Abstract

The derivation of backscatter ratio profiles from polarization lidar measurements is discussed. The method is based on differences in depolarization between molecular backscattering and backscattering from spherical aerosol particles. Simulations show that the polarization algorithms yield backscatter ratios with uncertainties comparable with those obtained by Klett’s method, provided that the backscattering process is dominated by molecular scattering. The technique could be utilized for monitoring the stratospheric sulfuric acid aerosol layer during periods of background conditions. The polarization analysis method is discussed in light of simulation results and is applied to polarization lidar profiles observed during the ALBATROSS 1996 field measurement campaign.

© 2000 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. S. R. Pal, A. I. Carswell, “Polarization properties of lidar backscattering from clouds,” Appl. Opt. 12, 1530–1535 (1973).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  9. K. Sassen, M. K. Griffin, G. C. Dodd, “Optical scattering and microphysical properties of subvisual cirrus clouds and climatic implications,” J. Appl. Meteorol. 28, 91–98 (1989).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  23. P. B. Russell, T. J. Swissler, M. P. McCormick, “Methodology for error analysis and simulation of lidar aerosol measurements,” Appl. Opt. 18, 3783–3797 (1979).
    [PubMed]
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    [CrossRef]
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    [CrossRef]
  27. G. Beyerle, H.-J. Schäfer, R. Neuber, O. Schrems, I. S. McDermid, “Dual wavelength lidar observation of tropical high-altitude cirrus clouds during the ALBATROSS 1996 campaign,” Geophys. Res. Lett. 25, 919–922 (1998).
    [CrossRef]
  28. H.-J. Schäfer, O. Schrems, G. Beyerle, B. Hofer, W. Mildner, F. A. Theopold, W. Lahmann, C. Weitkamp, M. Steinbach, “Modular and mobile multipurpose lidar system for observation of tropospheric and stratospheric aerosols,” in Lidar Techniques for Remote Sensing II, C. Werner, ed., Proc. SPIE2581, 128–136 (1995).
    [CrossRef]

1998 (2)

M. Mishchenko, K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25, 309–312 (1998).
[CrossRef]

G. Beyerle, H.-J. Schäfer, R. Neuber, O. Schrems, I. S. McDermid, “Dual wavelength lidar observation of tropical high-altitude cirrus clouds during the ALBATROSS 1996 campaign,” Geophys. Res. Lett. 25, 919–922 (1998).
[CrossRef]

1997 (1)

P. Hamill, E. J. Jensen, P. B. Russell, J. J. Bauman, “The life-cycle of stratospheric aerosol particles,” Bull. Am. Meteorol. Soc. 78, 1395–1410 (1997).
[CrossRef]

1995 (1)

1994 (1)

G. Beyerle, R. Neuber, O. Schrems, F. Wittrock, B. Knudsen, “Multiwavelength lidar measurements of stratospheric aerosols above Spitsbergen during winter 1992/93,” Geophys. Res. Lett. 21, 57–60 (1994).
[CrossRef]

1992 (1)

1991 (1)

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull Am. Meteorol. Soc. 72, 1848–1866 (1991).
[CrossRef]

1990 (2)

E. L. Fleming, S. Chandra, J. J. Barnett, M. Corney, “International Reference Atmosphere, Chapter 2: zonal mean temperature, pressure, zonal wind and geopotential height as functions of latitude,” Adv. Space Res. 10, 11–59 (1990).
[CrossRef]

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, A. F. Tuck, “Airborne lidar observations in the wintertime Arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

1989 (1)

K. Sassen, M. K. Griffin, G. C. Dodd, “Optical scattering and microphysical properties of subvisual cirrus clouds and climatic implications,” J. Appl. Meteorol. 28, 91–98 (1989).
[CrossRef]

1987 (1)

C. M. R. Platt, J. C. Scott, A. C. Dilley, “Remote sensing of high clouds. Part IV: Optical properties of midlatitude and tropical cirrus,” J. Atmos. Sci. 44, 729–747 (1987).
[CrossRef]

1981 (2)

1980 (1)

1979 (1)

1978 (1)

1977 (1)

C. M. R. Platt, “Lidar observations of a mixed-phase altostratus cloud,” J. Appl. Meteorol. 16, 339–345 (1977).
[CrossRef]

1975 (1)

K. Sassen, “Laser depolarization “bright band” from melting snowflakes,” Nature (London) 255, 316–318 (1975).
[CrossRef]

1974 (1)

K. Sassen, “Depolarization of laser light backscattered by artificial clouds,” J. Appl. Meteorol. 13, 923–933 (1974).
[CrossRef]

1973 (1)

1972 (1)

H. Inaba, T. Kobayasi, “Laser-Raman radar,” Opto-electronics 4, 101–123 (1972).
[CrossRef]

1971 (1)

R. M. Schotland, K. Sassen, R. J. Stone, “Observations by lidar of linear depolarization ratios by hydrometeors,” J. Appl. Meteorol. 10, 1011–1017 (1971).
[CrossRef]

Ansmann, A.

Barnett, J. J.

E. L. Fleming, S. Chandra, J. J. Barnett, M. Corney, “International Reference Atmosphere, Chapter 2: zonal mean temperature, pressure, zonal wind and geopotential height as functions of latitude,” Adv. Space Res. 10, 11–59 (1990).
[CrossRef]

Bauman, J. J.

P. Hamill, E. J. Jensen, P. B. Russell, J. J. Bauman, “The life-cycle of stratospheric aerosol particles,” Bull. Am. Meteorol. Soc. 78, 1395–1410 (1997).
[CrossRef]

Beyerle, G.

G. Beyerle, H.-J. Schäfer, R. Neuber, O. Schrems, I. S. McDermid, “Dual wavelength lidar observation of tropical high-altitude cirrus clouds during the ALBATROSS 1996 campaign,” Geophys. Res. Lett. 25, 919–922 (1998).
[CrossRef]

G. Beyerle, R. Neuber, O. Schrems, F. Wittrock, B. Knudsen, “Multiwavelength lidar measurements of stratospheric aerosols above Spitsbergen during winter 1992/93,” Geophys. Res. Lett. 21, 57–60 (1994).
[CrossRef]

H.-J. Schäfer, O. Schrems, G. Beyerle, B. Hofer, W. Mildner, F. A. Theopold, W. Lahmann, C. Weitkamp, M. Steinbach, “Modular and mobile multipurpose lidar system for observation of tropospheric and stratospheric aerosols,” in Lidar Techniques for Remote Sensing II, C. Werner, ed., Proc. SPIE2581, 128–136 (1995).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Browell, E. V.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, A. F. Tuck, “Airborne lidar observations in the wintertime Arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Butler, C. F.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, A. F. Tuck, “Airborne lidar observations in the wintertime Arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Carswell, A. I.

Carter, A. F.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, A. F. Tuck, “Airborne lidar observations in the wintertime Arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Chandra, S.

E. L. Fleming, S. Chandra, J. J. Barnett, M. Corney, “International Reference Atmosphere, Chapter 2: zonal mean temperature, pressure, zonal wind and geopotential height as functions of latitude,” Adv. Space Res. 10, 11–59 (1990).
[CrossRef]

Clarke, D.

D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, London, 1971).

Corney, M.

E. L. Fleming, S. Chandra, J. J. Barnett, M. Corney, “International Reference Atmosphere, Chapter 2: zonal mean temperature, pressure, zonal wind and geopotential height as functions of latitude,” Adv. Space Res. 10, 11–59 (1990).
[CrossRef]

Dilley, A. C.

C. M. R. Platt, J. C. Scott, A. C. Dilley, “Remote sensing of high clouds. Part IV: Optical properties of midlatitude and tropical cirrus,” J. Atmos. Sci. 44, 729–747 (1987).
[CrossRef]

Dodd, G. C.

K. Sassen, M. K. Griffin, G. C. Dodd, “Optical scattering and microphysical properties of subvisual cirrus clouds and climatic implications,” J. Appl. Meteorol. 28, 91–98 (1989).
[CrossRef]

Fleming, E. L.

E. L. Fleming, S. Chandra, J. J. Barnett, M. Corney, “International Reference Atmosphere, Chapter 2: zonal mean temperature, pressure, zonal wind and geopotential height as functions of latitude,” Adv. Space Res. 10, 11–59 (1990).
[CrossRef]

Grainger, J. F.

D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, London, 1971).

Griffin, M. K.

K. Sassen, M. K. Griffin, G. C. Dodd, “Optical scattering and microphysical properties of subvisual cirrus clouds and climatic implications,” J. Appl. Meteorol. 28, 91–98 (1989).
[CrossRef]

Hamill, P.

P. Hamill, E. J. Jensen, P. B. Russell, J. J. Bauman, “The life-cycle of stratospheric aerosol particles,” Bull. Am. Meteorol. Soc. 78, 1395–1410 (1997).
[CrossRef]

Higdon, N. S.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, A. F. Tuck, “Airborne lidar observations in the wintertime Arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Hofer, B.

H.-J. Schäfer, O. Schrems, G. Beyerle, B. Hofer, W. Mildner, F. A. Theopold, W. Lahmann, C. Weitkamp, M. Steinbach, “Modular and mobile multipurpose lidar system for observation of tropospheric and stratospheric aerosols,” in Lidar Techniques for Remote Sensing II, C. Werner, ed., Proc. SPIE2581, 128–136 (1995).
[CrossRef]

Houston, J. D.

Hovenier, J. W.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Inaba, H.

H. Inaba, T. Kobayasi, “Laser-Raman radar,” Opto-electronics 4, 101–123 (1972).
[CrossRef]

Ismail, S.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, A. F. Tuck, “Airborne lidar observations in the wintertime Arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Jensen, E. J.

P. Hamill, E. J. Jensen, P. B. Russell, J. J. Bauman, “The life-cycle of stratospheric aerosol particles,” Bull. Am. Meteorol. Soc. 78, 1395–1410 (1997).
[CrossRef]

Klett, J. D.

Knudsen, B.

G. Beyerle, R. Neuber, O. Schrems, F. Wittrock, B. Knudsen, “Multiwavelength lidar measurements of stratospheric aerosols above Spitsbergen during winter 1992/93,” Geophys. Res. Lett. 21, 57–60 (1994).
[CrossRef]

Kobayasi, T.

H. Inaba, T. Kobayasi, “Laser-Raman radar,” Opto-electronics 4, 101–123 (1972).
[CrossRef]

Lahmann, W.

H.-J. Schäfer, O. Schrems, G. Beyerle, B. Hofer, W. Mildner, F. A. Theopold, W. Lahmann, C. Weitkamp, M. Steinbach, “Modular and mobile multipurpose lidar system for observation of tropospheric and stratospheric aerosols,” in Lidar Techniques for Remote Sensing II, C. Werner, ed., Proc. SPIE2581, 128–136 (1995).
[CrossRef]

McCormick, M. P.

McDermid, I. S.

G. Beyerle, H.-J. Schäfer, R. Neuber, O. Schrems, I. S. McDermid, “Dual wavelength lidar observation of tropical high-altitude cirrus clouds during the ALBATROSS 1996 campaign,” Geophys. Res. Lett. 25, 919–922 (1998).
[CrossRef]

Measures, R.

R. Measures, Laser Remote Sensing, Fundamentals and Applications (Wiley, New York, 1984).

Michaelis, W.

Mildner, W.

H.-J. Schäfer, O. Schrems, G. Beyerle, B. Hofer, W. Mildner, F. A. Theopold, W. Lahmann, C. Weitkamp, M. Steinbach, “Modular and mobile multipurpose lidar system for observation of tropospheric and stratospheric aerosols,” in Lidar Techniques for Remote Sensing II, C. Werner, ed., Proc. SPIE2581, 128–136 (1995).
[CrossRef]

Mishchenko, M.

M. Mishchenko, K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25, 309–312 (1998).
[CrossRef]

Mishchenko, M. I.

Neuber, R.

G. Beyerle, H.-J. Schäfer, R. Neuber, O. Schrems, I. S. McDermid, “Dual wavelength lidar observation of tropical high-altitude cirrus clouds during the ALBATROSS 1996 campaign,” Geophys. Res. Lett. 25, 919–922 (1998).
[CrossRef]

G. Beyerle, R. Neuber, O. Schrems, F. Wittrock, B. Knudsen, “Multiwavelength lidar measurements of stratospheric aerosols above Spitsbergen during winter 1992/93,” Geophys. Res. Lett. 21, 57–60 (1994).
[CrossRef]

Pal, S. R.

Platt, C. M. R.

C. M. R. Platt, J. C. Scott, A. C. Dilley, “Remote sensing of high clouds. Part IV: Optical properties of midlatitude and tropical cirrus,” J. Atmos. Sci. 44, 729–747 (1987).
[CrossRef]

C. M. R. Platt, “Lidar observations of a mixed-phase altostratus cloud,” J. Appl. Meteorol. 16, 339–345 (1977).
[CrossRef]

Riebesell, M.

Robinette, P. A.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, A. F. Tuck, “Airborne lidar observations in the wintertime Arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Russell, P. B.

P. Hamill, E. J. Jensen, P. B. Russell, J. J. Bauman, “The life-cycle of stratospheric aerosol particles,” Bull. Am. Meteorol. Soc. 78, 1395–1410 (1997).
[CrossRef]

P. B. Russell, T. J. Swissler, M. P. McCormick, “Methodology for error analysis and simulation of lidar aerosol measurements,” Appl. Opt. 18, 3783–3797 (1979).
[PubMed]

Sassen, K.

M. Mishchenko, K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25, 309–312 (1998).
[CrossRef]

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull Am. Meteorol. Soc. 72, 1848–1866 (1991).
[CrossRef]

K. Sassen, M. K. Griffin, G. C. Dodd, “Optical scattering and microphysical properties of subvisual cirrus clouds and climatic implications,” J. Appl. Meteorol. 28, 91–98 (1989).
[CrossRef]

K. Sassen, “Laser depolarization “bright band” from melting snowflakes,” Nature (London) 255, 316–318 (1975).
[CrossRef]

K. Sassen, “Depolarization of laser light backscattered by artificial clouds,” J. Appl. Meteorol. 13, 923–933 (1974).
[CrossRef]

R. M. Schotland, K. Sassen, R. J. Stone, “Observations by lidar of linear depolarization ratios by hydrometeors,” J. Appl. Meteorol. 10, 1011–1017 (1971).
[CrossRef]

Schäfer, H.-J.

G. Beyerle, H.-J. Schäfer, R. Neuber, O. Schrems, I. S. McDermid, “Dual wavelength lidar observation of tropical high-altitude cirrus clouds during the ALBATROSS 1996 campaign,” Geophys. Res. Lett. 25, 919–922 (1998).
[CrossRef]

H.-J. Schäfer, O. Schrems, G. Beyerle, B. Hofer, W. Mildner, F. A. Theopold, W. Lahmann, C. Weitkamp, M. Steinbach, “Modular and mobile multipurpose lidar system for observation of tropospheric and stratospheric aerosols,” in Lidar Techniques for Remote Sensing II, C. Werner, ed., Proc. SPIE2581, 128–136 (1995).
[CrossRef]

Schoeberl, M. R.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, A. F. Tuck, “Airborne lidar observations in the wintertime Arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Schotland, R. M.

R. M. Schotland, K. Sassen, R. J. Stone, “Observations by lidar of linear depolarization ratios by hydrometeors,” J. Appl. Meteorol. 10, 1011–1017 (1971).
[CrossRef]

Schrems, O.

G. Beyerle, H.-J. Schäfer, R. Neuber, O. Schrems, I. S. McDermid, “Dual wavelength lidar observation of tropical high-altitude cirrus clouds during the ALBATROSS 1996 campaign,” Geophys. Res. Lett. 25, 919–922 (1998).
[CrossRef]

G. Beyerle, R. Neuber, O. Schrems, F. Wittrock, B. Knudsen, “Multiwavelength lidar measurements of stratospheric aerosols above Spitsbergen during winter 1992/93,” Geophys. Res. Lett. 21, 57–60 (1994).
[CrossRef]

H.-J. Schäfer, O. Schrems, G. Beyerle, B. Hofer, W. Mildner, F. A. Theopold, W. Lahmann, C. Weitkamp, M. Steinbach, “Modular and mobile multipurpose lidar system for observation of tropospheric and stratospheric aerosols,” in Lidar Techniques for Remote Sensing II, C. Werner, ed., Proc. SPIE2581, 128–136 (1995).
[CrossRef]

Scott, J. C.

C. M. R. Platt, J. C. Scott, A. C. Dilley, “Remote sensing of high clouds. Part IV: Optical properties of midlatitude and tropical cirrus,” J. Atmos. Sci. 44, 729–747 (1987).
[CrossRef]

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light: Production and Use (Harvard U. Press, Cambridge, Mass., 1962).

Steinbach, M.

H.-J. Schäfer, O. Schrems, G. Beyerle, B. Hofer, W. Mildner, F. A. Theopold, W. Lahmann, C. Weitkamp, M. Steinbach, “Modular and mobile multipurpose lidar system for observation of tropospheric and stratospheric aerosols,” in Lidar Techniques for Remote Sensing II, C. Werner, ed., Proc. SPIE2581, 128–136 (1995).
[CrossRef]

Stone, R. J.

R. M. Schotland, K. Sassen, R. J. Stone, “Observations by lidar of linear depolarization ratios by hydrometeors,” J. Appl. Meteorol. 10, 1011–1017 (1971).
[CrossRef]

Swissler, T. J.

Theopold, F. A.

H.-J. Schäfer, O. Schrems, G. Beyerle, B. Hofer, W. Mildner, F. A. Theopold, W. Lahmann, C. Weitkamp, M. Steinbach, “Modular and mobile multipurpose lidar system for observation of tropospheric and stratospheric aerosols,” in Lidar Techniques for Remote Sensing II, C. Werner, ed., Proc. SPIE2581, 128–136 (1995).
[CrossRef]

Toon, O. B.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, A. F. Tuck, “Airborne lidar observations in the wintertime Arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

Tuck, A. F.

E. V. Browell, C. F. Butler, S. Ismail, P. A. Robinette, A. F. Carter, N. S. Higdon, O. B. Toon, M. R. Schoeberl, A. F. Tuck, “Airborne lidar observations in the wintertime Arctic stratosphere: polar stratospheric clouds,” Geophys. Res. Lett. 17, 385–388 (1990).
[CrossRef]

van de Hulst, H. C.

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

Wandinger, U.

Weitkamp, C.

A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, W. Michaelis, “Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar,” Appl. Opt. 31, 7113–7131 (1992).
[CrossRef] [PubMed]

H.-J. Schäfer, O. Schrems, G. Beyerle, B. Hofer, W. Mildner, F. A. Theopold, W. Lahmann, C. Weitkamp, M. Steinbach, “Modular and mobile multipurpose lidar system for observation of tropospheric and stratospheric aerosols,” in Lidar Techniques for Remote Sensing II, C. Werner, ed., Proc. SPIE2581, 128–136 (1995).
[CrossRef]

Wittrock, F.

G. Beyerle, R. Neuber, O. Schrems, F. Wittrock, B. Knudsen, “Multiwavelength lidar measurements of stratospheric aerosols above Spitsbergen during winter 1992/93,” Geophys. Res. Lett. 21, 57–60 (1994).
[CrossRef]

Young, A. T.

Adv. Space Res. (1)

E. L. Fleming, S. Chandra, J. J. Barnett, M. Corney, “International Reference Atmosphere, Chapter 2: zonal mean temperature, pressure, zonal wind and geopotential height as functions of latitude,” Adv. Space Res. 10, 11–59 (1990).
[CrossRef]

Appl. Opt. (7)

Bull Am. Meteorol. Soc. (1)

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull Am. Meteorol. Soc. 72, 1848–1866 (1991).
[CrossRef]

Bull. Am. Meteorol. Soc. (1)

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Figures (5)

Fig. 1
Fig. 1

Relation between uncertainties ℰ(R) and ℰ(δ T L ) (solid line) and between ℰ(R) and ℰ(δ T C ) (dashed line) as a function of linear and circular volume depolarization, δ T L and δ T C . f L and f C are defined as f L = δ M L /[(δ T L )2 M L + 1)] and f C = δ M C /[(δ T C )2 M C + 1)]. For enhanced atmospheric aerosol content δ T L and δ T C decrease and thereby strongly increase errors ℰ(R). The circles mark δ T L = δ M L and δ T C = δ M C .

Fig. 2
Fig. 2

Deviations of molecular density between observed monthly mean density profiles and the CIRA (International Reference Atmosphere) model. The observations were derived from aerological soundings at Ny-Ålesund, Spitsbergen, Norway. Comparisons are shown for (a) January 1992–1998 profiles and (b) July 1993–1998 profiles. Note the different horizontal scales.

Fig. 3
Fig. 3

Backscatter ratio profiles for stratospheric background aerosols and their respective uncertainties obtained by simulations. (a) Backscatter ratio profiles derived from the circular (solid curve) and linear (dashed curve) polarization algorithms, Klett’s method (dash–dot curve), and the Raman lidar technique (dotted curve). (b) The corresponding 1-σ uncertainties.

Fig. 4
Fig. 4

Sensitivity of backscatter ratio profiles obtained by the linear polarization method with respect to misalignment of (b) transmitter and receiver polarization planes and (c) impure transmitter polarization. ΔR is the difference between simulated and true backscatter ratios. Misalignment is assumed to be 5° and transmitted signal depolarization is 0.5%. (a) The ideal case for comparison. The results represented by dashed lines were obtained with Eq. (19).

Fig. 5
Fig. 5

Backscatter ratio profiles calculated by (a) the linear polarization method and (b) Klett’s algorithm at 355 nm. This measurement of the stratospheric aerosol layer was performed during the ALBATROSS campaign aboard the research vessel Polarstern in 1996 between 25 October at 20:00 UTC and 26 October at 6:27 UTC. The 1-σ standard deviations are marked by dotted curves.

Equations (20)

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P,z=c,β,zz-z02 T2z0, z,
K PzPz=δTLzβzβz=βMz+βAzβMz+βAz,
δMLz=βMzβMz,
RzβAzβMz+1=βAz+βAzβMz+βMz+1
Rz=δTLzδML+δMLδTLzδML+δTLz=1+1/δTLz1+1/δML.
Rz=βAzβMz+1=βAz+βAzβMz+βMz+1,
Rz=δTCzδMC+δMCδTCzδMC+δTCz=1+1/δTCz1+1/δMC,
Sb=FSt.
Sdn=DnSb=DnFSt,
F=3Csca8πr24+M500002+3M500002+3M50000M,
M=9-9+2.
IdId=1-M3+2M=δML, IdId=2-2M2+3M=δMC, δMC=2δML/1-δML.
R=δML,CδTL,C2δML,C+1 δTL,CδML,CδTL,C2 δTL,C,
R1δML,C δTL,C.
RRPP, RRPP.
Rzz-z02Pzz-z02PzβMzβMz T2z, z,
RRz2PzPz2+NzNz2+PzPz2+NzNz2.
Rz=PzPRzPRzPz,
RzRz2PRzPRz2+PzPz2+PRzPRz2+PzPz2.
δTL=δML1+1-2-2M/4+Me cos2α1-1-2-2M/4+Me cos2α×R-R-2-2M/4+Me cos2αR+R-2-2M/4+Me cos2α,

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