Abstract

Identification and quantification of trace-gas sources is a major challenge for understanding and regulating air quality and greenhouse gas emissions. Current approaches provide either continuous but localized monitoring, or quasi-instantaneous “snapshot-in-time” regional monitoring. There is a need for emissions detection that provides both continuous and regional coverage, because sources and sinks can be episodic and spatially variable. We field deploy a dual frequency comb laser spectrometer for the first time, enabling an observing system that provides continuous detection of trace-gas sources over multiple-square-kilometer regions. Field tests simulating methane emissions from oil and gas production demonstrate detection and quantification of a 1.6  gmin1 source (less than the average emissions from a small pneumatic controller) from a distance of 1 km, and the ability to discern two leaks among a field of many potential sources. The technology achieves the goal of detecting, quantifying, and attributing emissions sources continuously through time, over large areas, and at emissions rates 1000× lower than current regional approaches. It therefore provides a useful tool for monitoring and mitigating undesirable sources and closes a major information gap in the atmospheric sciences.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]

2017 (7)

S. Schwietzke, G. Pétron, S. Conley, C. Pickering, I. Mielke-Maday, E. J. Dlugokencky, P. P. Tans, T. Vaughn, C. Bell, D. Zimmerle, S. Wolter, C. W. King, A. B. White, T. Coleman, L. Bianco, and R. C. Schnell, “Improved mechanistic understanding of natural gas methane emissions from spatially resolved aircraft measurements,” Environ. Sci. Technol. 51, 7286–7294 (2017).
[Crossref]

D. Zavala-Araiza, R. A. Alvarez, D. R. Lyon, D. T. Allen, A. J. Marchese, D. J. Zimmerle, and S. P. Hamburg, “Super-emitters in natural gas infrastructure are caused by abnormal process conditions,” Nat. Commun. 8, 14012 (2017).
[Crossref]

E. M. Waxman, K. C. Cossel, G.-W. Truong, F. R. Giorgetta, W. C. Swann, S. Coburn, R. J. Wright, G. B. Rieker, I. Coddington, and N. R. Newbury, “Intercomparison of open-path trace gas measurements with two dual-frequency-comb spectrometers,” Atmos. Meas. Tech. Katlenburg-Lindau 10, 3295–3311 (2017).
[Crossref]

P. J. Schroeder, R. J. Wright, S. Coburn, B. Sodergren, K. C. Cossel, S. Droste, G. W. Truong, E. Baumann, F. R. Giorgetta, I. Coddington, N. R. Newbury, and G. B. Rieker, “Dual frequency comb laser absorption spectroscopy in a 16  MW gas turbine exhaust,” Proc. Combust. Inst. 36, 4565–4573 (2017).
[Crossref]

A. P. Ravikumar, J. Wang, and A. R. Brandt, “Are optical gas imaging technologies effective for methane leak detection?” Environ. Sci. Technol. 51, 718–724 (2017).
[Crossref]

K. C. Cossel, E. M. Waxman, I. A. Finneran, G. A. Blake, J. Ye, and N. R. Newbury, “Gas-phase broadband spectroscopy using active sources: progress, status, and applications,” J. Opt. Soc. Am. B 34, 104–129 (2017).
[Crossref]

K. C. Cossel, E. M. Waxman, F. R. Giorgetta, M. Cermak, I. R. Coddington, D. Hesselius, S. Ruben, W. C. Swann, G.-W. Truong, G. B. Rieker, and N. R. Newbury, “Open-path dual-comb spectroscopy to an airborne retroreflector,” Optica 4, 724–728 (2017).
[Crossref]

2016 (5)

I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3, 414–426 (2016).
[Crossref]

G.-W. Truong, E. M. Waxman, K. C. Cossel, E. Baumann, A. Klose, F. R. Giorgetta, W. C. Swann, N. R. Newbury, and I. Coddington, “Accurate frequency referencing for fieldable dual-comb spectroscopy,” Opt. Express 24, 30495–30504 (2016).
[Crossref]

D. J. Jacob, A. J. Turner, J. D. Maasakkers, J. Sheng, K. Sun, X. Liu, K. Chance, I. Aben, J. McKeever, and C. Frankenberg, “Satellite observations of atmospheric methane and their value for quantifying methane emissions,” Atmos. Chem. Phys. 16, 14371–14396 (2016).
[Crossref]

S. Conley, G. Franco, I. Faloona, D. R. Blake, J. Peischl, and T. B. Ryerson, “Methane emissions from the 2015 Aliso Canyon blowout in Los Angeles, CA,” Science 351, 1317–1320 (2016).
[Crossref]

T. Lauvaux, N. L. Miles, A. Deng, S. J. Richardson, M. O. Cambaliza, K. J. Davis, B. Gaudet, K. R. Gurney, J. Huang, D. O’Keefe, Y. Song, A. Karion, T. Oda, R. Patarasuk, I. Razlivanov, D. Sarmiento, P. Shepson, C. Sweeney, J. Turnbull, and K. Wu, “High-resolution atmospheric inversion of urban CO2 emissions during the dormant season of the Indianapolis Flux Experiment (INFLUX),” J. Geophys. Res. Atmos. 121, 5213–5236 (2016).
[Crossref]

2015 (5)

D. T. Allen, A. P. Pacsi, D. W. Sullivan, D. Zavala-Araiza, M. Harrison, K. Keen, M. P. Fraser, A. Daniel Hill, R. F. Sawyer, and J. H. Seinfeld, “Methane emissions from process equipment at natural gas production sites in the United States: pneumatic controllers,” Environ. Sci. Technol. 49, 633–640 (2015).
[Crossref]

L. C. Sinclair, J.-D. Deschênes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “Invited article: a compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86, 081301 (2015).
[Crossref]

S. Okubo, K. Iwakuni, H. Inaba, K. Hosaka, A. Onae, H. Sasada, and F.-L. Hong, “Ultra-broadband dual-comb spectroscopy across 1.0-1.9 μm,” Appl. Phys. Express 8, 082402 (2015).
[Crossref]

T. I. Yacovitch, S. C. Herndon, G. Pétron, J. Kofler, D. Lyon, M. S. Zahniser, and C. E. Kolb, “Mobile laboratory observations of methane emissions in the Barnett Shale region,” Environ. Sci. Technol. 49, 7889–7895 (2015).
[Crossref]

J. R. Roscioli, T. I. Yacovitch, C. Floerchinger, A. L. Mitchell, D. S. Tkacik, R. Subramanian, D. M. Martinez, T. L. Vaughn, L. Williams, D. Zimmerle, A. L. Robinson, S. C. Herndon, and A. J. Marchese, “Measurements of methane emissions from natural gas gathering facilities and processing plants: measurement methods,” Atmos. Meas. Tech. 8, 2017–2035 (2015).
[Crossref]

2014 (9)

G. Pétron, A. Karion, C. Sweeney, B. R. Miller, S. A. Montzka, G. J. Frost, M. Trainer, P. Tans, A. Andrews, J. Kofler, D. Helmig, D. Guenther, E. Dlugokencky, P. Lang, T. Newberger, S. Wolter, B. Hall, P. Novelli, A. Brewer, S. Conley, M. Hardesty, R. Banta, A. White, D. Noone, D. Wolfe, and R. Schnell, “A new look at methane and nonmethane hydrocarbon emissions from oil and natural gas operations in the Colorado Denver-Julesburg Basin,” J. Geophys. Res. Atmospheres 119, 6836–6852 (2014).
[Crossref]

L. C. Sinclair, I. Coddington, W. C. Swann, G. B. Rieker, A. Hati, K. Iwakuni, and N. R. Newbury, “Operation of an optically coherent frequency comb outside the metrology lab,” Opt. Express 22, 6996–7006 (2014).
[Crossref]

G. B. Rieker, F. R. Giorgetta, W. C. Swann, J. Kofler, A. M. Zolot, L. C. Sinclair, E. Baumann, C. Cromer, G. Petron, C. Sweeney, P. P. Tans, I. Coddington, and N. R. Newbury, “Frequency-comb-based remote sensing of greenhouse gases over kilometer air paths,” Optica 1, 290–298 (2014).
[Crossref]

H. L. Brantley, E. D. Thoma, W. C. Squier, B. B. Guven, and D. Lyon, “Assessment of methane emissions from oil and gas production pads using mobile measurements,” Environ. Sci. Technol. 48, 14508–14515 (2014).
[Crossref]

M. O. L. Cambaliza, P. B. Shepson, D. R. Caulton, B. Stirm, D. Samarov, K. R. Gurney, J. Turnbull, K. J. Davis, A. Possolo, A. Karion, C. Sweeney, B. Moser, A. Hendricks, T. Lauvaux, K. Mays, J. Whetstone, J. Huang, I. Razlivanov, N. L. Miles, and S. J. Richardson, “Assessment of uncertainties of an aircraft-based mass balance approach for quantifying urban greenhouse gas emissions,” Atmos. Chem. Phys. 14, 9029–9050 (2014).
[Crossref]

M. Cassinerio, A. Gambetta, N. Coluccelli, P. Laporta, and G. Galzerano, “Absolute dual-comb spectroscopy at 1.55  μm by free-running Er:fiber lasers,” Appl. Phys. Lett. 104, 231102 (2014).
[Crossref]

C. W. Moore, B. Zielinska, G. Pétron, and R. B. Jackson, “Air impacts of increased natural gas acquisition, processing, and use: a critical review,” Environ. Sci. Technol. 48, 8349–8359 (2014).
[Crossref]

A. R. Brandt, G. A. Heath, E. A. Kort, F. O’Sullivan, G. Pétron, S. M. Jordaan, P. Tans, J. Wilcox, A. M. Gopstein, D. Arent, S. Wofsy, N. J. Brown, R. Bradley, G. D. Stucky, D. Eardley, and R. Harriss, “Methane leaks from North American natural gas systems,” Science 343, 733–735 (2014).
[Crossref]

T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5, 3375 (2014).
[Crossref]

2013 (1)

S. M. Miller, S. C. Wofsy, A. M. Michalak, E. A. Kort, A. E. Andrews, S. C. Biraud, E. J. Dlugokencky, J. Eluszkiewicz, M. L. Fischer, G. Janssens-Maenhout, B. R. Miller, J. B. Miller, S. A. Montzka, T. Nehrkorn, and C. Sweeney, “Anthropogenic emissions of methane in the United States,” Proc. Natl. Acad. Sci. USA 110, 20018–20022 (2013).
[Crossref]

2012 (4)

G. Pétron, G. Frost, B. R. Miller, A. I. Hirsch, S. A. Montzka, A. Karion, M. Trainer, C. Sweeney, A. E. Andrews, L. Miller, J. Kofler, A. Bar-Ilan, E. J. Dlugokencky, L. Patrick, C. T. Moore, T. B. Ryerson, C. Siso, W. Kolodzey, P. M. Lang, T. Conway, P. Novelli, K. Masarie, B. Hall, D. Guenther, D. Kitzis, J. Miller, D. Welsh, D. Wolfe, W. Neff, and P. Tans, “Hydrocarbon emissions characterization in the Colorado front range: a pilot study,” J. Geophys. Res. Atmos. 117, D04304 (2012).
[Crossref]

J. Roy, J.-D. Deschênes, S. Potvin, and J. Genest, “Continuous real-time correction and averaging for frequency comb interferometry,” Opt. Express 20, 21932–21939 (2012).
[Crossref]

R. A. Alvarez, S. W. Pacala, J. J. Winebrake, W. L. Chameides, and S. P. Hamburg, “Greater focus needed on methane leakage from natural gas infrastructure,” Proc. Natl. Acad. Sci. 109, 6435–6440 (2012).
[Crossref]

A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6, 440–449 (2012).
[Crossref]

2010 (1)

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: technology and applications,” Annu. Rev. Anal. Chem. 3, 175–205 (2010).
[Crossref]

2006 (2)

J. L. Hall, “Nobel lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279–1295 (2006).
[Crossref]

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[Crossref]

2005 (2)

A. Schliesser, M. Brehm, F. Keilmann, and D. W. van der Weide, “Frequency-comb infrared spectrometer for rapid, remote chemical sensing,” Opt. Express 13, 9029–9038 (2005).
[Crossref]

C. Frankenberg, J. F. Meirink, M. van Weele, U. Platt, and T. Wagner, “Assessing methane emissions from global space-borne observations,” Science 308, 1010–1014 (2005).
[Crossref]

Aben, I.

D. J. Jacob, A. J. Turner, J. D. Maasakkers, J. Sheng, K. Sun, X. Liu, K. Chance, I. Aben, J. McKeever, and C. Frankenberg, “Satellite observations of atmospheric methane and their value for quantifying methane emissions,” Atmos. Chem. Phys. 16, 14371–14396 (2016).
[Crossref]

Adler, F.

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: technology and applications,” Annu. Rev. Anal. Chem. 3, 175–205 (2010).
[Crossref]

Alden, C. B.

C. B. Alden, S. Ghosh, S. Coburn, C. Sweeney, A. Karion, R. Wright, I. Coddington, K. Prasad, and G. B. Rieker, “Methane leak detection and sizing over long distances using dual frequency comb laser spectroscopy and a bootstrap inversion technique,” Atmos. Meas. Tech. Discuss. (in review, 2017), DOI: 10.5194/amt-2017-262.
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D. Zavala-Araiza, R. A. Alvarez, D. R. Lyon, D. T. Allen, A. J. Marchese, D. J. Zimmerle, and S. P. Hamburg, “Super-emitters in natural gas infrastructure are caused by abnormal process conditions,” Nat. Commun. 8, 14012 (2017).
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D. T. Allen, A. P. Pacsi, D. W. Sullivan, D. Zavala-Araiza, M. Harrison, K. Keen, M. P. Fraser, A. Daniel Hill, R. F. Sawyer, and J. H. Seinfeld, “Methane emissions from process equipment at natural gas production sites in the United States: pneumatic controllers,” Environ. Sci. Technol. 49, 633–640 (2015).
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Alvarez, R. A.

D. Zavala-Araiza, R. A. Alvarez, D. R. Lyon, D. T. Allen, A. J. Marchese, D. J. Zimmerle, and S. P. Hamburg, “Super-emitters in natural gas infrastructure are caused by abnormal process conditions,” Nat. Commun. 8, 14012 (2017).
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R. A. Alvarez, S. W. Pacala, J. J. Winebrake, W. L. Chameides, and S. P. Hamburg, “Greater focus needed on methane leakage from natural gas infrastructure,” Proc. Natl. Acad. Sci. 109, 6435–6440 (2012).
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Andrews, A.

G. Pétron, A. Karion, C. Sweeney, B. R. Miller, S. A. Montzka, G. J. Frost, M. Trainer, P. Tans, A. Andrews, J. Kofler, D. Helmig, D. Guenther, E. Dlugokencky, P. Lang, T. Newberger, S. Wolter, B. Hall, P. Novelli, A. Brewer, S. Conley, M. Hardesty, R. Banta, A. White, D. Noone, D. Wolfe, and R. Schnell, “A new look at methane and nonmethane hydrocarbon emissions from oil and natural gas operations in the Colorado Denver-Julesburg Basin,” J. Geophys. Res. Atmospheres 119, 6836–6852 (2014).
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Andrews, A. E.

S. M. Miller, S. C. Wofsy, A. M. Michalak, E. A. Kort, A. E. Andrews, S. C. Biraud, E. J. Dlugokencky, J. Eluszkiewicz, M. L. Fischer, G. Janssens-Maenhout, B. R. Miller, J. B. Miller, S. A. Montzka, T. Nehrkorn, and C. Sweeney, “Anthropogenic emissions of methane in the United States,” Proc. Natl. Acad. Sci. USA 110, 20018–20022 (2013).
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G. Pétron, G. Frost, B. R. Miller, A. I. Hirsch, S. A. Montzka, A. Karion, M. Trainer, C. Sweeney, A. E. Andrews, L. Miller, J. Kofler, A. Bar-Ilan, E. J. Dlugokencky, L. Patrick, C. T. Moore, T. B. Ryerson, C. Siso, W. Kolodzey, P. M. Lang, T. Conway, P. Novelli, K. Masarie, B. Hall, D. Guenther, D. Kitzis, J. Miller, D. Welsh, D. Wolfe, W. Neff, and P. Tans, “Hydrocarbon emissions characterization in the Colorado front range: a pilot study,” J. Geophys. Res. Atmos. 117, D04304 (2012).
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Arent, D.

A. R. Brandt, G. A. Heath, E. A. Kort, F. O’Sullivan, G. Pétron, S. M. Jordaan, P. Tans, J. Wilcox, A. M. Gopstein, D. Arent, S. Wofsy, N. J. Brown, R. Bradley, G. D. Stucky, D. Eardley, and R. Harriss, “Methane leaks from North American natural gas systems,” Science 343, 733–735 (2014).
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Banta, R.

G. Pétron, A. Karion, C. Sweeney, B. R. Miller, S. A. Montzka, G. J. Frost, M. Trainer, P. Tans, A. Andrews, J. Kofler, D. Helmig, D. Guenther, E. Dlugokencky, P. Lang, T. Newberger, S. Wolter, B. Hall, P. Novelli, A. Brewer, S. Conley, M. Hardesty, R. Banta, A. White, D. Noone, D. Wolfe, and R. Schnell, “A new look at methane and nonmethane hydrocarbon emissions from oil and natural gas operations in the Colorado Denver-Julesburg Basin,” J. Geophys. Res. Atmospheres 119, 6836–6852 (2014).
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Bar-Ilan, A.

G. Pétron, G. Frost, B. R. Miller, A. I. Hirsch, S. A. Montzka, A. Karion, M. Trainer, C. Sweeney, A. E. Andrews, L. Miller, J. Kofler, A. Bar-Ilan, E. J. Dlugokencky, L. Patrick, C. T. Moore, T. B. Ryerson, C. Siso, W. Kolodzey, P. M. Lang, T. Conway, P. Novelli, K. Masarie, B. Hall, D. Guenther, D. Kitzis, J. Miller, D. Welsh, D. Wolfe, W. Neff, and P. Tans, “Hydrocarbon emissions characterization in the Colorado front range: a pilot study,” J. Geophys. Res. Atmos. 117, D04304 (2012).
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Baumann, E.

P. J. Schroeder, R. J. Wright, S. Coburn, B. Sodergren, K. C. Cossel, S. Droste, G. W. Truong, E. Baumann, F. R. Giorgetta, I. Coddington, N. R. Newbury, and G. B. Rieker, “Dual frequency comb laser absorption spectroscopy in a 16  MW gas turbine exhaust,” Proc. Combust. Inst. 36, 4565–4573 (2017).
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G.-W. Truong, E. M. Waxman, K. C. Cossel, E. Baumann, A. Klose, F. R. Giorgetta, W. C. Swann, N. R. Newbury, and I. Coddington, “Accurate frequency referencing for fieldable dual-comb spectroscopy,” Opt. Express 24, 30495–30504 (2016).
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L. C. Sinclair, J.-D. Deschênes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “Invited article: a compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86, 081301 (2015).
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G. B. Rieker, F. R. Giorgetta, W. C. Swann, J. Kofler, A. M. Zolot, L. C. Sinclair, E. Baumann, C. Cromer, G. Petron, C. Sweeney, P. P. Tans, I. Coddington, and N. R. Newbury, “Frequency-comb-based remote sensing of greenhouse gases over kilometer air paths,” Optica 1, 290–298 (2014).
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Bell, C.

S. Schwietzke, G. Pétron, S. Conley, C. Pickering, I. Mielke-Maday, E. J. Dlugokencky, P. P. Tans, T. Vaughn, C. Bell, D. Zimmerle, S. Wolter, C. W. King, A. B. White, T. Coleman, L. Bianco, and R. C. Schnell, “Improved mechanistic understanding of natural gas methane emissions from spatially resolved aircraft measurements,” Environ. Sci. Technol. 51, 7286–7294 (2017).
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Bianco, L.

S. Schwietzke, G. Pétron, S. Conley, C. Pickering, I. Mielke-Maday, E. J. Dlugokencky, P. P. Tans, T. Vaughn, C. Bell, D. Zimmerle, S. Wolter, C. W. King, A. B. White, T. Coleman, L. Bianco, and R. C. Schnell, “Improved mechanistic understanding of natural gas methane emissions from spatially resolved aircraft measurements,” Environ. Sci. Technol. 51, 7286–7294 (2017).
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S. M. Miller, S. C. Wofsy, A. M. Michalak, E. A. Kort, A. E. Andrews, S. C. Biraud, E. J. Dlugokencky, J. Eluszkiewicz, M. L. Fischer, G. Janssens-Maenhout, B. R. Miller, J. B. Miller, S. A. Montzka, T. Nehrkorn, and C. Sweeney, “Anthropogenic emissions of methane in the United States,” Proc. Natl. Acad. Sci. USA 110, 20018–20022 (2013).
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S. Conley, G. Franco, I. Faloona, D. R. Blake, J. Peischl, and T. B. Ryerson, “Methane emissions from the 2015 Aliso Canyon blowout in Los Angeles, CA,” Science 351, 1317–1320 (2016).
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Blake, G. A.

Bradley, R.

A. R. Brandt, G. A. Heath, E. A. Kort, F. O’Sullivan, G. Pétron, S. M. Jordaan, P. Tans, J. Wilcox, A. M. Gopstein, D. Arent, S. Wofsy, N. J. Brown, R. Bradley, G. D. Stucky, D. Eardley, and R. Harriss, “Methane leaks from North American natural gas systems,” Science 343, 733–735 (2014).
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A. P. Ravikumar, J. Wang, and A. R. Brandt, “Are optical gas imaging technologies effective for methane leak detection?” Environ. Sci. Technol. 51, 718–724 (2017).
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A. R. Brandt, G. A. Heath, E. A. Kort, F. O’Sullivan, G. Pétron, S. M. Jordaan, P. Tans, J. Wilcox, A. M. Gopstein, D. Arent, S. Wofsy, N. J. Brown, R. Bradley, G. D. Stucky, D. Eardley, and R. Harriss, “Methane leaks from North American natural gas systems,” Science 343, 733–735 (2014).
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H. L. Brantley, E. D. Thoma, W. C. Squier, B. B. Guven, and D. Lyon, “Assessment of methane emissions from oil and gas production pads using mobile measurements,” Environ. Sci. Technol. 48, 14508–14515 (2014).
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Brewer, A.

G. Pétron, A. Karion, C. Sweeney, B. R. Miller, S. A. Montzka, G. J. Frost, M. Trainer, P. Tans, A. Andrews, J. Kofler, D. Helmig, D. Guenther, E. Dlugokencky, P. Lang, T. Newberger, S. Wolter, B. Hall, P. Novelli, A. Brewer, S. Conley, M. Hardesty, R. Banta, A. White, D. Noone, D. Wolfe, and R. Schnell, “A new look at methane and nonmethane hydrocarbon emissions from oil and natural gas operations in the Colorado Denver-Julesburg Basin,” J. Geophys. Res. Atmospheres 119, 6836–6852 (2014).
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Brown, N. J.

A. R. Brandt, G. A. Heath, E. A. Kort, F. O’Sullivan, G. Pétron, S. M. Jordaan, P. Tans, J. Wilcox, A. M. Gopstein, D. Arent, S. Wofsy, N. J. Brown, R. Bradley, G. D. Stucky, D. Eardley, and R. Harriss, “Methane leaks from North American natural gas systems,” Science 343, 733–735 (2014).
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T. Lauvaux, N. L. Miles, A. Deng, S. J. Richardson, M. O. Cambaliza, K. J. Davis, B. Gaudet, K. R. Gurney, J. Huang, D. O’Keefe, Y. Song, A. Karion, T. Oda, R. Patarasuk, I. Razlivanov, D. Sarmiento, P. Shepson, C. Sweeney, J. Turnbull, and K. Wu, “High-resolution atmospheric inversion of urban CO2 emissions during the dormant season of the Indianapolis Flux Experiment (INFLUX),” J. Geophys. Res. Atmos. 121, 5213–5236 (2016).
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M. O. L. Cambaliza, P. B. Shepson, D. R. Caulton, B. Stirm, D. Samarov, K. R. Gurney, J. Turnbull, K. J. Davis, A. Possolo, A. Karion, C. Sweeney, B. Moser, A. Hendricks, T. Lauvaux, K. Mays, J. Whetstone, J. Huang, I. Razlivanov, N. L. Miles, and S. J. Richardson, “Assessment of uncertainties of an aircraft-based mass balance approach for quantifying urban greenhouse gas emissions,” Atmos. Chem. Phys. 14, 9029–9050 (2014).
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M. Cassinerio, A. Gambetta, N. Coluccelli, P. Laporta, and G. Galzerano, “Absolute dual-comb spectroscopy at 1.55  μm by free-running Er:fiber lasers,” Appl. Phys. Lett. 104, 231102 (2014).
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M. O. L. Cambaliza, P. B. Shepson, D. R. Caulton, B. Stirm, D. Samarov, K. R. Gurney, J. Turnbull, K. J. Davis, A. Possolo, A. Karion, C. Sweeney, B. Moser, A. Hendricks, T. Lauvaux, K. Mays, J. Whetstone, J. Huang, I. Razlivanov, N. L. Miles, and S. J. Richardson, “Assessment of uncertainties of an aircraft-based mass balance approach for quantifying urban greenhouse gas emissions,” Atmos. Chem. Phys. 14, 9029–9050 (2014).
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Cermak, M.

Chameides, W. L.

R. A. Alvarez, S. W. Pacala, J. J. Winebrake, W. L. Chameides, and S. P. Hamburg, “Greater focus needed on methane leakage from natural gas infrastructure,” Proc. Natl. Acad. Sci. 109, 6435–6440 (2012).
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D. J. Jacob, A. J. Turner, J. D. Maasakkers, J. Sheng, K. Sun, X. Liu, K. Chance, I. Aben, J. McKeever, and C. Frankenberg, “Satellite observations of atmospheric methane and their value for quantifying methane emissions,” Atmos. Chem. Phys. 16, 14371–14396 (2016).
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P. J. Schroeder, R. J. Wright, S. Coburn, B. Sodergren, K. C. Cossel, S. Droste, G. W. Truong, E. Baumann, F. R. Giorgetta, I. Coddington, N. R. Newbury, and G. B. Rieker, “Dual frequency comb laser absorption spectroscopy in a 16  MW gas turbine exhaust,” Proc. Combust. Inst. 36, 4565–4573 (2017).
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E. M. Waxman, K. C. Cossel, G.-W. Truong, F. R. Giorgetta, W. C. Swann, S. Coburn, R. J. Wright, G. B. Rieker, I. Coddington, and N. R. Newbury, “Intercomparison of open-path trace gas measurements with two dual-frequency-comb spectrometers,” Atmos. Meas. Tech. Katlenburg-Lindau 10, 3295–3311 (2017).
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C. B. Alden, S. Ghosh, S. Coburn, C. Sweeney, A. Karion, R. Wright, I. Coddington, K. Prasad, and G. B. Rieker, “Methane leak detection and sizing over long distances using dual frequency comb laser spectroscopy and a bootstrap inversion technique,” Atmos. Meas. Tech. Discuss. (in review, 2017), DOI: 10.5194/amt-2017-262.
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Coddington, I.

P. J. Schroeder, R. J. Wright, S. Coburn, B. Sodergren, K. C. Cossel, S. Droste, G. W. Truong, E. Baumann, F. R. Giorgetta, I. Coddington, N. R. Newbury, and G. B. Rieker, “Dual frequency comb laser absorption spectroscopy in a 16  MW gas turbine exhaust,” Proc. Combust. Inst. 36, 4565–4573 (2017).
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E. M. Waxman, K. C. Cossel, G.-W. Truong, F. R. Giorgetta, W. C. Swann, S. Coburn, R. J. Wright, G. B. Rieker, I. Coddington, and N. R. Newbury, “Intercomparison of open-path trace gas measurements with two dual-frequency-comb spectrometers,” Atmos. Meas. Tech. Katlenburg-Lindau 10, 3295–3311 (2017).
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I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3, 414–426 (2016).
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G.-W. Truong, E. M. Waxman, K. C. Cossel, E. Baumann, A. Klose, F. R. Giorgetta, W. C. Swann, N. R. Newbury, and I. Coddington, “Accurate frequency referencing for fieldable dual-comb spectroscopy,” Opt. Express 24, 30495–30504 (2016).
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L. C. Sinclair, J.-D. Deschênes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “Invited article: a compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86, 081301 (2015).
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G. B. Rieker, F. R. Giorgetta, W. C. Swann, J. Kofler, A. M. Zolot, L. C. Sinclair, E. Baumann, C. Cromer, G. Petron, C. Sweeney, P. P. Tans, I. Coddington, and N. R. Newbury, “Frequency-comb-based remote sensing of greenhouse gases over kilometer air paths,” Optica 1, 290–298 (2014).
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L. C. Sinclair, I. Coddington, W. C. Swann, G. B. Rieker, A. Hati, K. Iwakuni, and N. R. Newbury, “Operation of an optically coherent frequency comb outside the metrology lab,” Opt. Express 22, 6996–7006 (2014).
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C. B. Alden, S. Ghosh, S. Coburn, C. Sweeney, A. Karion, R. Wright, I. Coddington, K. Prasad, and G. B. Rieker, “Methane leak detection and sizing over long distances using dual frequency comb laser spectroscopy and a bootstrap inversion technique,” Atmos. Meas. Tech. Discuss. (in review, 2017), DOI: 10.5194/amt-2017-262.
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Coddington, I. R.

Coleman, T.

S. Schwietzke, G. Pétron, S. Conley, C. Pickering, I. Mielke-Maday, E. J. Dlugokencky, P. P. Tans, T. Vaughn, C. Bell, D. Zimmerle, S. Wolter, C. W. King, A. B. White, T. Coleman, L. Bianco, and R. C. Schnell, “Improved mechanistic understanding of natural gas methane emissions from spatially resolved aircraft measurements,” Environ. Sci. Technol. 51, 7286–7294 (2017).
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Coluccelli, N.

M. Cassinerio, A. Gambetta, N. Coluccelli, P. Laporta, and G. Galzerano, “Absolute dual-comb spectroscopy at 1.55  μm by free-running Er:fiber lasers,” Appl. Phys. Lett. 104, 231102 (2014).
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Conley, S.

S. Schwietzke, G. Pétron, S. Conley, C. Pickering, I. Mielke-Maday, E. J. Dlugokencky, P. P. Tans, T. Vaughn, C. Bell, D. Zimmerle, S. Wolter, C. W. King, A. B. White, T. Coleman, L. Bianco, and R. C. Schnell, “Improved mechanistic understanding of natural gas methane emissions from spatially resolved aircraft measurements,” Environ. Sci. Technol. 51, 7286–7294 (2017).
[Crossref]

S. Conley, G. Franco, I. Faloona, D. R. Blake, J. Peischl, and T. B. Ryerson, “Methane emissions from the 2015 Aliso Canyon blowout in Los Angeles, CA,” Science 351, 1317–1320 (2016).
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G. Pétron, A. Karion, C. Sweeney, B. R. Miller, S. A. Montzka, G. J. Frost, M. Trainer, P. Tans, A. Andrews, J. Kofler, D. Helmig, D. Guenther, E. Dlugokencky, P. Lang, T. Newberger, S. Wolter, B. Hall, P. Novelli, A. Brewer, S. Conley, M. Hardesty, R. Banta, A. White, D. Noone, D. Wolfe, and R. Schnell, “A new look at methane and nonmethane hydrocarbon emissions from oil and natural gas operations in the Colorado Denver-Julesburg Basin,” J. Geophys. Res. Atmospheres 119, 6836–6852 (2014).
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Conway, T.

G. Pétron, G. Frost, B. R. Miller, A. I. Hirsch, S. A. Montzka, A. Karion, M. Trainer, C. Sweeney, A. E. Andrews, L. Miller, J. Kofler, A. Bar-Ilan, E. J. Dlugokencky, L. Patrick, C. T. Moore, T. B. Ryerson, C. Siso, W. Kolodzey, P. M. Lang, T. Conway, P. Novelli, K. Masarie, B. Hall, D. Guenther, D. Kitzis, J. Miller, D. Welsh, D. Wolfe, W. Neff, and P. Tans, “Hydrocarbon emissions characterization in the Colorado front range: a pilot study,” J. Geophys. Res. Atmos. 117, D04304 (2012).
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Cossel, K. C.

K. C. Cossel, E. M. Waxman, F. R. Giorgetta, M. Cermak, I. R. Coddington, D. Hesselius, S. Ruben, W. C. Swann, G.-W. Truong, G. B. Rieker, and N. R. Newbury, “Open-path dual-comb spectroscopy to an airborne retroreflector,” Optica 4, 724–728 (2017).
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P. J. Schroeder, R. J. Wright, S. Coburn, B. Sodergren, K. C. Cossel, S. Droste, G. W. Truong, E. Baumann, F. R. Giorgetta, I. Coddington, N. R. Newbury, and G. B. Rieker, “Dual frequency comb laser absorption spectroscopy in a 16  MW gas turbine exhaust,” Proc. Combust. Inst. 36, 4565–4573 (2017).
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E. M. Waxman, K. C. Cossel, G.-W. Truong, F. R. Giorgetta, W. C. Swann, S. Coburn, R. J. Wright, G. B. Rieker, I. Coddington, and N. R. Newbury, “Intercomparison of open-path trace gas measurements with two dual-frequency-comb spectrometers,” Atmos. Meas. Tech. Katlenburg-Lindau 10, 3295–3311 (2017).
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K. C. Cossel, E. M. Waxman, I. A. Finneran, G. A. Blake, J. Ye, and N. R. Newbury, “Gas-phase broadband spectroscopy using active sources: progress, status, and applications,” J. Opt. Soc. Am. B 34, 104–129 (2017).
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G.-W. Truong, E. M. Waxman, K. C. Cossel, E. Baumann, A. Klose, F. R. Giorgetta, W. C. Swann, N. R. Newbury, and I. Coddington, “Accurate frequency referencing for fieldable dual-comb spectroscopy,” Opt. Express 24, 30495–30504 (2016).
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F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: technology and applications,” Annu. Rev. Anal. Chem. 3, 175–205 (2010).
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Cromer, C.

Daniel Hill, A.

D. T. Allen, A. P. Pacsi, D. W. Sullivan, D. Zavala-Araiza, M. Harrison, K. Keen, M. P. Fraser, A. Daniel Hill, R. F. Sawyer, and J. H. Seinfeld, “Methane emissions from process equipment at natural gas production sites in the United States: pneumatic controllers,” Environ. Sci. Technol. 49, 633–640 (2015).
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Davis, K. J.

T. Lauvaux, N. L. Miles, A. Deng, S. J. Richardson, M. O. Cambaliza, K. J. Davis, B. Gaudet, K. R. Gurney, J. Huang, D. O’Keefe, Y. Song, A. Karion, T. Oda, R. Patarasuk, I. Razlivanov, D. Sarmiento, P. Shepson, C. Sweeney, J. Turnbull, and K. Wu, “High-resolution atmospheric inversion of urban CO2 emissions during the dormant season of the Indianapolis Flux Experiment (INFLUX),” J. Geophys. Res. Atmos. 121, 5213–5236 (2016).
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M. O. L. Cambaliza, P. B. Shepson, D. R. Caulton, B. Stirm, D. Samarov, K. R. Gurney, J. Turnbull, K. J. Davis, A. Possolo, A. Karion, C. Sweeney, B. Moser, A. Hendricks, T. Lauvaux, K. Mays, J. Whetstone, J. Huang, I. Razlivanov, N. L. Miles, and S. J. Richardson, “Assessment of uncertainties of an aircraft-based mass balance approach for quantifying urban greenhouse gas emissions,” Atmos. Chem. Phys. 14, 9029–9050 (2014).
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Deng, A.

T. Lauvaux, N. L. Miles, A. Deng, S. J. Richardson, M. O. Cambaliza, K. J. Davis, B. Gaudet, K. R. Gurney, J. Huang, D. O’Keefe, Y. Song, A. Karion, T. Oda, R. Patarasuk, I. Razlivanov, D. Sarmiento, P. Shepson, C. Sweeney, J. Turnbull, and K. Wu, “High-resolution atmospheric inversion of urban CO2 emissions during the dormant season of the Indianapolis Flux Experiment (INFLUX),” J. Geophys. Res. Atmos. 121, 5213–5236 (2016).
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Deschênes, J.-D.

L. C. Sinclair, J.-D. Deschênes, L. Sonderhouse, W. C. Swann, I. H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, “Invited article: a compact optically coherent fiber frequency comb,” Rev. Sci. Instrum. 86, 081301 (2015).
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J. Roy, J.-D. Deschênes, S. Potvin, and J. Genest, “Continuous real-time correction and averaging for frequency comb interferometry,” Opt. Express 20, 21932–21939 (2012).
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Dlugokencky, E.

G. Pétron, A. Karion, C. Sweeney, B. R. Miller, S. A. Montzka, G. J. Frost, M. Trainer, P. Tans, A. Andrews, J. Kofler, D. Helmig, D. Guenther, E. Dlugokencky, P. Lang, T. Newberger, S. Wolter, B. Hall, P. Novelli, A. Brewer, S. Conley, M. Hardesty, R. Banta, A. White, D. Noone, D. Wolfe, and R. Schnell, “A new look at methane and nonmethane hydrocarbon emissions from oil and natural gas operations in the Colorado Denver-Julesburg Basin,” J. Geophys. Res. Atmospheres 119, 6836–6852 (2014).
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Dlugokencky, E. J.

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S. M. Miller, S. C. Wofsy, A. M. Michalak, E. A. Kort, A. E. Andrews, S. C. Biraud, E. J. Dlugokencky, J. Eluszkiewicz, M. L. Fischer, G. Janssens-Maenhout, B. R. Miller, J. B. Miller, S. A. Montzka, T. Nehrkorn, and C. Sweeney, “Anthropogenic emissions of methane in the United States,” Proc. Natl. Acad. Sci. USA 110, 20018–20022 (2013).
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G. Pétron, G. Frost, B. R. Miller, A. I. Hirsch, S. A. Montzka, A. Karion, M. Trainer, C. Sweeney, A. E. Andrews, L. Miller, J. Kofler, A. Bar-Ilan, E. J. Dlugokencky, L. Patrick, C. T. Moore, T. B. Ryerson, C. Siso, W. Kolodzey, P. M. Lang, T. Conway, P. Novelli, K. Masarie, B. Hall, D. Guenther, D. Kitzis, J. Miller, D. Welsh, D. Wolfe, W. Neff, and P. Tans, “Hydrocarbon emissions characterization in the Colorado front range: a pilot study,” J. Geophys. Res. Atmos. 117, D04304 (2012).
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S. M. Miller, S. C. Wofsy, A. M. Michalak, E. A. Kort, A. E. Andrews, S. C. Biraud, E. J. Dlugokencky, J. Eluszkiewicz, M. L. Fischer, G. Janssens-Maenhout, B. R. Miller, J. B. Miller, S. A. Montzka, T. Nehrkorn, and C. Sweeney, “Anthropogenic emissions of methane in the United States,” Proc. Natl. Acad. Sci. USA 110, 20018–20022 (2013).
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G. Pétron, G. Frost, B. R. Miller, A. I. Hirsch, S. A. Montzka, A. Karion, M. Trainer, C. Sweeney, A. E. Andrews, L. Miller, J. Kofler, A. Bar-Ilan, E. J. Dlugokencky, L. Patrick, C. T. Moore, T. B. Ryerson, C. Siso, W. Kolodzey, P. M. Lang, T. Conway, P. Novelli, K. Masarie, B. Hall, D. Guenther, D. Kitzis, J. Miller, D. Welsh, D. Wolfe, W. Neff, and P. Tans, “Hydrocarbon emissions characterization in the Colorado front range: a pilot study,” J. Geophys. Res. Atmos. 117, D04304 (2012).
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Neff, W.

G. Pétron, G. Frost, B. R. Miller, A. I. Hirsch, S. A. Montzka, A. Karion, M. Trainer, C. Sweeney, A. E. Andrews, L. Miller, J. Kofler, A. Bar-Ilan, E. J. Dlugokencky, L. Patrick, C. T. Moore, T. B. Ryerson, C. Siso, W. Kolodzey, P. M. Lang, T. Conway, P. Novelli, K. Masarie, B. Hall, D. Guenther, D. Kitzis, J. Miller, D. Welsh, D. Wolfe, W. Neff, and P. Tans, “Hydrocarbon emissions characterization in the Colorado front range: a pilot study,” J. Geophys. Res. Atmos. 117, D04304 (2012).
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S. Schwietzke, G. Pétron, S. Conley, C. Pickering, I. Mielke-Maday, E. J. Dlugokencky, P. P. Tans, T. Vaughn, C. Bell, D. Zimmerle, S. Wolter, C. W. King, A. B. White, T. Coleman, L. Bianco, and R. C. Schnell, “Improved mechanistic understanding of natural gas methane emissions from spatially resolved aircraft measurements,” Environ. Sci. Technol. 51, 7286–7294 (2017).
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G. Pétron, A. Karion, C. Sweeney, B. R. Miller, S. A. Montzka, G. J. Frost, M. Trainer, P. Tans, A. Andrews, J. Kofler, D. Helmig, D. Guenther, E. Dlugokencky, P. Lang, T. Newberger, S. Wolter, B. Hall, P. Novelli, A. Brewer, S. Conley, M. Hardesty, R. Banta, A. White, D. Noone, D. Wolfe, and R. Schnell, “A new look at methane and nonmethane hydrocarbon emissions from oil and natural gas operations in the Colorado Denver-Julesburg Basin,” J. Geophys. Res. Atmospheres 119, 6836–6852 (2014).
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Wright, R.

C. B. Alden, S. Ghosh, S. Coburn, C. Sweeney, A. Karion, R. Wright, I. Coddington, K. Prasad, and G. B. Rieker, “Methane leak detection and sizing over long distances using dual frequency comb laser spectroscopy and a bootstrap inversion technique,” Atmos. Meas. Tech. Discuss. (in review, 2017), DOI: 10.5194/amt-2017-262.
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T. Lauvaux, N. L. Miles, A. Deng, S. J. Richardson, M. O. Cambaliza, K. J. Davis, B. Gaudet, K. R. Gurney, J. Huang, D. O’Keefe, Y. Song, A. Karion, T. Oda, R. Patarasuk, I. Razlivanov, D. Sarmiento, P. Shepson, C. Sweeney, J. Turnbull, and K. Wu, “High-resolution atmospheric inversion of urban CO2 emissions during the dormant season of the Indianapolis Flux Experiment (INFLUX),” J. Geophys. Res. Atmos. 121, 5213–5236 (2016).
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T. I. Yacovitch, S. C. Herndon, G. Pétron, J. Kofler, D. Lyon, M. S. Zahniser, and C. E. Kolb, “Mobile laboratory observations of methane emissions in the Barnett Shale region,” Environ. Sci. Technol. 49, 7889–7895 (2015).
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D. Zavala-Araiza, R. A. Alvarez, D. R. Lyon, D. T. Allen, A. J. Marchese, D. J. Zimmerle, and S. P. Hamburg, “Super-emitters in natural gas infrastructure are caused by abnormal process conditions,” Nat. Commun. 8, 14012 (2017).
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S. Schwietzke, G. Pétron, S. Conley, C. Pickering, I. Mielke-Maday, E. J. Dlugokencky, P. P. Tans, T. Vaughn, C. Bell, D. Zimmerle, S. Wolter, C. W. King, A. B. White, T. Coleman, L. Bianco, and R. C. Schnell, “Improved mechanistic understanding of natural gas methane emissions from spatially resolved aircraft measurements,” Environ. Sci. Technol. 51, 7286–7294 (2017).
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J. R. Roscioli, T. I. Yacovitch, C. Floerchinger, A. L. Mitchell, D. S. Tkacik, R. Subramanian, D. M. Martinez, T. L. Vaughn, L. Williams, D. Zimmerle, A. L. Robinson, S. C. Herndon, and A. J. Marchese, “Measurements of methane emissions from natural gas gathering facilities and processing plants: measurement methods,” Atmos. Meas. Tech. 8, 2017–2035 (2015).
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D. Zavala-Araiza, R. A. Alvarez, D. R. Lyon, D. T. Allen, A. J. Marchese, D. J. Zimmerle, and S. P. Hamburg, “Super-emitters in natural gas infrastructure are caused by abnormal process conditions,” Nat. Commun. 8, 14012 (2017).
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[Crossref]

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[Crossref]

H. L. Brantley, E. D. Thoma, W. C. Squier, B. B. Guven, and D. Lyon, “Assessment of methane emissions from oil and gas production pads using mobile measurements,” Environ. Sci. Technol. 48, 14508–14515 (2014).
[Crossref]

T. I. Yacovitch, S. C. Herndon, G. Pétron, J. Kofler, D. Lyon, M. S. Zahniser, and C. E. Kolb, “Mobile laboratory observations of methane emissions in the Barnett Shale region,” Environ. Sci. Technol. 49, 7889–7895 (2015).
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[Crossref]

D. T. Allen, A. P. Pacsi, D. W. Sullivan, D. Zavala-Araiza, M. Harrison, K. Keen, M. P. Fraser, A. Daniel Hill, R. F. Sawyer, and J. H. Seinfeld, “Methane emissions from process equipment at natural gas production sites in the United States: pneumatic controllers,” Environ. Sci. Technol. 49, 633–640 (2015).
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T. Lauvaux, N. L. Miles, A. Deng, S. J. Richardson, M. O. Cambaliza, K. J. Davis, B. Gaudet, K. R. Gurney, J. Huang, D. O’Keefe, Y. Song, A. Karion, T. Oda, R. Patarasuk, I. Razlivanov, D. Sarmiento, P. Shepson, C. Sweeney, J. Turnbull, and K. Wu, “High-resolution atmospheric inversion of urban CO2 emissions during the dormant season of the Indianapolis Flux Experiment (INFLUX),” J. Geophys. Res. Atmos. 121, 5213–5236 (2016).
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Supplementary Material (1)

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Figures (5)

Fig. 1.
Fig. 1. Regional source monitoring with a centralized DCS. (a) The DCS measures trace gas absorption over an array of long-distance beam paths. (b) Time-resolved trace gas concentrations are determined from fits to the absorption spectra with ppb-km sensitivity and stability. (c) An atmospheric transport model and inversion determines source location and time-resolved emission rate.
Fig. 2.
Fig. 2. (a) Raw transmission spectrum. (b) Result of fit with absorbance model including CH4, CO2, and H2O. The fit residual is largest near water vapor features in the spectrum. (a) and (b) share horizontal axes. (c) Allan deviation for methane mole fraction data collected during well-mixed atmospheric conditions and without nearby leak sources. Also included in (c) is an Allan deviation trace from open-path DCS measurements using the original laboratory-based system [13].
Fig. 3.
Fig. 3. Overview of the field site. (a) Table Mountain field site location. (b) Zoomed view of the site including mobile laboratory (yellow square) and the area over which tests were conducted (black circle). (c) Field deployed DCS, (d) gimbal/telescope, and (e) retroreflector.
Fig. 4.
Fig. 4. Detection of a small, time-varying methane source from 1 km. (a) Map showing the site configuration including retroreflectors (blue diamonds) and source (red circle). (b) Methane concentrations measured on beam paths shown in (a). The light blue line denotes the background measurement (the upwind beam depends on wind direction). (c) Retrieved emission rate (blue line; error bars are 1σ posterior uncertainty), compared with true emission rate (black dotted line). Also shown is the prior estimate of the emission (thin gray line at zero) used in the inversion and the average values for both the true emission rate (maroon dashed line) and the posterior (thick gray line with mean uncertainty).
Fig. 5.
Fig. 5. Detection of two sources from among multiple potential sources. Layout of (a) and (b) in this figure follow that of Fig. 4. (c) True emission rates (sources 2 and 4, solid gray lines; sources 1, 3, and 5, dotted black lines) and retrieved emission rates (sources 1, gray squares; 2, red diamonds; 3, orange diamonds; 4, purple hourglasses; 5, gold asterisks).

Equations (1)

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s^=sp+QHT(HQHT+R)1(zHsp).

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