Abstract

A near-infrared airborne-laser transmission model for thin cirrus clouds has been developed on the basis of the successive-order-of-scattering approach to account for multiple scattering by randomly and horizontally oriented ice crystals associated with an aircraft–target system. Direct transmission and transmission due to multiple scattering are formulated specifically for this geometric system, in which scattering and absorption associated with aerosols, water vapor, and air are accounted for. A number of sensitivity experiments have been performed for investigation of the effect of aircraft–target position, cirrus cloud optical depth, and ice crystal size on laser transmission for tactical applications. We show that transmission contributions produced by orders of scattering higher than 1 are small and can be neglected. The possibility of horizontal orientation of ice crystals can enhance transmission of laser beams in the aircraft–target geometry. Transmitted energy is strongly dependent on the horizontal distance between the aircraft and the target and on the cloud optical depth as well as on whether the cloud is above or below the aircraft.

© 2000 Optical Society of America

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  1. K. N. Liou, Y. Takano, S. C. Ou, A. Heymsfield, W. Kreiss, “Infrared transmission through cirrus clouds: a radiative model for target detection,” Appl. Opt. 29, 1886–1896 (1990).
    [CrossRef] [PubMed]
  2. K. N. Liou, S. C. Ou, G. Koenig, “An investigation on the climatic effect of contrail cirrus,” in Air Traffic and the Environment—Background, Tendencies and Potential Global Atmospheric Effects, U. Schumann, ed. (Springer-Verlag, Berlin, 1990), pp. 154–169.
    [CrossRef]
  3. D. Frankel, K. N. Liou, S. C. Ou, D. P. Wylie, W. P. Menzel, “Observation of cirrus cloud extent and their impacts to climate,” in Proceedings of the Ninth Conference on Atmospheric Radiation (American Meteorological Society, Boston, Mass., 1997), pp. 414–417.
  4. D. P. Wylie, W. P. Menzel, H. M. Woolf, K. I. Strabala, “Four years of global cirrus cloud statistics using HIRS,” J. Climate 7, 1972–1986 (1994).
    [CrossRef]
  5. Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
    [CrossRef]
  6. P. Yang, K. N. Liou, “Geometric-optics integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
    [CrossRef] [PubMed]
  7. P. Yang, K. N. Liou, “Finite-difference time-domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A 13, 2072–2085 (1996).
    [CrossRef]
  8. P. Yang, K. N. Liou, “An efficient algorithm for truncating spatial domain in modeling light scattering by finite-difference technique,” J. Comput. Phys. 140, 346–369 (1998).
    [CrossRef]
  9. K. N. Liou, Radiation and Cloud Processes in the Atmosphere: Theory, Observation, and Modeling (Oxford U. Press, Oxford, 1992).
  10. K. N. Liou, P. Yang, Y. Takano, K. Sassen, T. P. Charlock, W. P. Arnott, “On the radiative properties of contrail cirrus,” Geophys. Res. Lett. 25, 1161–1164 (1998).
    [CrossRef]
  11. K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: applications to climate research,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Geophysical Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 1999), Chap. 15.
  12. H. Gerber, Y. Takano, T. J. Garret, P. V. Hobbs, “Nephelometer measurements of the asymmetry parameter, volume extinction coefficient and backscatter ratio in arctic clouds,” J. Atmos. Sci. (to be published).
  13. Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. I. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
    [CrossRef]
  14. G. P. Anderson, R. H. Picard, J. H. Chetwynd, “Proceedings of the 17th Annual Review Conference on Atmospheric Transmission Models,” (Phillips Laboratory/Geophysics Directorate, Hanscom Air Force Base, Mass., 1995).
  15. G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols: Global Climatology and Radiative Characteristics (Deepak, Hampton, Va., 1991).
  16. Q. Fu, K. N. Liou, “On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres,” J. Atmos. Sci. 49, 2139–2156 (1992).
    [CrossRef]
  17. L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
    [CrossRef]
  18. Y. Takano, K. N. Liou, “Transfer of polarized infrared radiation in optically anisotropic media: application to horizontally oriented ice crystals,” J. Opt. Soc. Am. A 10, 1243–1256 (1993).
    [CrossRef]

1998 (2)

P. Yang, K. N. Liou, “An efficient algorithm for truncating spatial domain in modeling light scattering by finite-difference technique,” J. Comput. Phys. 140, 346–369 (1998).
[CrossRef]

K. N. Liou, P. Yang, Y. Takano, K. Sassen, T. P. Charlock, W. P. Arnott, “On the radiative properties of contrail cirrus,” Geophys. Res. Lett. 25, 1161–1164 (1998).
[CrossRef]

1996 (2)

1995 (1)

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

1994 (1)

D. P. Wylie, W. P. Menzel, H. M. Woolf, K. I. Strabala, “Four years of global cirrus cloud statistics using HIRS,” J. Climate 7, 1972–1986 (1994).
[CrossRef]

1993 (1)

1992 (2)

Q. Fu, K. N. Liou, “On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres,” J. Atmos. Sci. 49, 2139–2156 (1992).
[CrossRef]

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

1990 (1)

1989 (1)

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. I. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Anderson, G. P.

G. P. Anderson, R. H. Picard, J. H. Chetwynd, “Proceedings of the 17th Annual Review Conference on Atmospheric Transmission Models,” (Phillips Laboratory/Geophysics Directorate, Hanscom Air Force Base, Mass., 1995).

Arnott, W. P.

K. N. Liou, P. Yang, Y. Takano, K. Sassen, T. P. Charlock, W. P. Arnott, “On the radiative properties of contrail cirrus,” Geophys. Res. Lett. 25, 1161–1164 (1998).
[CrossRef]

Benner, D. C.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Brown, L. R.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Camy-Peyret, C.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Charlock, T. P.

K. N. Liou, P. Yang, Y. Takano, K. Sassen, T. P. Charlock, W. P. Arnott, “On the radiative properties of contrail cirrus,” Geophys. Res. Lett. 25, 1161–1164 (1998).
[CrossRef]

Chetwynd, J. H.

G. P. Anderson, R. H. Picard, J. H. Chetwynd, “Proceedings of the 17th Annual Review Conference on Atmospheric Transmission Models,” (Phillips Laboratory/Geophysics Directorate, Hanscom Air Force Base, Mass., 1995).

d’Almeida, G. A.

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols: Global Climatology and Radiative Characteristics (Deepak, Hampton, Va., 1991).

Devi, V. M.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Flaud, J.-M.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Frankel, D.

D. Frankel, K. N. Liou, S. C. Ou, D. P. Wylie, W. P. Menzel, “Observation of cirrus cloud extent and their impacts to climate,” in Proceedings of the Ninth Conference on Atmospheric Radiation (American Meteorological Society, Boston, Mass., 1997), pp. 414–417.

Fu, Q.

Q. Fu, K. N. Liou, “On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres,” J. Atmos. Sci. 49, 2139–2156 (1992).
[CrossRef]

Gamache, R. R.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Garret, T. J.

H. Gerber, Y. Takano, T. J. Garret, P. V. Hobbs, “Nephelometer measurements of the asymmetry parameter, volume extinction coefficient and backscatter ratio in arctic clouds,” J. Atmos. Sci. (to be published).

Gerber, H.

H. Gerber, Y. Takano, T. J. Garret, P. V. Hobbs, “Nephelometer measurements of the asymmetry parameter, volume extinction coefficient and backscatter ratio in arctic clouds,” J. Atmos. Sci. (to be published).

Goldman, A.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Heymsfield, A.

Hobbs, P. V.

H. Gerber, Y. Takano, T. J. Garret, P. V. Hobbs, “Nephelometer measurements of the asymmetry parameter, volume extinction coefficient and backscatter ratio in arctic clouds,” J. Atmos. Sci. (to be published).

Koenig, G.

K. N. Liou, S. C. Ou, G. Koenig, “An investigation on the climatic effect of contrail cirrus,” in Air Traffic and the Environment—Background, Tendencies and Potential Global Atmospheric Effects, U. Schumann, ed. (Springer-Verlag, Berlin, 1990), pp. 154–169.
[CrossRef]

Koepke, P.

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols: Global Climatology and Radiative Characteristics (Deepak, Hampton, Va., 1991).

Kreiss, W.

Liou, K. N.

P. Yang, K. N. Liou, “An efficient algorithm for truncating spatial domain in modeling light scattering by finite-difference technique,” J. Comput. Phys. 140, 346–369 (1998).
[CrossRef]

K. N. Liou, P. Yang, Y. Takano, K. Sassen, T. P. Charlock, W. P. Arnott, “On the radiative properties of contrail cirrus,” Geophys. Res. Lett. 25, 1161–1164 (1998).
[CrossRef]

P. Yang, K. N. Liou, “Geometric-optics integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[CrossRef] [PubMed]

P. Yang, K. N. Liou, “Finite-difference time-domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A 13, 2072–2085 (1996).
[CrossRef]

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

Y. Takano, K. N. Liou, “Transfer of polarized infrared radiation in optically anisotropic media: application to horizontally oriented ice crystals,” J. Opt. Soc. Am. A 10, 1243–1256 (1993).
[CrossRef]

Q. Fu, K. N. Liou, “On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres,” J. Atmos. Sci. 49, 2139–2156 (1992).
[CrossRef]

K. N. Liou, Y. Takano, S. C. Ou, A. Heymsfield, W. Kreiss, “Infrared transmission through cirrus clouds: a radiative model for target detection,” Appl. Opt. 29, 1886–1896 (1990).
[CrossRef] [PubMed]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. I. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

K. N. Liou, S. C. Ou, G. Koenig, “An investigation on the climatic effect of contrail cirrus,” in Air Traffic and the Environment—Background, Tendencies and Potential Global Atmospheric Effects, U. Schumann, ed. (Springer-Verlag, Berlin, 1990), pp. 154–169.
[CrossRef]

D. Frankel, K. N. Liou, S. C. Ou, D. P. Wylie, W. P. Menzel, “Observation of cirrus cloud extent and their impacts to climate,” in Proceedings of the Ninth Conference on Atmospheric Radiation (American Meteorological Society, Boston, Mass., 1997), pp. 414–417.

K. N. Liou, Radiation and Cloud Processes in the Atmosphere: Theory, Observation, and Modeling (Oxford U. Press, Oxford, 1992).

K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: applications to climate research,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Geophysical Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 1999), Chap. 15.

Massie, S. T.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Menzel, W. P.

D. P. Wylie, W. P. Menzel, H. M. Woolf, K. I. Strabala, “Four years of global cirrus cloud statistics using HIRS,” J. Climate 7, 1972–1986 (1994).
[CrossRef]

D. Frankel, K. N. Liou, S. C. Ou, D. P. Wylie, W. P. Menzel, “Observation of cirrus cloud extent and their impacts to climate,” in Proceedings of the Ninth Conference on Atmospheric Radiation (American Meteorological Society, Boston, Mass., 1997), pp. 414–417.

Ou, S. C.

K. N. Liou, Y. Takano, S. C. Ou, A. Heymsfield, W. Kreiss, “Infrared transmission through cirrus clouds: a radiative model for target detection,” Appl. Opt. 29, 1886–1896 (1990).
[CrossRef] [PubMed]

D. Frankel, K. N. Liou, S. C. Ou, D. P. Wylie, W. P. Menzel, “Observation of cirrus cloud extent and their impacts to climate,” in Proceedings of the Ninth Conference on Atmospheric Radiation (American Meteorological Society, Boston, Mass., 1997), pp. 414–417.

K. N. Liou, S. C. Ou, G. Koenig, “An investigation on the climatic effect of contrail cirrus,” in Air Traffic and the Environment—Background, Tendencies and Potential Global Atmospheric Effects, U. Schumann, ed. (Springer-Verlag, Berlin, 1990), pp. 154–169.
[CrossRef]

Perrin, A.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Picard, R. H.

G. P. Anderson, R. H. Picard, J. H. Chetwynd, “Proceedings of the 17th Annual Review Conference on Atmospheric Transmission Models,” (Phillips Laboratory/Geophysics Directorate, Hanscom Air Force Base, Mass., 1995).

Rinsland, C. P.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Rothman, L. S.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Sassen, K.

K. N. Liou, P. Yang, Y. Takano, K. Sassen, T. P. Charlock, W. P. Arnott, “On the radiative properties of contrail cirrus,” Geophys. Res. Lett. 25, 1161–1164 (1998).
[CrossRef]

Shettle, E. P.

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols: Global Climatology and Radiative Characteristics (Deepak, Hampton, Va., 1991).

Smith, M. A. H.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Strabala, K. I.

D. P. Wylie, W. P. Menzel, H. M. Woolf, K. I. Strabala, “Four years of global cirrus cloud statistics using HIRS,” J. Climate 7, 1972–1986 (1994).
[CrossRef]

Takano, Y.

K. N. Liou, P. Yang, Y. Takano, K. Sassen, T. P. Charlock, W. P. Arnott, “On the radiative properties of contrail cirrus,” Geophys. Res. Lett. 25, 1161–1164 (1998).
[CrossRef]

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

Y. Takano, K. N. Liou, “Transfer of polarized infrared radiation in optically anisotropic media: application to horizontally oriented ice crystals,” J. Opt. Soc. Am. A 10, 1243–1256 (1993).
[CrossRef]

K. N. Liou, Y. Takano, S. C. Ou, A. Heymsfield, W. Kreiss, “Infrared transmission through cirrus clouds: a radiative model for target detection,” Appl. Opt. 29, 1886–1896 (1990).
[CrossRef] [PubMed]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. I. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: applications to climate research,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Geophysical Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 1999), Chap. 15.

H. Gerber, Y. Takano, T. J. Garret, P. V. Hobbs, “Nephelometer measurements of the asymmetry parameter, volume extinction coefficient and backscatter ratio in arctic clouds,” J. Atmos. Sci. (to be published).

Tipping, R. H.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Toth, R. A.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Woolf, H. M.

D. P. Wylie, W. P. Menzel, H. M. Woolf, K. I. Strabala, “Four years of global cirrus cloud statistics using HIRS,” J. Climate 7, 1972–1986 (1994).
[CrossRef]

Wylie, D. P.

D. P. Wylie, W. P. Menzel, H. M. Woolf, K. I. Strabala, “Four years of global cirrus cloud statistics using HIRS,” J. Climate 7, 1972–1986 (1994).
[CrossRef]

D. Frankel, K. N. Liou, S. C. Ou, D. P. Wylie, W. P. Menzel, “Observation of cirrus cloud extent and their impacts to climate,” in Proceedings of the Ninth Conference on Atmospheric Radiation (American Meteorological Society, Boston, Mass., 1997), pp. 414–417.

Yang, P.

P. Yang, K. N. Liou, “An efficient algorithm for truncating spatial domain in modeling light scattering by finite-difference technique,” J. Comput. Phys. 140, 346–369 (1998).
[CrossRef]

K. N. Liou, P. Yang, Y. Takano, K. Sassen, T. P. Charlock, W. P. Arnott, “On the radiative properties of contrail cirrus,” Geophys. Res. Lett. 25, 1161–1164 (1998).
[CrossRef]

P. Yang, K. N. Liou, “Geometric-optics integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[CrossRef] [PubMed]

P. Yang, K. N. Liou, “Finite-difference time-domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A 13, 2072–2085 (1996).
[CrossRef]

K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: applications to climate research,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Geophysical Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 1999), Chap. 15.

Appl. Opt. (2)

Geophys. Res. Lett. (1)

K. N. Liou, P. Yang, Y. Takano, K. Sassen, T. P. Charlock, W. P. Arnott, “On the radiative properties of contrail cirrus,” Geophys. Res. Lett. 25, 1161–1164 (1998).
[CrossRef]

J. Atmos. Sci. (3)

Q. Fu, K. N. Liou, “On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres,” J. Atmos. Sci. 49, 2139–2156 (1992).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. I. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

J. Climate (1)

D. P. Wylie, W. P. Menzel, H. M. Woolf, K. I. Strabala, “Four years of global cirrus cloud statistics using HIRS,” J. Climate 7, 1972–1986 (1994).
[CrossRef]

J. Comput. Phys. (1)

P. Yang, K. N. Liou, “An efficient algorithm for truncating spatial domain in modeling light scattering by finite-difference technique,” J. Comput. Phys. 140, 346–369 (1998).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. M. Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Other (7)

K. N. Liou, S. C. Ou, G. Koenig, “An investigation on the climatic effect of contrail cirrus,” in Air Traffic and the Environment—Background, Tendencies and Potential Global Atmospheric Effects, U. Schumann, ed. (Springer-Verlag, Berlin, 1990), pp. 154–169.
[CrossRef]

D. Frankel, K. N. Liou, S. C. Ou, D. P. Wylie, W. P. Menzel, “Observation of cirrus cloud extent and their impacts to climate,” in Proceedings of the Ninth Conference on Atmospheric Radiation (American Meteorological Society, Boston, Mass., 1997), pp. 414–417.

K. N. Liou, Radiation and Cloud Processes in the Atmosphere: Theory, Observation, and Modeling (Oxford U. Press, Oxford, 1992).

K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: applications to climate research,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Geophysical Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 1999), Chap. 15.

H. Gerber, Y. Takano, T. J. Garret, P. V. Hobbs, “Nephelometer measurements of the asymmetry parameter, volume extinction coefficient and backscatter ratio in arctic clouds,” J. Atmos. Sci. (to be published).

G. P. Anderson, R. H. Picard, J. H. Chetwynd, “Proceedings of the 17th Annual Review Conference on Atmospheric Transmission Models,” (Phillips Laboratory/Geophysics Directorate, Hanscom Air Force Base, Mass., 1995).

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols: Global Climatology and Radiative Characteristics (Deepak, Hampton, Va., 1991).

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Figures (9)

Fig. 1
Fig. 1

(a) First-order scattering contribution and definitions of scan angle θ and path length s in an aircraft–target system. s′ = BE, s - s′ = ET, u = BM, and v = AT. (b) Second-order scattering contribution in an aircraft–target system. s - s′ = ET, s′ = EB, s″ = DB, u = BM, v = AT, s 1 = EF, s 2 = FB′, and s 3 = BM.

Fig. 2
Fig. 2

Phase functions for six laser wavelengths corresponding to four typical cirrus clouds. Ice crystal mean effective sizes D e for cirrus cloud models are shown in parentheses.

Fig. 3
Fig. 3

Extinction coefficients, single-scattering albedos, and asymmetry factors that correspond to the phase functions depicted in Fig. 2. Also included are a measured asymmetry factor at 0.63 µm taken from Ref. 12 for aggregates that occur in arctic ice clouds and a corresponding theoretical interpretation.

Fig. 4
Fig. 4

Direct transmission and transmission owing to first- and second-order scattering through cirrus clouds in the US1976 standard atmosphere as a function of target height z m . The parameters used in the calculation are λ = 1.315 µm, D e = 42 µm, F 0 = 106 W, r t = 3 m, and d = 100 km. The cirrus cloud is located between z t = 9.5 and z b = 9 km, and the position of the aircraft, z a , is 11 km.

Fig. 5
Fig. 5

Same as Fig. 4 but with the position of the aircraft set at z a = 8 km; second-order scattering results are not shown.

Fig. 6
Fig. 6

Same as Fig. 5 but with the position of the aircraft set at z a = 9.25 km. This is an in-cloud configuration.

Fig. 7
Fig. 7

Direct transmission and transmission owing to first-order scattering through cirrus clouds for several ice crystal mean effective sizes as a function of target height z m . The parameters used are the same as in Fig. 4. Aerosols and water vapor are included in the calculation.

Fig. 8
Fig. 8

Normalized extinction coefficient, single-scattering albedo, and delta-function transmission for Parry columns and two-dimensional (2-D) plates as a function of the laser scan angle θ at a wavelength of 1.315 µm.

Fig. 9
Fig. 9

Direct transmission and transmission owing to first-order scattering through cirrus clouds for horizontally and randomly oriented ice crystals in the US1976 standard atmosphere. The parameters used are the same as in Fig. 4. 2-D and 3-D, two- and three-dimensional, respectively.

Equations (19)

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Fd=F0 exp-βes=F0 exp-βair+βaer+kvρ+βclds,
s=zt-zb/μ,
Fn0, Ω=0s Jns, Ωexp-βesβeds, n=1, 2,,
Jns, Ω=ω˜4πΔΩ Fn-1s, ΩPΩ, ΩdΩ,
F0s, Ω=F0 exp-βes-s.
J1s, Ω=ω˜2 F0s, Ω0Ψ1 PΘsinΘdΘ,
Ψ1=tan-1rtu+s,
F10, Ω=exp-βnc,aν+βnc,bu0s J1s, Ω×exp-βesβeds.
J1s, Ω=ω˜2 F0s, Ω0Θ1t PΘ1sinΘ1dΘ1,
Θ1t=mintan-1zt-zbcos θs-s, tan-1zt-zb1/cos θ-cos θs-s,
F1s, Ω=0s J1s, Ωexp-βes1βeds,
J2s, Ω=ω˜2Θ2-Ψ2Θ2+Ψ2 F1s, ΩPΘsin ΘdΘ,
Θ2=π2+Θ1-tan-1s+us-stan Θ1,
Ψ2=tan-1rts2+s3,
s2+s3=s+ucosΘ2-Θ1,
s3=u sin θsinθ+Θ2-Θ1.
F20, Ω=exp-βnc,aν+βnc,bs30s J2s, Ω×exp-βes2βeds.
De= VnDdD AnDdD,
βair=τairΔz=0.008569λ-41+0.0113λ-2+0.00013λ-4×ΔpΔzp0,

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