Abstract

A method is presented that permits the determination of atmospheric depolarization-ratio profiles from three elastic-backscatter lidar signals with different sensitivity to the state of polarization of the backscattered light. The three-signal method is far less sensitive to experimental errors and does not require calibration of the measurement, as is the case of the two-signal lidar technique conventionally used for the observation of depolarization ratios. The three-signal method is applied to a polar stratospheric cloud observation. In the analysis we show that, depending on the statistical error of the measurement and on the lidar system parameters, the new method requires minimum cloud volume depolarization ratios to be applicable; in the case study presented, this threshold is ∼0.2. Depolarization ratios determined with the three-signal method can be used to accurately calibrate measurements with the conventional two-signal technique.

© 2003 Optical Society of America

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References

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  1. K. Sassen, S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. II: microphysical properties derived from lidar depolarization,” J. Atmos. Sci. 58, 2103–2112 (2001).
    [CrossRef]
  2. M. Del Guasta, “Simulation of LIDAR returns from pristine and deformed hexagonal ice prisms in cold cirrus by means of ‘face tracing’,” J. Geophys. Res. 106, 12589–12602 (2001).
    [CrossRef]
  3. J. Reichardt, S. Reichardt, M. Hess, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: microphysical interpretation,” J. Geophys. Res. 107D, 10.1029/2002JD002589 (2002).
    [CrossRef]
  4. U. Wandinger, A. Ansmann, C. Weitkamp, “Atmospheric Raman depolarization-ratio measurements,” Appl. Opt. 33, 5671–5673 (1994).
    [CrossRef] [PubMed]
  5. G. Roy, L. Bissonnette, C. Bastille, G. Vallée, “Retrieval of droplet-size density distribution from multiple-field-of-view cross-polarized lidar signals: theory and experimental validation,” Appl. Opt. 38, 5202–5211 (1999).
    [CrossRef]
  6. R. M. Schotland, K. Sassen, R. Stone, “Observations by lidar of linear depolarization ratios for hydrometeors,” J. Appl. Meteorol. 10, 1011–1017 (1971).
    [CrossRef]
  7. H. Adachi, T. Shibata, Y. Iwasaka, M. Fujiwara, “Calibration method for the lidar-observed stratospheric depolarization ratio in the presence of liquid aerosol particles,” Appl. Opt. 40, 6587–6595 (2001).
    [CrossRef]
  8. C. Schulze, “Untersuchung der Polarisationseigenschaften der optischen Elemente eines Polarisations-Raman-Lidars,” Diploma thesis (Universität Hamburg, Hamburg, Germany, 1994).
  9. J. Reichardt, U. Wandinger, M. Serwazi, C. Weitkamp, “Combined Raman lidar for aerosol, ozone, and moisture measurements,” Opt. Eng. 35, 1457–1465 (1996).
    [CrossRef]
  10. 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]
  11. M. J. Walker, “Matrix calculus and the Stokes parameters of polarized radiation,” Am. J. Phys. 22, 170–174 (1954).
    [CrossRef]

2002 (1)

J. Reichardt, S. Reichardt, M. Hess, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: microphysical interpretation,” J. Geophys. Res. 107D, 10.1029/2002JD002589 (2002).
[CrossRef]

2001 (3)

K. Sassen, S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. II: microphysical properties derived from lidar depolarization,” J. Atmos. Sci. 58, 2103–2112 (2001).
[CrossRef]

M. Del Guasta, “Simulation of LIDAR returns from pristine and deformed hexagonal ice prisms in cold cirrus by means of ‘face tracing’,” J. Geophys. Res. 106, 12589–12602 (2001).
[CrossRef]

H. Adachi, T. Shibata, Y. Iwasaka, M. Fujiwara, “Calibration method for the lidar-observed stratospheric depolarization ratio in the presence of liquid aerosol particles,” Appl. Opt. 40, 6587–6595 (2001).
[CrossRef]

1999 (1)

1996 (1)

J. Reichardt, U. Wandinger, M. Serwazi, C. Weitkamp, “Combined Raman lidar for aerosol, ozone, and moisture measurements,” Opt. Eng. 35, 1457–1465 (1996).
[CrossRef]

1994 (1)

1990 (1)

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]

1971 (1)

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

1954 (1)

M. J. Walker, “Matrix calculus and the Stokes parameters of polarized radiation,” Am. J. Phys. 22, 170–174 (1954).
[CrossRef]

Adachi, H.

Ansmann, A.

Bastille, C.

Benson, S.

K. Sassen, S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. II: microphysical properties derived from lidar depolarization,” J. Atmos. Sci. 58, 2103–2112 (2001).
[CrossRef]

Bissonnette, L.

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]

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]

Del Guasta, M.

M. Del Guasta, “Simulation of LIDAR returns from pristine and deformed hexagonal ice prisms in cold cirrus by means of ‘face tracing’,” J. Geophys. Res. 106, 12589–12602 (2001).
[CrossRef]

Fujiwara, M.

Hess, M.

J. Reichardt, S. Reichardt, M. Hess, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: microphysical interpretation,” J. Geophys. Res. 107D, 10.1029/2002JD002589 (2002).
[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]

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]

Iwasaka, Y.

McGee, T. J.

J. Reichardt, S. Reichardt, M. Hess, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: microphysical interpretation,” J. Geophys. Res. 107D, 10.1029/2002JD002589 (2002).
[CrossRef]

Reichardt, J.

J. Reichardt, S. Reichardt, M. Hess, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: microphysical interpretation,” J. Geophys. Res. 107D, 10.1029/2002JD002589 (2002).
[CrossRef]

J. Reichardt, U. Wandinger, M. Serwazi, C. Weitkamp, “Combined Raman lidar for aerosol, ozone, and moisture measurements,” Opt. Eng. 35, 1457–1465 (1996).
[CrossRef]

Reichardt, S.

J. Reichardt, S. Reichardt, M. Hess, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: microphysical interpretation,” J. Geophys. Res. 107D, 10.1029/2002JD002589 (2002).
[CrossRef]

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]

Roy, G.

Sassen, K.

K. Sassen, S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. II: microphysical properties derived from lidar depolarization,” J. Atmos. Sci. 58, 2103–2112 (2001).
[CrossRef]

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

Schulze, C.

C. Schulze, “Untersuchung der Polarisationseigenschaften der optischen Elemente eines Polarisations-Raman-Lidars,” Diploma thesis (Universität Hamburg, Hamburg, Germany, 1994).

Serwazi, M.

J. Reichardt, U. Wandinger, M. Serwazi, C. Weitkamp, “Combined Raman lidar for aerosol, ozone, and moisture measurements,” Opt. Eng. 35, 1457–1465 (1996).
[CrossRef]

Shibata, T.

Stone, R.

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

Vallée, G.

Walker, M. J.

M. J. Walker, “Matrix calculus and the Stokes parameters of polarized radiation,” Am. J. Phys. 22, 170–174 (1954).
[CrossRef]

Wandinger, U.

J. Reichardt, U. Wandinger, M. Serwazi, C. Weitkamp, “Combined Raman lidar for aerosol, ozone, and moisture measurements,” Opt. Eng. 35, 1457–1465 (1996).
[CrossRef]

U. Wandinger, A. Ansmann, C. Weitkamp, “Atmospheric Raman depolarization-ratio measurements,” Appl. Opt. 33, 5671–5673 (1994).
[CrossRef] [PubMed]

Weitkamp, C.

J. Reichardt, U. Wandinger, M. Serwazi, C. Weitkamp, “Combined Raman lidar for aerosol, ozone, and moisture measurements,” Opt. Eng. 35, 1457–1465 (1996).
[CrossRef]

U. Wandinger, A. Ansmann, C. Weitkamp, “Atmospheric Raman depolarization-ratio measurements,” Appl. Opt. 33, 5671–5673 (1994).
[CrossRef] [PubMed]

Am. J. Phys. (1)

M. J. Walker, “Matrix calculus and the Stokes parameters of polarized radiation,” Am. J. Phys. 22, 170–174 (1954).
[CrossRef]

Appl. Opt. (3)

Geophys. Res. Lett. (1)

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]

J. Appl. Meteorol. (1)

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

J. Atmos. Sci. (1)

K. Sassen, S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. II: microphysical properties derived from lidar depolarization,” J. Atmos. Sci. 58, 2103–2112 (2001).
[CrossRef]

J. Geophys. Res. (2)

M. Del Guasta, “Simulation of LIDAR returns from pristine and deformed hexagonal ice prisms in cold cirrus by means of ‘face tracing’,” J. Geophys. Res. 106, 12589–12602 (2001).
[CrossRef]

J. Reichardt, S. Reichardt, M. Hess, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: microphysical interpretation,” J. Geophys. Res. 107D, 10.1029/2002JD002589 (2002).
[CrossRef]

Opt. Eng. (1)

J. Reichardt, U. Wandinger, M. Serwazi, C. Weitkamp, “Combined Raman lidar for aerosol, ozone, and moisture measurements,” Opt. Eng. 35, 1457–1465 (1996).
[CrossRef]

Other (1)

C. Schulze, “Untersuchung der Polarisationseigenschaften der optischen Elemente eines Polarisations-Raman-Lidars,” Diploma thesis (Universität Hamburg, Hamburg, Germany, 1994).

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Figures (3)

Fig. 1
Fig. 1

Depolarization-ratio measurement with the three-signal method (fixed reference height, z0 = 20.5 km) in a water-ice PSC observed over the Swedish research facility Esrange (67.9 °N, 21.1 °E) on 16 January 1997 between 16:55 and 17:55 UT. The mean value of δ(z0) is 0.0127 ± 0.0002. The lidar data were background subtracted; the vertical resolution is 120 m. Error bars indicate uncertainties that are due to signal noise. Normalized signal ratio V23 was multiplied by a factor of ten. The depolarization observation with the conventional two-signal technique is also shown (thin solid curve, right-hand plot). It was calibrated with a fit to the δ profile in the PSC layer. The resultant two-signal-technique depolarization ratio at reference height is 0.0139.

Fig. 2
Fig. 2

Error in depolarization ratio as a function of tilt angle between transmitter and receiver polarization-measurement reference systems for different volume depolarization ratios.

Fig. 3
Fig. 3

Depolarization-ratio measurement with the three-signal method (variable reference height) for the same PSC as in Fig. 1. To determine the composite δ(z0) profile, the reference height is increased consecutively from cloud base to cloud top in height-bin increments and δ and δ(z0) are evaluated. As examples, results of the analysis are presented for reference heights of 23.2 km (left plot), and 24.9 km (center plot). Mean δ(z0) values and corresponding averaging intervals are indicated (vertical thin solid lines). Along with the composite δ(z0) profile (right plot), the depolarization observations with the three-signal method (fixed reference height) and with the conventional two-signal technique are shown for comparison. Error bars indicate uncertainties that are due to signal noise.

Equations (7)

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

Niz=ηiηiβz+ηiβzT2z/z2.
NizNiz0=Kzηiβz+ηiβzηiβz0+ηiβz0
=Kz1+δz01+Diδz1+δz1+Diδz0βzβz0,
Vij=NizNjz0Niz0Njz=1+Djδz01+Diδz1+Diδz01+Djδz.
δz0=1-V231+D3δz/1+D2δzD2V231+D3δz/1+D2δz-D3,
δz=1-V131+D1δz0/1+D3δz0D3V131+D1δz0/1+D3δz0-D1.
δφ=R-1δparφ/1+δparφ+δmolφ/1+δmolφR-1/1+δparφ+1/1+δmolφ,

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