Abstract

An analytical model based on the integration of the scattering-angle and light-path manifold has been developed to quantify the effect of multiple scattering on cirrus measurements obtained with elastic polarization lidars from space. Light scattering by molecules and by a horizontally homogeneous cloud is taken into account. Lidar parameters, including laser beam divergence, can be freely chosen. Up to 3 orders of scattering are calculated. Furthermore, an inversion technique for the retrieval of cloud extinction profiles from measurements with elastic-backscatter lidars is proposed that explicitly takes multiple scattering into account. It is found that for typical lidar system parameters such as those of the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) instrument multiple scattering does not significantly affect depolarization-ratio measurements in cirrus clouds with small to moderate optical depths. For all simulated clouds, the absolute value of the difference between measured and single-scattering volume depolarization ratio is <0.006. The particle depolarization ratio can be calculated from the measured volume depolarization ratio and the retrieved backscatter ratio without degradation of accuracy; thus characterization of the various cirrus categories in terms of the particle depolarization ratio and retrieval of cloud microphysical properties is feasible from space. The results of this study apply to polar stratospheric clouds as well.

© 2003 Optical Society of America

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    [CrossRef]
  45. J. Reichardt, S. Reichardt, A. Behrendt, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: implications for spaceborne remote sensing,” Geophys. Res. Lett. 29, 1668, 10.1029/2002GL014836 (2002).
  46. 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]

2002 (4)

P. Völger, Z. Liu, N. Sugimoto, “Multiple scattering simulations for the Japanese space lidar project ELISE,” IEEE Trans. Geosci. Remote Sens. 40, 550–559 (2002).
[CrossRef]

J. Reichardt, S. Reichardt, M. Hess, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: microphysical interpretation,” J. Geophys. Res. 107, 4562, 10.1029/2002JD002589 (2002).

J. Reichardt, S. Reichardt, A. Behrendt, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: implications for spaceborne remote sensing,” Geophys. Res. Lett. 29, 1668, 10.1029/2002GL014836 (2002).

V. Noel, H. Chepfer, G. Ledanois, A. Delaval, P. H. Flamant, “Classification of particle effective shape ratios in cirrus clouds based on the lidar depolarization ratio,” Appl. Opt. 41, 4245–4257 (2002).
[CrossRef] [PubMed]

2001 (6)

K. Sassen, J. M. Comstock, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part III: radiative properties,” J. Atmos. Sci. 58, 2113–2127 (2001).
[CrossRef]

K. Sassen, S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part 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]

Y.-X. Hu, D. Winker, P. Yang, B. Baum, L. Poole, L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: a multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569–579 (2001).
[CrossRef]

W. Widada, H. Kinjo, H. Kuze, N. Takeuchi, M. Sasaki, “Effect of multiple scattering in the lidar measurement of tropospheric aerosol extinction profiles,” Opt. Rev. 8, 382–387 (2001).
[CrossRef]

D. P. Duda, J. D. Spinhirne, E. W. Eloranta, “Atmospheric multiple scattering effects on GLAS altimetry—Part I: calculations of single pulse bias,” IEEE Trans. Geosci. Remote Sens. 39, 92–101 (2001).
[CrossRef]

2000 (2)

1999 (4)

Y. S. Balin, S. V. Samoilova, M. M. Krekova, D. M. Winker, “Retrieval of cloud optical parameters from space-based backscatter lidar data,” Appl. Opt. 38, 6365–6373 (1999).
[CrossRef]

S. D. Miller, G. L. Stephens, “Multiple scattering effects in the lidar pulse stretching problem,” J. Geophys. Res. 104, 22205–22219 (1999).
[CrossRef]

H. Chepfer, J. Pelon, G. Brogniez, C. Flamant, V. Trouillet, P. H. Flamant, “Impact of cirrus cloud ice crystal shape and size on multiple scattering effects: application to spaceborne and airborne backscatter lidar measurements during LITE mission and E LITE campaign,” Geophys. Res. Lett. 26, 2203–2206 (1999).
[CrossRef]

J. Reichardt, “Optical and geometrical properties of northern midlatitude cirrus clouds observed with a UV Raman lidar,” Phys. Chem. Earth 24, 255–260 (1999).
[CrossRef]

1998 (5)

1997 (2)

F. Nicolas, L. R. Bissonnette, P. H. Flamant, “Lidar effective multiple-scattering coefficients in cirrus clouds,” Appl. Opt. 36, 3458–3468 (1997).
[CrossRef] [PubMed]

G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering on lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Contrib. Atmos. Phys. 70, 91–107 (1997).

1996 (3)

D. M. Winker, R. H. Couch, M. P. McCormick, “An overview of LITE: NASA’s lidar in-space technology experiment,” Proc. IEEE 84, 164–180 (1996).
[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]

C. Flesia, A. V. Starkov, “Multiple scattering from clear atmosphere obscured by transparent crystal clouds in satellite-borne lidar sensing,” Appl. Opt. 35, 2637–2641 (1996).
[CrossRef] [PubMed]

1995 (3)

L. R. Bissonnette, D. L. Hutt, “Multiply scattered aerosol lidar returns—Inversion method and comparison with in situ measurements,” Appl. Opt. 34, 6959–6975 (1995).
[CrossRef] [PubMed]

D. M. Winker, L. R. Poole, “Monte-Carlo calculations of cloud returns for ground-based and space-based LIDARs,” Appl. Phys. B 60, 341–344 (1995).
[CrossRef]

A. V. Starkow, M. Noormohammadian, U. G. Oppel, “A stochastic-model and a variance-reduction Monte-Carlo method for the calculation of light transport,” Appl. Phys. B 60, 335–340 (1995).
[CrossRef]

1994 (1)

1993 (1)

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 (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]

1986 (1)

1985 (1)

1984 (1)

1981 (2)

J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981).
[CrossRef] [PubMed]

C. M. R. Platt, “Remote sounding of high clouds: III. Monte Carlo calculations of multiple-scattered lidar returns,” J. Atmos. Sci. 38, 156–167 (1981).
[CrossRef]

1976 (2)

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

S. R. Pal, A. I. Carswell, “Multiple scattering in atmospheric clouds: lidar observations,” Appl. Opt. 15, 1990–1995 (1976).
[CrossRef]

1972 (1)

J. A. Weinman, S. T. Shipley, “Effects of multiple scattering on laser pulses transmitted through clouds,” J. Geophys. Res. 77, 7123–7128 (1972).
[CrossRef]

1971 (1)

K. N. Liou, R. M. Schotland, “Multiple backscattering and depolarization from water clouds for a pulsed lidar system,” J. Atmos. Sci. 28, 772–784 (1971).
[CrossRef]

Ansmann, A.

Balin, Y. S.

Baum, B.

Y.-X. Hu, D. Winker, P. Yang, B. Baum, L. Poole, L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: a multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569–579 (2001).
[CrossRef]

Behrendt, A.

J. Reichardt, S. Reichardt, A. Behrendt, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: implications for spaceborne remote sensing,” Geophys. Res. Lett. 29, 1668, 10.1029/2002GL014836 (2002).

Benson, S.

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

Bissonnette, L. R.

Brogniez, G.

H. Chepfer, J. Pelon, G. Brogniez, C. Flamant, V. Trouillet, P. H. Flamant, “Impact of cirrus cloud ice crystal shape and size on multiple scattering effects: application to spaceborne and airborne backscatter lidar measurements during LITE mission and E LITE campaign,” Geophys. Res. Lett. 26, 2203–2206 (1999).
[CrossRef]

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]

Y. Sasano, E. V. Browell, S. Ismail, “Error caused by using a constant extinction/backscattering ratio in the lidar solution,” Appl. Opt. 24, 3929–3932 (1985).
[CrossRef] [PubMed]

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]

Carnuth, W.

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]

Chepfer, H.

V. Noel, H. Chepfer, G. Ledanois, A. Delaval, P. H. Flamant, “Classification of particle effective shape ratios in cirrus clouds based on the lidar depolarization ratio,” Appl. Opt. 41, 4245–4257 (2002).
[CrossRef] [PubMed]

H. Chepfer, J. Pelon, G. Brogniez, C. Flamant, V. Trouillet, P. H. Flamant, “Impact of cirrus cloud ice crystal shape and size on multiple scattering effects: application to spaceborne and airborne backscatter lidar measurements during LITE mission and E LITE campaign,” Geophys. Res. Lett. 26, 2203–2206 (1999).
[CrossRef]

Comstock, J. M.

K. Sassen, J. M. Comstock, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part III: radiative properties,” J. Atmos. Sci. 58, 2113–2127 (2001).
[CrossRef]

Couch, R. H.

D. M. Winker, R. H. Couch, M. P. McCormick, “An overview of LITE: NASA’s lidar in-space technology experiment,” Proc. IEEE 84, 164–180 (1996).
[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]

Delaval, A.

Duda, D. P.

D. P. Duda, J. D. Spinhirne, E. W. Eloranta, “Atmospheric multiple scattering effects on GLAS altimetry—Part I: calculations of single pulse bias,” IEEE Trans. Geosci. Remote Sens. 39, 92–101 (2001).
[CrossRef]

Eloranta, E. W.

D. P. Duda, J. D. Spinhirne, E. W. Eloranta, “Atmospheric multiple scattering effects on GLAS altimetry—Part I: calculations of single pulse bias,” IEEE Trans. Geosci. Remote Sens. 39, 92–101 (2001).
[CrossRef]

E. W. Eloranta, “Practical model for the calculation of multiply scattered lidar returns,” Appl. Opt. 37, 2464–2472 (1998).
[CrossRef]

E. W. Eloranta, P. Piironen, “Measurements of cirrus cloud optical properties and particle size with the University of Wisconsin High Spectral Resolution Lidar,” in Advances in Atmospheric Remote Sensing with Lidar, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer, New York, 1997), pp. 83–86.
[CrossRef]

Fernald, F. G.

Flamant, C.

H. Chepfer, J. Pelon, G. Brogniez, C. Flamant, V. Trouillet, P. H. Flamant, “Impact of cirrus cloud ice crystal shape and size on multiple scattering effects: application to spaceborne and airborne backscatter lidar measurements during LITE mission and E LITE campaign,” Geophys. Res. Lett. 26, 2203–2206 (1999).
[CrossRef]

Flamant, P. H.

V. Noel, H. Chepfer, G. Ledanois, A. Delaval, P. H. Flamant, “Classification of particle effective shape ratios in cirrus clouds based on the lidar depolarization ratio,” Appl. Opt. 41, 4245–4257 (2002).
[CrossRef] [PubMed]

H. Chepfer, J. Pelon, G. Brogniez, C. Flamant, V. Trouillet, P. H. Flamant, “Impact of cirrus cloud ice crystal shape and size on multiple scattering effects: application to spaceborne and airborne backscatter lidar measurements during LITE mission and E LITE campaign,” Geophys. Res. Lett. 26, 2203–2206 (1999).
[CrossRef]

F. Nicolas, L. R. Bissonnette, P. H. Flamant, “Lidar effective multiple-scattering coefficients in cirrus clouds,” Appl. Opt. 36, 3458–3468 (1997).
[CrossRef] [PubMed]

Flesia, C.

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. 107, 4562, 10.1029/2002JD002589 (2002).

J. Reichardt, M. Hess, A. Macke, “Lidar inelastic multiple-scattering parameters of cirrus particle ensembles determined with geometrical-optics crystal phase functions,” Appl. Opt. 39, 1895–1910 (2000).
[CrossRef]

M. Hess, R. B. A. Koelemeijer, P. Stammes, “Scattering matrices of imperfect hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 60, 301–308 (1998).
[CrossRef]

M. Hess, M. Wiegner, “COP: a data library of optical properties of hexagonal ice crystals,” Appl. Opt. 33, 7740–7746 (1994).
[CrossRef] [PubMed]

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]

Hu, Y.-X.

Y.-X. Hu, D. Winker, P. Yang, B. Baum, L. Poole, L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: a multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569–579 (2001).
[CrossRef]

Hutt, D. L.

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]

Y. Sasano, E. V. Browell, S. Ismail, “Error caused by using a constant extinction/backscattering ratio in the lidar solution,” Appl. Opt. 24, 3929–3932 (1985).
[CrossRef] [PubMed]

Kerscher, M.

G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering on lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Contrib. Atmos. Phys. 70, 91–107 (1997).

Kinjo, H.

W. Widada, H. Kinjo, H. Kuze, N. Takeuchi, M. Sasaki, “Effect of multiple scattering in the lidar measurement of tropospheric aerosol extinction profiles,” Opt. Rev. 8, 382–387 (2001).
[CrossRef]

Klett, J. D.

Koelemeijer, R. B. A.

M. Hess, R. B. A. Koelemeijer, P. Stammes, “Scattering matrices of imperfect hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 60, 301–308 (1998).
[CrossRef]

Krekova, M. M.

Kunkel, K. E.

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

Kuze, H.

W. Widada, H. Kinjo, H. Kuze, N. Takeuchi, M. Sasaki, “Effect of multiple scattering in the lidar measurement of tropospheric aerosol extinction profiles,” Opt. Rev. 8, 382–387 (2001).
[CrossRef]

Ledanois, G.

Liou, K. N.

P. Yang, K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmosphere,” Contrib. Atmos. Phys. 71, 223–248 (1998).

K. N. Liou, R. M. Schotland, “Multiple backscattering and depolarization from water clouds for a pulsed lidar system,” J. Atmos. Sci. 28, 772–784 (1971).
[CrossRef]

Liu, Z.

P. Völger, Z. Liu, N. Sugimoto, “Multiple scattering simulations for the Japanese space lidar project ELISE,” IEEE Trans. Geosci. Remote Sens. 40, 550–559 (2002).
[CrossRef]

Macke, A.

McCormick, M. P.

D. M. Winker, R. H. Couch, M. P. McCormick, “An overview of LITE: NASA’s lidar in-space technology experiment,” Proc. IEEE 84, 164–180 (1996).
[CrossRef]

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. 107, 4562, 10.1029/2002JD002589 (2002).

J. Reichardt, S. Reichardt, A. Behrendt, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: implications for spaceborne remote sensing,” Geophys. Res. Lett. 29, 1668, 10.1029/2002GL014836 (2002).

J. Reichardt, S. Reichardt, T. J. McGee, “Scattering-angle distributions of the multiple-scattering contribution to the return signals of spaceborne lidars,” in Extended Abstracts of the Eleventh International Workshop on Multiple Scattering Lidar Experiments, D. Winker, ed. (NASA Langley Research Center, Hampton, Virginia, 2001), pp. 117–121.

Michaelis, W.

Miller, S. D.

S. D. Miller, G. L. Stephens, “Multiple scattering effects in the lidar pulse stretching problem,” J. Geophys. Res. 104, 22205–22219 (1999).
[CrossRef]

Nicolas, F.

Noel, V.

Noormohammadian, M.

G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering on lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Contrib. Atmos. Phys. 70, 91–107 (1997).

A. V. Starkow, M. Noormohammadian, U. G. Oppel, “A stochastic-model and a variance-reduction Monte-Carlo method for the calculation of light transport,” Appl. Phys. B 60, 335–340 (1995).
[CrossRef]

Oppel, U. G.

G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering on lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Contrib. Atmos. Phys. 70, 91–107 (1997).

A. V. Starkow, M. Noormohammadian, U. G. Oppel, “A stochastic-model and a variance-reduction Monte-Carlo method for the calculation of light transport,” Appl. Phys. B 60, 335–340 (1995).
[CrossRef]

Pal, S. R.

Pelon, J.

H. Chepfer, J. Pelon, G. Brogniez, C. Flamant, V. Trouillet, P. H. Flamant, “Impact of cirrus cloud ice crystal shape and size on multiple scattering effects: application to spaceborne and airborne backscatter lidar measurements during LITE mission and E LITE campaign,” Geophys. Res. Lett. 26, 2203–2206 (1999).
[CrossRef]

Piironen, P.

E. W. Eloranta, P. Piironen, “Measurements of cirrus cloud optical properties and particle size with the University of Wisconsin High Spectral Resolution Lidar,” in Advances in Atmospheric Remote Sensing with Lidar, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer, New York, 1997), pp. 83–86.
[CrossRef]

Platt, C. M. R.

C. M. R. Platt, “Remote sounding of high clouds: III. Monte Carlo calculations of multiple-scattered lidar returns,” J. Atmos. Sci. 38, 156–167 (1981).
[CrossRef]

Poole, L.

Y.-X. Hu, D. Winker, P. Yang, B. Baum, L. Poole, L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: a multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569–579 (2001).
[CrossRef]

Poole, L. R.

D. M. Winker, L. R. Poole, “Monte-Carlo calculations of cloud returns for ground-based and space-based LIDARs,” Appl. Phys. B 60, 341–344 (1995).
[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. 107, 4562, 10.1029/2002JD002589 (2002).

J. Reichardt, S. Reichardt, A. Behrendt, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: implications for spaceborne remote sensing,” Geophys. Res. Lett. 29, 1668, 10.1029/2002GL014836 (2002).

J. Reichardt, “Error analysis of Raman differential absorption lidar ozone measurements in ice clouds,” Appl. Opt. 39, 6058–6071 (2000).
[CrossRef]

J. Reichardt, M. Hess, A. Macke, “Lidar inelastic multiple-scattering parameters of cirrus particle ensembles determined with geometrical-optics crystal phase functions,” Appl. Opt. 39, 1895–1910 (2000).
[CrossRef]

J. Reichardt, “Optical and geometrical properties of northern midlatitude cirrus clouds observed with a UV Raman lidar,” Phys. Chem. Earth 24, 255–260 (1999).
[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]

J. Reichardt, S. Reichardt, T. J. McGee, “Scattering-angle distributions of the multiple-scattering contribution to the return signals of spaceborne lidars,” in Extended Abstracts of the Eleventh International Workshop on Multiple Scattering Lidar Experiments, D. Winker, ed. (NASA Langley Research Center, Hampton, Virginia, 2001), pp. 117–121.

Reichardt, S.

J. Reichardt, S. Reichardt, A. Behrendt, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: implications for spaceborne remote sensing,” Geophys. Res. Lett. 29, 1668, 10.1029/2002GL014836 (2002).

J. Reichardt, S. Reichardt, M. Hess, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: microphysical interpretation,” J. Geophys. Res. 107, 4562, 10.1029/2002JD002589 (2002).

J. Reichardt, S. Reichardt, T. J. McGee, “Scattering-angle distributions of the multiple-scattering contribution to the return signals of spaceborne lidars,” in Extended Abstracts of the Eleventh International Workshop on Multiple Scattering Lidar Experiments, D. Winker, ed. (NASA Langley Research Center, Hampton, Virginia, 2001), pp. 117–121.

Reiter, R.

Renger, W.

G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering on lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Contrib. Atmos. Phys. 70, 91–107 (1997).

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]

Ruppersberg, G. H.

G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering on lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Contrib. Atmos. Phys. 70, 91–107 (1997).

Samoilova, S. V.

Sasaki, M.

W. Widada, H. Kinjo, H. Kuze, N. Takeuchi, M. Sasaki, “Effect of multiple scattering in the lidar measurement of tropospheric aerosol extinction profiles,” Opt. Rev. 8, 382–387 (2001).
[CrossRef]

Sasano, Y.

Sassen, K.

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

K. Sassen, J. M. Comstock, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part III: radiative properties,” J. Atmos. Sci. 58, 2113–2127 (2001).
[CrossRef]

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

K. N. Liou, R. M. Schotland, “Multiple backscattering and depolarization from water clouds for a pulsed lidar system,” J. Atmos. Sci. 28, 772–784 (1971).
[CrossRef]

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]

Shipley, S. T.

J. A. Weinman, S. T. Shipley, “Effects of multiple scattering on laser pulses transmitted through clouds,” J. Geophys. Res. 77, 7123–7128 (1972).
[CrossRef]

Spinhirne, J. D.

D. P. Duda, J. D. Spinhirne, E. W. Eloranta, “Atmospheric multiple scattering effects on GLAS altimetry—Part I: calculations of single pulse bias,” IEEE Trans. Geosci. Remote Sens. 39, 92–101 (2001).
[CrossRef]

Stammes, P.

M. Hess, R. B. A. Koelemeijer, P. Stammes, “Scattering matrices of imperfect hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 60, 301–308 (1998).
[CrossRef]

Starkov, A. V.

Starkow, A. V.

A. V. Starkow, M. Noormohammadian, U. G. Oppel, “A stochastic-model and a variance-reduction Monte-Carlo method for the calculation of light transport,” Appl. Phys. B 60, 335–340 (1995).
[CrossRef]

Stephens, G. L.

S. D. Miller, G. L. Stephens, “Multiple scattering effects in the lidar pulse stretching problem,” J. Geophys. Res. 104, 22205–22219 (1999).
[CrossRef]

Sugimoto, N.

P. Völger, Z. Liu, N. Sugimoto, “Multiple scattering simulations for the Japanese space lidar project ELISE,” IEEE Trans. Geosci. Remote Sens. 40, 550–559 (2002).
[CrossRef]

Takeuchi, N.

W. Widada, H. Kinjo, H. Kuze, N. Takeuchi, M. Sasaki, “Effect of multiple scattering in the lidar measurement of tropospheric aerosol extinction profiles,” Opt. Rev. 8, 382–387 (2001).
[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]

Trouillet, V.

H. Chepfer, J. Pelon, G. Brogniez, C. Flamant, V. Trouillet, P. H. Flamant, “Impact of cirrus cloud ice crystal shape and size on multiple scattering effects: application to spaceborne and airborne backscatter lidar measurements during LITE mission and E LITE campaign,” Geophys. Res. Lett. 26, 2203–2206 (1999).
[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]

Vann, L.

Y.-X. Hu, D. Winker, P. Yang, B. Baum, L. Poole, L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: a multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569–579 (2001).
[CrossRef]

Völger, P.

P. Völger, Z. Liu, N. Sugimoto, “Multiple scattering simulations for the Japanese space lidar project ELISE,” IEEE Trans. Geosci. Remote Sens. 40, 550–559 (2002).
[CrossRef]

Wandinger, U.

Weinman, J. A.

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

J. A. Weinman, S. T. Shipley, “Effects of multiple scattering on laser pulses transmitted through clouds,” J. Geophys. Res. 77, 7123–7128 (1972).
[CrossRef]

Weitkamp, C.

Widada, W.

W. Widada, H. Kinjo, H. Kuze, N. Takeuchi, M. Sasaki, “Effect of multiple scattering in the lidar measurement of tropospheric aerosol extinction profiles,” Opt. Rev. 8, 382–387 (2001).
[CrossRef]

Wiegner, M.

Wielicki, B. A.

D. M. Winker, B. A. Wielicki, “The PICASSO-CENA mission,” in Sensors, Systems, and Next Generation Satellites, H. Fujisada, J. B. Lurie, eds., Proc. SPIE3870, 26–36 (1999).

Winker, D.

Y.-X. Hu, D. Winker, P. Yang, B. Baum, L. Poole, L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: a multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569–579 (2001).
[CrossRef]

Winker, D. M.

Y. S. Balin, S. V. Samoilova, M. M. Krekova, D. M. Winker, “Retrieval of cloud optical parameters from space-based backscatter lidar data,” Appl. Opt. 38, 6365–6373 (1999).
[CrossRef]

D. M. Winker, R. H. Couch, M. P. McCormick, “An overview of LITE: NASA’s lidar in-space technology experiment,” Proc. IEEE 84, 164–180 (1996).
[CrossRef]

D. M. Winker, L. R. Poole, “Monte-Carlo calculations of cloud returns for ground-based and space-based LIDARs,” Appl. Phys. B 60, 341–344 (1995).
[CrossRef]

D. M. Winker, B. A. Wielicki, “The PICASSO-CENA mission,” in Sensors, Systems, and Next Generation Satellites, H. Fujisada, J. B. Lurie, eds., Proc. SPIE3870, 26–36 (1999).

Yang, P.

Y.-X. Hu, D. Winker, P. Yang, B. Baum, L. Poole, L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: a multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569–579 (2001).
[CrossRef]

P. Yang, K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmosphere,” Contrib. Atmos. Phys. 71, 223–248 (1998).

Appl. Opt. (18)

S. R. Pal, A. I. Carswell, “Multiple scattering in atmospheric clouds: lidar observations,” Appl. Opt. 15, 1990–1995 (1976).
[CrossRef]

J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981).
[CrossRef] [PubMed]

F. G. Fernald, “Analysis of atmospheric lidar observations: some comments,” Appl. Opt. 23, 652–653 (1984).
[CrossRef] [PubMed]

Y. Sasano, E. V. Browell, S. Ismail, “Error caused by using a constant extinction/backscattering ratio in the lidar solution,” Appl. Opt. 24, 3929–3932 (1985).
[CrossRef] [PubMed]

W. Carnuth, R. Reiter, “Cloud extinction profile measurements by lidar using Klett’s inversion method,” Appl. Opt. 25, 2899–2907 (1986).
[CrossRef]

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]

A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
[CrossRef] [PubMed]

M. Hess, M. Wiegner, “COP: a data library of optical properties of hexagonal ice crystals,” Appl. Opt. 33, 7740–7746 (1994).
[CrossRef] [PubMed]

E. W. Eloranta, “Practical model for the calculation of multiply scattered lidar returns,” Appl. Opt. 37, 2464–2472 (1998).
[CrossRef]

S. R. Pal, L. R. Bissonnette, “Multiple-scattering effect on ozone retrieval from space-based differential absorption lidar measurements,” Appl. Opt. 37, 6500–6510 (1998).
[CrossRef]

L. R. Bissonnette, D. L. Hutt, “Multiply scattered aerosol lidar returns—Inversion method and comparison with in situ measurements,” Appl. Opt. 34, 6959–6975 (1995).
[CrossRef] [PubMed]

C. Flesia, A. V. Starkov, “Multiple scattering from clear atmosphere obscured by transparent crystal clouds in satellite-borne lidar sensing,” Appl. Opt. 35, 2637–2641 (1996).
[CrossRef] [PubMed]

F. Nicolas, L. R. Bissonnette, P. H. Flamant, “Lidar effective multiple-scattering coefficients in cirrus clouds,” Appl. Opt. 36, 3458–3468 (1997).
[CrossRef] [PubMed]

Y. S. Balin, S. V. Samoilova, M. M. Krekova, D. M. Winker, “Retrieval of cloud optical parameters from space-based backscatter lidar data,” Appl. Opt. 38, 6365–6373 (1999).
[CrossRef]

J. Reichardt, M. Hess, A. Macke, “Lidar inelastic multiple-scattering parameters of cirrus particle ensembles determined with geometrical-optics crystal phase functions,” Appl. Opt. 39, 1895–1910 (2000).
[CrossRef]

J. Reichardt, “Error analysis of Raman differential absorption lidar ozone measurements in ice clouds,” Appl. Opt. 39, 6058–6071 (2000).
[CrossRef]

U. Wandinger, “Multiple-scattering influence on extinction- and backscatter-coefficient measurements with Raman and high-spectral-resolution lidars,” Appl. Opt. 37, 417–427 (1998).
[CrossRef]

V. Noel, H. Chepfer, G. Ledanois, A. Delaval, P. H. Flamant, “Classification of particle effective shape ratios in cirrus clouds based on the lidar depolarization ratio,” Appl. Opt. 41, 4245–4257 (2002).
[CrossRef] [PubMed]

Appl. Phys. B (2)

D. M. Winker, L. R. Poole, “Monte-Carlo calculations of cloud returns for ground-based and space-based LIDARs,” Appl. Phys. B 60, 341–344 (1995).
[CrossRef]

A. V. Starkow, M. Noormohammadian, U. G. Oppel, “A stochastic-model and a variance-reduction Monte-Carlo method for the calculation of light transport,” Appl. Phys. B 60, 335–340 (1995).
[CrossRef]

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]

Contrib. Atmos. Phys. (2)

P. Yang, K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmosphere,” Contrib. Atmos. Phys. 71, 223–248 (1998).

G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering on lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Contrib. Atmos. Phys. 70, 91–107 (1997).

Geophys. Res. Lett. (3)

H. Chepfer, J. Pelon, G. Brogniez, C. Flamant, V. Trouillet, P. H. Flamant, “Impact of cirrus cloud ice crystal shape and size on multiple scattering effects: application to spaceborne and airborne backscatter lidar measurements during LITE mission and E LITE campaign,” Geophys. Res. Lett. 26, 2203–2206 (1999).
[CrossRef]

J. Reichardt, S. Reichardt, A. Behrendt, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: implications for spaceborne remote sensing,” Geophys. Res. Lett. 29, 1668, 10.1029/2002GL014836 (2002).

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]

IEEE Trans. Geosci. Remote Sens. (2)

P. Völger, Z. Liu, N. Sugimoto, “Multiple scattering simulations for the Japanese space lidar project ELISE,” IEEE Trans. Geosci. Remote Sens. 40, 550–559 (2002).
[CrossRef]

D. P. Duda, J. D. Spinhirne, E. W. Eloranta, “Atmospheric multiple scattering effects on GLAS altimetry—Part I: calculations of single pulse bias,” IEEE Trans. Geosci. Remote Sens. 39, 92–101 (2001).
[CrossRef]

J. Atmos. Sci. (5)

K. N. Liou, R. M. Schotland, “Multiple backscattering and depolarization from water clouds for a pulsed lidar system,” J. Atmos. Sci. 28, 772–784 (1971).
[CrossRef]

C. M. R. Platt, “Remote sounding of high clouds: III. Monte Carlo calculations of multiple-scattered lidar returns,” J. Atmos. Sci. 38, 156–167 (1981).
[CrossRef]

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

K. Sassen, J. M. Comstock, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part III: radiative properties,” J. Atmos. Sci. 58, 2113–2127 (2001).
[CrossRef]

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

J. Geophys. Res. (4)

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]

S. D. Miller, G. L. Stephens, “Multiple scattering effects in the lidar pulse stretching problem,” J. Geophys. Res. 104, 22205–22219 (1999).
[CrossRef]

J. A. Weinman, S. T. Shipley, “Effects of multiple scattering on laser pulses transmitted through clouds,” J. Geophys. Res. 77, 7123–7128 (1972).
[CrossRef]

J. Reichardt, S. Reichardt, M. Hess, T. J. McGee, “Correlations among the optical properties of cirrus-cloud particles: microphysical interpretation,” J. Geophys. Res. 107, 4562, 10.1029/2002JD002589 (2002).

J. Quant. Spectrosc. Radiat. Transfer (2)

Y.-X. Hu, D. Winker, P. Yang, B. Baum, L. Poole, L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: a multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569–579 (2001).
[CrossRef]

M. Hess, R. B. A. Koelemeijer, P. Stammes, “Scattering matrices of imperfect hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 60, 301–308 (1998).
[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]

Opt. Rev. (1)

W. Widada, H. Kinjo, H. Kuze, N. Takeuchi, M. Sasaki, “Effect of multiple scattering in the lidar measurement of tropospheric aerosol extinction profiles,” Opt. Rev. 8, 382–387 (2001).
[CrossRef]

Phys. Chem. Earth (1)

J. Reichardt, “Optical and geometrical properties of northern midlatitude cirrus clouds observed with a UV Raman lidar,” Phys. Chem. Earth 24, 255–260 (1999).
[CrossRef]

Proc. IEEE (1)

D. M. Winker, R. H. Couch, M. P. McCormick, “An overview of LITE: NASA’s lidar in-space technology experiment,” Proc. IEEE 84, 164–180 (1996).
[CrossRef]

Other (3)

D. M. Winker, B. A. Wielicki, “The PICASSO-CENA mission,” in Sensors, Systems, and Next Generation Satellites, H. Fujisada, J. B. Lurie, eds., Proc. SPIE3870, 26–36 (1999).

E. W. Eloranta, P. Piironen, “Measurements of cirrus cloud optical properties and particle size with the University of Wisconsin High Spectral Resolution Lidar,” in Advances in Atmospheric Remote Sensing with Lidar, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer, New York, 1997), pp. 83–86.
[CrossRef]

J. Reichardt, S. Reichardt, T. J. McGee, “Scattering-angle distributions of the multiple-scattering contribution to the return signals of spaceborne lidars,” in Extended Abstracts of the Eleventh International Workshop on Multiple Scattering Lidar Experiments, D. Winker, ed. (NASA Langley Research Center, Hampton, Virginia, 2001), pp. 117–121.

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Figures (9)

Fig. 1
Fig. 1

Model results for a reference cirrus cloud (cloud base of 10 km, geometrical depth of 2 km) with a height-independent particle extinction coefficient (αpar = 0.3 km-1) consisting of 130-μm long imperfect (1° distortion) hexagonal solid ice columns. Laser wavelength, lidar field of view (FOVL) and orbit height (z L) of the spaceborne lidar are 532 nm, 130 μrad (full angle), and 700 km, respectively. Left panel, total extinction coefficient (α = αpar + αmol) and multiple-scattering parameters F L; second from left, ratios of multiply to singly scattered light; third from left, volume depolarization ratio of the singly scattered photons δvol1, of the multiply scattered photons δvolMS, and the difference Δδvol (multiplied by a factor of 100) between measured depolarization ratio δvol1+MS and δvol1. Right panel, probability density of scattering angle θ for multiply scattered photons at various heights.

Fig. 2
Fig. 2

Relative difference between the ratios of doubly- to singly-scattered light obtained for a nondiverging laser beam and for a laser beam divergence of 100 μrad (full angle, CALIPSO specification) with a Gaussian profile. FOVL varies between 40 and 400 μrad; 130 μm is the FOVL of the CALIPSO lidar. Cirrus-cloud properties, laser wavelength, and orbit height are the same as in Fig. 1.

Fig. 3
Fig. 3

Ratios of multiple-scattering to single-scattering lidar signal at cloud base versus optical depth of the cirrus cloud. Except for the varying optical depth, all parameters are the same as in Fig. 1. Right, results obtained for various particle sizes, particle shape distortions, and FOVLs for an optical depth of 0.6 (triangles).

Fig. 4
Fig. 4

Volume depolarization ratios of the single-scattering and multiple-scattering contributions to the lidar signal, and the measured volume depolarization ratio at cloud base versus optical depth (τC) of the cirrus cloud. Except for τC, all parameters are the same as in Fig. 1. Results obtained for various particle sizes, particle shape distortions, and FOVLs are shown as well for τC = 0.6 (triangles).

Fig. 5
Fig. 5

Top, PD of incidence angle ∊ for multiply scattered photons; bottom, volume depolarization ratio of the multiple-scattering contribution to the lidar signal as a function of incidence angle at various heights. The maximum incidence angle of 200 μrad corresponds to a FOVL of 400 μrad. Except for the wider field of view, all parameters are the same as in Fig. 1. The maximum CALIPSO-lidar incidence angle is indicated by arrows.

Fig. 6
Fig. 6

Left column, single-scattering particle extinction coefficient αpar; second column, multiple-scattering parameter F L; third column, measured volume depolarization ratio δvol1+MS; fourth column, difference between measured and single-scattering volume depolarization ratio for three cirrus clouds. Results are shown for ice clouds consisting of hexagonal solid columns of three different sizes (1° shape distortion). Orbit height, field of view, and laser wavelength of the spaceborne lidar are 700 km, 130 μm, and 532 nm, respectively. The extinction profiles have been taken from the cirrus data set measured with the ground-based GKSS Raman lidar.35

Fig. 7
Fig. 7

Top, PD of scattering angle near the backward-scattering direction for multiply scattered photons; bottom, the dependence of the volume depolarization ratio on the scattering angle for various cirrus-particle sizes. The data are drawn from the multiple-scattering calculation for the lowest cloud in Fig. 6 at 4.5 km (height of the lower maximum of the extinction-coefficient profile).

Fig. 8
Fig. 8

Left, true extinction coefficient αpar; right, differences between true and inversion-derived extinction coefficients. The cirrus cloud is assumed to consist of 130-μm particles (1° shape distortion). Inversion is performed iteratively. Multiple scattering is accounted for only in the second iteration; results are presented for various assumptions about particle size. Initial and retrieved S par are indicated.

Fig. 9
Fig. 9

Left, true backscatter ratio R; right, absolute values of the relative differences between true and inversion-derived backscatter ratios. The cirrus cloud is assumed to consist of 130-μm particles (1° shape distortion). Inversion is performed iteratively. Multiple scattering is accounted for only in the second iteration; results are presented for various assumptions about particle size.

Equations (15)

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S1=P1θ1·L01φ1S0.
S3=P3θ3·L23φ3S2.
S3= dz1  dθ1sin θ1  dφ1  dz2 dθ2sin θ2  dφ2  dz3 ΔΩRecαz1αz2αz3exp-τ01+τ12+τ23+τ30L30φ4·P3θ3·L23φ3·P2θ2·L12φ2·P1θ1·L01φ1S0,
α=αpar+αmol
S2= dz1  dθ1sin θ1  dφ1  dz2 ΔΩRecαz1αz2exp-τ01+τ12+τ20L10π-φ1·P2θ2·P1θ1·L01φ1S0.
S1+2+3=S1+MS=S1+S2+S3.
δvol1+MS=I1+MS-Q1+MS/I1+MS+Q1+MS.
αeffz=1-FLzαz,
FLz=-12αzddzln1+NzN1z,
δpar=1+δmoldetR-1δvol+δvol-δmoldet1+δmoldetR-1-δvol+δmoldet,
Xz=z2Nz=kβparz+βmolzexp-2 0zαparζ+αmolζdζ,
Xz=Xz+Vz0δmoldet Xz,
βparz+βmolz=Xzexp-2 z0zSparζ-SmolβmolζdζAz0-2 z0z SparζXζexp-2 z0ζSparξ-Smolβmolξdξdζ,
Xz=kβparz+βmolzexp-2 0z1-FLζ×αparζ+αmolζdζ.
βparz+βmolz=Xzexp-2 z0z1-FLζSparζ-SmolβmolζdζAz0-2 z0z1-FLζSparζXζexp-2 z0ζ1-FLξSparξ-Smolβmolξdξdζ.

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