Abstract

Classical optics holds that the extinction cross of particles should be equal to twice their geometric cross section, in the limit where the particles are much larger than the wavelength. It follows that the extinction coefficient of such large scatterers should be independent of wavelength. Snowflakes are much larger than the wavelengths of visible and infrared radiation, yet many investigators have found that the visible and infrared extinction coefficient of falling snow measured with transmissometers is wavelength dependent. This dependency is known to be a result of the scattering contribution to the transmissometer signal. Furthermore, many measurements in the visible and infrared show that extinction values measured simultaneously with two transmissometers are linearly related up to at least 12 km−1. The slope depends on the wavelengths and optical characteristics of the transmissometers. We show that for small values of extinction, the observations can be explained by taking into account single-scattering contributions to transmissometer signals. For high values of extinction, a multiple-scattering model gives good agreement with measurements.

© 1992 Optical Society of America

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References

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  1. L. A. Poliakov, V. D. Tretjakov, “Visibility in falling snow,” Tr. Gl. Geofiz. Obs. 100, 53–57 (1960).
  2. O. Lillesaeter, “Parallel-beam attenuation of light, particularly by falling snow,” J. Appl. Meteorol. 4, 607–613 (1965).
    [CrossRef]
  3. H. W. O’Brien, “Visibility and light attenuation in falling snow,” J. Appl. Meteorol. 9, 671–683 (1970).
    [CrossRef]
  4. M. C. Sola, R. J. Bergmann, “Multi-spectral propagation measurements through snow” in Topical Meeting on Optical Propagation Through Turbulence, Rain and Fog, 1977 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1977), paper ThB4.
  5. M. J. Persky, W. O. Gallery, “Validation and analysis of SNOW-ONE-A transmission data,” in Proceedings of SNOW Symposium IV, G. W. Aitken, ed. (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1984), p. 9.
  6. J. A. Curcio, P. Lebow, “Spectral transmittance measurements at SNOW-TWO,” Spec. Rep. 84-20, 3-16 (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1984).
  7. S. T. Hanley, B. L. Bean, R. Soulon, J. Randhawa, R. A. Dise, “SMART transmission support at SNOW IV,” in Proceedings of SNOW Symposium VI, A. W. Hogan, R. Redfield, eds. (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1987), p. 69.
  8. J. D. Mill, E. P. Shettle, “A preliminary LOWTRAN snow model,” in Proceedings of SNOW Symposium II, G. W. Aitken, ed. (U. S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1983), p. 239.
  9. D. L. Hutt, L. R. Bissonnette, D. St. Germain, “Multi-wavelength transmittance through falling snow,” in Propagation Engineering, N. S. Kopeika, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1115, 254 (1989).
  10. W. E. K. Middleton, “The effect of the angular aperture of a telescope on the telephotometry of collimated and non-collimated beams,” J. Opt. Soc. Am. 39, 576–581 (1949).
    [CrossRef]
  11. J. R. Hodkinson, I. Greenleaves, “Computations of light-scattering and extinction by spheres according to diffraction and geometrical optics,” J. Opt. Soc. Am. 53, 577–588 (1963).
    [CrossRef]
  12. V. E. Zuev, Laser Beams in the Atmosphere (Consultants Bureau, New York, 1982), Chap. 3, p. 150.
  13. L. W. Winchester, G. G. Gimmestad, “Scattering corrections to extinction coefficients measured in falling snow,” Opt. Eng. 22, 86–89 (1983).
  14. M. A. Seagraves, J. F. Ebersole, “Visible and infrared transmission through snow,” Opt. Eng. 22, 90–93 (1983).
  15. M. A. Seagraves, “Visible and infrared extinction in falling snow,” Appl. Opt. 25, 1166–1169 (1986).
    [CrossRef] [PubMed]
  16. C. F. Bohren, G. Koh, “Forward-scattering corrected extinction by nonspherical particles,” Appl. Opt. 24, 1023–1029 (1985).
    [CrossRef] [PubMed]
  17. L. R. Bissonnette, “Multiscattering model for propagation of narrow light beams in aerosol media,” Appl. Opt. 27, 2478–2484 (1988).
    [CrossRef] [PubMed]
  18. V. J. Schaefer, J. A. Day, A Field Guide to the Atmosphere (Houghton Mifflin, Boston, Mass., 1981), p. 324.
  19. K. Liou, J. E. Hansen, “Intensity and polarization for single scattering by polydisperse spheres: a comparison of ray optics and Mie theory,” J. Atmos. Sci 28, 995–1004 (1971).
    [CrossRef]
  20. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957), Chap. 8, p. 108.
  21. J. R. Hodkinson, “Light scattering and extinction by irregular particles larger than the wavelength,” in Electromagnetic Scattering, M. Kerker, ed. (Macmillan, New York, 1963), pp. 87–100.
  22. D. S. Bochkov, “Attenuation of a finite optical beam in a medium with large scatterers,” Atmos. Opt. 2, 468–472 (1989).
  23. V. E. Zuev, M. V. Kabanov, B. A. Savelev, “Propagation of laser beams in scattering media,” Appl. Opt. 8, 137–142 (1969).
    [CrossRef] [PubMed]
  24. L. R. Bissonnette, R. B. Smith, A. Ulitsky, J. D. Houston, A. I. Carswell, “Transmitted beam profiles, integrated backscatter and range resolved backscatter in inhomogeneous laboratory water droplet clouds,” Appl. Opt. 27, 2485–2494 (1988).
    [CrossRef] [PubMed]
  25. F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” Rep. AFGL-TR-83-0187 (U. S. Air Force Geophysics Laboratory, Cambridge, Mass., 1983).
  26. D. St. Germain, “Polar nephelometer for measuring snowflake phase functions,” in Proceedings of SNOW Symposium VII, R. E. Bates, A. W. Hogan, E. A. Wright, eds. (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1987), p. 77.
  27. C. F. Bohren, “Colors of snow, frozen waterfalls and icebergs,” J. Opt. Soc. Am. 73, 1646–1652 (1983).
    [CrossRef]
  28. C. F. Bohren, T. J. Nevitt, “Absorption by a sphere: a simple approximation,” Appl. Opt. 22, 774–775 (1983).
    [CrossRef] [PubMed]
  29. S. J. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
    [CrossRef] [PubMed]

1989 (1)

D. S. Bochkov, “Attenuation of a finite optical beam in a medium with large scatterers,” Atmos. Opt. 2, 468–472 (1989).

1988 (2)

1986 (1)

1985 (1)

1984 (1)

1983 (4)

C. F. Bohren, “Colors of snow, frozen waterfalls and icebergs,” J. Opt. Soc. Am. 73, 1646–1652 (1983).
[CrossRef]

C. F. Bohren, T. J. Nevitt, “Absorption by a sphere: a simple approximation,” Appl. Opt. 22, 774–775 (1983).
[CrossRef] [PubMed]

L. W. Winchester, G. G. Gimmestad, “Scattering corrections to extinction coefficients measured in falling snow,” Opt. Eng. 22, 86–89 (1983).

M. A. Seagraves, J. F. Ebersole, “Visible and infrared transmission through snow,” Opt. Eng. 22, 90–93 (1983).

1971 (1)

K. Liou, J. E. Hansen, “Intensity and polarization for single scattering by polydisperse spheres: a comparison of ray optics and Mie theory,” J. Atmos. Sci 28, 995–1004 (1971).
[CrossRef]

1970 (1)

H. W. O’Brien, “Visibility and light attenuation in falling snow,” J. Appl. Meteorol. 9, 671–683 (1970).
[CrossRef]

1969 (1)

1965 (1)

O. Lillesaeter, “Parallel-beam attenuation of light, particularly by falling snow,” J. Appl. Meteorol. 4, 607–613 (1965).
[CrossRef]

1963 (1)

1960 (1)

L. A. Poliakov, V. D. Tretjakov, “Visibility in falling snow,” Tr. Gl. Geofiz. Obs. 100, 53–57 (1960).

1949 (1)

Abreu, L. W.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” Rep. AFGL-TR-83-0187 (U. S. Air Force Geophysics Laboratory, Cambridge, Mass., 1983).

Bean, B. L.

S. T. Hanley, B. L. Bean, R. Soulon, J. Randhawa, R. A. Dise, “SMART transmission support at SNOW IV,” in Proceedings of SNOW Symposium VI, A. W. Hogan, R. Redfield, eds. (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1987), p. 69.

Bergmann, R. J.

M. C. Sola, R. J. Bergmann, “Multi-spectral propagation measurements through snow” in Topical Meeting on Optical Propagation Through Turbulence, Rain and Fog, 1977 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1977), paper ThB4.

Bissonnette, L. R.

Bochkov, D. S.

D. S. Bochkov, “Attenuation of a finite optical beam in a medium with large scatterers,” Atmos. Opt. 2, 468–472 (1989).

Bohren, C. F.

Carswell, A. I.

Chetwynd, J. H.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” Rep. AFGL-TR-83-0187 (U. S. Air Force Geophysics Laboratory, Cambridge, Mass., 1983).

Clough, S. A.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” Rep. AFGL-TR-83-0187 (U. S. Air Force Geophysics Laboratory, Cambridge, Mass., 1983).

Curcio, J. A.

J. A. Curcio, P. Lebow, “Spectral transmittance measurements at SNOW-TWO,” Spec. Rep. 84-20, 3-16 (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1984).

Day, J. A.

V. J. Schaefer, J. A. Day, A Field Guide to the Atmosphere (Houghton Mifflin, Boston, Mass., 1981), p. 324.

Dise, R. A.

S. T. Hanley, B. L. Bean, R. Soulon, J. Randhawa, R. A. Dise, “SMART transmission support at SNOW IV,” in Proceedings of SNOW Symposium VI, A. W. Hogan, R. Redfield, eds. (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1987), p. 69.

Ebersole, J. F.

M. A. Seagraves, J. F. Ebersole, “Visible and infrared transmission through snow,” Opt. Eng. 22, 90–93 (1983).

Fenn, R. W.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” Rep. AFGL-TR-83-0187 (U. S. Air Force Geophysics Laboratory, Cambridge, Mass., 1983).

Gallery, W. O.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” Rep. AFGL-TR-83-0187 (U. S. Air Force Geophysics Laboratory, Cambridge, Mass., 1983).

M. J. Persky, W. O. Gallery, “Validation and analysis of SNOW-ONE-A transmission data,” in Proceedings of SNOW Symposium IV, G. W. Aitken, ed. (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1984), p. 9.

Germain, D. St.

D. St. Germain, “Polar nephelometer for measuring snowflake phase functions,” in Proceedings of SNOW Symposium VII, R. E. Bates, A. W. Hogan, E. A. Wright, eds. (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1987), p. 77.

D. L. Hutt, L. R. Bissonnette, D. St. Germain, “Multi-wavelength transmittance through falling snow,” in Propagation Engineering, N. S. Kopeika, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1115, 254 (1989).

Gimmestad, G. G.

L. W. Winchester, G. G. Gimmestad, “Scattering corrections to extinction coefficients measured in falling snow,” Opt. Eng. 22, 86–89 (1983).

Greenleaves, I.

Hanley, S. T.

S. T. Hanley, B. L. Bean, R. Soulon, J. Randhawa, R. A. Dise, “SMART transmission support at SNOW IV,” in Proceedings of SNOW Symposium VI, A. W. Hogan, R. Redfield, eds. (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1987), p. 69.

Hansen, J. E.

K. Liou, J. E. Hansen, “Intensity and polarization for single scattering by polydisperse spheres: a comparison of ray optics and Mie theory,” J. Atmos. Sci 28, 995–1004 (1971).
[CrossRef]

Hodkinson, J. R.

J. R. Hodkinson, I. Greenleaves, “Computations of light-scattering and extinction by spheres according to diffraction and geometrical optics,” J. Opt. Soc. Am. 53, 577–588 (1963).
[CrossRef]

J. R. Hodkinson, “Light scattering and extinction by irregular particles larger than the wavelength,” in Electromagnetic Scattering, M. Kerker, ed. (Macmillan, New York, 1963), pp. 87–100.

Houston, J. D.

Hutt, D. L.

D. L. Hutt, L. R. Bissonnette, D. St. Germain, “Multi-wavelength transmittance through falling snow,” in Propagation Engineering, N. S. Kopeika, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1115, 254 (1989).

Kabanov, M. V.

Kneizys, F. X.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” Rep. AFGL-TR-83-0187 (U. S. Air Force Geophysics Laboratory, Cambridge, Mass., 1983).

Koh, G.

Lebow, P.

J. A. Curcio, P. Lebow, “Spectral transmittance measurements at SNOW-TWO,” Spec. Rep. 84-20, 3-16 (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1984).

Lillesaeter, O.

O. Lillesaeter, “Parallel-beam attenuation of light, particularly by falling snow,” J. Appl. Meteorol. 4, 607–613 (1965).
[CrossRef]

Liou, K.

K. Liou, J. E. Hansen, “Intensity and polarization for single scattering by polydisperse spheres: a comparison of ray optics and Mie theory,” J. Atmos. Sci 28, 995–1004 (1971).
[CrossRef]

Middleton, W. E. K.

Mill, J. D.

J. D. Mill, E. P. Shettle, “A preliminary LOWTRAN snow model,” in Proceedings of SNOW Symposium II, G. W. Aitken, ed. (U. S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1983), p. 239.

Nevitt, T. J.

O’Brien, H. W.

H. W. O’Brien, “Visibility and light attenuation in falling snow,” J. Appl. Meteorol. 9, 671–683 (1970).
[CrossRef]

Persky, M. J.

M. J. Persky, W. O. Gallery, “Validation and analysis of SNOW-ONE-A transmission data,” in Proceedings of SNOW Symposium IV, G. W. Aitken, ed. (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1984), p. 9.

Poliakov, L. A.

L. A. Poliakov, V. D. Tretjakov, “Visibility in falling snow,” Tr. Gl. Geofiz. Obs. 100, 53–57 (1960).

Randhawa, J.

S. T. Hanley, B. L. Bean, R. Soulon, J. Randhawa, R. A. Dise, “SMART transmission support at SNOW IV,” in Proceedings of SNOW Symposium VI, A. W. Hogan, R. Redfield, eds. (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1987), p. 69.

Savelev, B. A.

Schaefer, V. J.

V. J. Schaefer, J. A. Day, A Field Guide to the Atmosphere (Houghton Mifflin, Boston, Mass., 1981), p. 324.

Seagraves, M. A.

M. A. Seagraves, “Visible and infrared extinction in falling snow,” Appl. Opt. 25, 1166–1169 (1986).
[CrossRef] [PubMed]

M. A. Seagraves, J. F. Ebersole, “Visible and infrared transmission through snow,” Opt. Eng. 22, 90–93 (1983).

Selby, J. E. A.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” Rep. AFGL-TR-83-0187 (U. S. Air Force Geophysics Laboratory, Cambridge, Mass., 1983).

Shettle, E. P.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” Rep. AFGL-TR-83-0187 (U. S. Air Force Geophysics Laboratory, Cambridge, Mass., 1983).

J. D. Mill, E. P. Shettle, “A preliminary LOWTRAN snow model,” in Proceedings of SNOW Symposium II, G. W. Aitken, ed. (U. S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1983), p. 239.

Smith, R. B.

Sola, M. C.

M. C. Sola, R. J. Bergmann, “Multi-spectral propagation measurements through snow” in Topical Meeting on Optical Propagation Through Turbulence, Rain and Fog, 1977 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1977), paper ThB4.

Soulon, R.

S. T. Hanley, B. L. Bean, R. Soulon, J. Randhawa, R. A. Dise, “SMART transmission support at SNOW IV,” in Proceedings of SNOW Symposium VI, A. W. Hogan, R. Redfield, eds. (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1987), p. 69.

Tretjakov, V. D.

L. A. Poliakov, V. D. Tretjakov, “Visibility in falling snow,” Tr. Gl. Geofiz. Obs. 100, 53–57 (1960).

Ulitsky, A.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957), Chap. 8, p. 108.

Warren, S. J.

Winchester, L. W.

L. W. Winchester, G. G. Gimmestad, “Scattering corrections to extinction coefficients measured in falling snow,” Opt. Eng. 22, 86–89 (1983).

Zuev, V. E.

V. E. Zuev, M. V. Kabanov, B. A. Savelev, “Propagation of laser beams in scattering media,” Appl. Opt. 8, 137–142 (1969).
[CrossRef] [PubMed]

V. E. Zuev, Laser Beams in the Atmosphere (Consultants Bureau, New York, 1982), Chap. 3, p. 150.

Appl. Opt. (7)

Atmos. Opt. (1)

D. S. Bochkov, “Attenuation of a finite optical beam in a medium with large scatterers,” Atmos. Opt. 2, 468–472 (1989).

J. Appl. Meteorol. (2)

O. Lillesaeter, “Parallel-beam attenuation of light, particularly by falling snow,” J. Appl. Meteorol. 4, 607–613 (1965).
[CrossRef]

H. W. O’Brien, “Visibility and light attenuation in falling snow,” J. Appl. Meteorol. 9, 671–683 (1970).
[CrossRef]

J. Atmos. Sci (1)

K. Liou, J. E. Hansen, “Intensity and polarization for single scattering by polydisperse spheres: a comparison of ray optics and Mie theory,” J. Atmos. Sci 28, 995–1004 (1971).
[CrossRef]

J. Opt. Soc. Am. (3)

Opt. Eng. (2)

L. W. Winchester, G. G. Gimmestad, “Scattering corrections to extinction coefficients measured in falling snow,” Opt. Eng. 22, 86–89 (1983).

M. A. Seagraves, J. F. Ebersole, “Visible and infrared transmission through snow,” Opt. Eng. 22, 90–93 (1983).

Tr. Gl. Geofiz. Obs. (1)

L. A. Poliakov, V. D. Tretjakov, “Visibility in falling snow,” Tr. Gl. Geofiz. Obs. 100, 53–57 (1960).

Other (12)

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran 6,” Rep. AFGL-TR-83-0187 (U. S. Air Force Geophysics Laboratory, Cambridge, Mass., 1983).

D. St. Germain, “Polar nephelometer for measuring snowflake phase functions,” in Proceedings of SNOW Symposium VII, R. E. Bates, A. W. Hogan, E. A. Wright, eds. (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1987), p. 77.

V. J. Schaefer, J. A. Day, A Field Guide to the Atmosphere (Houghton Mifflin, Boston, Mass., 1981), p. 324.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957), Chap. 8, p. 108.

J. R. Hodkinson, “Light scattering and extinction by irregular particles larger than the wavelength,” in Electromagnetic Scattering, M. Kerker, ed. (Macmillan, New York, 1963), pp. 87–100.

M. C. Sola, R. J. Bergmann, “Multi-spectral propagation measurements through snow” in Topical Meeting on Optical Propagation Through Turbulence, Rain and Fog, 1977 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1977), paper ThB4.

M. J. Persky, W. O. Gallery, “Validation and analysis of SNOW-ONE-A transmission data,” in Proceedings of SNOW Symposium IV, G. W. Aitken, ed. (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1984), p. 9.

J. A. Curcio, P. Lebow, “Spectral transmittance measurements at SNOW-TWO,” Spec. Rep. 84-20, 3-16 (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1984).

S. T. Hanley, B. L. Bean, R. Soulon, J. Randhawa, R. A. Dise, “SMART transmission support at SNOW IV,” in Proceedings of SNOW Symposium VI, A. W. Hogan, R. Redfield, eds. (U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1987), p. 69.

J. D. Mill, E. P. Shettle, “A preliminary LOWTRAN snow model,” in Proceedings of SNOW Symposium II, G. W. Aitken, ed. (U. S. Army Cold Regions Research and Engineering Laboratory, Hanover, N. H., 1983), p. 239.

D. L. Hutt, L. R. Bissonnette, D. St. Germain, “Multi-wavelength transmittance through falling snow,” in Propagation Engineering, N. S. Kopeika, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1115, 254 (1989).

V. E. Zuev, Laser Beams in the Atmosphere (Consultants Bureau, New York, 1982), Chap. 3, p. 150.

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Figures (13)

Fig. 1
Fig. 1

Simultaneous measurements of visible and infrared extinction in falling snow plotted as a function of He–Ne laser beam extinction. The measurements were made with closely spaced transmissometers with a path length of 538 m.

Fig. 2
Fig. 2

Frequency of occurrence of mean snowflake size.

Fig. 3
Fig. 3

(a) Ratios of visible extinction measured with a wide-beam transmissometer (0.4–0.7 μm) and a narrow-beam He–Ne laser transmissometer (0.633 μm) as a function of snowflake size observed during the measurements; (b) frequency of occurrence of visible extinction ratios according to snow type.

Fig. 4
Fig. 4

(a) Ratios of 3- to 5-μm extinction to the He–Ne laser extinction as a function of snowflake size; (b) frequency of occurrence of ratios of 3- to 5-μm extinction to He–Ne laser extinction according to snow type.

Fig. 5
Fig. 5

(a) Ratios of 8- to 12-μm extinction to the He–Ne laser extinction as a function of snowflake size; (b) frequency of occurrence of ratios of 8- to 12-μm extinction to the He–Ne laser extinction according to snow type.

Fig. 6
Fig. 6

(a) Ratios of infrared extinction measured in the 3- to 5-μm and 8- to 12-μm bands with identical transmissometers as a function of snowflake size; (b) frequency of occurrence of infrared extinction ratios according to snow type.

Fig. 7
Fig. 7

Geometry used in Mill and Shettle8 model to calculate the contribution of single-scattered power to transmission measurements. The dimensions of the source and receiver are assumed to be negligible compared with the path length Z.

Fig. 8
Fig. 8

Forward-scatter coefficient D as a function of beam divergence and receiver FOV for spheres of different size parameters. For convenience, the divergence and FOV are kept equal in calculating D.

Fig. 9
Fig. 9

Apparent extinction of 0.4- to 0.7-μm, 3-to 5-μm, and 8-to 12-μm beams versus apparent extinction of the He–Ne laser. Measurements are shown as symbols and results of single-scattering calculations are shown as curves. Only low values of extinction are shown for which the agreement between the model and measurements is good.

Fig. 10
Fig. 10

Apparent extinction of 0.4- to 0.7-μm, 3- to 5-μm, and 8-to 12-μm beams versus apparent extinction of the He–Ne laser. For high values of extinction the agreement between the single-scattering model and measurements is poor.

Fig. 11
Fig. 11

Apparent extinction of 0.4- to 0.7-μm, 3- to 5-μm, and 8-to 12-μm beams versus apparent extinction of the He–Ne laser The multiple-scattering model is in good agreement with the measurements over the entire range of extinction shown.

Fig. 12
Fig. 12

Phase function of an equivalent sphere used in multiple-scattering calculations and a snow phase function measured by Ref. 26. The differences in the two curves are evident.

Fig. 13
Fig. 13

Apparent extinction calculated with the multiple-scattering model versus the single-scattering extinction for the four DREV transmissometers.

Tables (5)

Tables Icon

Table 1 Measured Extinction Ratios for Different Wavelengths and Transmissometer Geometriesa

Tables Icon

Table 2 Extinction Ratios Measured with DREV Transmissometers for Different Snow Types

Tables Icon

Table 3 Extinction Ratios for DREV Transmissometers from the Single-Scattering Model

Tables Icon

Table 4 Extinction Ratios for DREV Transmissometers from the Multiple-Scattering Model

Tables Icon

Table 5 Optical Characteristics of Icea

Equations (22)

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α = 0 d N ( r ) d r σ E ( r ) d r ,
T = ( P u + P s ) / P 0 .
α a = - [ ln ( T ) / Z ] ,
4 π P ( θ ) d ω = 1.
σ S P ( θ ) = σ D P D ( θ ) + σ G P G ( θ ) .
P ( θ ) = σ D σ S P D ( θ ) + ( 1 - σ D σ S ) P G ( θ ) .
σ D = σ E 2 ,
P ( θ ) = 1 2 σ E σ S P D ( θ ) + ( 1 - 1 2 σ E σ S ) P G ( θ ) .
ω 0 = σ S / σ E .
P ( θ ) = 1 2 ω 0 P D ( θ ) + ( 1 - 1 2 ω 0 ) P G ( θ ) .
α a = α k ( δ , ϕ , Z , λ , l , ω 0 ) .
T = exp ( - α Z ) [ 1 + ω 0 α Z D ( δ , ϕ , λ , l ) ] ,
D ( δ , ϕ , λ , l ) = 2 π 0 ϕ 0 δ P ( ϕ + δ , λ , l ) d ϕ d δ .
α a = α - ( 1 / Z ) ln ( 1 + ω 0 α Z D ) .
α a α ( 1 - ω 0 D ) .
P ( θ ) 1 2 ω 0 P D ( θ ) .
I ( θ ) = I 0 x 2 4 π [ 2 J 1 ( x sin θ ) x sin θ ] 2 ,
P D ( θ ) = x 2 2 π [ J 1 ( x sin θ ) x sin θ ] 2 .
D ( δ , x ) = 2 π 0 δ P ( δ , x ) sin δ d δ .
α a = α - 1 Z ln ( P s + P u P u ) .
ω 0 = σ E - σ A σ E .
σ A = 4 π r 3 3 κ i n [ n 3 - ( n 2 - 1 ) 3 / 2 ] ,

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