Abstract

A line-by-line radiative-transfer model to quantify the Ring effect as caused by rotational Raman scattering has been developed for the 310–550-nm spectral interval. The solar zenith angle and the resolution are key input parameters, as is the sky spectrum (excluding inelastic atmospheric scattering), which was modeled with modtran3.5. The filling in is modeled for ground-based viewing geometry and includes surface reflection and single inelastic scattering. It is shown that O2 contributes half of the filling in of N2. A strong inverse relationship with wavelength is noted in the filling in. A comparison with observations shows moderate agreement. The largest filling in occurs in the Ca ii K and H lines.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. R. Grainger, J. Ring, “Anomalous Fraunhofer line profiles,” Nature (London) 193, 762 (1962).
    [CrossRef]
  2. J. Burrows, M. Vountas, H. Haug, K. Chance, L. Marquard, K. Muirhead, U. Platt, A. Richter, V. Rozanov, “Study of the Ring Effect,” (European Space Agency, Noordivijk, The Netherlands, 1996).
  3. R. T. Brinkmann, “Rotational Raman Scattering in planetary atmospheres,” Astrophys. J. 154, 1087–1093 (1968).
    [CrossRef]
  4. G. W. Kattawar, A. T. Young, T. J. Humphreys, “Inelastic scattering in planetary atmospheres. I. The Ring effect, without aerosols,” Astrophys. J. 243, 1049–1057 (1981).
    [CrossRef]
  5. J. Joiner, P. K. Bhartia, R. P. Cebula, E. Hilsenrath, R. D. McPeters, H. Park, “Rotational Raman Scattering (Ring effect) in satellite ultraviolet measurements,” Appl. Opt. 34, 4513–4525 (1995).
    [CrossRef] [PubMed]
  6. K. V. Chance, R. J. Spurr, “Ring effect studies: Rayleigh scattering, including molecular parameters for rotational Raman scattering, and the Fraunhofer spectrum,” Appl. Opt. 36, 5224–5230 (1997).
    [CrossRef] [PubMed]
  7. M. Vountas, V. V. Rozanov, J. P. Burrows, “Ring effect: impact of rotational Raman scattering on radiative transfer in Earth’s atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 60, 943–961 (1998).
    [CrossRef]
  8. D. S. Renschler, J. L. Hunt, T. K. McCubbin, S. R. Polo, “Triplet structure of the rotational Raman spectrum of oxygen,” J. Mol. Spectrosc. 31, 173–176 (1969).
    [CrossRef]
  9. R. P. Wayne, Chemistry of Atmospheres, 2nd ed. (Oxford University, Oxford, 1991).
  10. A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: a moderate resolution model for lowtran 7,” (U.S. Air Force Phillips Laboratory, Hanscom Air Force Base, Mass., 1989).
  11. A. W. Harrison, “Diurnal variation of the Ring effect,” Can. J. Phys. 54, 1000–1005 (1976).
    [CrossRef]
  12. D. J. Fish, R. L. Jones, “Rotational Raman scattering and the ring effect in zenith-sky spectra,” Geophys. Res. Lett. 22, 811–814 (1995).
    [CrossRef]
  13. A. W. Harrison, “Computed filling in of Fraunhofer lines 3850–4450 Å,” Can. J. Phys. 52, 2030–2036 (1974).
  14. J. F. Noxon, R. Goody, “Noncoherent scattering of skylight,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 1, 163–166 (1965).
  15. A. W. Harrison, D. J. W. Kendall, “Fraunhofer line filling in (3855–4455 Å),” Can. J. Phys. 52, 940–944 (1974).
  16. S. Solomon, A. L. Schmeltekopf, R. W. Sanders, “On the interpretation of zenith sky absorption measurements,” J. Geophys. Res. 92, 8311–8319 (1987).
    [CrossRef]
  17. K. N. Liou, An Introduction to Atmospheric Radiation (Academic, San Diego, Calif., 1980).
  18. F. E. Barmore, “The filling-in of Fraunhofer lines in the day sky,” J. Atmos. Sci. 32, 1489–1493 (1975).
    [CrossRef]
  19. I. Aben, F. Helderman, D. M. Stam, P. Stammes, “High-spectral resolution measurements of the atmosphere with the GOME BBM,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 446–453 (1997).
  20. K. R. Lang, Astrophysical Formulae (Springer Verlag, New York, 1986).
  21. I. Kostadinov, G. Giovanelli, F. Ravegnani, F. Evangelisti, P. Bonasoni, R. Werner, U. Bonafe, “Polarization and Ring effect influences upon stratospheric DOAS measurements,” in Spectroscopic Atmospheric Monitoring Techniques, K. Schäfer, ed., Proc. SPIE3106, 74–83 (1997).
    [CrossRef]

1998 (1)

M. Vountas, V. V. Rozanov, J. P. Burrows, “Ring effect: impact of rotational Raman scattering on radiative transfer in Earth’s atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 60, 943–961 (1998).
[CrossRef]

1997 (1)

1995 (2)

1987 (1)

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

1981 (1)

G. W. Kattawar, A. T. Young, T. J. Humphreys, “Inelastic scattering in planetary atmospheres. I. The Ring effect, without aerosols,” Astrophys. J. 243, 1049–1057 (1981).
[CrossRef]

1976 (1)

A. W. Harrison, “Diurnal variation of the Ring effect,” Can. J. Phys. 54, 1000–1005 (1976).
[CrossRef]

1975 (1)

F. E. Barmore, “The filling-in of Fraunhofer lines in the day sky,” J. Atmos. Sci. 32, 1489–1493 (1975).
[CrossRef]

1974 (2)

A. W. Harrison, D. J. W. Kendall, “Fraunhofer line filling in (3855–4455 Å),” Can. J. Phys. 52, 940–944 (1974).

A. W. Harrison, “Computed filling in of Fraunhofer lines 3850–4450 Å,” Can. J. Phys. 52, 2030–2036 (1974).

1969 (1)

D. S. Renschler, J. L. Hunt, T. K. McCubbin, S. R. Polo, “Triplet structure of the rotational Raman spectrum of oxygen,” J. Mol. Spectrosc. 31, 173–176 (1969).
[CrossRef]

1968 (1)

R. T. Brinkmann, “Rotational Raman Scattering in planetary atmospheres,” Astrophys. J. 154, 1087–1093 (1968).
[CrossRef]

1965 (1)

J. F. Noxon, R. Goody, “Noncoherent scattering of skylight,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 1, 163–166 (1965).

1962 (1)

J. R. Grainger, J. Ring, “Anomalous Fraunhofer line profiles,” Nature (London) 193, 762 (1962).
[CrossRef]

Aben, I.

I. Aben, F. Helderman, D. M. Stam, P. Stammes, “High-spectral resolution measurements of the atmosphere with the GOME BBM,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 446–453 (1997).

Barmore, F. E.

F. E. Barmore, “The filling-in of Fraunhofer lines in the day sky,” J. Atmos. Sci. 32, 1489–1493 (1975).
[CrossRef]

Berk, A.

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: a moderate resolution model for lowtran 7,” (U.S. Air Force Phillips Laboratory, Hanscom Air Force Base, Mass., 1989).

Bernstein, L. S.

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: a moderate resolution model for lowtran 7,” (U.S. Air Force Phillips Laboratory, Hanscom Air Force Base, Mass., 1989).

Bhartia, P. K.

Bonafe, U.

I. Kostadinov, G. Giovanelli, F. Ravegnani, F. Evangelisti, P. Bonasoni, R. Werner, U. Bonafe, “Polarization and Ring effect influences upon stratospheric DOAS measurements,” in Spectroscopic Atmospheric Monitoring Techniques, K. Schäfer, ed., Proc. SPIE3106, 74–83 (1997).
[CrossRef]

Bonasoni, P.

I. Kostadinov, G. Giovanelli, F. Ravegnani, F. Evangelisti, P. Bonasoni, R. Werner, U. Bonafe, “Polarization and Ring effect influences upon stratospheric DOAS measurements,” in Spectroscopic Atmospheric Monitoring Techniques, K. Schäfer, ed., Proc. SPIE3106, 74–83 (1997).
[CrossRef]

Brinkmann, R. T.

R. T. Brinkmann, “Rotational Raman Scattering in planetary atmospheres,” Astrophys. J. 154, 1087–1093 (1968).
[CrossRef]

Burrows, J.

J. Burrows, M. Vountas, H. Haug, K. Chance, L. Marquard, K. Muirhead, U. Platt, A. Richter, V. Rozanov, “Study of the Ring Effect,” (European Space Agency, Noordivijk, The Netherlands, 1996).

Burrows, J. P.

M. Vountas, V. V. Rozanov, J. P. Burrows, “Ring effect: impact of rotational Raman scattering on radiative transfer in Earth’s atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 60, 943–961 (1998).
[CrossRef]

Cebula, R. P.

Chance, K.

J. Burrows, M. Vountas, H. Haug, K. Chance, L. Marquard, K. Muirhead, U. Platt, A. Richter, V. Rozanov, “Study of the Ring Effect,” (European Space Agency, Noordivijk, The Netherlands, 1996).

Chance, K. V.

Evangelisti, F.

I. Kostadinov, G. Giovanelli, F. Ravegnani, F. Evangelisti, P. Bonasoni, R. Werner, U. Bonafe, “Polarization and Ring effect influences upon stratospheric DOAS measurements,” in Spectroscopic Atmospheric Monitoring Techniques, K. Schäfer, ed., Proc. SPIE3106, 74–83 (1997).
[CrossRef]

Fish, D. J.

D. J. Fish, R. L. Jones, “Rotational Raman scattering and the ring effect in zenith-sky spectra,” Geophys. Res. Lett. 22, 811–814 (1995).
[CrossRef]

Giovanelli, G.

I. Kostadinov, G. Giovanelli, F. Ravegnani, F. Evangelisti, P. Bonasoni, R. Werner, U. Bonafe, “Polarization and Ring effect influences upon stratospheric DOAS measurements,” in Spectroscopic Atmospheric Monitoring Techniques, K. Schäfer, ed., Proc. SPIE3106, 74–83 (1997).
[CrossRef]

Goody, R.

J. F. Noxon, R. Goody, “Noncoherent scattering of skylight,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 1, 163–166 (1965).

Grainger, J. R.

J. R. Grainger, J. Ring, “Anomalous Fraunhofer line profiles,” Nature (London) 193, 762 (1962).
[CrossRef]

Harrison, A. W.

A. W. Harrison, “Diurnal variation of the Ring effect,” Can. J. Phys. 54, 1000–1005 (1976).
[CrossRef]

A. W. Harrison, “Computed filling in of Fraunhofer lines 3850–4450 Å,” Can. J. Phys. 52, 2030–2036 (1974).

A. W. Harrison, D. J. W. Kendall, “Fraunhofer line filling in (3855–4455 Å),” Can. J. Phys. 52, 940–944 (1974).

Haug, H.

J. Burrows, M. Vountas, H. Haug, K. Chance, L. Marquard, K. Muirhead, U. Platt, A. Richter, V. Rozanov, “Study of the Ring Effect,” (European Space Agency, Noordivijk, The Netherlands, 1996).

Helderman, F.

I. Aben, F. Helderman, D. M. Stam, P. Stammes, “High-spectral resolution measurements of the atmosphere with the GOME BBM,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 446–453 (1997).

Hilsenrath, E.

Humphreys, T. J.

G. W. Kattawar, A. T. Young, T. J. Humphreys, “Inelastic scattering in planetary atmospheres. I. The Ring effect, without aerosols,” Astrophys. J. 243, 1049–1057 (1981).
[CrossRef]

Hunt, J. L.

D. S. Renschler, J. L. Hunt, T. K. McCubbin, S. R. Polo, “Triplet structure of the rotational Raman spectrum of oxygen,” J. Mol. Spectrosc. 31, 173–176 (1969).
[CrossRef]

Joiner, J.

Jones, R. L.

D. J. Fish, R. L. Jones, “Rotational Raman scattering and the ring effect in zenith-sky spectra,” Geophys. Res. Lett. 22, 811–814 (1995).
[CrossRef]

Kattawar, G. W.

G. W. Kattawar, A. T. Young, T. J. Humphreys, “Inelastic scattering in planetary atmospheres. I. The Ring effect, without aerosols,” Astrophys. J. 243, 1049–1057 (1981).
[CrossRef]

Kendall, D. J. W.

A. W. Harrison, D. J. W. Kendall, “Fraunhofer line filling in (3855–4455 Å),” Can. J. Phys. 52, 940–944 (1974).

Kostadinov, I.

I. Kostadinov, G. Giovanelli, F. Ravegnani, F. Evangelisti, P. Bonasoni, R. Werner, U. Bonafe, “Polarization and Ring effect influences upon stratospheric DOAS measurements,” in Spectroscopic Atmospheric Monitoring Techniques, K. Schäfer, ed., Proc. SPIE3106, 74–83 (1997).
[CrossRef]

Lang, K. R.

K. R. Lang, Astrophysical Formulae (Springer Verlag, New York, 1986).

Liou, K. N.

K. N. Liou, An Introduction to Atmospheric Radiation (Academic, San Diego, Calif., 1980).

Marquard, L.

J. Burrows, M. Vountas, H. Haug, K. Chance, L. Marquard, K. Muirhead, U. Platt, A. Richter, V. Rozanov, “Study of the Ring Effect,” (European Space Agency, Noordivijk, The Netherlands, 1996).

McCubbin, T. K.

D. S. Renschler, J. L. Hunt, T. K. McCubbin, S. R. Polo, “Triplet structure of the rotational Raman spectrum of oxygen,” J. Mol. Spectrosc. 31, 173–176 (1969).
[CrossRef]

McPeters, R. D.

Muirhead, K.

J. Burrows, M. Vountas, H. Haug, K. Chance, L. Marquard, K. Muirhead, U. Platt, A. Richter, V. Rozanov, “Study of the Ring Effect,” (European Space Agency, Noordivijk, The Netherlands, 1996).

Noxon, J. F.

J. F. Noxon, R. Goody, “Noncoherent scattering of skylight,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 1, 163–166 (1965).

Park, H.

Platt, U.

J. Burrows, M. Vountas, H. Haug, K. Chance, L. Marquard, K. Muirhead, U. Platt, A. Richter, V. Rozanov, “Study of the Ring Effect,” (European Space Agency, Noordivijk, The Netherlands, 1996).

Polo, S. R.

D. S. Renschler, J. L. Hunt, T. K. McCubbin, S. R. Polo, “Triplet structure of the rotational Raman spectrum of oxygen,” J. Mol. Spectrosc. 31, 173–176 (1969).
[CrossRef]

Ravegnani, F.

I. Kostadinov, G. Giovanelli, F. Ravegnani, F. Evangelisti, P. Bonasoni, R. Werner, U. Bonafe, “Polarization and Ring effect influences upon stratospheric DOAS measurements,” in Spectroscopic Atmospheric Monitoring Techniques, K. Schäfer, ed., Proc. SPIE3106, 74–83 (1997).
[CrossRef]

Renschler, D. S.

D. S. Renschler, J. L. Hunt, T. K. McCubbin, S. R. Polo, “Triplet structure of the rotational Raman spectrum of oxygen,” J. Mol. Spectrosc. 31, 173–176 (1969).
[CrossRef]

Richter, A.

J. Burrows, M. Vountas, H. Haug, K. Chance, L. Marquard, K. Muirhead, U. Platt, A. Richter, V. Rozanov, “Study of the Ring Effect,” (European Space Agency, Noordivijk, The Netherlands, 1996).

Ring, J.

J. R. Grainger, J. Ring, “Anomalous Fraunhofer line profiles,” Nature (London) 193, 762 (1962).
[CrossRef]

Robertson, D. C.

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: a moderate resolution model for lowtran 7,” (U.S. Air Force Phillips Laboratory, Hanscom Air Force Base, Mass., 1989).

Rozanov, V.

J. Burrows, M. Vountas, H. Haug, K. Chance, L. Marquard, K. Muirhead, U. Platt, A. Richter, V. Rozanov, “Study of the Ring Effect,” (European Space Agency, Noordivijk, The Netherlands, 1996).

Rozanov, V. V.

M. Vountas, V. V. Rozanov, J. P. Burrows, “Ring effect: impact of rotational Raman scattering on radiative transfer in Earth’s atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 60, 943–961 (1998).
[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]

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]

Spurr, R. J.

Stam, D. M.

I. Aben, F. Helderman, D. M. Stam, P. Stammes, “High-spectral resolution measurements of the atmosphere with the GOME BBM,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 446–453 (1997).

Stammes, P.

I. Aben, F. Helderman, D. M. Stam, P. Stammes, “High-spectral resolution measurements of the atmosphere with the GOME BBM,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 446–453 (1997).

Vountas, M.

M. Vountas, V. V. Rozanov, J. P. Burrows, “Ring effect: impact of rotational Raman scattering on radiative transfer in Earth’s atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 60, 943–961 (1998).
[CrossRef]

J. Burrows, M. Vountas, H. Haug, K. Chance, L. Marquard, K. Muirhead, U. Platt, A. Richter, V. Rozanov, “Study of the Ring Effect,” (European Space Agency, Noordivijk, The Netherlands, 1996).

Wayne, R. P.

R. P. Wayne, Chemistry of Atmospheres, 2nd ed. (Oxford University, Oxford, 1991).

Werner, R.

I. Kostadinov, G. Giovanelli, F. Ravegnani, F. Evangelisti, P. Bonasoni, R. Werner, U. Bonafe, “Polarization and Ring effect influences upon stratospheric DOAS measurements,” in Spectroscopic Atmospheric Monitoring Techniques, K. Schäfer, ed., Proc. SPIE3106, 74–83 (1997).
[CrossRef]

Young, A. T.

G. W. Kattawar, A. T. Young, T. J. Humphreys, “Inelastic scattering in planetary atmospheres. I. The Ring effect, without aerosols,” Astrophys. J. 243, 1049–1057 (1981).
[CrossRef]

Appl. Opt. (2)

Astrophys. J. (2)

R. T. Brinkmann, “Rotational Raman Scattering in planetary atmospheres,” Astrophys. J. 154, 1087–1093 (1968).
[CrossRef]

G. W. Kattawar, A. T. Young, T. J. Humphreys, “Inelastic scattering in planetary atmospheres. I. The Ring effect, without aerosols,” Astrophys. J. 243, 1049–1057 (1981).
[CrossRef]

Can. J. Phys. (3)

A. W. Harrison, “Diurnal variation of the Ring effect,” Can. J. Phys. 54, 1000–1005 (1976).
[CrossRef]

A. W. Harrison, “Computed filling in of Fraunhofer lines 3850–4450 Å,” Can. J. Phys. 52, 2030–2036 (1974).

A. W. Harrison, D. J. W. Kendall, “Fraunhofer line filling in (3855–4455 Å),” Can. J. Phys. 52, 940–944 (1974).

Geophys. Res. Lett. (1)

D. J. Fish, R. L. Jones, “Rotational Raman scattering and the ring effect in zenith-sky spectra,” Geophys. Res. Lett. 22, 811–814 (1995).
[CrossRef]

Izv. Acad. Sci. USSR Atmos. Oceanic Phys. (1)

J. F. Noxon, R. Goody, “Noncoherent scattering of skylight,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 1, 163–166 (1965).

J. Atmos. Sci. (1)

F. E. Barmore, “The filling-in of Fraunhofer lines in the day sky,” J. Atmos. Sci. 32, 1489–1493 (1975).
[CrossRef]

J. Geophys. Res. (1)

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

J. Mol. Spectrosc. (1)

D. S. Renschler, J. L. Hunt, T. K. McCubbin, S. R. Polo, “Triplet structure of the rotational Raman spectrum of oxygen,” J. Mol. Spectrosc. 31, 173–176 (1969).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

M. Vountas, V. V. Rozanov, J. P. Burrows, “Ring effect: impact of rotational Raman scattering on radiative transfer in Earth’s atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 60, 943–961 (1998).
[CrossRef]

Nature (London) (1)

J. R. Grainger, J. Ring, “Anomalous Fraunhofer line profiles,” Nature (London) 193, 762 (1962).
[CrossRef]

Other (7)

J. Burrows, M. Vountas, H. Haug, K. Chance, L. Marquard, K. Muirhead, U. Platt, A. Richter, V. Rozanov, “Study of the Ring Effect,” (European Space Agency, Noordivijk, The Netherlands, 1996).

I. Aben, F. Helderman, D. M. Stam, P. Stammes, “High-spectral resolution measurements of the atmosphere with the GOME BBM,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 446–453 (1997).

K. R. Lang, Astrophysical Formulae (Springer Verlag, New York, 1986).

I. Kostadinov, G. Giovanelli, F. Ravegnani, F. Evangelisti, P. Bonasoni, R. Werner, U. Bonafe, “Polarization and Ring effect influences upon stratospheric DOAS measurements,” in Spectroscopic Atmospheric Monitoring Techniques, K. Schäfer, ed., Proc. SPIE3106, 74–83 (1997).
[CrossRef]

R. P. Wayne, Chemistry of Atmospheres, 2nd ed. (Oxford University, Oxford, 1991).

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: a moderate resolution model for lowtran 7,” (U.S. Air Force Phillips Laboratory, Hanscom Air Force Base, Mass., 1989).

K. N. Liou, An Introduction to Atmospheric Radiation (Academic, San Diego, Calif., 1980).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

(a) Rotational Raman spectrum of N2 at 258 K, 310 nm. Anti-Stokes lines are shifted to shorter wavelengths (negative wave numbers), and Stokes shifting is to longer wavelengths (positive wave numbers). Stokes clearly dominates anti-Stokes at 258 K. (b) Rotational Raman spectrum of O2 (at 258 K, 310 nm), which contains more lines than for N2 owing to the effects of electronic spin on angular momentum.

Fig. 2
Fig. 2

Radiance of the sky convolved with a triangular slit function with a FWHM of 22 cm-1 interpolated to 1 cm-1 at a SZA of 61.07°. This is the input spectrum created in modtran3.5 from 310 to 413 nm.

Fig. 3
Fig. 3

Effect of ignoring terrestrial absorption on FI values. The sky spectrum and the solar spectrum (both with a resolution of 22 cm-1 (a FWHM of a triangular slit function) (at a SZA of 60°) are compared. The difference in FI occurring in the near-UV region is primarily due to Huggins band gas absorption lines (O3).

Fig. 4
Fig. 4

Sum of cross sections shifting radiance due to RRS (σ in versus σout), O2, 410–434 nm. Each point on the thick line represents the sum of the rotational Raman cross sections for the lines shifting light out of that wavelength. The points on the thin line indicate the intensity-weighted cross sections for lines shifting light into a particular wavelength. Note the inverse wavelength dependence for both. The difference between corresponding points on the thick and the thin lines is the cross section inputted into the Beer’s law formalism to obtain the frequency-redistributed intensity at a particular wavelength.

Fig. 5
Fig. 5

RRS/Rayleigh phase function ratio versus scattering angle. The weaker dependence of Raman scattering on the cosine of the scattering angle is responsible for the maximum (at 90°) in the ratio of phase functions (RRS/Rayleigh) versus scattering angle.

Fig. 6
Fig. 6

FI spectrum in the 310–410-nm spectral interval at a resolution of 22 cm-1 (FWHM of the triangular slit function); SZA, 30°. Note the large FI for the Ca ii K and H lines at approximately 393 and 397 nm, respectively.

Fig. 7
Fig. 7

FI spectrum (410–550 nm) at a resolution of 22 cm-1 (FWHM of a triangular slit function); SZA, 30°. No gas-absorption line or Fraunhofer line is filled in above 2.5%.

Fig. 8
Fig. 8

Radiance spectrum of scattered skylight including RRS and the FI spectrum in the 312–320-nm region at a SZA of 30°. Note the mirror-image pairing of Fraunhofer lines with maxima on the FI spectrum.

Fig. 9
Fig. 9

Spectral radiance of skylight (Wcm-2 cm-1 sr-1) with and without RRS (thin and thick lines, respectively) for the Ni i line near 313 nm at an SZA of 30°. There is FI in the line core and the opposite effect in the wings of the line (at ∼313.9 nm) and in the nearby continuum.

Tables (1)

Tables Icon

Table 1 FI Comparison (Harrisona versus Model) at SZA’s of 30° and 90°

Equations (14)

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

QN,JN,J=256π5γ2fNbN,JN,J/27λ4
γO2=7.149×10-26 cm3+4.59364×10-15 cm/4.82716×109 cm-2-ν2,
γN2=-6.01466×10-25 cm3+2.38557×10-14 cm/1.86099×1010 cm-2-ν2.
QNN=256π5γ2fNbNN/27λ4.
fN=gN/Z2J+1exp-E/kT,
Z=J,N fN.
σin=1/IλJ,N=0 IλQN,JN,J;λ,
σout=J,N=0 QN,JN,J;λ.
FIλ=Iλ-Rλ/Iλ,
PRRS=3/4013+cos2θ,
P=31+ρ+1-ρcos2 θ/4+2ρ.
ρRayleigh=6ε/180+7ε,
α=m2-1/4πN0,
mair=1+7.041×10-5+3.159×106 cm-2/1.5739×1010 cm-2-ν2+8.4127×104 cm-2/5.0429×109 cm-2-ν2,

Metrics