Abstract

Differential-optical-absorption spectroscopy (DOAS) permits the sensitive measurement of concentrations of trace gases in the atmosphere. DOAS is a technique of well-defined accuracy; however, the calculation of a statistically sound measurement precision is still an unsolved problem. Usually one evaluates DOAS spectra by performing least-squares fits of reference absorption spectra to the measured atmospheric absorption spectra. Inasmuch as the absorbance from atmospheric trace gases is usually very weak, with optical densities in the range from 10-5 to 10-3, interference caused by the occurrence of nonreproducible spectral artifacts often determines the detection limit and the measurement precision. These spectral artifacts bias the least-squares fitting result in two respects. First, spectral artifacts to some extent are falsely interpreted as real absorption, and second, spectral artifacts add nonstatistical noise to spectral residuals, which results in a significant misestimation of the least-squares fitting error. We introduce two new approaches to investigate the evaluation errors of DOAS spectra accurately. The first method, residual inspection by cyclic displacement, estimates the effect of false interpretation of the artifact structures. The second method applies a statistical bootstrap algorithm to estimate properly the error of fitting, even in cases when the condition of random and independent scatter of the residual signal is not fulfilled. Evaluation of simulated atmospheric measurement spectra shows that a combination of the results of both methods yields a good estimate of the spectra evaluation error to within an uncertainty of ∼10%.

© 1999 Optical Society of America

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    [CrossRef]
  2. U. Platt, D. Perner, “Direct measurements of atmospheric CH2O, HNO2, O3, NO2, SO2, by differential optical absorption in the near UV,” J. Geophys. Res. 85, 7453–7458 (1980).
    [CrossRef]
  3. U. Platt, M. Hausmann, “Spectroscopic measurements of the free radicals NO3, BrO, IO, and OH in the troposphere,” Res. Chem. Intermed. 20, 557–578 (1994).
    [CrossRef]
  4. B. Trost, J. Stutz, U. Platt, “UV-absorption cross section of a series of monocyclic aromatic compounds,” Atmos. Environ. 31, 3999–4008 (1997).
    [CrossRef]
  5. U. Platt, “Differential optical absorption spectroscopy,” in Air Monitoring by Spectroscopic Techniques, M. W. Sigrist, ed. (Wiley, New York, 1994).
  6. W. H. Press, B. P. Flannery, S. A. Teukolskey, W. T. Vetting, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1986).
  7. U. Brandenburger, T. Brauers, H.-P. Dorn, M. Hausmann, D. H. Ehhalt, “In-situ measurements of thropospheric hydroxyl radicals by folded long-path laser absorption during the field campaign POPCORN in 1994,” J. Atmos. Chem. 31, 181–204 (1998).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  15. M. Hausmann, U. Brandenburger, T. Brauers, H.-P. Dorn, “Detection of tropospheric OH radicals by long-path differential-optical-absorption spectroscopy: Experimental setup, accuracy, and precision,” J. Geophys. Res. 102, 16,011–16,022 (1997).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. J. Harder, G. Mount, “Long path differential absorption measurements of tropospheric molecules,” in Remote Sensing of Atmospheric Chemistry, J. L. McElroy, R. J. McNeal, eds., Proc. SPIE1491, 33–42 (1991).
    [CrossRef]
  26. J. Callis, “Absorptionsspektroskopischer Nachweis von Hydroxylradikalen in der Troposphäre,” Ph.D. dissertation (University of Cologne, Cologne, Germany, 1988).
  27. T. Gomer, T. Brauers, F. Heintz, J. Stutz, U. Platt, MFC Version 1.98 User Manual (University of Heidelberg and Forschungszentrum Jülich, Jülich, Germany, 1993).
  28. B. Efron, “Bootstrap methods: another look at the jacknife,” Ann. Statist. 7, 1–26 (1979).
    [CrossRef]
  29. B. Efron, R. J. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall, New York, 1993).
    [CrossRef]
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1998

U. Brandenburger, T. Brauers, H.-P. Dorn, M. Hausmann, D. H. Ehhalt, “In-situ measurements of thropospheric hydroxyl radicals by folded long-path laser absorption during the field campaign POPCORN in 1994,” J. Atmos. Chem. 31, 181–204 (1998).
[CrossRef]

1997

U. Platt, L. Marquard, T. Wagner, D. Perner, “Corrections for zenith scattered light DOAS,” Geophys. Res. Lett. 24, 1759–1762 (1997).
[CrossRef]

B. Trost, J. Stutz, U. Platt, “UV-absorption cross section of a series of monocyclic aromatic compounds,” Atmos. Environ. 31, 3999–4008 (1997).
[CrossRef]

M. Hausmann, U. Brandenburger, T. Brauers, H.-P. Dorn, “Detection of tropospheric OH radicals by long-path differential-optical-absorption spectroscopy: Experimental setup, accuracy, and precision,” J. Geophys. Res. 102, 16,011–16,022 (1997).
[CrossRef]

J. W. Harder, R. O. Jakoubek, G. H. Mount, “Measurement of tropospheric trace gases by long-path differential absorption spectroscopy during the 1993 OH photochemistry experiment,” J. Geophys. Res. 102, 6215–6226 (1997).
[CrossRef]

J. Stutz, U. Platt, “Improving long-path differential optical absorption spectroscopy (DOAS) with a quartz-fiber mode mixer,” Appl. Opt. 36, 1105–1115 (1997).
[CrossRef] [PubMed]

1996

J. Stutz, U. Platt, “Numerical analysis and error estimation of differential optical absorption spectroscopy measurements with least-squares methods,” Appl. Opt. 35, 6041–6053 (1996).
[CrossRef] [PubMed]

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

T. Brauers, U. Aschmutat, U. Brandenburger, H.-P. Dorn, M. Hausmann, M. Hessling, A. Hofzumahaus, F. Holland, C. Plass-Dülmer, D. H. Ehhalt, “Intercomparison of the tropospheric OH radical measurements by multiple folded laser long-path absorption and laser induced fluorescence,” Geophys. Res. Lett. 23, 2545–2548 (1996).
[CrossRef]

1995

J. M. C. Plane, N. Smith, “Differential optical absorption spectrometer for measuring atmospheric trace gases,” Rev. Sci. Instrum. 63, 1867–1876 (1995).
[CrossRef]

N. Smith, J. M. C. Plane, C.-F. Nien, P. A. Solomon, “Nighttime radical chemistry in the San Joaquin Valley,” Atmos. Environ. 29, 2887–2897 (1995).
[CrossRef]

H.-P. Dorn, U. Brandenburger, T. Brauers, M. Hausmann, “A new in situ laser long-path absorption instrument for the measurement of tropospheric OH radicals,” J. Atmos. Sci. 52, 3373–3380 (1995).
[CrossRef]

T. Brauers, M. Hausmann, U. Brandenburger, H.-P. Dorn, “Improvement of differential optical absorption spectroscopy using multi-channel-scanning-technique,” Appl. Opt. 34, 4472–4479 (1995).
[CrossRef] [PubMed]

1994

U. Platt, M. Hausmann, “Spectroscopic measurements of the free radicals NO3, BrO, IO, and OH in the troposphere,” Res. Chem. Intermed. 20, 557–578 (1994).
[CrossRef]

1992

G. H. Mount, “The measurement of tropospheric OH by long path absorption. 1. Instrumentation,” J. Geophys. Res. 97, 2427–2444 (1992).
[CrossRef]

1989

A. Pierson, J. Goldstein, “Stray light in spectrometers: causes and cures,” Laser Optron., 67–74 (September1989).

1988

H.-P. Dorn, J. Callies, U. Platt, D. H. Ehhalt, “Measurement of tropospheric OH concentration by laser long-path absorption spectroscopy,” Tellus 40B, 437–445 (1988).
[CrossRef]

1987

S. Solomon, A. L. Schmeltekopf, R. W. Sanders, “On the interpretation of zenith sky absorption measurements,” J. Geophys. Res. 92, 8311–8319 (1987).
[CrossRef]

1980

U. Platt, D. Perner, “Direct measurements of atmospheric CH2O, HNO2, O3, NO2, SO2, by differential optical absorption in the near UV,” J. Geophys. Res. 85, 7453–7458 (1980).
[CrossRef]

1979

U. Platt, D. Perner, H. W. Pätz, “Simultaneous measurements of atmospheric CH2O, O3, and NO2 by differential optical absorption,” J. Geophys. Res. 84, 6329–6335 (1979).
[CrossRef]

B. Efron, “Bootstrap methods: another look at the jacknife,” Ann. Statist. 7, 1–26 (1979).
[CrossRef]

Aschmutat, U.

T. Brauers, U. Aschmutat, U. Brandenburger, H.-P. Dorn, M. Hausmann, M. Hessling, A. Hofzumahaus, F. Holland, C. Plass-Dülmer, D. H. Ehhalt, “Intercomparison of the tropospheric OH radical measurements by multiple folded laser long-path absorption and laser induced fluorescence,” Geophys. Res. Lett. 23, 2545–2548 (1996).
[CrossRef]

Bergquisk, B.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Brandenburger, U.

U. Brandenburger, T. Brauers, H.-P. Dorn, M. Hausmann, D. H. Ehhalt, “In-situ measurements of thropospheric hydroxyl radicals by folded long-path laser absorption during the field campaign POPCORN in 1994,” J. Atmos. Chem. 31, 181–204 (1998).
[CrossRef]

M. Hausmann, U. Brandenburger, T. Brauers, H.-P. Dorn, “Detection of tropospheric OH radicals by long-path differential-optical-absorption spectroscopy: Experimental setup, accuracy, and precision,” J. Geophys. Res. 102, 16,011–16,022 (1997).
[CrossRef]

T. Brauers, U. Aschmutat, U. Brandenburger, H.-P. Dorn, M. Hausmann, M. Hessling, A. Hofzumahaus, F. Holland, C. Plass-Dülmer, D. H. Ehhalt, “Intercomparison of the tropospheric OH radical measurements by multiple folded laser long-path absorption and laser induced fluorescence,” Geophys. Res. Lett. 23, 2545–2548 (1996).
[CrossRef]

T. Brauers, M. Hausmann, U. Brandenburger, H.-P. Dorn, “Improvement of differential optical absorption spectroscopy using multi-channel-scanning-technique,” Appl. Opt. 34, 4472–4479 (1995).
[CrossRef] [PubMed]

H.-P. Dorn, U. Brandenburger, T. Brauers, M. Hausmann, “A new in situ laser long-path absorption instrument for the measurement of tropospheric OH radicals,” J. Atmos. Sci. 52, 3373–3380 (1995).
[CrossRef]

Brauers, T.

U. Brandenburger, T. Brauers, H.-P. Dorn, M. Hausmann, D. H. Ehhalt, “In-situ measurements of thropospheric hydroxyl radicals by folded long-path laser absorption during the field campaign POPCORN in 1994,” J. Atmos. Chem. 31, 181–204 (1998).
[CrossRef]

M. Hausmann, U. Brandenburger, T. Brauers, H.-P. Dorn, “Detection of tropospheric OH radicals by long-path differential-optical-absorption spectroscopy: Experimental setup, accuracy, and precision,” J. Geophys. Res. 102, 16,011–16,022 (1997).
[CrossRef]

T. Brauers, U. Aschmutat, U. Brandenburger, H.-P. Dorn, M. Hausmann, M. Hessling, A. Hofzumahaus, F. Holland, C. Plass-Dülmer, D. H. Ehhalt, “Intercomparison of the tropospheric OH radical measurements by multiple folded laser long-path absorption and laser induced fluorescence,” Geophys. Res. Lett. 23, 2545–2548 (1996).
[CrossRef]

T. Brauers, M. Hausmann, U. Brandenburger, H.-P. Dorn, “Improvement of differential optical absorption spectroscopy using multi-channel-scanning-technique,” Appl. Opt. 34, 4472–4479 (1995).
[CrossRef] [PubMed]

H.-P. Dorn, U. Brandenburger, T. Brauers, M. Hausmann, “A new in situ laser long-path absorption instrument for the measurement of tropospheric OH radicals,” J. Atmos. Sci. 52, 3373–3380 (1995).
[CrossRef]

T. Gomer, T. Brauers, F. Heintz, J. Stutz, U. Platt, MFC Version 1.98 User Manual (University of Heidelberg and Forschungszentrum Jülich, Jülich, Germany, 1993).

Callies, J.

H.-P. Dorn, J. Callies, U. Platt, D. H. Ehhalt, “Measurement of tropospheric OH concentration by laser long-path absorption spectroscopy,” Tellus 40B, 437–445 (1988).
[CrossRef]

Callis, J.

J. Callis, “Absorptionsspektroskopischer Nachweis von Hydroxylradikalen in der Troposphäre,” Ph.D. dissertation (University of Cologne, Cologne, Germany, 1988).

Camy-Peyret, C.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Carleer, M.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Clerbaux, C.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Colin, R. C.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Dorn, H.-P.

U. Brandenburger, T. Brauers, H.-P. Dorn, M. Hausmann, D. H. Ehhalt, “In-situ measurements of thropospheric hydroxyl radicals by folded long-path laser absorption during the field campaign POPCORN in 1994,” J. Atmos. Chem. 31, 181–204 (1998).
[CrossRef]

M. Hausmann, U. Brandenburger, T. Brauers, H.-P. Dorn, “Detection of tropospheric OH radicals by long-path differential-optical-absorption spectroscopy: Experimental setup, accuracy, and precision,” J. Geophys. Res. 102, 16,011–16,022 (1997).
[CrossRef]

T. Brauers, U. Aschmutat, U. Brandenburger, H.-P. Dorn, M. Hausmann, M. Hessling, A. Hofzumahaus, F. Holland, C. Plass-Dülmer, D. H. Ehhalt, “Intercomparison of the tropospheric OH radical measurements by multiple folded laser long-path absorption and laser induced fluorescence,” Geophys. Res. Lett. 23, 2545–2548 (1996).
[CrossRef]

T. Brauers, M. Hausmann, U. Brandenburger, H.-P. Dorn, “Improvement of differential optical absorption spectroscopy using multi-channel-scanning-technique,” Appl. Opt. 34, 4472–4479 (1995).
[CrossRef] [PubMed]

H.-P. Dorn, U. Brandenburger, T. Brauers, M. Hausmann, “A new in situ laser long-path absorption instrument for the measurement of tropospheric OH radicals,” J. Atmos. Sci. 52, 3373–3380 (1995).
[CrossRef]

H.-P. Dorn, J. Callies, U. Platt, D. H. Ehhalt, “Measurement of tropospheric OH concentration by laser long-path absorption spectroscopy,” Tellus 40B, 437–445 (1988).
[CrossRef]

Efron, B.

B. Efron, “Bootstrap methods: another look at the jacknife,” Ann. Statist. 7, 1–26 (1979).
[CrossRef]

B. Efron, R. J. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall, New York, 1993).
[CrossRef]

Ehhalt, D. H.

U. Brandenburger, T. Brauers, H.-P. Dorn, M. Hausmann, D. H. Ehhalt, “In-situ measurements of thropospheric hydroxyl radicals by folded long-path laser absorption during the field campaign POPCORN in 1994,” J. Atmos. Chem. 31, 181–204 (1998).
[CrossRef]

T. Brauers, U. Aschmutat, U. Brandenburger, H.-P. Dorn, M. Hausmann, M. Hessling, A. Hofzumahaus, F. Holland, C. Plass-Dülmer, D. H. Ehhalt, “Intercomparison of the tropospheric OH radical measurements by multiple folded laser long-path absorption and laser induced fluorescence,” Geophys. Res. Lett. 23, 2545–2548 (1996).
[CrossRef]

H.-P. Dorn, J. Callies, U. Platt, D. H. Ehhalt, “Measurement of tropospheric OH concentration by laser long-path absorption spectroscopy,” Tellus 40B, 437–445 (1988).
[CrossRef]

Fayt, C.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolskey, W. T. Vetting, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1986).

Galle, B.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Goldstein, J.

A. Pierson, J. Goldstein, “Stray light in spectrometers: causes and cures,” Laser Optron., 67–74 (September1989).

Gomer, T.

T. Gomer, T. Brauers, F. Heintz, J. Stutz, U. Platt, MFC Version 1.98 User Manual (University of Heidelberg and Forschungszentrum Jülich, Jülich, Germany, 1993).

Goutail, F.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Harder, J.

J. Harder, G. Mount, “Long path differential absorption measurements of tropospheric molecules,” in Remote Sensing of Atmospheric Chemistry, J. L. McElroy, R. J. McNeal, eds., Proc. SPIE1491, 33–42 (1991).
[CrossRef]

Harder, J. W.

J. W. Harder, R. O. Jakoubek, G. H. Mount, “Measurement of tropospheric trace gases by long-path differential absorption spectroscopy during the 1993 OH photochemistry experiment,” J. Geophys. Res. 102, 6215–6226 (1997).
[CrossRef]

Hausmann, M.

U. Brandenburger, T. Brauers, H.-P. Dorn, M. Hausmann, D. H. Ehhalt, “In-situ measurements of thropospheric hydroxyl radicals by folded long-path laser absorption during the field campaign POPCORN in 1994,” J. Atmos. Chem. 31, 181–204 (1998).
[CrossRef]

M. Hausmann, U. Brandenburger, T. Brauers, H.-P. Dorn, “Detection of tropospheric OH radicals by long-path differential-optical-absorption spectroscopy: Experimental setup, accuracy, and precision,” J. Geophys. Res. 102, 16,011–16,022 (1997).
[CrossRef]

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

T. Brauers, U. Aschmutat, U. Brandenburger, H.-P. Dorn, M. Hausmann, M. Hessling, A. Hofzumahaus, F. Holland, C. Plass-Dülmer, D. H. Ehhalt, “Intercomparison of the tropospheric OH radical measurements by multiple folded laser long-path absorption and laser induced fluorescence,” Geophys. Res. Lett. 23, 2545–2548 (1996).
[CrossRef]

H.-P. Dorn, U. Brandenburger, T. Brauers, M. Hausmann, “A new in situ laser long-path absorption instrument for the measurement of tropospheric OH radicals,” J. Atmos. Sci. 52, 3373–3380 (1995).
[CrossRef]

T. Brauers, M. Hausmann, U. Brandenburger, H.-P. Dorn, “Improvement of differential optical absorption spectroscopy using multi-channel-scanning-technique,” Appl. Opt. 34, 4472–4479 (1995).
[CrossRef] [PubMed]

U. Platt, M. Hausmann, “Spectroscopic measurements of the free radicals NO3, BrO, IO, and OH in the troposphere,” Res. Chem. Intermed. 20, 557–578 (1994).
[CrossRef]

Heintz, F.

T. Gomer, T. Brauers, F. Heintz, J. Stutz, U. Platt, MFC Version 1.98 User Manual (University of Heidelberg and Forschungszentrum Jülich, Jülich, Germany, 1993).

Herman, C.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Hessling, M.

T. Brauers, U. Aschmutat, U. Brandenburger, H.-P. Dorn, M. Hausmann, M. Hessling, A. Hofzumahaus, F. Holland, C. Plass-Dülmer, D. H. Ehhalt, “Intercomparison of the tropospheric OH radical measurements by multiple folded laser long-path absorption and laser induced fluorescence,” Geophys. Res. Lett. 23, 2545–2548 (1996).
[CrossRef]

Hofzumahaus, A.

T. Brauers, U. Aschmutat, U. Brandenburger, H.-P. Dorn, M. Hausmann, M. Hessling, A. Hofzumahaus, F. Holland, C. Plass-Dülmer, D. H. Ehhalt, “Intercomparison of the tropospheric OH radical measurements by multiple folded laser long-path absorption and laser induced fluorescence,” Geophys. Res. Lett. 23, 2545–2548 (1996).
[CrossRef]

Holland, F.

T. Brauers, U. Aschmutat, U. Brandenburger, H.-P. Dorn, M. Hausmann, M. Hessling, A. Hofzumahaus, F. Holland, C. Plass-Dülmer, D. H. Ehhalt, “Intercomparison of the tropospheric OH radical measurements by multiple folded laser long-path absorption and laser induced fluorescence,” Geophys. Res. Lett. 23, 2545–2548 (1996).
[CrossRef]

Jakoubek, R. O.

J. W. Harder, R. O. Jakoubek, G. H. Mount, “Measurement of tropospheric trace gases by long-path differential absorption spectroscopy during the 1993 OH photochemistry experiment,” J. Geophys. Res. 102, 6215–6226 (1997).
[CrossRef]

Marquard, L.

U. Platt, L. Marquard, T. Wagner, D. Perner, “Corrections for zenith scattered light DOAS,” Geophys. Res. Lett. 24, 1759–1762 (1997).
[CrossRef]

Mount, G.

J. Harder, G. Mount, “Long path differential absorption measurements of tropospheric molecules,” in Remote Sensing of Atmospheric Chemistry, J. L. McElroy, R. J. McNeal, eds., Proc. SPIE1491, 33–42 (1991).
[CrossRef]

Mount, G. H.

J. W. Harder, R. O. Jakoubek, G. H. Mount, “Measurement of tropospheric trace gases by long-path differential absorption spectroscopy during the 1993 OH photochemistry experiment,” J. Geophys. Res. 102, 6215–6226 (1997).
[CrossRef]

G. H. Mount, “The measurement of tropospheric OH by long path absorption. 1. Instrumentation,” J. Geophys. Res. 97, 2427–2444 (1992).
[CrossRef]

Nien, C.-F.

N. Smith, J. M. C. Plane, C.-F. Nien, P. A. Solomon, “Nighttime radical chemistry in the San Joaquin Valley,” Atmos. Environ. 29, 2887–2897 (1995).
[CrossRef]

J. M. C. Plane, C.-F. Nien, “Atmospheric monitoring by differential optical absorption spectrometry,” in Advances in Spectroscopy, Vol. 24 of Spectroscopy in Environmental Science, R. J. H. Clark, R. E. Hester, ed. (Wiley, New York, 1992).

Nunes Pinharanda, M.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Pätz, H. W.

U. Platt, D. Perner, H. W. Pätz, “Simultaneous measurements of atmospheric CH2O, O3, and NO2 by differential optical absorption,” J. Geophys. Res. 84, 6329–6335 (1979).
[CrossRef]

Perner, D.

U. Platt, L. Marquard, T. Wagner, D. Perner, “Corrections for zenith scattered light DOAS,” Geophys. Res. Lett. 24, 1759–1762 (1997).
[CrossRef]

U. Platt, D. Perner, “Direct measurements of atmospheric CH2O, HNO2, O3, NO2, SO2, by differential optical absorption in the near UV,” J. Geophys. Res. 85, 7453–7458 (1980).
[CrossRef]

U. Platt, D. Perner, H. W. Pätz, “Simultaneous measurements of atmospheric CH2O, O3, and NO2 by differential optical absorption,” J. Geophys. Res. 84, 6329–6335 (1979).
[CrossRef]

Pierson, A.

A. Pierson, J. Goldstein, “Stray light in spectrometers: causes and cures,” Laser Optron., 67–74 (September1989).

Plane, J. M. C.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

N. Smith, J. M. C. Plane, C.-F. Nien, P. A. Solomon, “Nighttime radical chemistry in the San Joaquin Valley,” Atmos. Environ. 29, 2887–2897 (1995).
[CrossRef]

J. M. C. Plane, N. Smith, “Differential optical absorption spectrometer for measuring atmospheric trace gases,” Rev. Sci. Instrum. 63, 1867–1876 (1995).
[CrossRef]

J. M. C. Plane, C.-F. Nien, “Atmospheric monitoring by differential optical absorption spectrometry,” in Advances in Spectroscopy, Vol. 24 of Spectroscopy in Environmental Science, R. J. H. Clark, R. E. Hester, ed. (Wiley, New York, 1992).

Plass-Dülmer, C.

T. Brauers, U. Aschmutat, U. Brandenburger, H.-P. Dorn, M. Hausmann, M. Hessling, A. Hofzumahaus, F. Holland, C. Plass-Dülmer, D. H. Ehhalt, “Intercomparison of the tropospheric OH radical measurements by multiple folded laser long-path absorption and laser induced fluorescence,” Geophys. Res. Lett. 23, 2545–2548 (1996).
[CrossRef]

Platt, U.

U. Platt, L. Marquard, T. Wagner, D. Perner, “Corrections for zenith scattered light DOAS,” Geophys. Res. Lett. 24, 1759–1762 (1997).
[CrossRef]

J. Stutz, U. Platt, “Improving long-path differential optical absorption spectroscopy (DOAS) with a quartz-fiber mode mixer,” Appl. Opt. 36, 1105–1115 (1997).
[CrossRef] [PubMed]

B. Trost, J. Stutz, U. Platt, “UV-absorption cross section of a series of monocyclic aromatic compounds,” Atmos. Environ. 31, 3999–4008 (1997).
[CrossRef]

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

J. Stutz, U. Platt, “Numerical analysis and error estimation of differential optical absorption spectroscopy measurements with least-squares methods,” Appl. Opt. 35, 6041–6053 (1996).
[CrossRef] [PubMed]

U. Platt, M. Hausmann, “Spectroscopic measurements of the free radicals NO3, BrO, IO, and OH in the troposphere,” Res. Chem. Intermed. 20, 557–578 (1994).
[CrossRef]

H.-P. Dorn, J. Callies, U. Platt, D. H. Ehhalt, “Measurement of tropospheric OH concentration by laser long-path absorption spectroscopy,” Tellus 40B, 437–445 (1988).
[CrossRef]

U. Platt, D. Perner, “Direct measurements of atmospheric CH2O, HNO2, O3, NO2, SO2, by differential optical absorption in the near UV,” J. Geophys. Res. 85, 7453–7458 (1980).
[CrossRef]

U. Platt, D. Perner, H. W. Pätz, “Simultaneous measurements of atmospheric CH2O, O3, and NO2 by differential optical absorption,” J. Geophys. Res. 84, 6329–6335 (1979).
[CrossRef]

T. Gomer, T. Brauers, F. Heintz, J. Stutz, U. Platt, MFC Version 1.98 User Manual (University of Heidelberg and Forschungszentrum Jülich, Jülich, Germany, 1993).

U. Platt, “Differential optical absorption spectroscopy,” in Air Monitoring by Spectroscopic Techniques, M. W. Sigrist, ed. (Wiley, New York, 1994).

Politis, D. N.

D. N. Politis, J. P. Romano, “A circular block-re-sampling procedure for stationary data,” in Exploring the Limits of Bootstrap, R. Lepage, L. Billard, eds. (Wiley, New York, 1992).

Pommereau, J. P.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolskey, W. T. Vetting, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1986).

Pundt, I.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Romano, J. P.

D. N. Politis, J. P. Romano, “A circular block-re-sampling procedure for stationary data,” in Exploring the Limits of Bootstrap, R. Lepage, L. Billard, eds. (Wiley, New York, 1992).

Rudolph, T.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Sanders, R. W.

S. Solomon, A. L. Schmeltekopf, R. W. Sanders, “On the interpretation of zenith sky absorption measurements,” J. Geophys. Res. 92, 8311–8319 (1987).
[CrossRef]

Schmeltekopf, A. L.

S. Solomon, A. L. Schmeltekopf, R. W. Sanders, “On the interpretation of zenith sky absorption measurements,” J. Geophys. Res. 92, 8311–8319 (1987).
[CrossRef]

Simon, P. C.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Smith, N.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

J. M. C. Plane, N. Smith, “Differential optical absorption spectrometer for measuring atmospheric trace gases,” Rev. Sci. Instrum. 63, 1867–1876 (1995).
[CrossRef]

N. Smith, J. M. C. Plane, C.-F. Nien, P. A. Solomon, “Nighttime radical chemistry in the San Joaquin Valley,” Atmos. Environ. 29, 2887–2897 (1995).
[CrossRef]

Solomon, P. A.

N. Smith, J. M. C. Plane, C.-F. Nien, P. A. Solomon, “Nighttime radical chemistry in the San Joaquin Valley,” Atmos. Environ. 29, 2887–2897 (1995).
[CrossRef]

Solomon, S.

S. Solomon, A. L. Schmeltekopf, R. W. Sanders, “On the interpretation of zenith sky absorption measurements,” J. Geophys. Res. 92, 8311–8319 (1987).
[CrossRef]

Stutz, J.

B. Trost, J. Stutz, U. Platt, “UV-absorption cross section of a series of monocyclic aromatic compounds,” Atmos. Environ. 31, 3999–4008 (1997).
[CrossRef]

J. Stutz, U. Platt, “Improving long-path differential optical absorption spectroscopy (DOAS) with a quartz-fiber mode mixer,” Appl. Opt. 36, 1105–1115 (1997).
[CrossRef] [PubMed]

J. Stutz, U. Platt, “Numerical analysis and error estimation of differential optical absorption spectroscopy measurements with least-squares methods,” Appl. Opt. 35, 6041–6053 (1996).
[CrossRef] [PubMed]

T. Gomer, T. Brauers, F. Heintz, J. Stutz, U. Platt, MFC Version 1.98 User Manual (University of Heidelberg and Forschungszentrum Jülich, Jülich, Germany, 1993).

Teukolskey, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolskey, W. T. Vetting, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1986).

Tibshirani, R. J.

B. Efron, R. J. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall, New York, 1993).
[CrossRef]

Trost, B.

B. Trost, J. Stutz, U. Platt, “UV-absorption cross section of a series of monocyclic aromatic compounds,” Atmos. Environ. 31, 3999–4008 (1997).
[CrossRef]

Vandaele, A. C.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

Vetting, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolskey, W. T. Vetting, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1986).

Wagner, T.

U. Platt, L. Marquard, T. Wagner, D. Perner, “Corrections for zenith scattered light DOAS,” Geophys. Res. Lett. 24, 1759–1762 (1997).
[CrossRef]

Weichsel, H.

H. Weichsel, Laser Beam Propagation in the Atmosphere (SPIE Optical Engineering Press, Bellingham, Wash., 1990).

Ann. Statist.

B. Efron, “Bootstrap methods: another look at the jacknife,” Ann. Statist. 7, 1–26 (1979).
[CrossRef]

Appl. Opt.

Atmos. Environ.

B. Trost, J. Stutz, U. Platt, “UV-absorption cross section of a series of monocyclic aromatic compounds,” Atmos. Environ. 31, 3999–4008 (1997).
[CrossRef]

N. Smith, J. M. C. Plane, C.-F. Nien, P. A. Solomon, “Nighttime radical chemistry in the San Joaquin Valley,” Atmos. Environ. 29, 2887–2897 (1995).
[CrossRef]

Geophys. Res. Lett.

T. Brauers, U. Aschmutat, U. Brandenburger, H.-P. Dorn, M. Hausmann, M. Hessling, A. Hofzumahaus, F. Holland, C. Plass-Dülmer, D. H. Ehhalt, “Intercomparison of the tropospheric OH radical measurements by multiple folded laser long-path absorption and laser induced fluorescence,” Geophys. Res. Lett. 23, 2545–2548 (1996).
[CrossRef]

U. Platt, L. Marquard, T. Wagner, D. Perner, “Corrections for zenith scattered light DOAS,” Geophys. Res. Lett. 24, 1759–1762 (1997).
[CrossRef]

J. Atmos. Chem.

C. Camy-Peyret, B. Bergquisk, B. Galle, M. Carleer, C. Clerbaux, R. C. Colin, C. Fayt, F. Goutail, M. Nunes Pinharanda, J. P. Pommereau, M. Hausmann, U. Platt, I. Pundt, T. Rudolph, C. Herman, P. C. Simon, A. C. Vandaele, J. M. C. Plane, N. Smith, “Intercomparison of instruments for tropospheric measurements using differential optical absorption spectroscopy,” J. Atmos. Chem. 23, 51–80 (1996).
[CrossRef]

U. Brandenburger, T. Brauers, H.-P. Dorn, M. Hausmann, D. H. Ehhalt, “In-situ measurements of thropospheric hydroxyl radicals by folded long-path laser absorption during the field campaign POPCORN in 1994,” J. Atmos. Chem. 31, 181–204 (1998).
[CrossRef]

J. Atmos. Sci.

H.-P. Dorn, U. Brandenburger, T. Brauers, M. Hausmann, “A new in situ laser long-path absorption instrument for the measurement of tropospheric OH radicals,” J. Atmos. Sci. 52, 3373–3380 (1995).
[CrossRef]

J. Geophys. Res.

G. H. Mount, “The measurement of tropospheric OH by long path absorption. 1. Instrumentation,” J. Geophys. Res. 97, 2427–2444 (1992).
[CrossRef]

S. Solomon, A. L. Schmeltekopf, R. W. Sanders, “On the interpretation of zenith sky absorption measurements,” J. Geophys. Res. 92, 8311–8319 (1987).
[CrossRef]

M. Hausmann, U. Brandenburger, T. Brauers, H.-P. Dorn, “Detection of tropospheric OH radicals by long-path differential-optical-absorption spectroscopy: Experimental setup, accuracy, and precision,” J. Geophys. Res. 102, 16,011–16,022 (1997).
[CrossRef]

J. W. Harder, R. O. Jakoubek, G. H. Mount, “Measurement of tropospheric trace gases by long-path differential absorption spectroscopy during the 1993 OH photochemistry experiment,” J. Geophys. Res. 102, 6215–6226 (1997).
[CrossRef]

U. Platt, D. Perner, H. W. Pätz, “Simultaneous measurements of atmospheric CH2O, O3, and NO2 by differential optical absorption,” J. Geophys. Res. 84, 6329–6335 (1979).
[CrossRef]

U. Platt, D. Perner, “Direct measurements of atmospheric CH2O, HNO2, O3, NO2, SO2, by differential optical absorption in the near UV,” J. Geophys. Res. 85, 7453–7458 (1980).
[CrossRef]

Laser Optron.

A. Pierson, J. Goldstein, “Stray light in spectrometers: causes and cures,” Laser Optron., 67–74 (September1989).

Res. Chem. Intermed.

U. Platt, M. Hausmann, “Spectroscopic measurements of the free radicals NO3, BrO, IO, and OH in the troposphere,” Res. Chem. Intermed. 20, 557–578 (1994).
[CrossRef]

Rev. Sci. Instrum.

J. M. C. Plane, N. Smith, “Differential optical absorption spectrometer for measuring atmospheric trace gases,” Rev. Sci. Instrum. 63, 1867–1876 (1995).
[CrossRef]

Tellus

H.-P. Dorn, J. Callies, U. Platt, D. H. Ehhalt, “Measurement of tropospheric OH concentration by laser long-path absorption spectroscopy,” Tellus 40B, 437–445 (1988).
[CrossRef]

Other

H. Weichsel, Laser Beam Propagation in the Atmosphere (SPIE Optical Engineering Press, Bellingham, Wash., 1990).

B. Efron, R. J. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall, New York, 1993).
[CrossRef]

D. N. Politis, J. P. Romano, “A circular block-re-sampling procedure for stationary data,” in Exploring the Limits of Bootstrap, R. Lepage, L. Billard, eds. (Wiley, New York, 1992).

J. Harder, G. Mount, “Long path differential absorption measurements of tropospheric molecules,” in Remote Sensing of Atmospheric Chemistry, J. L. McElroy, R. J. McNeal, eds., Proc. SPIE1491, 33–42 (1991).
[CrossRef]

J. Callis, “Absorptionsspektroskopischer Nachweis von Hydroxylradikalen in der Troposphäre,” Ph.D. dissertation (University of Cologne, Cologne, Germany, 1988).

T. Gomer, T. Brauers, F. Heintz, J. Stutz, U. Platt, MFC Version 1.98 User Manual (University of Heidelberg and Forschungszentrum Jülich, Jülich, Germany, 1993).

J. M. C. Plane, C.-F. Nien, “Atmospheric monitoring by differential optical absorption spectrometry,” in Advances in Spectroscopy, Vol. 24 of Spectroscopy in Environmental Science, R. J. H. Clark, R. E. Hester, ed. (Wiley, New York, 1992).

U. Platt, “Differential optical absorption spectroscopy,” in Air Monitoring by Spectroscopic Techniques, M. W. Sigrist, ed. (Wiley, New York, 1994).

W. H. Press, B. P. Flannery, S. A. Teukolskey, W. T. Vetting, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1986).

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Figures (13)

Fig. 1
Fig. 1

Example of the evaluation of an atmospheric absorption spectrum recorded by long-path laser absorption. Absorptions of SO2 and OH are shown.7 Here the channel numbers (pixels of a diode array detector, 0.25 pm/pixel) instead of the wavelength scale are given. The top trace shows the atmospheric absorption spectrum superimposed upon the simultaneously fitted reference spectra of OH and SO2 (see Fig. 3 below). The atmospheric absorption is dominated by SO2 in this case (polluted air). The middle trace shows the same spectrum after subtraction of the fitted SO2 reference. Superimposed is an OH reference spectrum. The bottom trace exhibits the residual after subtraction of all known trace-gas absorption features.

Fig. 2
Fig. 2

Four examples of simulated spectra (based on residuals of atmospheric absorption spectra; see Section 4), showing pure artifact structures with no absorption by trace gases (traces a–d). The spectra are superimposed upon a fitted OH reference spectrum to demonstrate examples of fit failure. Because the simulated spectra are free from absorption the fit result is equal to the true error of the fit. For comparison a pure noise spectrum is added (trace e).

Fig. 3
Fig. 3

Reference absorption spectra of molecules that can be observed in the atmosphere by the long-path laser absorption instrument,7 showing distinct spectral features. They serve as test spectra for investigation of the new methods for error calculation.

Fig. 4
Fig. 4

Flow chart of the RICD method; see text. stdev, Standard deviation.

Fig. 5
Fig. 5

Two examples of spectra with displaced residuals as obtained by the RICD method. The top trace shows a measured air absorption spectrum, containing absorption of ambient OH radicals, and a superimposed fit of an OH reference spectrum. The center and the bottom traces show the same spectrum but with the residual cyclically displaced (indicated by arrows). The corresponding OH fits of the reevaluation are superimposed.

Fig. 6
Fig. 6

Flow chart of the bootstrap method; see text. stdev, Standard deviation.

Fig. 7
Fig. 7

Schematic examples of the resampling technique by the bootstrap method. In (a) Ten single channels are resampled from the original spectrum. (b) Block resampling with four blocks, each five channels wide, to replicate a spectrum of twenty-channel width.

Fig. 8
Fig. 8

Ratios of bootstrap (BS) error (based on 100 bootstrap replications) and fit error [err(LSQ)] determined by the LSQ algorithm versus bootstrap block size. Data points are mean values averaged over the results obtained from 100 simulated spectra and 100 noise spectra (see text). Open circles, noise spectra results; filled circles, results for the simulated measurement spectra; filled triangles, results ignoring the contribution of the single-line spectrum; filled triangles in boxes, results from fitting the reference individually to the simulated spectra (see text). Dotted lines are guides to the eye to indicate the plateau (see text).

Fig. 9
Fig. 9

Imprecision of the bootstrap error versus bootstrap block size. The values correspond to the relative 1-σ scatter of the bootstrap results for 100 individual noise spectra investigated (see Section 4). Filled circles, standard deviations of the bootstrap results of the noise spectra, each replicated by 100 bootstrap replicas. Open circles, results for 10 and 1000 replicas.

Fig. 10
Fig. 10

Probability plots of the empirical cumulative frequency function of the evaluation of noise spectra. Straight lines, theoretical error functions for an N(0,1) distribution. Here and Fig. 11, BS means bootstrap.

Fig. 11
Fig. 11

Probability plots of the empirical cumulative frequency function of the evaluation of the simulated spectra. Unity slope, theoretical result for an N(0,1) distribution (Gaussian distribution with standard deviation 1).

Fig. 12
Fig. 12

err(LSQ) versus BS ⊕ RICD error for the sample of simulated measurement spectra, indicating a factor of 2–8 underestimation of err(LSQ). Axis numbers are given in absorbance, indicating typical uncertainties of the applied DOAS instrument.15

Fig. 13
Fig. 13

Bootstrap error versus RICD error normalized by err(LSQ) for the simulated measurement spectra, showing that the bootstrap and RICD are nearly independent methods (r 2 = 0.1–0.3 for the different reference spectra applied).

Tables (2)

Tables Icon

Table 1 Standard Deviation (stdev) of the Ratio ci,bi,b of the 100 Noise Spectraa

Tables Icon

Table 2 Standard Deviation (stdev) of the Ratio ci,bi,b of the 100 Simulated Measurement Spectraa

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

Aλ=IλI0λ=exp-Dλ,  Dλ=i CiσiλL,
Sxk=IxkPxkAxkRxk,
sxk=ln Sxk=-i CiσiλL+rxk,  rxk=ln Rxk,
χ2=ksxk-sˆxk2σ2[sxk],
sˆxk=co+ici ln Mixk,  i=1,2,3....
θi=1N-1n=1Ncˆi,n*-c¯i*21/2,  c¯i*=1Nn=1N cˆi,n*,
rˆxk=sxk-sˆxk.
Fa=1Bb=1a fz˜i,b,  z˜i,bzi,b=ci,bΘi,b,  a=1, 2, , B,
erfA=1σ2π-A exp-z22σ2 dz.
stdevci,bΘi,b=1,
BS  RICD=BS2 + RICD21/2.
BS  RICD  0.85×BS  RICD,
χ2=k wksxk-sxk2σ2[sxk], withk=1K wk=K,

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