Garrett Garrett NW Gate Lake NE Gate Lake N Gate Lake NW Gate NE Gate N Geary NW Geary SW Georgia Georgia S Georgia SW Gerty Gerty E Gerty N Gerty NW Gerty W Gibbon NE Gibbon N Gibbon Spur E Gibbon Spur NE Gibbon Spur N Gibbon Spur NW Gibson Gibson W Gilbert N Gilbert SE Gilbert S Gilcrease Gilcrease District East Gilcrease SW Gilliland Gilliland W Glencoe E Glencoe NE Glencoe SE Glencoe S Glencoe SW Glencoe W Glennpool Glover NE Golden Trend Goldsby E Goldsby N Goldsby NW Goltry NE Goltry N Goodnight NE Goodnight SE Goodnight S Goodwell SE Goodwin E Goodwin SE Goodwin S Goodwin W Goose Neck Gotebo Gotebo District South Gotebo E Gotebo N Gotebo NW Gould S Gracemont N Grainola SW Grand Center NW Grand E Grand NW Grand S Grand Valley East District Grand Valley N Grand Valley SE Grand W Granite Granite W Grant-Pond Creek Grant-Pond Creek E Grant-Pond Creek NE Grant-Pond Creek N Grant-Pond Creek SE Gray Grayhorse District Grayhorse N Grayhorse SE Grayhorse W Grayson N Grayson S Greasy Creek Green NW Green Valley Green Valley E Green Valley SE Greenfield NW Greenfield W Greenlease Greenlease S Greenough Greenough Middle Greenough W Greenup Greenup N Greenville NW Gregory Grey Noret Grey Noret SW Griggs SE Griggs S Grimes Grisso Grisso SW Grisso W Grove NE Guthrie Guthrie E Guthrie Lake Guthrie Lake E Guthrie Lake SE Guthrie NE Guthrie NW 22N 22N 21N 5N 6N 18N 18N 11N 11N 10N 10N 20N 21N 22N 22N 24N 21N 23N 23N 10N 11N 11N 15N 19N 20N 19N 19N 26N 27N 28N 6N 6N 5N 6N 14N 13N 18N 17N 17N 4N 4N 5N 5N 4N 29N 29N 7N 7N 7N 7N 16N 16N 27N 27N 26N 9N 9N 9N 23N 23N 20N 20N 20N 20N 20N 20N 17N 5S 4N 8N 8N 8N 24N 25N 17N 17N 17N 1N 20N 19N 19N 20N 28N 7N 7N 7N 7N 7N 2N 9N 28N 16N 17N 18N 17N 2N 3N 2N 18N 7N 6N 26N 25N 26N 26N 25N 6N 24N 24N 24N 24N 6N 6N 8N 22N 21N 22N 21N 15N 14N 11N 11N 5N 6N 6N 21N 22N 6S 10N 29N 29N 2N 11N 8N 8N 8N 12N 17N 16N 16N 16N 15N 17N 17N 10E 10E 20E 24W 24W 7W 6W 23W 24W 9E 9E 21W 21W 21W 3W 3W 3W 3W 2W 3W 12W 23C 23C 26W 8W 7E 7E 6W 7E 7E 3E 2E 3E 3E 3E 3W 25W 25W 25W 11W 11W 17E 16E 12C 11C 10C 12C 11C 10C 1E 1W 12W 23W 24W 24W 16E 16E 5E 25E 25E 25E 24E 2W 2W 4W 3W 4W 3W 4W 4W 7E 7E 6E 1E 5E 5E 4E 4E 2E 1E 26W 28C 27C 28C 28C 11W 11W 4E 4E 4E 10E 10E 10E 9E 9E 7W 7W 2W 2W 2W 2W 18E 18E 7W 7W 7W 9E 9E 9E 7E 7E 4E 4E 4E 3E 3E 3E 12E 23E 3W 2W 3W 3W 9W 9W 2E 2E 2E 14C 25W 24W 25W 26W 16E 16W 16W 15W 16W 16W 25W 10W 6E 2E 24W 24W 25W 20C 20C 22C 25W 21W 21W 6W 5W 5W 6W 5W 4E 6E 6E 6E 6E 5E 5E 10E 18E 3W 2W 3W 11W 12W 9E 9E 22C 21C 21C 7E 7E 11E 3E 3E 9C 9C 24W 4E 4E 4E 18E 1W 2W 2W 2W 2W 1W 3W 1201 1202 1203 1204 1205 1206 1207 1208 1209 Guthrie Townsite Guthrie W Guymon NE Guymon N Guymon NW Guymon S Guymon Townsite Guymon-Hugoton Gas Area Gypsy SW 16N 16N 3N 3N 3N 2N 3N 3N 14N 2W 3W 15C 15C 14C 15C 15C 16C 7E 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 Haileyville SW Halfway Halfway NW Hallett Hallett NW Hallett W Halsell Hamburg Hamburg N Hamilton Switch Hammon E Hammon S Hanbury District Hanbury NE Hanbury SE Haney N Hanna Hanna N Hanna NW Happy Hill Happy Hill E Happy Hill NE Happy Hill SE Happy Hill SW Happy Hill W Happy Hollow NE Happy Star N Happy Valley Happy Valley N Happy Valley S Hardesty Hardesty NE Hardesty N Hardesty W Hardscrabble SE Hardscrabble W Hardy Hardy NE Harmon E Harmon N Harmon NW Harmon SE Harmon S Harmony Harmony SW Harness Harness NW Harrah E Harrah N Harrisburg NW Hart E Hart NE Hart S Hart SW Hartshorne S Haskell Hatton NE Hatton N Hawley Hawley E Hawley SE Hawley S Hawley SW Haydenville District Hayward Hayward N Hayward S Hayward SW Hayward Townsite Hayward W Hazel NW Healdton Hector Helena Helsel Helsel N Helsel NW Helsel SE Helsel SW Helsel W Henderson E Hennepin Hennepin E Henryetta District Henryetta E Henryetta SE Henryetta S Hewitt Hewitt E Hickory Ridge Hickory Ridge N Hickory Ridge SW Higbee N Higgins S Hill NW Hill S Hill Top Hill Top N Hill Top SW Hill W Hilliby E Hillsdale NE Hillsdale N Hillsdale NW Hillsdale SE Hillsdale SW Hillside S Hitchita NE Hitchland N Hobart Hobart NE Hobart Townsite Hoffman Hoffman District NW Hoffman W Hogshooter Holdenville Holdenville NE Holdenville N Holdenville SE Holdenville S Holdenville SW Holland Holland NE Hollister SW Hollow NW Homer Hominy Hominy E Hominy Falls Hominy Lake S Hominy S Hominy W Hooker Hooker District North Hooker E Hooker NE Hooker SW Hoover Hoover SE Hoover W Hope Hope NW Hope SE Hope SW Hopeton N Horns Corner Horns Corner N Horntown SE Hotulke-West Earlsboro Hough Hough S House Creek House Creek N Howe Howe NW Hubbard Hubbard N Hucmac Hucmac N Hucmac NW Hucmac SE Hucmac S Hucmac SW Hulah Hulah N Hulah S Hulbert S Hulen E Hulen SW Hull Hull NE Hull N Hunnewell E Hunter Hunter N Hunter NW Hunter S Hunter Townsite Huntley E Huntley W Hutchie Hydro Hydro W 4N 13N 13N 20N 21N 20N 27N 15N 15N 14N 14N 13N 2N 2N 1N 10N 8N 9N 9N 13N 13N 13N 13N 13N 13N 25N 24N 17N 17N 16N 2N 3N 3N 2N 15N 15N 25N 29N 19N 21N 20N 18N 19N 17N 17N 5N 5N 12N 12N 1S 3N 3N 2N 3N 4N 16N 6N 6N 27N 26N 26N 26N 26N 13N 21N 21N 21N 21N 21N 21N 7N 4S 16N 24N 7N 7N 7N 7N 7N 7N 3S 1N 1S 11N 12N 11N 11N 4S 4S 10N 10N 10N 14N 18N 11N 10N 5N 6N 5N 10N 13N 24N 24N 24N 24N 24N 22N 12N 1N 7N 7N 7N 12N 12N 12N 25N 7N 8N 8N 7N 7N 7N 2N 2N 3S 29N 1S 22N 22N 21N 22N 22N 22N 5N 6N 5N 5N 4N 1N 1N 1N 1N 2N 1N 1N 26N 7N 7N 7N 9N 4N 4N 20N 20N 6N 6N 26N 27N 18N 19N 18N 17N 17N 18N 28N 29N 28N 16N 1S 1S 18N 19N 19N 29N 24N 25N 24N 22N 24N 6N 16N 12N 12N 15E 7E 7E 7E 7E 6E 17E 25W 25W 13E 20W 21W 9W 9W 9W 7E 13E 13E 13E 3E 3E 3E 3E 3E 8E 2W 5E 5E 5E 17C 18C 17C 16C 4E 4E 3E 5E 21W 21W 22W 21W 22W 5E 5E 7W 7W 2E 1E 6W 4E 4E 4E 3E 17E 15E 24C 24C 8W 7W 7W 8W 8W 10E 3W 3W 3W 3W 3W 3W 5E 3W 13E 10W 1E 1E 1E 1E 1E 1E 17W 1W 1W 12E 12E 13E 12E 2W 2W 10E 10E 10E 3W 26W 1E 11E 11E 11E 8E 7W 8W 8W 7W 8W 13E 15E 16C 17W 17W 18W 14E 14E 13E 14E 8E 9E 9E 9E 9E 8E 28C 28C 16W 18E 2W 8E 9E 11E 8E 9E 8E 17C 17C 18C 18C 17C 1W 1E 1W 6W 6W 6W 7W 14W 10E 10E 11E 4E 14C 14C 8E 8E 25E 25E 2W 2W 15W 15W 15W 15W 15W 15W 12E 12E 12E 20E 9W 10W 4W 3W 4W 2W 5W 4W 5W 4W 4W 10W 11W 18E 13W 13W 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 Iconium Iconium NW Iconium SE Iconium S Iconium W Idabel NE Idabel W Indianapolis Indianola Indianola E Indianola SE Ingalls Ingalls S Ingalls SW Ingersoll S Inola District Ioland NE Ioland N Ioland NW Iona Iona NE Iron Chapel Iron Chapel SE Iron Post Iron Post District SE Isom Springs Isom Springs SW Ivanhoe Ivanhoe W 16N 16N 16N 16N 16N 7S 7S 12N 8N 8N 8N 19N 18N 18N 26N 19N 18N 18N 18N 2N 2N 7N 6N 14N 14N 7S 8S 1N 1N 1E 1E 1E 1E 1E 24E 23E 16W 14E 15E 15E 4E 4E 4E 11W 17E 22W 22W 22W 2E 3E 3W 3W 8E 9E 5E 5E 26C 27C 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 Jarvis N Javine District Jefferson N Jefferson W Jefferson-Grant NE Jefferson-Grant NW Jennings Jennings E Jennings SE Jennings S Jennings SW Jesse E Jester SE Jester S Jimtown N Johnson W Johnsonville Johnsonville NW Johnsonville W Joiner City Joiner City SE Jolly-Patton Jones Jones Chapel Jones Chapel SW Jones E Jones S Jones SW Jones W Jumbo S 29N 22N 8N 26N 26N 26N 19N 19N 19N 19N 19N 1N 6N 6N 7S 26N 5N 5N 5N 5S 6S 14N 13N 4N 13N 12N 12N 13N 2S 6W 11E 8E 6W 5W 6W 7E 8E 7E 7E 7E 8E 23W 24W 2W 10E 2E 2E 2E 3W 2W 19E 1E 5E 5E 2E 1E 1E 1W 15E 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 Katie SE Katie S Kaw Kaw S Keaton Keaton W Keefeton Keenan SW Keller Keller N Keller SE Kellyville District Kellyville District NW Kellyville District West Kendrick Kendrick S Keokuk Keokuk E Keokuk NE Keokuk NW Keokuk SE Keokuk W Keota Ketchum Keyes District Keyes E Keyes Gas Area Keyes W Keylon NE Keystone Keystone District East Keystone District NE Kibby S Kibby SW Kickapoo Kickapoo E Kickapoo N Kiersey S Kildare NW Kildare S King King E Kingfisher SE Kingston Kingston NE Kingston SE Kinta Kiowa 1N 1N 26N 25N 12N 12N 13N 20N 4S 4S 4S 17N 18N 17N 15N 15N 10N 10N 11N 11N 10N 10N 9N 24N 5N 4N 5N 5N 3N 19N 20N 20N 25N 26N 12N 12N 12N 7S 27N 27N 10N 10N 16N 7S 6S 7S 8N 3N 1W 2W 4E 4E 9E 10E 18E 23W 1W 2W 1W 10E 10E 10E 5E 5E 6E 6E 6E 6E 6E 6E 23E 21E 7C 8C 9C 7C 11C 10E 10E 9E 22W 22W 2E 2E 2E 8E 2E 2E 4E 5E 6W 6E 6E 6E 22E 13E 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 Kiowa Flats Kiowa Flats N Kiowa Flats NW Kiowa NW Kline NE Klondike Klondike N 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 Figure S16. Oklahoma oil and gas wells. Plot adapted from Oklahoma Geological Survey16: http://www.ogs.ou.edu/fossilfuels/MAPS/GM-36.pdf. 62 Figure S17. Oklahoma oil and gas production by county. Plot was created by Joe Wertz of StateImpact Oklahoma17. Below, we include a plot by Water Education Colorado showing the value of oil and gas production value by county (Figure S18). If we compare it to Figure S6, it is evident that much of the FRAPPE observations were taken around nearby oil-producing wells that produce significant revenue. This is consistent with the large C2 and C3 to C1 emission ratios observed during the FRAPPE campaign (Figure 13, main text). Figure S18. Oil and gas production value by county in Colorado. The plot was obtained from Water Education Colorado (founded by Colorado State Legislature).18 63 S2.5 Comparison to Lan et al. 2019 study Lan et al. 2019 investigated C3H8/CH4 and C2H6/CH4 ratios using NOAA-ongoing observations. Consistent with their study, we find increasing C3H8/CH4 and C2H6/CH4 ratios over time with relatively similar slopes. However, we find no statistically significant temporal trend in C3H8/C2H6. As shown in Figure S9 and in the additional cross plot of C3H8 and C2H6 colored by time (Figure S19, left), the correlation of these gases in the ‘fresh emissions’ regime is identical within error. Even when excluding aircraft data for SGP site, the ratio remains nearly the same (Figure S19, right). Figure S19. C3H8 and C2H6 correlation at NOAA SGP site– yearly and tower observations. Left: C3H8 vs C2H6 colored by all years for the NOAA SGP site. Slope: [0.63, 0.70] (95% CI), R2=0.98. Right: Slope of C3H8 vs C2H6 for ground- and tower-based measurements NOAA SGP site. (The highest tower sampling is 374m sampling at SGP.) The slope is [0.66, 0.70], and R2=0.99, comparable to [0.63, 0.70] 95% CI slope of the correlation that includes both aircraft and tower observations (this Figure, left side). We bootstrapped the samples to obtain a 95% CI (see methods, main text). Our C3H8 anomalies are calculated in a different fashion than in Lan et al. 2019. Given the curvature of the correlation (Figure 1, main text) and its seasonal dependence, we determine the slope of the C3H8 and CH4 anomalies only within the fresh emission regime (C3H8 > 103 ppt, along with co-measurements of CH4, see Section 2.2). Since we only focus on the linear part of the curve, our analysis is not terribly sensitive to how the CH4 anomaly is determined (it simply produces varying intercepts). To estimate C3H8/C2H6, we also only consider the fresh emission regime (beyond 103 ppt C3H8). We replicate Figure 3a,b from Lan et al. 2019 using our methods in Figure S20. Even with very different methodology, our results for the central value of the emissions ratio between C3H8 and C2H6 and CH4 anomalies are similar, albeit Lan et al. claims a much smaller uncertainty in these 64 ratios (51.2 ± 0.6ppt/ppb and 80.5 ± 2.5ppt/ppb, respectively) such that the interannual variation and the trend over the record far exceed the stated uncertainty. Our 95% CI of the slope for C3H8/CH4 is [42.57, 49.87] and for C2H6/CH4 is [64.66, 74.89] (both in ppt/ppb) where most of the CI spread results from the temporal trend (see Figure S20). Figure S20. NOAA C3H8 and C2H6 vs CH4 anomaly colored by year. Data is for SGP site only. C3H8/∆CH4 slope: [0.43, 0.50] ppb/ppb, R2= 0.83. C2H6/∆CH4 slope: [0.65, 0.75] ppb/ppb, R2= 0.86. We use data within the fresh emission regime (see Section 2.2). Our methods for determining CH4 anomalies are described in detail in section 2.3, and our methods for determining the 95% CI via bootstrapping is described in the methods section of the main text. We reproduce Figure 3e from Lan et al. 2019 in Figure S21, below. In Figure S21, the variability in ratios each year is constructed from the 95% confidence interval of the slopes from samples of a pairs bootstrap, described in more detail in section 2.1 As in Lan et al., we find significant trends in C3H8/CH4 anomalies (3.12 ± 0.63 ppt/ppb/year), and C2H6/CH4 anomalies (3.89 ± 0.84 ppt/ppb/year), which are comparable to their result. On the right side of Figure S21, we plot the fractional change relative to the mean. Instead, we find that both ratios are fractionally increasing at the same rate. The reported error in the slope is simply the standard error calculated from a linear regression of the yearly slopes vs year (that includes the upper and lower CI points). We use the linear trend of anomalies/year (Figure S21, left) to calculate mean anomaly ratios for SGP during 2016-2018 to be [0.060, 0.061] ppb/ppb (and C2H6/CH4 to be 0.086, 0.088]), where the interval is determined using the standard error in the slope. 65 Figure S21. Yearly correlation between NOAA hydrocarbon vs CH4 anomaly. Left: Average hydrocarbon vs CH4 anomaly for each year for NOAA SGP site. C3H8/CH4 anomaly slope: 3.12 ± 0.63 ppt/ppb/year (R2=0.71), and C2H6/CH4 anomaly trend is 3.89 ± 0.84 ppt/ppb/year (R2=0.69). The variability in the trend (ppt/ppb/year) comes from the standard error of a linear regression. The variability in the yearly slope (ppt/ppb) comes from the 95% confidence interval of a pairs bootstrap (we ran a pairs bootstrap for co-measurements of C3H8 and ∆CH4 and compute the slope of the correlation for each bootstrap sample and repeated this for every year in the data; please see the methods section of the main text for more information about pairs bootstrapping). Right: Same as left, but in units of percent change with respect to the mean hydrocarbon and methane anomalies. The resulting trend for C3H8/CH4 is 7.13 ± 1.44 % with an R2 of 0.71. The trend for C2H6/CH4 is 5.87 ± 1.26 % with an R2=0.69. Both trends are calculated in the same way as the left figure. Our analysis of the NOAA data suggests that the C3H8/C2H6 ratio is quite static in the U.S. over this 12-year record. That the ratios C2H6/CH4 (and C3H8/CH4) are increasing over time is completely consistent with Lan et al. 2019, and as they point out, studies that assume these ratios are invariant will overestimate the rate of oil/gas CH4 emissions. Here, we use C3H8 vs CH4 and C2H6 vs CH4 between 2012 and 2018 to estimate the CH4 emissions from the US as this is the period when most of the top-down and bottom-up estimates of CH4 have been performed. That the ratios are getting “wetter” (higher hydrocarbon content in pre-processed gas) over time is consistent with an increasing contribution from oil exploration. That the atmospheric C2H6 and C3H8 increase fractionally the same, suggests that the ratio of the alkanes in the reservoirs producing these emissions do not change significantly over the time of this record. S3. ATom & HIPPO aircraft observations The HIPPO campaign was a sequence of five global measurement campaigns which sampled from near the North Pole to the coastal waters of Antarctica, covering different seasons and years: 66 HIPPO 1: 8-30 January 2009, HIPPO 2: 31 October – 22 November 2009, HIPPO 3: 24 March – 16 April, HIPPO 4: 14 June – 11 July 2011. ATom was a sequence of four global campaigns that took place from 29 July – 12 August 2016, 26 January – 10 February 2017, 28 September 201711 October 2017, and 24 April 2018 – 6 May 2018. Flight paths of HIPPO and ATom campaigns are illustrated in Figure S22. Figure S22. Truncated ATom and HIPPO flight paths. Flight paths used in this analysis are shown above (Top: ATom, Bottom: HIPPO). We split the data into Pacific (left column) and Atlantic (right column) “curtains” shown above for ATom, but HIPPO only offered Pacific curtains over remote ocean. The flight paths shown above do not encompass the entire dataset due to filtering out measurements south of 20 latitude north, those obtained over land, and those associated with very recent emissions. A summary of the filtering parameters we use in the main text are shown in Table S2. Table S2. Filters for Aircraft Measurements. Parameter ATom HIPPO Aircraft Aircraft Altitude > 1000 meters > 1000 meters N2 O > 0.327 ppb > 0.320 ppb Tropopause > 100 hPa > 100 hPa Pressure 67 Summer season exclude exclude HIPPO data were accessed from https://www.eol.ucar.edu/field_projects/hippo on 12/18/18, using the “discrete continuous merge” file. ATom data were accessed from the WAS-Discrete merged file from espo.nasa.gov/atom/archive/browse/atom/DC8/MER-WAS in August, 2021. Data taken over landmass for both aircraft campaigns were filtered away using global-land-mask version 1.0.0,19 available from Python Package Index. Here, we outline additional information on processing ATom and HIPPO aircraft observations used to compare with the GEOS-Chem model. HIPPO measurements were filtered for AWAS/UM instrument measurements to avoid measurement bias in C3H8 over C2H6, as the NOAA instrument only measured one of those species. All measurement species of HIPPO and ATom were filtered for consistent measurements of C3H8 and C2H6 within their respective campaigns; i.e., when those constituents were either both null or non-zero. This requires filtering data to remove plumes from highly local sources (including both energy infrastructure and wildfires), and to exclude regions and times where the lifetime of the alkanes is very short and thus regional / local sources dominate the variance. To reduce the influence of local sources, we only analyze observations in the free troposphere over the ocean at altitudes above 1000 meters (this filter excludes less than 20% of the dataset). To diagnose tropical air, we use tropopause pressure as a filter. We use the NASA Global Modeling and Assimilation Office GEOS FP-IT (version 5.12.4) tropopause pressure product at 0.5 x 0.67 resolution,20 and linearly interpolate it to the HIPPO aircraft path (for ATom, we use the product already included in the dataset). We only analyze measurements with tropopause pressure above 100 hPa (about 5% of the data was excluded under this constraint) for both ATom and HIPPO, which was sufficient to reduce the influence of tropical intrusions. Because C2H6 and C3H8 are relatively short-lived gases, their abundance in the stratosphere is low and poorly connected to the underlying fluxes. To exclude stratospheric observations, we use N2O which is inert and generally well-mixed in the troposphere, but is destroyed in the stratosphere by photolysis and reaction with O1D.21 Thus, we exclude data associated with low N2O mole fraction (Figure S23). We use nearest neighbor interpolation to estimate missing N2O observations. In Figure S23, we compare N2O observations and GEOS-Chem simulations of N2O and determine a common filter for both datasets. (Note that we generate GEOS-Chem N2O simulations shown in Figure S23 by interpolating GEOS-Chem to aircraft latitude, longitude, time and potential temperature, but for all subsequent analysis, we filter GEOS-Chem by N2O before interpolating to the aircraft potential temperature). To account for biomass burning, we use HCN as a tracer and did not use data with high HCN (Figure S24-26) for ATom observations only, as HIPPO did not provide HCN observations. 68 Figure S23. Stratospheric filter using N2O. Left: ATom. Right: HIPPO. In both figures, GEOSChem simulations were interpolated to aircraft latitude, longitude, time, and potential temperature in order to compare N2O. However, for all subsequent analysis, GEOS-Chem was filtered by N2O before interpolating simulations to aircraft potential temperature. We use these figures to arbitrarily choose 0.327 and 0.320 N2O mole fractions as a filter cutoff for ATom and HIPPO, respectively, as described in the main text. To account for biomass burning, we use HCN as a tracer. We see elevated HCN over the Atlantic ocean on several campaigns (Figure S21). In the cross plot of HCN and C2H6 (Figure S23), we observe distinct plumes of elevated HCN and C2H6 that suggest biomass burning, and we deweighted and excluded samples with high HCN (see description in Figure S23). 69 Figure S24. ATom HCN Pacific transects. HCN (left column), Ethane (middle column), and tropopause height (right column). 70 Figure S25. ATom HCN Atlantic transects. HCN (left column), Ethane (middle column), and tropopause height (right column). Figure S26. ATom HCN vs C2H6. This data includes all four ATom campaigns and ocean transects and has been filtered using the specifications outlined in the methods section in the main text. The 71 few points with very high HCN and C2H6 are associated with biomass burning. We assigned a weak percentile score for each datapoint, and the values greater than or equal to equal to the 87th percentile are highlighted in black. Those points were replaced with NaN and then interpolated using the “backfill” method for C3H8 and C2H6. S4. GEOS-Chem Simulations We simulated HIPPO and ATom measurements using the GEOS-Chem “classic” global 3-D chemical transport model in v12.1.1 (doi:10.5281/zenodo.2249246). The simulations were driven by MERRA-2 reanalysis meteorology product by the Global Modeling and Assimilation Office (GMAO) at NASA Goddard Space Flight Center.22 MERRA-2 has a native resolution of 0.5 lat x 0.625 lon x 72 hybrid sigma/pressure levels, of which we degrade to a 4 x 5 x 72 resolution. We simulate time periods that encompass the HIPPO and ATom aircraft measurements with a 1-year spin-up period. In all cases, we use a standard chemistry simulation with no changes to the chemistry regimes. Simulations were collected over every hour over every day of each campaign period (~2 months of results for each campaign time period). Hydrocarbons were converted from units of carbon to molx/moldry air. All emissions are computed using the Harmonized Emissions Component (HEMCO) Standalone23 version 3.0.0 (DOI: 10.5281/zenodo.4429214)24 with GEOS-Chem development version 13.0.0, cloned on 9/2020 at https://github.com/geoschem/geos-chem). This Standalone utilizes the most up-to-date versions of emissions as of September, 2020. As such, even though we utilize an older version of GEOS-Chem classic for the simulations, we implement up-to-date emissions. Relevant inventories that cover the oil and natural gas sector that are used in the default emissions configuration for GEOS-Chem v13.0.0 are Tzompa-Sosa et al. 2017 for C2H6, and Xiao et al. 2008 for C3H8.4,25 In Figure S27, we show that GEOS-Chem “synoptic replicates” (GEOS-Chem sampled several days before and after the aircraft in situ sampling time) show less consistency in latitude compared to the coordinate, potential temperature. 72 Figure S27. GEOS-Chem simulated C2H6 vs potential temperature and latitude during 2017. These data are analyzed for Pacific and Atlantic transects during January-Feburary 2017. Aircraft observations are shown in black. GEOS-Chem simulations are colored by the sampling time, in days beyond the flight path. (We found the median time of in-situ sampling of the aircraft, and then sampled the GEOS-Chem model for several days before and after the median to generate what we call “synoptic replicates” here. Each of the synoptic replicates were sampled along the flight path latitude, longitude, time and potential temperature using nearest neighbor interpolation.) In this figure we include ± 5 days to demonstrate the variance, but we use up to ± 2 days of the GEOS-Chem replicates in the Bayesian model. All remaining simulations of ATom and HIPPO C2H6 and C3H8 are included in the SI. As discussed in Section 3.2 in the main text, we revise C3H8 emissions using GEOS-Chem v13.0.0 default C2H6 emissions scaled by the observed C3H8/C2H6 ratio estimated from the NOAA data. In Figure S28, we show the default C2H6 and C3H8 emissions, as well as the revised C3H8 emissions. 0 1 2 3 4 5 Default C2H6 Emissions (kg/m2/s) 6 7 1e-11 73 0 1 2 4 3 5 7 6 Default C3H8 Emissions (kg/m2/s) 0 1 2 4 3 5 1e-11 7 6 Revised C3H8 Emissions (kg/m2/s) -6 -4 -2 0 2 Revised – Default C3H8 Emissions (kg/m2/s) 1e-11 4 6 1e-11 Figure S28. GEOS-Chem v13.0.0 default and revised emissions. Top: Default C3H8 emissions. Upper middle: Default C2H6 emissions. Bottom middle: Revised C3H8 emissions scaled by the observed NOAA C3H8/C2H6 ratio (0.67 mol/mol, Figure S9). Bottom: Difference between revised and default C3H8 emissions used by GEOS-Chem v13.0.0. In the GEOS-Chem simulations, both ethane and propane have the most variability and lowest mole fraction, as expected, since their oxidative chemistry is much faster. During the summer, 74 tropical intrusions with very low mixing ratios are prominent (see Atom summer Pacific transect, Figure S29.). Figure S29. GEOS-Chem simulated C2H6 vs potential temperature during ATom campaign. Each plot is specific to the ocean transect. GEOS-Chem simulations are colored by the sampling time, 75 in the number of days from the day of the flight. (We found the median time of in-situ sampling of the aircraft, and then sampled the GEOS-Chem model for several days before and after the median to generate “synoptic replicates.” Each of the synoptic replicates were sampled along the flight path latitude, longitude, time of day and potential temperature using nearest neighbor interpolation.) 76 Figure S30. GEOS-Chem simulated C3H8 vs potential temperature during ATom campaign. Each plot is specific to the ocean transect. GEOS-Chem simulations are colored by the sampling time, in the number of days from the day of the flight. (We found the median time of in-situ sampling of the aircraft, and then sampled the GEOS-Chem model for several days before and after the median to generate “synoptic replicates.” Each of the synoptic replicates were sampled along the 77 flight path latitude, longitude, time of day and potential temperature using nearest neighbor interpolation.) Figure S31. GEOS-Chem simulated C2H6 vs potential temperature during HIPPO aircraft campaign. Each plot is specific to the ocean transect. GEOS-Chem simulations are colored by the sampling time, in the number of days from the day of the flight. (We found the median time of insitu sampling of the aircraft, and then sampled the GEOS-Chem model for several days before and after the median to generate “synoptic replicates.” Each of the synoptic replicates were sampled along the flight path latitude, longitude, time of day and potential temperature using nearest neighbor interpolation.) 78 Figure S32. GEOS-Chem simulated C3H8 vs potential temperature during HIPPO aircraft campaign. Each plot is specific to the ocean transect. GEOS-Chem simulations are colored by the sampling time, in the number of days from the day of the flight. (We found the median time of insitu sampling of the aircraft, and then sampled the GEOS-Chem model for several days before and after the median to generate “synoptic replicates.” Each of the synoptic replicates were sampled along the flight path latitude, longitude, time of day and potential temperature using nearest neighbor interpolation.) We compare the cross plot of C3H8 to C2H6 from the aircraft measurements and GEOS-Chem simulations to the NOAA measurements. As expected, both the aircraft and GEOS-Chem simulations fall under the photochemically aged emissions part of the NOAA curve. While the aircraft data overlays the NOAA measurements almost perfectly (especially in the winter when the lifetimes of both gases are longest), GEOS-Chem underestimates C3H8, particularly over the Atlantic curtain (Figure S33). The same conclusion is drawn for HIPPO time periods (Figure S 34). 79 Figure S33. Comparison of C3H8 vs C2H6 for NOAA, ATom aircraft, and GEOS-Chem (GC) simulations. NOAA photochemically-aged measurements (all sites, 2005-2018), as explained in the text, are shown on the heat map (colored by density of data). Note the distinction between winter/fall and spring/summer seasons. HIPPO is included in the SI, Section 3. 80 Figure S34. C3H8 vs C2H6 for HIPPO aircraft and GEOS-Chem simulations. Please see section 3.2 in the main text for a discussion. In the main text, we show, in Figure 4, the impact of the revised C3H8 emissions on GEOS-Chem simulations during the ATom 4 campaign time period. Below, in Figure S35, we show the impact of the revised C3H8 emissions for all four ATom campaigns. In Figure S36, we show the impact of the revised C3H8 emissions during all 5 HIPPO campaigns. 81 Figure S35. GEOS-Chem simulations using the default and revised C3H8 emissions during all four ATom campaigns. Please see section 3.2 in the main text for more discussion. Figure S36. GEOS-Chem simulations using the default and revised C3H8 emissions during all 5 HIPPO campaigns. Please see section 3.2 in the main text for more discussion. 82 S5. Bayesian Inference S5.1 Background and Priors We wish to use the ATom and HIPPO aircraft observations to quantify C3H8 and C2H6 emissions. We use hierarchical Bayesian modeling to estimate what global scalar would minimize the difference between the simulated C3H8 and C2H6 from the updated GEOS-Chem v13.0.0 emissions and the observations made during the ATom and HIPPO aircraft campaigns. Using Bayesian probability, we can quantify a degree of certainty about a hypothesis or parameter value. Using probability rules, one can derive Bayes’s Theorem: 𝑃(𝜃 ∣ 𝑦) = 𝑝𝑜𝑠𝑡𝑒𝑟𝑖𝑜𝑟 = 𝑃(𝑦 ∣ 𝜃)𝑃(𝜃) 𝑃(𝑦) 𝑙𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 × 𝑝𝑟𝑖𝑜𝑟 𝑒𝑣𝑖𝑑𝑒𝑛𝑐𝑒 The likelihood tells us how likely it is to acquire the observed data, y, given the parameter, 𝜃. The prior is a measure of plausibility of the hypothesis 𝜃 before the experiment was conducted. The evidence is a marginal likelihood that is computed from the likelihood and the prior. The posterior contains the information we want about the parameters we are after. The ambient mole fraction of C3H8 and C2H6 is more linearly related to its underlying emissions pattern during the winter/fall/spring when there is decreased sunlight/oxidation. As such, we assume differences between the GEOS-Chem simulations and the aircraft observations can largely be attributed to the underlying emissions grid, such that, a = gcs ⋅ 𝛼 (1) where a is the aircraft C2H6 or C3H8, gcs stands for GEOS-Chem simulation of C2H6 or C3H8, and 𝛼 is a scalar that represents the most likely mismatch between the underlying C3H8 and C2H6 emissions as transported through GEOS-Chem v13.0.0 relative to ATom and HIPPO observations. This assumption forms the heart of our hierarchical Bayesian model. We can reasonably approximate C2H6 and C3H8 measured by the aircraft to be Lognormally distributed with an approximate error. Lognormal distributions have longer tails, which is appropriate given the outliers we see in the measurements. We can model the GEOS-Chem simulated results as follows: 83 gcs" 𝜎 𝛽 ∼ LogNorm(𝛽 ⋅ a" , 𝜎) ∼ Prior ∼ Prior (2) where gcs" represents GEOS-Chem simulated C3H8 and C2H6, a" represents the jth datum of aircraft-observed C3H8 or C2H6. Here, 𝛽 parameter (equivalent to 1/ 𝛼) estimates error in the default GEOS-Chem emissions, and 𝜎 is the approximate uncertainty in the GEOS-Chem simulations. In this case, we expect 𝛽 to be less than one since the aircraft observations are usually greater than the GEOS-Chem simulations. We organized the Bayesian model this way because we consider the aircraft observations to be unchanging, while treating the GEOS-Chem simulations as the experimental dataset. To obtain the GEOS-Chem missing emissions, we can invert the 𝛽 parameter. We sampled the GEOS-Chem model several days before and after the aircraft path to estimate uncertainty in the simulations due to meteorology, as explained in Section 2.3 in the main text. If we were to pool all the data together, each experiment would be governed by identical parameters. However, each replicate is subject to differences mainly due to meteorology and we conclude that the parameters in each replicate experiment should vary from one another, such that we have 𝑖 separate models to fit, each looking like equations 2, above. Under this scenario, we organize our model into a hierarchical structure, pictured in Figure S37. Level 0 Level 1 1 2 3 4 Measured Data Figure S37. Schematic of hierarchical Bayesian model. Level 0 contains the hyperparameter β, the parameter we ultimately wish to get estimates for. Level 1 corresponds to the day the GEOS-Chem model was sampled (there are 5 days because we sampled 2 days before and after the mean flight path). There will be variability from day to day, and the location and scale parameters for a given day are conditioned on the hyperparameters. We can consider a hierarchical model in which there is a hyperparameter, which we call 𝛽 (corresponds to level 0, Figure S32), and the values of the scaling parameters of the replicates, 84 which we now call 𝛽# (corresponds to level 1, Figure S37), may vary from this 𝛽 according to some probability distribution, 𝑔(𝛽#,! |𝛽). We now have parameters 𝛽#,# , 𝛽#,5 , … 𝛽#,! and 𝛽. The posterior can be written using Bayes’ theorem, defining 𝛽# = (𝛽#,# , 𝛽#,5 , … ), 𝑔(𝛽, 𝛽# |a, gcs) = 𝑓(a, gcs|𝛽, 𝛽# )𝑔(𝛽, 𝛽# ) 𝑓(a, gcs) (3) Note though that the observed values of gcs do not directly depend on 𝛽, only on 𝛽# and as such, the observations are only indirectly dependent on 𝛽. So, we can write: 𝑔(𝛽, 𝛽# |a, gcs) = 𝑓(a, gcs|𝛽# )𝑔(𝛽, 𝛽# ) 𝑓(a, gcs) (4) Next, we can rewrite the prior using the definition of conditional probability: 𝑔(𝛽, 𝛽# ) = 𝑔(𝛽# |𝛽)𝑔(𝛽) (5) Substituting this back into the previous expression for the posterior, we have: 𝑔(𝛽, 𝛽# |a, gcs) = 𝑓(a, gcs|𝛽# )𝑔(𝛽# |𝛽)𝑔(𝛽) 𝑓(a, gcs) (6) In the numerator, we see a chain of dependencies. The gcs simulations depend on 𝛽# . Parameters 𝛽# depend on hyperparameter 𝛽. Hyperparameter 𝛽 then has some hyperprior distribution. As such, this hierarchical model captures both the sample day-to-day variability, as well as the hyperparameter. We must specify a hyperprior, and a conditional prior, 𝑔(𝛽# |𝛽). Here, we have no reason to believe that we can distinguish any one 𝛽#,! from another prior to the experiment. As such, we can assume the conditional prior to behave in an exchangeable manner, where the label 𝑖 is not dependent on the permutations of the indices. Our expression for the posterior is: 2 𝑔(𝛽# , 𝛽 ∣ a, gcs) = 𝑓(a, gcs ∣ 𝛽# ) 9i!1# 𝑔(𝛽#,! ∣ 𝛽): 𝑔(𝛽) 𝑓(a, gcs) (7) The full hierarchical model is given by one additional level above Level 0 in Figure 37 that corresponds to individual aircraft campaign/season and ocean transect. This additional level 85 contains the parameter 𝛼, the overall parameter that is a result of the sampling replicates and the season/ocean transect. It is very difficult to sample the full hierarchical model with so many levels, and for practical reasons, we were not able to. However, given that each season/ocean transect is assumed to be independent, we can treat each season/ocean transect with a separate hierarchical model (that is shown in Figure 37), and then sample the posterior samples of those separate models to define a credible interval for overall 𝛼. Our statistical model is defined for campaign/transect, i, and the observed mole fraction, j, as follows: 𝜏!" = 0.05|Δ𝑡|!" + 0.01 𝛽! ∼ Norm(0.7,0.2) 𝛽#,!" ∼ Norm(𝛽! , 𝜏!" ) 𝛼! = 1/𝛽! 𝜎!" = 0.14 ⋅ tropht !" + 0.8 gcs!" ∼ LogNorm(𝛽#,!" ⋅ a!" , 𝜎!" ) (8) The likelihood is given by gcs!" , which represents the ijth mole fraction of GEOS-Chem simulated C3H8 and C2H6, and a!" represents the ijth C3H8 or C2H6 mole fraction observed by the aircraft. The uncertainty in gcs!" is given by 𝜎!" , which increases linearly with tropopause height, tropht !" , since we expect more variability in C3H8 or C2H6 mole fraction with high tropopause height that is often related with tropical intrusions. The conditional parameter, 𝛽#,!" , depends on a hyperprior distribution for the emissions scalar, 𝛽! (which is equivalent to 1/𝛼! ), and 𝜏!" , which describes variability in the emissions scalar due to transport errors in GEOS-Chem. As such, 𝜏!" depends on the difference between the original aircraft sampling time and the GEOS-Chem sampling replicate time (∆𝑡!" ) and increases with deviation between them. Development of this hierarchical model and our process for selecting priors are included in the SI. We assume each 𝛼! parameter from individual aircraft campaign season and ocean transect to be independent of one another. As such, to estimate a credible interval for an overall 𝛼, we draw a random sample of the posterior of hyperparameter 𝛼! for each campaign season and ocean transect. We take the mean of these samples and repeat this 10,000 times. (Note that we do not use the summer estimates for this calculation, for reasons described in Section 2.2, main text.) Details on the software used are described below. The 𝜏!" parameter has the effect of weighting the GEOS-Chem simulation replicate that falls on the plane path higher than the other replicates that do not. As such, GEOS-Chem simulation replicate that falls on the exact aircraft data collection time has more influence on the final result of 𝛽! parameter (the emission scalar). We would not expect meteorology to cause more than ± 0.5 86 variation in parameter 𝛽#,!" , as this would imply a very large variation in Tg after scaling emissions. As such, we vary 𝜏!" from 0.05 (the plane path day), to 0.33 for the furthest day from the plane path (± 2 days), (Figure S38). Figure S38. Prior for 𝜏!" parameter for the GEOS-Chem simulations in the Bayesian hierarchical model. The x-axis corresponds to the GEOS-Chem sample replicate, in units of days above or below the aircraft path (day 0). We define 𝜎!" parameter as a function of tropopause height. As discussed earlier, tropical air masses are characterized by very low mole fractions of C3H8 and C2H6 because in the tropics they have short lifetimes relative to transport. We assign higher 𝜎!" (lower weight) to GEOS-Chem simulations that have higher tropopause height, which extends the width of the lognormal distribution likelihood for those measurements. This de-weights the samples that have more tropical influence. (In practice, the model is quite robust against changes in 𝜎!" , so this implementation has a small impact – see results of the sampling the posterior in Section 4.7). We somewhat arbitrarily define 𝜎!" = 0.14 ⋅ tropht !" + 0.8, where tropht !" is the tropopause height in km associated for the jth aircraft observation. This equation results in 𝜎!" typically ranging from 1- 1.5 and implementing this range as the variance in a lognormal distribution centered at 1𝑥106) or 1𝑥1067 (typical of C2H6 or C3H8 measured mole fractions in remote atmospheres) results in a broad distribution that is consistent with mole fractions that we would expect for short-lived gases in remote atmospheres. The 1st and 99th percentiles of the resulting C3H8 distribution are 3𝑥1068 and 3𝑥106) , respectively, which is two orders of magnitude below and one order of magnitude above an average C3H8 mole fraction we would expect in the remote atmosphere. We find similar results for C2H6, except that it is centered at a value that is one magnitude larger. We use the same 𝜎!" when modeling both C3H8 and C2H6. An example of the value of 𝜎!" for ATom 2 observations over the Atlantic is shown in Figure S39. 87 Figure S39. Prior for the 𝝈𝒊𝒋 parameter for ATom 2 observations in the Bayesian hierarchical model. We expect the 𝛽! to be less than 1 since GEOS-Chem typically underestimates the aircraft observations. The prior for 𝛽! is weakly informative, centered at 0.7 with the 1st percentile at 0.23 and 99th percentile at 1.17 (Figure S40). Figure S40. Prior distribution for 𝜷𝒊 parameter in the Bayesian hierarchical model. We performed prior predictive checks26 to visualize the data our Bayesian model would generate given our priors. This check includes drawing parameter values from the prior distributions, plugging those parameters into the likelihood to generate pseudo data, and saving those data. These simulations gave us insight as to whether this was an appropriate model given our prior knowledge. The results of are satisfactory, as the empirical cumulative distribution functions are within what we expect given our prior knowledge. The results are shown in Figure S41. 88 Figure S41. Prior predictive checks during ATom 2, Atlantic curtain. Top: Empirical cumulative distribution function of pseudo data of GEOS-Chem simulations given our priors. Bottom: Empirical cumulative distribution function of pseudo data of the 𝛽#,!" parameter given our priors. We run our statistical model using Stan software27 (version 2.26) with CmdStanPy Python interface (version 0.9.67)28. We parse Markov chain sampling using ArviZ (version 0.11.1).29 We validate our hierarchical model using simulation-based calibration,30 and posterior predictive checks26 (described more below). We use bebi103 package (version 0.1.0)31 to execute simulation-based calibration, prepare data for Stan sampling, parse MCMC samples, plot posteriors and plot posterior predictive checks. We also use iqplot (version 0.1.6)32 to visualize empirical cumulative distribution functions of our priors. Finally, other software we use in our analysis includes Holoviews version 1.14.5,33 Bokeh version 2.3.3,34 Pandas version 1.3.1,35 SciPy version 1.6.2,36 and NumPy version 1.20.3.37 89 S5.2 Simulation based calibration Often, the posterior distribution is impossible to calculate analytically. Markov chain Monte Carlo (MCMC) allows us to sample out of an arbitrary probability distribution, where the probability of choosing a given value of a parameter is proportional to the posterior probability or probability density. Here, we use Stan to sample the posterior. Stan is a free, open source, state-of-the-art probabilistic programming language that has interfaces for many other programming languages. Stan translates the model into C++, which is then compiled into machine code. It uses Hamiltonian Monte Carlo (HMC),26 which allows for more efficient sampling of the posterior by taking large step sizes while taking into account the shape of the target distribution and tracing trajectories along it. We use CmdStanPy to install Stan, version 0.9.67. We use the bebi103 package31 to execute simulation-based calibration. Simulation-based calibration30 consists of the following general steps: 1) Draw a parameter set 𝜃w out of the prior; 2) Use 𝜃w to draw a data set 𝑦x out of the likelihood; 3) Perform HMC sampling of the posterior using 𝑦x as if it were the actual measured data set, and draw L HMC samples of the parameters; 4) Do steps 1-3 N times, on order of N = 1000. In step 3, we are using a data set for which we know the underlying parameters that generated it. Because the data were generated using 𝜃w as the parameter set, 𝜃w is now the ground truth parameter set. As such, we can check to see if we uncover the ground truth in the posterior sampling by calculating the z-score. We can also check whether the posterior is narrower than the prior (shrinkage), indicating that the data are informing the model. We compute a z-score for each parameter, 𝜃! , which measures how close the mean sampled parameter value is to the ground truth, relative to the posterior uncertainty in the parameter value: 𝑧! = 〈𝜃! 〉,:;< − 𝜃w! 𝜎!,,:;< (9) Here, 〈𝜃! 〉,:;< is the average value of 𝜃! over all posterior samples, and 𝜎!,,:;< is the standard deviation of 𝜃! over all posterior samples. The z-score should be symmetric about zero to indicate that there is no bias in estimating the ground truth, and should have a magnitude less than 5.30 Our z-score calculations are satisfactory, shown in Figure S42. 90 Figure S42. Z-score and shrinkage. Top: C2H6 during ATom 2 Atlantic curtain. Bottom: C3H8 during ATom 4 Atlantic curtain. Satisfactory z-score is symmetric about zero with a magnitude less than 5, while shrinkage should be around 1. S5.3 Posterior samples – ATom observations Below are our results for our HMC sampling of the posterior (Figure S43 and S44). The posterior of hierarchical models inherently has regions of high curvature, which can cause difficulties for HMC sampling. If HMC trajectories veer sharply due to this curvature, the Monte Carlo step ends in a divergence. We decreased the step size of the sampler to sample the areas of high curvature (increased the adapt_delta parameter to 0.99 in Stan). To further reduce problems with high curvature, we implemented a non-centered parametrization of 𝛽#,!" . We also set the warmup iterations to 2000 and conducted 1000 samples. Using bebi103’s stan.check_all_diagnostics() function, our sampling had effective sample size for all parameters (based on the suggestion of 50 effective samples per split chain):30 0 out of 4000 iterations ended with a divergence or saturated the maximum tree depth and the energy-Bayes fraction of missing information indicated no pathological behavior. We achieved these diagnostics for all runs of ATom and HIPPO. 91 Figure S43. HMC Posterior samples for 𝛽#,!" and 𝛽! parameters using C2H6 ATom 4 aircraft and GEOS-Chem simulations. Beta_1 parameter is a vector of length 5, corresponding to the synoptic replicates of GEOS-Chem. Beta_1[0] and beta_1[1] correspond to 2 days before the aircraft, beta_1[2] is the plane path, and beta_1[3] and beta_1[4] correspond to 2 days after the aircraft. The hyperparameter 𝛽! is represented by beta_. 92 Figure S44. HMC Posterior samples for 𝛽#,!" and 𝛽! parameters using C3H8 ATom 4 aircraft and GEOS-Chem simulations. Beta_1 parameter is a vector of length 5, corresponding to the synoptic replicates of GEOS-Chem. Beta_1[0] and beta_1[1] correspond to 2 days before the aircraft, beta_1[2] is the plane path, and beta_1[3] and beta_1[4] correspond to 2 days after the aircraft. The hyperparameter, 𝛽! , is represented by beta_. In Figure S45, we show a cross plot of our hyperparameter, 𝛽! and 𝛽#,!" , in inverse form, for a single ATom campaign, which directly corresponds to the scaling of our adjusted default emissions under the GEOS-Chem v13.0.0 simulations. This shows an example of the variability due to GEOS-Chem meteorology compared to the hyperparameter that we use to scale the emissions. In 93 Figure S46, we show the results of the Bayesian model for the 𝛼! emissions scalar estimate for all 4 ATom campaigns and ocean transects. Figure S45. Posterior samples of 𝛼#,!" vs 𝛼! during ATom 4. Top: C2H6 observations. Bottom: C3H8 observations. 94 Figure S46. 𝛼! hyperparameter estimate for each season during the ATom campaign. We do not include the summer values to calculate an overall 𝛼 estimate as discussed in the methods in the main text. Top: C2H6, Bottom: C3H8. S5.4 Posterior predictive check – ATom observations Posterior predictive checks involve drawing parameter values out of the posterior, using those parameters in the likelihood to generate a pseudo dataset, and repeat. We can see whether our Bayesian model can produce the observed data. Below, we show all posterior predictive checks for all ATom aircraft campaigns (Figures S47, S48). The majority of the measured data fell into the 30th and 50th percentile of the simulated Bayesian model data. The exception to this was the summer season, where the Bayesian model does not capture the measured aircraft data. This is expected, since during the summer we do not observe a robust relationship between potential temperature and C3H8 or C2H6. 95 Figure S47. Posterior predictive check of C2H6 using ATom data. Posterior predictive checks are explained in the text above. The pseudo data are shown in blue with 30, 50, 70, 99th percentiles. Please see Figure S46 for the estimated values of 𝛼! that were used to scale the GCS data in each season/transect. 96 97 Figure S48. Posterior predictive check of C3H8 using ATom data. (Posterior predictive checks are explained in the text above.) The pseudo data are shown in blue with 30, 50, 70, 99th percentiles. Please see Figure S46 for the estimated values of 𝛼! that were used to scale the GCS data in each season/transect. Both C3H8 and C2H6 aircraft observations feature high mole fractions during ATom 2 winter measurements at low potential temperature. The largest differences between the aircraft and GEOS-Chem simulations occur at high latitude and low altitude (Figure S49), subject to low altitude and cold environments. GEOS-Chem does not able to capture this variability, as discussed in Section 3.3 in the main text. 98 Figure S49. Difference between aircraft and GEOS-Chem C3H8 simulations. Simulations and aircraft observations during ATom 2, Atlantic transect, are shown. Points are colored by altitude (left) and potential temperature (right). S5.5 Posterior samples – HIPPO observations We show an example of our posterior sampling for our Bayesian model using HIPPO C2H6 and C3H8 observations in Figures S50 and S51 below. 99 Figure S50. HMC Posterior samples for 𝛽#,!" and 𝛽! parameters using C2H6 HIPPO 5 aircraft and GEOS-Chem simulations. Beta_1 parameter is a vector of length 5, corresponding to the synoptic replicates of GEOS-Chem. Beta_1[0] and beta_1[1] correspond to 2 days before the aircraft, beta_1[2] is the plane path, and beta_1[3] and beta_1[4] correspond to 2 days after the aircraft. The hyperparameter, 𝛽! , is represented by beta_. 100 Figure S51. HMC Posterior samples for 𝛽#,!" and 𝛽! parameters using C3H8 HIPPO 5 aircraft and GEOS-Chem simulations. Beta_1 parameter is a vector of length 5, corresponding to the synoptic replicates of GEOS-Chem. Beta_1[0] and beta_1[1] correspond to 2 days before the aircraft, beta_1[2] is the plane path, and beta_1[3] and beta_1[4] correspond to 2 days after the aircraft. The hyperparameter, 𝛽! , is represented by beta_. In Figure S52, we show a cross plot of our hyperparameter, 𝛽#,!" and 𝛽! , in inverse form, for a single HIPPO campaign, which directly corresponds to the scaling of the GEOS-Chem v13.0.0 emissions. This shows an example of the variability due to GEOS-Chem meteorology compared 101 to the hyperparameter that we use to scale the emissions. In Figure S53, we show the results of the Bayesian model for the 𝛼! emissions scalar estimate for all 5 HIPPO campaigns. Figure S52. Posterior samples of 𝛼#,!" vs 𝛼! during HIPPO 5. Top: C2H6 observations. Bottom: C3H8 observations. Figure S53. 𝛼! hyperparameter estimate for each season during the HIPPO campaign. We do not include the summer values to calculate an overall 𝛼 estimate as discussed in the methods in the 102 main text. Top: C2H6, Bottom: C3H8. There are many fewer observations during HIPPO than ATom resulting in a much larger spread and bigger uncertainty in defining 𝛼! . S5.6. Posterior predictive check – HIPPO observations Posterior predictive checks involve drawing parameter values out of the posterior, using those parameters in the likelihood to generate a pseudo dataset, and repeat. We can see whether our Bayesian model can produce the observed data. Below, we show all posterior predictive checks for all HIPPO aircraft campaigns (Figures S54, S55). 103 Figure S54. Posterior predictive check of C2H6 using HIPPO data. (Posterior predictive check method is described in the text above.) The pseudo data are shown in blue with 30, 50, 70, 99th percentiles. Please see Figure S53 for the estimated values of 𝛼! that were used to scale the GCS data in each season/transect. 104 Figure S55. Posterior predictive check of C3H8 using HIPPO data. (Posterior predictive check method is described in the text above.) The pseudo data are shown in blue with 30, 50, 70, 99th percentiles. Please see Figure S53 for the estimated values of 𝛼! that were used to scale the GCS data in each season/transect. During HIPPO 1 (winter 2009), observations are biased towards high latitudes and are subject to arctic conditions. Furthermore, the revised emissions may be missing a high latitude source. This, combined with a relatively lower number of HIPPO aircraft observations at lower latitudes, results in a substantial bias on the overall Bayesian emissions scalar estimate for C3H8 during winter 2009 (Figure S53). To illustrate sampling biases at high latitudes during the winter 2009 campaign, we obtain two Bayesian estimates of 𝛼! during each season: one estimate using aircraft observations restricted above 300 K (potential temperature) and those below 300 K. We see that observations restricted to values less than 300 K result in very high 𝛼! estimates that bias the overall 𝛼 scalar estimate (Figure S56-S57). 105 Figure S56. Bayesian 𝛼! hyperparameter estimate and posterior predictive checks using HIPPO aircraft observations > 300 K. 106 Figure S57. Bayesian 𝜶𝒊 hyperparameter estimate and posterior predictive checks using HIPPO aircraft observations < 300 K. 107 S5.7. Sigma parameter sensitivity analysis We use ATom aircraft/GEOS-Chem simulations of C3H8 to observe the effect of implementing an unchanging, large 𝜎!" parameter. (As a reminder, the 𝜎!" parameter has the effect of de-weighting GEOS-Chem simulations with higher tropopause height, since samples with high tropopause height tend to originate from the tropics, which is not useful for the purposes of our study. Please see Section 5.1 for more background on the parameters and the selected prior.) Here, we show that in practice, our model is quite robust against changes in 𝜎!" . Using an unchanging, relatively large 𝜎!" parameter equal to 3.5 in the lognormal likelihood yields 𝛼! hyperparameter estimates (Figure S58, S59) that are nearly identical to our results shown previously in which 𝜎!" varies according to tropopause height (Figure S45, S46). Furthermore, we obtain similar posterior predictive checks (Figure S60) as our previous results (Figure S48). Figure S58. Posterior samples of 𝛼#,!" vs 𝛼! using a scalar 𝜎!" parameter. We use 𝜎!" = 3.5 instead of the usual distribution in the lognormal likelihood during ATom 4 time period. Figure S59. Estimate of 𝛼 hyperparameter after using a scalar 𝜎!" parameter. We use 𝜎!" = 3.5 in the lognormal likelihood during ATom 4 time period. 108 109 Figure S60. Posterior predictive check for C3H8 using a scalar 𝜎!" parameter. We use 𝜎!" = 3.5 in the lognormal likelihood. S5.8. Estimating an overall emissions scalar To estimate a credible interval for an overall 𝛼, we draw a random sample of the posterior of hyperparameter 𝛼! for each campaign season and ocean transect. We take the mean of these samples and repeat this 10,000 times. (Note that we do not use the summer estimates for this calculation, for reasons described in the main text.) For ATom, the 95% confidence interval for 𝛼 of C2H6 is [1.02, 1.13] and for 𝛼 of C3H8, [1.15, 1.27]. For HIPPO, the confidence interval for 𝛼 of C2H6 is [1.06, 1.28] and for 𝛼 of C3H8, [1.45, 1.98]. S5.9 Estimating C2H6 and C3H8 Emissions GEOS-Chem v13.0.0 emissions were calculated using the Harmonized Emissions Component (HEMCO) v3.0.0, as described in section 2.3 in the main text. To estimate emissions over the Northern Hemisphere and the U.S., we calculate a simple integration by defining a rectangle that describes the latitude and longitude boundaries that approximately encloses the geographical region of interest. (Table S3 shows those boundary estimates.) We approximate latitude and longitude to meters using the Haversine formula. We then integrate the region of the emission grid computed by HEMCO of the anthropogenic variable using trapezoidal integration along latitude and longitude. When estimating global emissions, we do not impose any boundaries on latitude or longitude. After integration, we simply convert the resulting units of kg/second to Tg/year. 110 Table S3. Boundary estimates for emissions grid. Region US Northern Hemisphere Latitude Min 20 0 Latitude Max 50 80 Longitude Min -130 -165 Longitude Max -60 180 The anthropogenic variable does not include biomass burning or biofuel emissions, according to GEOS-Chem documentation. Finally, we scale the emissions estimate for each boundary region with an overall hyperparameter, 𝛼, estimated during ATom from section 5.8. We report fossil emissions using 95% CI of 𝛼 to define the variability. Our estimates for global fossil fuel emissions of C2H6 and C3H8 are [12.67, 13.98] (13.3 ± 0.7, 95% CI) and [13.89, 15.44] (14.7 ± 0.8, 95% CI) Tg/year, respectively (during the median year of 2017). Northern hemisphere emissions of C2H6 and C3H8 from fossil fuel production to be [11.18, 12.30] and [12.23, 13.60] Tg/year, respectively. In the U.S., we estimate C2H6 and C3H8 fossil fuel emissions at [1.29, 1.42] and [1.41, 1.56] Tg/year. Note that the global C2H6 emissions estimated in 2016-2018 are about 15% larger than in 2009-2011 ([10.55, 12.57] Tg/yr, Figure S61). Our C3H8 emissions are about 65% larger than in 2009-2011 ([7.31, 12.2] Tg/yr when not including the biased winter 2009 estimate that is impacted by arctic conditions and few observations. Our results are comparable to other studies (Figure S62). Figure S61. Global ethane and propane emissions during 2009-2018. “Unscaled” represent integrated default emissions from GEOS-Chem v13.0.0. “Revised C3” represent the revised C3H8 emissions after implementing the default v13.0.0 C2H6 proxy. “Scaled+Revised C3” represents the revised C3H8 emissions after scaling with our mean Bayesian estimate (Section 5.8). “Scaled C2” represent the revised emissions after scaling with our mean Bayesian estimate (Section 5.8). ∗: Note that our mean scaled C3 estimate shown here are skewed, as the 2009 winter HIPPO 111 observations are latitudinally biased. We show that C3 emissions increase by 65% from 2010 to 2017 when excluding the bias below in Figure S62. Figure S62. Global revised ethane and propane anthropogenic fossil emissions compared to other studies. Our emissions estimate in 2016-2018 (during ATom) and 2009-2011 (during HIPPO) includes GEOS-Chem v13.0.0 emissions for winter, fall and spring seasons scaled by 𝛼, that we determined with our Bayesian model during each season. As discussed in the text, fewer samples were obtained during HIPPO, resulting in a sampling bias that we test by restricting observations and simulations to ± 300K potential temperature (Figure S51-S52). This test affects the estimate about ± 1 Tg during 2010-2011 but affects our estimate by up to 12 Tg in 2009. ∗∶ This 2009 estimate is highly biased, as the latitudinal coverage of aircraft observations is not representative 112 of the global spatial distribution of methane emissions from oil and gas processes and the confidence interval stretches to nearly 40 Tg (please see Section 3.3 text and Figure S51-52). We compare our revised ethane and propane emissions to the default emissions from GEOS-Chem v13.0.0 (relevant anthropogenic inventories include Tzompa-Sosa et al. 201725 for C2H6, and Xiao et al. 20084 for C3H8). ‡∶ The studies included here38–41 represent anthropogenic fossil emissions, except Dalsøren et al. 2018 which also includes biofuel, agriculture, and waste. We obtained the CEDS CMIP6 estimate from Dalsøren et al. 2018. Our emissions estimates do not include biomass burning or biofuels. Please see Section 5 in the SI for more information on estimating these emissions. S6. Oil & Gas Emissions S6.1. Hydrocarbon wellhead composition We gathered hydrocarbon wellhead compositions reported in the literature for the top five natural gas-producing countries in the world (Table S4 and S5). Table S4. Statistical summaries of hydrocarbon wellhead composition for the globe. Units are in mole % for the US,42–49 Russia,50–56 Qatar,57 Iran,58 and Canada 59–62. Top: C1; Middle: C2; Bottom: C3. 113 Table S5. Statistical summaries of hydrocarbon wellhead composition in the U.S. Units are in mole %.42–49 Top: C1; Middle: C2; Bottom: C3. 114 Using Equation 2 (main text), we combine literature estimates of dry natural gas production and hydrocarbon composition measurements from a variety of basins (Table S4 and Table S5) to arrive at a global and U.S. C3/C1 emission ratio. We refer to this value as a “literature” emission ratio. For our global literature emission ratio, we use hydrocarbon and dry natural gas production data from the top 5 producing natural gas basins around the world that made up 50% of the total natural gas production in 2019. For our U.S. emission ratio, we include the top 7 natural gas producing basins that account for 86% of total U.S. natural gas production. The literature emission ratio of C2/C1 is calculated similarly. We arrive at a single literature emission estimate for both the US and globe (Figure 13, main text). Due to the limited published data on hydrocarbon composition, we compile data we found for a range of years: U.S. (2003-2020), Russia (1995-2018), Qatar (2005), Iran (2006), Canada (2004-2020). We calculate confidence intervals for each basin by performing a pairs bootstrap with co-measurements of hydrocarbon composition using the same bootstrap methods used with the NOAA and FRAPPE data as described in the methods section of the main text. Separately, we calculate an “implied” emission ratio by taking the ratio between our revised C3H8 emissions with several literature estimates of CH4 emissions from oil and natural gas processes. The results are shown in Figure S63. The implied emission ratio for our revised C2H6 is calculated similarly. For the EPA U.S. CH4 emissions estimate,63 we sum the categories “Natural Gas Systems”, “Petroleum Systems”, and “Abandoned Oil and Gas Wells” from Table 3-1 using the 2017 estimates (to match NOAA/ATom time period during 2016-2018). 115 Figure S63. Literature and Observationally-Informed Emission ratios. Top: U.S. basins; Bottom: Global basins. The weighted raw gas ratio represents the “literature ratio” described in the main text. OIER, ratios between our revised C2H6 and C3H8 emissions and literature CH4 emission estimates, are shown for several literature CH4 estimates, including Alvarez et al. 2018 (13 Tg/yr)64 and EPA 2017 estimate (7.8 Tg/yr, 2021 report)63 for U.S. basins, and IEA 2021 (76.4 Tg/yr),65 Scarpelli et al. 2020 (65.7 Tg/yr),66 and Global Carbon Project 2020 bottom-up estimate67 (128 Tg/yr, 2008-2017 average) for global basins. The variability in the literature ratio is attributed to the 95% CI of pairs bootstrap samples of hydrocarbon composition measurements (see main text for more detail). The variability in the OIER is attributed to the 95% CI of our revised C3H8 and C2H6 emission estimates. We also compare C3H8/CH4 and C2H6/CH4 correlations from in-situ observations, including NOAA observations from Northern Oklahoma (2017 average from Figure S21, units of kg/kg) and FRAPPE observations from Northern Colorado (2014 from Figure S9, units of kg/kg). The variability in the NOAA ratio is relatively low because it is calculated from a multi-year average slope, and the error in the slope is low (see Figure S21, left). The variability in the FRAPPE ratio is relatively high because we use the 95% CI derived directly from our bootstrap samples described in the main text. S6.2. Impact of reallocation of CH4 emissions on the transportation sector footprint There has been much debate about the greenhouse gas mitigation impact of switching from coal to natural gas energy in electricity production. The impact depends on how much CH4 is lost during natural gas production, processing, and transport as these losses will offset some of the benefits of the lower CO2 emissions. A study by the Environmental Defense Fund suggested that a CH4 leak rate greater than 3% would negate the climate benefits of switching from coal to gas in the near term (the current leak rate is estimated at 2.3%).68 As described here and in other studies, although CH4 emissions associated with dry natural gas production likely remain underestimated, flared and 116 vented associated gas from petroleum exploration contributes significantly to the total emissions. Since global oil production has continually increased over the past 3 decades (Figure S2), and our findings suggest that CH4 losses are at least proportional to production (but likely greater and biased towards oil-producing sites), a significant fraction of the estimated CH4 emissions may be misallocated to dry CH4 production and should instead be included with the oil production sector. Correctly attributing CH4 emissions from oil production to the transportation sector, rather than the power sector, increases the greenhouse gas footprint of petroleum-based transportation, while decreasing the greenhouse gas emissions ascribed to natural gas-powered power plants. As an example, if we assume that 20% of natural gas losses are associated with petroleum exploration (associated natural gas makes up 20% of total natural gas marketed production in the U.S.69), the CO2 equivalent footprint of the global transportation sector would increase by roughly 5%, using IEA’s estimate of 76 Tg/year CH4 emissions from oil and natural gas and recent transportation CO2 emission estimates.70,71 Equivalently, the U.S. transportation sector CO2 footprint would increase by 2%, using the EPA’s U.S. 2017 estimate (2021 report)63 of 7.8 Tg/year CH4 emissions and the U.S. petroleum/transportation sector CO2 (equivalent) footprint as reported by the EPA (2017 estimate, 2021 report)63. Both of our estimates are lower bounds that will only increase when accounting for vented and flared losses of associated natural gas that is not accounted for in marketed associated gas. Methods: For a global estimate, we estimate the transportation footprint from Figure 4 from Liu et al. 202071 and multiply it by 365 to get 7,300 Mmt (million metric tones) CO2 equivalents/year. We use 76 Tg/year of CH4 from (IEA)65 as a global estimate from oil and natural gas and find that 20% of that number results in 15.2 Tg, multiplied by 25 GWP, yields 6% of the transportation sector. Using the same process for the U.S., the EPA estimates the transportation sector at 1,740.2 Mmt CO2/year (Table 3-5, Petroleum fuel/Transportation sector for 2017).63 We use the EPA’s 7.8 Tg/year64 of CH4 for the oil and gas estimate and find that 20% of 7.8 Tg/year multiplied by 25 GWP results in 2.2% of the U.S. transportation sector. References (1) U.S. Energy Information Administration. Where our natural gas comes from https://www.eia.gov/energyexplained/natural-gas/where-our-natural-gas-comes-from.php (accessed 2022 -03 -18). (2) U.S. Energy Information Administration. 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All GEOS-Chem simulations were sampled along aircraft latitude and aduring single median time/longitude 6 “curtain” pressure and latitude. All GEOS-Chem simulations were sampled along aircraft latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 shows simulations sampled 5 days after the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the median aircraft time. FIRST row: 4x5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. SECOND row: 2x2.5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed 124 illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black. C3H8 is included in the main body. Figure A2. GEOS-Chem-simulated C3H8 “curtain” during ATom 1 summer 2016 campaign, along pressure and latitude. All GEOS-Chem simulations were sampled along aircraft latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 shows simulations sampled 5 days after the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the median aircraft time. FIRST row: 4x5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. SECOND row: 2x2.5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black. 125 Figure A3. GEOS-Chem-simulated C2H6 “curtain” during ATom 1 summer 2016 campaign, along pressure and latitude. All GEOS-Chem simulations were sampled along aircraft latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 shows simulations sampled 5 days after the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the median 126 aircraft time. FIRST row: 4x5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. SECOND row: 2x2.5 resolution, interpolated to 0.5x0.625 grid using latitude and pressure coordinates. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black. 127 Figure A4. GEOS-Chem-simulated C2H6 “curtain” during ATom 2 winter 2017 campaign, along potential temperature and latitude. All GEOS-Chem simulations were sampled along aircraft latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 shows simulations sampled 5 days after the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the median aircraft time. FIRST row: 4x5 resolution. SECOND row: 2x2.5 resolution. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black. C3H8 is included in the main body. 128 Figure A5. GEOS-Chem-simulated C3H8 “curtain” during ATom 1 summer 2016 campaign, along potential temperature and latitude. All GEOS-Chem simulations were sampled along aircraft latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 shows simulations sampled 5 days after the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the median aircraft time. FIRST row: 4x5 resolution. SECOND row: 2x2.5 resolution. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black. 129 130 Figure A6. GEOS-Chem-simulated C2H6 “curtain” during ATom 1 summer 2016 campaign, along potential temperature and latitude. All GEOS-Chem simulations were sampled along aircraft latitude and a single median time/longitude during the flight over the Atlantic ocean. Column 1 shows simulations sampled 5 days after the median aircraft time; Column 2 shows simulations sampled on the median aircraft time; Column 3 shows simulations sampled 5 days before the median aircraft time. FIRST row: 4x5 resolution. SECOND row: 2x2.5 resolution. THIRD row: 0.5x0.625 resolution. FOURTH row: a more detailed illustration of plot number r3,c2, with aircraft flight path shown in grey, the aircraft observations shown by triangle markers, and potential temperature contours shown in black. Figure A7. GEOS-Chem simulations and ATom aircraft C2H6 vs potential temperature. Left: Includes aircraft observations and simulations sampled 5 days after the aircraft flight path. Middle: Includes aircraft observations and simulations sampled during the aircraft flight path. Right: Includes aircraft observations and simulations 5 days before the aircraft flight path. C3H8 included in the main body. 131 Figure A8. C3H8 posterior samples for the conditional parameter and the hyperparameter during ATom 2 winter 2017. Top: 4x5. Middle: 2x2.5. Bottom: 0.5x0.625. 132 Figure A9. C2H6 posterior samples for the conditional parameter and the hyperparameter during ATom 2 winter 2017. Top: 4x5. Middle: 2x2.5. Bottom: 0.5x0.625. 133 As in Tribby et al. 2022, we conduct posterior predictive checks, which involve drawing parameter values out of the posterior, using those parameters in the likelihood to generate a pseudo dataset, and continue repeating. This allows us to see whether the Bayesian model reproduces the observed data. Below, we show all posterior predictive checks for ATom 2 atlantic aircraft campaign. The majority of the measured data fell into the 30th and 50th percentile of the simulated Bayesian model data. Figure A10. Posterior predictive check of C3H8 using ATom data. Left: 4x5. Middle: 2x2.5. Right: 0.5x0.625. Samples are during ATom 2 winter 2017. Pseudo data are shown in blue with 30, 50, 70, 99th percentiles. Please see Table 1 for values used to scale GCS data. Figure A11. Posterior predictive check of C2H6 using ATom data. Left: 4x5. Middle: 2x2.5. Right: 0.5x0.625. Samples are during ATom 2 winter 2017. Pseudo data are shown in blue with 30, 50, 70, 99th percentiles. Please see Table 1 for values used to scale GCS data. 134 Table A1. Bayesian inference 97.5% confidence interval. 𝛼 C3H8 𝛼 C2H6 4x5 [0.803 0.995] [0.878 1.094] 2 x 2.5 [0.809 1.012] [0.909 1.141] 0.5 x 0.625 [0.900 1.134] [0.952 1.204] 135 Appendix B Supplementary Information for “Towards Constraining Methane Emissions in Southern Oklahoma Using STILT Analysis of Remote Sensing and Flask Observations of Hydrocarbon Tracers” Figure B1. Temporal intersection between NOAA flask (aircraft + tower) and TCCON observations. Figure B2. Oil and gas well geospatial data from FrackTracker.org. 136 Figure B3. Density of oil and gas wells per .1x.1 degree grid. Figure B4. Well density (zoom in). The blue circles are the footprint lat/lon, and the squares are the 0.1x0.1 degree bins in which the density was calculated. The colorbar is in units of wells/cell. 137 Figure B5. Emissions of methane, ethane, and propane used as a prior for the STILT analysis. These emissions were computed as described in the main text. Emissions comparison to Alvarez et al. 2018 and Zhang et al. 2020 Our total emissions over the footprint area for CH4, in units of Tg/yr, are 7.63 +/- 1.4. We calcula ted the uncertainty by scaling the 0.5Tg/yr uncertainty from Zhang et al. 2020 to our density calc ulation. In comparison, We sum several southwestern basin estimates from Alvarez et al. 2018 wi th the Permian 2.7 Tg (from Zhang et al. 2020) to obtain 5.5 Tg/yr. This sum is missing several k ey basins that would affect our receptor site, including Anadarko (northern Oklahoma), Ardmore (southern Oklahoma), Gulf Coast (of Texas), Cherokee Platform (central Oklahoma). 138 Figure B6. Priors for key parameters in our Bayesian analysis. Our methodology for choosing these priors is explained in the main text.