Abstract

Differential optical absorption spectroscopy (DOAS) has become a widely used method to measure trace gases in the atmosphere. Their concentration is retrieved by a numerical analysis of the atmospheric absorption spectra, which often are a combination of overlapping absorption structures of several trace gases. A new analysis procedure was developed, modeling atmospheric spectra with the absorption structures of the individual trace gases, to determine their concentrations. The procedure also corrects differences in the wavelength–pixel mapping of these spectra. A new method to estimate the error of the concentrations considers the uncertainty of this correction and the influence of random residual structures in the absorption spectra.

© 1996 Optical Society of America

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  1. G. M. B. Dobson, D. N. Harrison, “Measurements of the amount of ozone in the earth’s atmosphere and its relation to other geophysical conditions, Part 1,” Proc. R. Soc. London 110, 660–693 (1926).
    [CrossRef]
  2. J. F. Noxon, “Nitrogen dioxide in the stratosphere and troposphere measured by ground-based absorption spectroscopy,” Science 189, 547–549 (1975).
    [CrossRef] [PubMed]
  3. J. F. Noxon, E. C. Whipple, R. S. Hyde, “Stratospheric NO2. 1. Observational method and behavior at midlatitudes,” J. Geophys. Res. 84, 5047–5076 (1979).
    [CrossRef]
  4. U. Platt, D. Perner, H. Pätz, “Simultaneous measurements of atmospheric CH2O, O3 and NO2 by differential optical absorption,” J. Geophys. Res. 84, 6329–6335 (1979).
    [CrossRef]
  5. U. Platt, “Differential optical absorption spectroscopy (DOAS),” in Air Monitoring by Spectroscopic Techniques, M. W. Sigrist, ed., Chemical Analysis Series (Wiley, New York, 1994), Vol. 127.
  6. S. Solomon, A. L. Schmeltekopf, R. W. Sanders, “On the interpretation of zenith sky absorption measurements,” J. Geophys. Res. 92, 8311–8319 (1987).
    [CrossRef]
  7. D. Perner, U. Platt, “Detection of nitrous acid in the atmosphere by differential optical absorption,” Geophys. Res. Lett. 6, 917–920 (1979).
    [CrossRef]
  8. D. Perner, D. H. Ehhalt, H. W. Paetz, U. Platt, E. P. Roeth, A. Volz, “OH-radicals in the lower troposphere,” Geophys. Res. Lett. 3, 466–468 (1976).
    [CrossRef]
  9. U. Platt, D. Perner, G. W. Harris, A. M. Winer, J. N. Pitts, “Detection of NO3 in the polluted troposphere by differential optical absorption,” Geophys. Res. Lett. 7, 89–92 (1980).
    [CrossRef]
  10. M. Hausmann, U. Platt, “Spectroscopic measurement of bromine oxide and ozone in the high arctic during Polar Sunrise Experiment 1992,” J. Geophys. Res. 99, 25399–25413 (1994).
    [CrossRef]
  11. R. W. Sanders, S. Solomon, M. A. Carroll, A. L. Schmeltekopf, “Ground-based measurements of O3, NO2, OClO, and BrO during the 1987 Antarctic ozone depletion event,” in Ozone in the Atmosphere, Proceedings of the Quadrennial Ozone Symposium 1988, R. D. Bojkov, P. Fabian, eds. (Deepak Publishing, Hampton, Va., 1989), pp. 65–70.
  12. K. Pfeilsticker, U. Platt, “Airborne measurements during the Arctic stratospheric experiment: observation of O3 and NO2,” Geophys. Res. Lett. 21, 1375–1378 (1994).
    [CrossRef]
  13. U. Platt, D. Perner, “Measurements of atmospheric trace gases by long path differential UV/visible absorption spectroscopy,” in Optical and Laser Remote Sensing, D. K. Killinger, A. Mooradian, eds. (Springer-Verlag, New York, 1983), pp. 95–105.
  14. A. M. Bass, R. J. Paur, “The ultraviolet cross-sections of ozone. I. The measurements,” in Atmospheric Ozone (Reidel, Dordrecht, The Netherlands, 1985), pp. 606–629.
    [CrossRef]
  15. W. Schneider, G. K. Moortgat, G. S. Tyndall, J. P. Burrows, “Absorption cross-sections of NO2 in the UV and visible region (200–700 nm) at 298 K,” J. Photochem. Photobiol. 40, 195–217 (1987).
    [CrossRef]
  16. A. C. Vandaele, P. C. Simon, J. M. Guilmot, M. Carleer, R. Colin, “SO2 absorption cross section measurements in the UV using a Fourier transform spectrometer,” J. Geophys. Res. 99, 25599–25605 (1994).
    [CrossRef]
  17. C. A. Cantrell, J. A. Davidson, A. H. McDaniel, R. E. Shetter, J. G. Calvert, “Temperature-dependent formaldehyde cross section in the near-ultraviolet spectral region,” J. Phys. Chem. 94, 3902–3908 (1990).
    [CrossRef]
  18. K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Quart. Appl. Math 2, 164–168 (1944).
  19. D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Indust. Appl. Math. 11, 431–441 (1963).
    [CrossRef]
  20. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge University, Cambridge, England, 1986).
  21. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).
  22. D. L. Albritton, A. L. Schmeltekopf, R. N. Zare, “An introduction to the least-squares fitting of spectroscopic data,” in Molecular Spectroscopy: Modern Research, R. K. Narahari, M. W. Weldon, eds. (Academic, Orlando, Florida, 1976).
  23. R. W. Cunningham, “Comparison of three methods for determining fit parameter uncertainies for the Marquardt compromise,” Comput. Phys. 7, 570–576 (1993).
    [CrossRef]
  24. J. Stutz, U. Platt, “A new generation of DOAS instruments,” TOPAS/EUROTRAC, in press.

1994 (3)

M. Hausmann, U. Platt, “Spectroscopic measurement of bromine oxide and ozone in the high arctic during Polar Sunrise Experiment 1992,” J. Geophys. Res. 99, 25399–25413 (1994).
[CrossRef]

K. Pfeilsticker, U. Platt, “Airborne measurements during the Arctic stratospheric experiment: observation of O3 and NO2,” Geophys. Res. Lett. 21, 1375–1378 (1994).
[CrossRef]

A. C. Vandaele, P. C. Simon, J. M. Guilmot, M. Carleer, R. Colin, “SO2 absorption cross section measurements in the UV using a Fourier transform spectrometer,” J. Geophys. Res. 99, 25599–25605 (1994).
[CrossRef]

1993 (1)

R. W. Cunningham, “Comparison of three methods for determining fit parameter uncertainies for the Marquardt compromise,” Comput. Phys. 7, 570–576 (1993).
[CrossRef]

1990 (1)

C. A. Cantrell, J. A. Davidson, A. H. McDaniel, R. E. Shetter, J. G. Calvert, “Temperature-dependent formaldehyde cross section in the near-ultraviolet spectral region,” J. Phys. Chem. 94, 3902–3908 (1990).
[CrossRef]

1987 (2)

W. Schneider, G. K. Moortgat, G. S. Tyndall, J. P. Burrows, “Absorption cross-sections of NO2 in the UV and visible region (200–700 nm) at 298 K,” J. Photochem. Photobiol. 40, 195–217 (1987).
[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]

1980 (1)

U. Platt, D. Perner, G. W. Harris, A. M. Winer, J. N. Pitts, “Detection of NO3 in the polluted troposphere by differential optical absorption,” Geophys. Res. Lett. 7, 89–92 (1980).
[CrossRef]

1979 (3)

D. Perner, U. Platt, “Detection of nitrous acid in the atmosphere by differential optical absorption,” Geophys. Res. Lett. 6, 917–920 (1979).
[CrossRef]

J. F. Noxon, E. C. Whipple, R. S. Hyde, “Stratospheric NO2. 1. Observational method and behavior at midlatitudes,” J. Geophys. Res. 84, 5047–5076 (1979).
[CrossRef]

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

1976 (1)

D. Perner, D. H. Ehhalt, H. W. Paetz, U. Platt, E. P. Roeth, A. Volz, “OH-radicals in the lower troposphere,” Geophys. Res. Lett. 3, 466–468 (1976).
[CrossRef]

1975 (1)

J. F. Noxon, “Nitrogen dioxide in the stratosphere and troposphere measured by ground-based absorption spectroscopy,” Science 189, 547–549 (1975).
[CrossRef] [PubMed]

1963 (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Indust. Appl. Math. 11, 431–441 (1963).
[CrossRef]

1944 (1)

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Quart. Appl. Math 2, 164–168 (1944).

1926 (1)

G. M. B. Dobson, D. N. Harrison, “Measurements of the amount of ozone in the earth’s atmosphere and its relation to other geophysical conditions, Part 1,” Proc. R. Soc. London 110, 660–693 (1926).
[CrossRef]

Albritton, D. L.

D. L. Albritton, A. L. Schmeltekopf, R. N. Zare, “An introduction to the least-squares fitting of spectroscopic data,” in Molecular Spectroscopy: Modern Research, R. K. Narahari, M. W. Weldon, eds. (Academic, Orlando, Florida, 1976).

Bass, A. M.

A. M. Bass, R. J. Paur, “The ultraviolet cross-sections of ozone. I. The measurements,” in Atmospheric Ozone (Reidel, Dordrecht, The Netherlands, 1985), pp. 606–629.
[CrossRef]

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

Burrows, J. P.

W. Schneider, G. K. Moortgat, G. S. Tyndall, J. P. Burrows, “Absorption cross-sections of NO2 in the UV and visible region (200–700 nm) at 298 K,” J. Photochem. Photobiol. 40, 195–217 (1987).
[CrossRef]

Calvert, J. G.

C. A. Cantrell, J. A. Davidson, A. H. McDaniel, R. E. Shetter, J. G. Calvert, “Temperature-dependent formaldehyde cross section in the near-ultraviolet spectral region,” J. Phys. Chem. 94, 3902–3908 (1990).
[CrossRef]

Cantrell, C. A.

C. A. Cantrell, J. A. Davidson, A. H. McDaniel, R. E. Shetter, J. G. Calvert, “Temperature-dependent formaldehyde cross section in the near-ultraviolet spectral region,” J. Phys. Chem. 94, 3902–3908 (1990).
[CrossRef]

Carleer, M.

A. C. Vandaele, P. C. Simon, J. M. Guilmot, M. Carleer, R. Colin, “SO2 absorption cross section measurements in the UV using a Fourier transform spectrometer,” J. Geophys. Res. 99, 25599–25605 (1994).
[CrossRef]

Carroll, M. A.

R. W. Sanders, S. Solomon, M. A. Carroll, A. L. Schmeltekopf, “Ground-based measurements of O3, NO2, OClO, and BrO during the 1987 Antarctic ozone depletion event,” in Ozone in the Atmosphere, Proceedings of the Quadrennial Ozone Symposium 1988, R. D. Bojkov, P. Fabian, eds. (Deepak Publishing, Hampton, Va., 1989), pp. 65–70.

Colin, R.

A. C. Vandaele, P. C. Simon, J. M. Guilmot, M. Carleer, R. Colin, “SO2 absorption cross section measurements in the UV using a Fourier transform spectrometer,” J. Geophys. Res. 99, 25599–25605 (1994).
[CrossRef]

Cunningham, R. W.

R. W. Cunningham, “Comparison of three methods for determining fit parameter uncertainies for the Marquardt compromise,” Comput. Phys. 7, 570–576 (1993).
[CrossRef]

Davidson, J. A.

C. A. Cantrell, J. A. Davidson, A. H. McDaniel, R. E. Shetter, J. G. Calvert, “Temperature-dependent formaldehyde cross section in the near-ultraviolet spectral region,” J. Phys. Chem. 94, 3902–3908 (1990).
[CrossRef]

Dobson, G. M. B.

G. M. B. Dobson, D. N. Harrison, “Measurements of the amount of ozone in the earth’s atmosphere and its relation to other geophysical conditions, Part 1,” Proc. R. Soc. London 110, 660–693 (1926).
[CrossRef]

Ehhalt, D. H.

D. Perner, D. H. Ehhalt, H. W. Paetz, U. Platt, E. P. Roeth, A. Volz, “OH-radicals in the lower troposphere,” Geophys. Res. Lett. 3, 466–468 (1976).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge University, Cambridge, England, 1986).

Guilmot, J. M.

A. C. Vandaele, P. C. Simon, J. M. Guilmot, M. Carleer, R. Colin, “SO2 absorption cross section measurements in the UV using a Fourier transform spectrometer,” J. Geophys. Res. 99, 25599–25605 (1994).
[CrossRef]

Harris, G. W.

U. Platt, D. Perner, G. W. Harris, A. M. Winer, J. N. Pitts, “Detection of NO3 in the polluted troposphere by differential optical absorption,” Geophys. Res. Lett. 7, 89–92 (1980).
[CrossRef]

Harrison, D. N.

G. M. B. Dobson, D. N. Harrison, “Measurements of the amount of ozone in the earth’s atmosphere and its relation to other geophysical conditions, Part 1,” Proc. R. Soc. London 110, 660–693 (1926).
[CrossRef]

Hausmann, M.

M. Hausmann, U. Platt, “Spectroscopic measurement of bromine oxide and ozone in the high arctic during Polar Sunrise Experiment 1992,” J. Geophys. Res. 99, 25399–25413 (1994).
[CrossRef]

Hyde, R. S.

J. F. Noxon, E. C. Whipple, R. S. Hyde, “Stratospheric NO2. 1. Observational method and behavior at midlatitudes,” J. Geophys. Res. 84, 5047–5076 (1979).
[CrossRef]

Levenberg, K.

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Quart. Appl. Math 2, 164–168 (1944).

Marquardt, D. W.

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Indust. Appl. Math. 11, 431–441 (1963).
[CrossRef]

McDaniel, A. H.

C. A. Cantrell, J. A. Davidson, A. H. McDaniel, R. E. Shetter, J. G. Calvert, “Temperature-dependent formaldehyde cross section in the near-ultraviolet spectral region,” J. Phys. Chem. 94, 3902–3908 (1990).
[CrossRef]

Moortgat, G. K.

W. Schneider, G. K. Moortgat, G. S. Tyndall, J. P. Burrows, “Absorption cross-sections of NO2 in the UV and visible region (200–700 nm) at 298 K,” J. Photochem. Photobiol. 40, 195–217 (1987).
[CrossRef]

Noxon, J. F.

J. F. Noxon, E. C. Whipple, R. S. Hyde, “Stratospheric NO2. 1. Observational method and behavior at midlatitudes,” J. Geophys. Res. 84, 5047–5076 (1979).
[CrossRef]

J. F. Noxon, “Nitrogen dioxide in the stratosphere and troposphere measured by ground-based absorption spectroscopy,” Science 189, 547–549 (1975).
[CrossRef] [PubMed]

Paetz, H. W.

D. Perner, D. H. Ehhalt, H. W. Paetz, U. Platt, E. P. Roeth, A. Volz, “OH-radicals in the lower troposphere,” Geophys. Res. Lett. 3, 466–468 (1976).
[CrossRef]

Pätz, H.

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

Paur, R. J.

A. M. Bass, R. J. Paur, “The ultraviolet cross-sections of ozone. I. The measurements,” in Atmospheric Ozone (Reidel, Dordrecht, The Netherlands, 1985), pp. 606–629.
[CrossRef]

Perner, D.

U. Platt, D. Perner, G. W. Harris, A. M. Winer, J. N. Pitts, “Detection of NO3 in the polluted troposphere by differential optical absorption,” Geophys. Res. Lett. 7, 89–92 (1980).
[CrossRef]

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

D. Perner, U. Platt, “Detection of nitrous acid in the atmosphere by differential optical absorption,” Geophys. Res. Lett. 6, 917–920 (1979).
[CrossRef]

D. Perner, D. H. Ehhalt, H. W. Paetz, U. Platt, E. P. Roeth, A. Volz, “OH-radicals in the lower troposphere,” Geophys. Res. Lett. 3, 466–468 (1976).
[CrossRef]

U. Platt, D. Perner, “Measurements of atmospheric trace gases by long path differential UV/visible absorption spectroscopy,” in Optical and Laser Remote Sensing, D. K. Killinger, A. Mooradian, eds. (Springer-Verlag, New York, 1983), pp. 95–105.

Pfeilsticker, K.

K. Pfeilsticker, U. Platt, “Airborne measurements during the Arctic stratospheric experiment: observation of O3 and NO2,” Geophys. Res. Lett. 21, 1375–1378 (1994).
[CrossRef]

Pitts, J. N.

U. Platt, D. Perner, G. W. Harris, A. M. Winer, J. N. Pitts, “Detection of NO3 in the polluted troposphere by differential optical absorption,” Geophys. Res. Lett. 7, 89–92 (1980).
[CrossRef]

Platt, U.

K. Pfeilsticker, U. Platt, “Airborne measurements during the Arctic stratospheric experiment: observation of O3 and NO2,” Geophys. Res. Lett. 21, 1375–1378 (1994).
[CrossRef]

M. Hausmann, U. Platt, “Spectroscopic measurement of bromine oxide and ozone in the high arctic during Polar Sunrise Experiment 1992,” J. Geophys. Res. 99, 25399–25413 (1994).
[CrossRef]

U. Platt, D. Perner, G. W. Harris, A. M. Winer, J. N. Pitts, “Detection of NO3 in the polluted troposphere by differential optical absorption,” Geophys. Res. Lett. 7, 89–92 (1980).
[CrossRef]

D. Perner, U. Platt, “Detection of nitrous acid in the atmosphere by differential optical absorption,” Geophys. Res. Lett. 6, 917–920 (1979).
[CrossRef]

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

D. Perner, D. H. Ehhalt, H. W. Paetz, U. Platt, E. P. Roeth, A. Volz, “OH-radicals in the lower troposphere,” Geophys. Res. Lett. 3, 466–468 (1976).
[CrossRef]

U. Platt, “Differential optical absorption spectroscopy (DOAS),” in Air Monitoring by Spectroscopic Techniques, M. W. Sigrist, ed., Chemical Analysis Series (Wiley, New York, 1994), Vol. 127.

U. Platt, D. Perner, “Measurements of atmospheric trace gases by long path differential UV/visible absorption spectroscopy,” in Optical and Laser Remote Sensing, D. K. Killinger, A. Mooradian, eds. (Springer-Verlag, New York, 1983), pp. 95–105.

J. Stutz, U. Platt, “A new generation of DOAS instruments,” TOPAS/EUROTRAC, in press.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge University, Cambridge, England, 1986).

Roeth, E. P.

D. Perner, D. H. Ehhalt, H. W. Paetz, U. Platt, E. P. Roeth, A. Volz, “OH-radicals in the lower troposphere,” Geophys. Res. Lett. 3, 466–468 (1976).
[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]

R. W. Sanders, S. Solomon, M. A. Carroll, A. L. Schmeltekopf, “Ground-based measurements of O3, NO2, OClO, and BrO during the 1987 Antarctic ozone depletion event,” in Ozone in the Atmosphere, Proceedings of the Quadrennial Ozone Symposium 1988, R. D. Bojkov, P. Fabian, eds. (Deepak Publishing, Hampton, Va., 1989), pp. 65–70.

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]

R. W. Sanders, S. Solomon, M. A. Carroll, A. L. Schmeltekopf, “Ground-based measurements of O3, NO2, OClO, and BrO during the 1987 Antarctic ozone depletion event,” in Ozone in the Atmosphere, Proceedings of the Quadrennial Ozone Symposium 1988, R. D. Bojkov, P. Fabian, eds. (Deepak Publishing, Hampton, Va., 1989), pp. 65–70.

D. L. Albritton, A. L. Schmeltekopf, R. N. Zare, “An introduction to the least-squares fitting of spectroscopic data,” in Molecular Spectroscopy: Modern Research, R. K. Narahari, M. W. Weldon, eds. (Academic, Orlando, Florida, 1976).

Schneider, W.

W. Schneider, G. K. Moortgat, G. S. Tyndall, J. P. Burrows, “Absorption cross-sections of NO2 in the UV and visible region (200–700 nm) at 298 K,” J. Photochem. Photobiol. 40, 195–217 (1987).
[CrossRef]

Shetter, R. E.

C. A. Cantrell, J. A. Davidson, A. H. McDaniel, R. E. Shetter, J. G. Calvert, “Temperature-dependent formaldehyde cross section in the near-ultraviolet spectral region,” J. Phys. Chem. 94, 3902–3908 (1990).
[CrossRef]

Simon, P. C.

A. C. Vandaele, P. C. Simon, J. M. Guilmot, M. Carleer, R. Colin, “SO2 absorption cross section measurements in the UV using a Fourier transform spectrometer,” J. Geophys. Res. 99, 25599–25605 (1994).
[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]

R. W. Sanders, S. Solomon, M. A. Carroll, A. L. Schmeltekopf, “Ground-based measurements of O3, NO2, OClO, and BrO during the 1987 Antarctic ozone depletion event,” in Ozone in the Atmosphere, Proceedings of the Quadrennial Ozone Symposium 1988, R. D. Bojkov, P. Fabian, eds. (Deepak Publishing, Hampton, Va., 1989), pp. 65–70.

Stutz, J.

J. Stutz, U. Platt, “A new generation of DOAS instruments,” TOPAS/EUROTRAC, in press.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge University, Cambridge, England, 1986).

Tyndall, G. S.

W. Schneider, G. K. Moortgat, G. S. Tyndall, J. P. Burrows, “Absorption cross-sections of NO2 in the UV and visible region (200–700 nm) at 298 K,” J. Photochem. Photobiol. 40, 195–217 (1987).
[CrossRef]

Vandaele, A. C.

A. C. Vandaele, P. C. Simon, J. M. Guilmot, M. Carleer, R. Colin, “SO2 absorption cross section measurements in the UV using a Fourier transform spectrometer,” J. Geophys. Res. 99, 25599–25605 (1994).
[CrossRef]

Vettering, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge University, Cambridge, England, 1986).

Volz, A.

D. Perner, D. H. Ehhalt, H. W. Paetz, U. Platt, E. P. Roeth, A. Volz, “OH-radicals in the lower troposphere,” Geophys. Res. Lett. 3, 466–468 (1976).
[CrossRef]

Whipple, E. C.

J. F. Noxon, E. C. Whipple, R. S. Hyde, “Stratospheric NO2. 1. Observational method and behavior at midlatitudes,” J. Geophys. Res. 84, 5047–5076 (1979).
[CrossRef]

Winer, A. M.

U. Platt, D. Perner, G. W. Harris, A. M. Winer, J. N. Pitts, “Detection of NO3 in the polluted troposphere by differential optical absorption,” Geophys. Res. Lett. 7, 89–92 (1980).
[CrossRef]

Zare, R. N.

D. L. Albritton, A. L. Schmeltekopf, R. N. Zare, “An introduction to the least-squares fitting of spectroscopic data,” in Molecular Spectroscopy: Modern Research, R. K. Narahari, M. W. Weldon, eds. (Academic, Orlando, Florida, 1976).

Comput. Phys. (1)

R. W. Cunningham, “Comparison of three methods for determining fit parameter uncertainies for the Marquardt compromise,” Comput. Phys. 7, 570–576 (1993).
[CrossRef]

Geophys. Res. Lett. (4)

D. Perner, U. Platt, “Detection of nitrous acid in the atmosphere by differential optical absorption,” Geophys. Res. Lett. 6, 917–920 (1979).
[CrossRef]

D. Perner, D. H. Ehhalt, H. W. Paetz, U. Platt, E. P. Roeth, A. Volz, “OH-radicals in the lower troposphere,” Geophys. Res. Lett. 3, 466–468 (1976).
[CrossRef]

U. Platt, D. Perner, G. W. Harris, A. M. Winer, J. N. Pitts, “Detection of NO3 in the polluted troposphere by differential optical absorption,” Geophys. Res. Lett. 7, 89–92 (1980).
[CrossRef]

K. Pfeilsticker, U. Platt, “Airborne measurements during the Arctic stratospheric experiment: observation of O3 and NO2,” Geophys. Res. Lett. 21, 1375–1378 (1994).
[CrossRef]

J. Geophys. Res. (5)

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. Platt, “Spectroscopic measurement of bromine oxide and ozone in the high arctic during Polar Sunrise Experiment 1992,” J. Geophys. Res. 99, 25399–25413 (1994).
[CrossRef]

J. F. Noxon, E. C. Whipple, R. S. Hyde, “Stratospheric NO2. 1. Observational method and behavior at midlatitudes,” J. Geophys. Res. 84, 5047–5076 (1979).
[CrossRef]

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

A. C. Vandaele, P. C. Simon, J. M. Guilmot, M. Carleer, R. Colin, “SO2 absorption cross section measurements in the UV using a Fourier transform spectrometer,” J. Geophys. Res. 99, 25599–25605 (1994).
[CrossRef]

J. Photochem. Photobiol. (1)

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Figures (11)

Fig. 1
Fig. 1

Schematic view of a DOAS instrument used to measure tropospheric trace-gas concentrations. Collimated light undergoes absorption processes on its way through the atmosphere. In a, an example of this light entering the spectrograph is given when HCHO is assumed to be the only absorber. This absorption spectrum shows the rotational structure of the absorption bands. b, the same spectrum convoluted by the spectrographs instrumental function reaches the detector. In the detector the wavelength is mapped to discrete pixels. This spectrum, c, is then stored in the computer and can be analyzed numerically.

Fig. 2
Fig. 2

Absorption spectra used for the Monte Carlo tests. We calculated the spectra by convoluting high-resolution cross sections with an Gaussian-shaped instrument function of 1.3-nm half-width. The average optical density D ¯ [Eq. (5)] of the spectra, 0.0195 for O3, 0.00066 for NO2, 0.0023 for SO2, and 0.00051 for HCHO, is marked with bars on the right axis. This corresponds to atmospheric concentrations of 100 × 10−9 (ppb) for O3, 2.5 ppb for NO2, 0.5 ppb for SO2, and 0.5 ppb for HCHO for a light path of 7.5 km in the troposphere.

Fig. 3
Fig. 3

Overview of the analysis procedure. As stopping conditions for the iteration, a maximum number of steps or the convergence of χ2 can be used. In the second case, the iteration stops if the change of χ2 from one step to another is smaller than a factor φ, which is typically set to 10−6.

Fig. 4
Fig. 4

Φj,k [see Eq. (14)] describes the influence on the fit results aj of the misalignment of spectrum Sk. The Φj,k shown in this figure was calculated with the spectra of Fig. 2. (a) shows the influence of the shift of the four different Sj on a1 of O3. (b), (c), and (d) show the influence on NO2, SO2, and HCHO, respectively. The highest influence is found for the shift of O3 on SO23,1 in (c)], where a shift of one pixel changes a3 by 70%.

Fig. 5
Fig. 5

J (Fig. 2) with added noise spectra N(σ) of different magnitudes. The magnitude is defined by the standard deviation σ over the pixel intensities. For high σ, the spectrum J cannot be identified in the noise.

Fig. 6
Fig. 6

Results of the Monte Carlo tests. (a) The average shift error Δ d j , 0 ¯ shows a linear behavior until the noise is much higher than the absorption structure. (b) Δ d j , 0 ¯ is usually underestimated by 20% compared with the statistical fluctuation δ(dj,0). For NO2, a 50% underestimation was found.

Fig. 7
Fig. 7

Results of the Monte Carlo test of the new method to estimate the total error Δtotaj. a: The relative error of aj shows a linear behavior. The arrows indicate where D ¯ j of the spectra Sj is equal to the 1-σ noise. The error is near the theoretical value of the detection limit 0.5. b: The standard deviation of the results δ(aj) is found within 10% by the total error Δ tot a j ¯. Higher values correspond to errors higher then 0.5 that are beyond the detection limit. (c) The ratio of the error Δ tot a j ¯ of the test of the complete analysis procedure with Δ a j lin ¯ of the Monte Carlo test of the linear procedure. In the case of O3 and SO2, the influence of the shift uncertainty is about 10%.

Fig. 8
Fig. 8

Comparison of a residuum of tropospheric NO2 measurements at 430 nm with a noise spectrum smoothed with a running mean of width W = 10 pixels. The measured spectrum looks similar to the theoretical spectrum.

Fig. 9
Fig. 9

Result of the Monte Carlo test with residuum. The values calculated with an ordinary linear least-squares procedure Δ a j ¯ underestimates the statistical error δ(aj) by a factor of 3. Δ a j ¯ calculated with the correlated linear least-squares procedure in contrast show a good agreement with δ(aj).

Fig. 10
Fig. 10

To correct the influence of random residual structures, a correction factor C(τ, W) can be calculated by Monte Carlo experiments. (a) C(τ, W) for the normal linear least-squares fit depending on the width of the absorption structures τ in the reference spectrum and the smoothing width W. (b) C(τ, W) for the shift error in the nonlinear fit.

Fig. 11
Fig. 11

Example of the analysis of an atmospheric absorption spectrum. The atmospheric spectrum was measured in Heidelberg on 27 August 1994 over a light path of 7.5 km. The fitted reference spectra and the residual spectrum after the removal of the absorption structures of the references are also shown.

Tables (1)

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Table 1 Results of the Analysis of the Spectrum in Fig. 10a

Equations (23)

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I ( λ , L ) = I 0 ( λ ) exp { 0 L j [ - σ j ABS ( λ , p , T ) × ρ j ( l ) ] - ɛ R ( λ , l ) - ɛ M ( λ , l ) d l } + N ( λ ) .
I ( i ) = λ ( i ) λ ( i + 1 ) I * ( λ ) d λ .
Γ I :             λ ( i ) = k = 0 q γ k × i k .
J ( i ) = J 0 ( i ) + j = 1 m a j × S j ( i ) + B ( i ) + R ( i ) + A ( i ) + N ( i ) .
D ¯ j = 3 × [ 1 n - 1 × i = 1 n ( S j ( i ) - S j ¯ ) 2 ] 1 / 2 .
F ( i ) = P r ( i ) + j = 1 m a j × S j ( d j , 0 , d j , 1 , ) ( i ) .
P r ( i ) = h = 0 r c h × ( i - i c ) h .
S j ( i ) interpolation S j ( x ) Γ j - 1 S j ( λ ) Γ J S j * ( i ) .
x ( i ) = x [ λ ( i ) ] = k = 0 q s × q I δ k × i k .
x = i + f j ( i )             with             f j ( i ) = k = 0 p j d j , k × ( i - i c ) k .
β = [ X T X ] - 1 X T J , Θ = σ ^ 2 [ X T X ] - 1 , σ ^ 2 = [ n - ( m + r ) ] - 1 [ J - X β ] T [ J - X β ] .
X = ( 1 ( - i c ) 1 ( - i c ) 2 ( - i c ) r S 1 ( 0 ) S 2 ( 0 ) S m ( 0 ) 1 ( 1 - i c ) 1 ( 1 - i c ) 2 ( 1 - i c ) r S 1 ( 1 ) S 2 ( 1 ) S m ( 1 ) 1 ( 2 - i c ) 1 ( 2 - i c ) 2 ( 2 - i c ) r S 1 ( 2 ) S 2 ( 2 ) S m ( 2 ) 1 ( n - i c ) 1 ( n - i c ) 2 ( n - i c ) r S 1 ( n ) S 2 ( n ) S m ( n ) ) .
J = 1 + S 1 * ( 0 ) + + S g * ( d g , 0 , d g , 1 , ) + + S m * ( 0 ) .
Φ j , g ( d g , 0 , d g , 1 , ) = 1 - a j * .
x ± = i ± Δ f g ( i ) with             Δ f g ( i ) = { k = 0 p j [ Δ d g , k × ( i - i c ) k ] 2 } 1 / 2 .
Φ j , g ( Δ f g ) = ½ × [ Φ j , g ( + Δ f g ) + Φ j , g ( - Δ f g ) ] .
Δ s h a j a j = { g = 1 m [ Φ j , g ( Δ f g ) ] 2 } 1 / 2 .
Δ tot a j = [ ( Δ a j ) 2 + ( Δ s h a j ) 2 ] 1 / 2 .
D ¯ limit σ × 6 ( n - 1 ) 1 / 2 .
σ limit ( n - 1 ) 1 / 2 6 × D ¯ .
( M ) i j = E ( ɛ i × ɛ j ) .
M 9 = 1 81 × ( 1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1 0 0 0 0 1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1 0 0 0 0 1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1 0 ) ,
β = [ X T M - 1 X ] - 1 X T M - 1 J , Θ = σ ^ 2 [ X T M - 1 X ] - 1 , σ ^ 2 = ( n - m ) - 1 [ J - X β ] T M - 1 [ J - X β ] .

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