Abstract

We present an approach to estimating the multiple-scattering (MS) contribution to lidar return signals from clouds recorded from space that enables us to describe in more detail the return formation at the depth where first orders of scattering dominate. Estimates made have enabled us to propose a method for correcting solutions of single-scattering lidar equations for the MS contribution. We also describe an algorithm for reconstructing the profiles of the cloud scattering coefficient and the optical thickness τ under conditions of a priori uncertainties. The approach proposed is illustrated with results for optical parameters of cirrus and stratiform clouds determined from return signals calculated by the Monte Carlo method as well as from return signals acquired with the American spaceborne lidar during the Lidar In-Space Technology Experiment (LITE).

© 1999 Optical Society of America

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  1. Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. V. Samokhvalov, S. V. Samoilova, “On laser sounding of clouds and underlying surface from space,” Atmos. Opt. 1, 93–99 (1988).
  2. G. M. Krekov, M. M. Krekova, I. V. Samokhvalov, “Spaceborne lidar signals in stratus sounding,” Earth Res. Space 6, 77–83 (1986).
  3. G. M. Krekov, M. M. Krekova, “Structure of spaceborne lidar signal reflected by upper-level clouds. II. Optically inhomogeneous clouds,” Atm. Oceanic Opt. 11, 51–54 (1998).
  4. B. Kaul, Yu. Arshinov, D. Romashov, I. Samokhvalov, Ch. Werner, J. Streicher, H. Herrmann, U. Oppel, H. Krasting, Crystal Clouds (Spektr, Tomsk, Russia), Chap. 4, pp. 48–77 (1997).
  5. Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. A. Razenkov, “Noise-proof inversion of lidar equation,” Opt. Lett. 12, 13–15 (1987).
    [CrossRef] [PubMed]
  6. J. D. Klett, “Lidar inversion with variable backscatter/extinction ratios,” Appl. Opt. 24, 1638–1643 (1985).
    [CrossRef] [PubMed]
  7. L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
    [CrossRef]
  8. E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B 60, 345–353 (1995).
    [CrossRef]
  9. G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering of lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Beitr. Phys. Atmos. 70, 93–105 (1997).
  10. V. A. Kovalev, “Lidar measurements of the vertical aerosol extinction profiles with range-dependent backscatter-to-extinction ratios,” Appl. Opt. 32, 6053–6065 (1993).
    [CrossRef] [PubMed]
  11. Yu. S. Balin, I. V. Samokhvalov, “Statistical characteristics of the back scattering vertical structure in the lower troposphere,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 19, 937–943 (1983).
  12. A. N. Tikhonov, V. A. Arsenin, Methods for Solution of Incorrect Problems (Nauka, Moscow, 1974).
  13. D. M. Winker, “Simulation and modeling of multiple scattering effects observed in LITE data,” in Advances in Atmospheric Remote Sensing with Lidar, Selected papers of the 18th International Laser Radar Conference, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1997), pp. 185–188.
  14. M. Wiegner, U. Oppel, H. Krasting, W. Renger, Ch. Kiemle, M. Wirth, “Cirrus measurements from a spaceborne lidar: influence of multiple scattering,” in Advances in Atmospheric Remote Sensing with Lidar, Selected papers of the 18th International Laser Radar Conference, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1997), pp. 189–192.
  15. A. V. Starkov, C. Flesia, “Correction of spaceborne lidar signal for multiple scattering from high clouds,” in Nineteenth International Laser Radar Conference, U. N. Singh, S. Ismail, G. K. Schwemmer, eds., NASA/CP-1998-207671/PT 2 (NASA, Washington, D.C., 1998), pp. 967–969.
  16. I. V. Samokhvalov, “Double scattering approximation of lidar equation for inhomogeneous atmosphere,” Opt. Lett. 4, 12–14 (1979).
    [CrossRef]
  17. M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
    [CrossRef]
  18. W. Renger, C. Kiemle, H.-G. Schreiber, M. Wirth, P. Moerl, “Airborne backscatter lidar measurements at 3 wavelengths during ELITE,” in ELITE-94, The European ‘LITE’ Correlative Measurement Campaign, P. Fletcher, F. Lodge, E. Attema, eds., esaWPP-107 (European Space Agency/European Space Telecommunication, Postbus 299 AG Noordwijk, The Netherlands, 1995), pp. 15–30.
  19. C. I. Marchuk, G. M. Mikhailov, T. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, E. P. Elepov, “Monte Carlo algorithms for solving nonstationary problems on propagation of narrow light beams in the atmosphere and ocean,” in Monte-Carlo Methods in Atmospheric Optics, G. I. Marchuk, ed. (Springer-Verlag, Berlin, 1980), Chap. 5.
    [CrossRef]
  20. G. M. Krekov, M. M. Krekova, V. S. Shamanaev, “Laser sensing of a subsurface oceanic layer. I. Effect of atmosphere and wind-driven sea waves,” Appl. Opt. 37, 1589–1595 (1998).
    [CrossRef]
  21. Qiu Jinhuan, H. Quenzel, M. Wenger, Parameterized Multiple-Scatter Lidar Equation and Its Application (Institute of Atmospheric Optics, Tomsk, Russia, 1990), P. I, pp. 345–348.
  22. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).
  23. Yo. Takano, K.-N. Liou, “Solar radiation transfer in cirrus clouds. 1. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
    [CrossRef]
  24. V. E. Zuev, G. O. Zadde, S. I. Kavkyanov, B. V. Kaul, “Interpretation of lidar return signals from the regions of large optical depths,” in Remote Sensing of the Atmosphere, V. Zuev, ed. (Nauka, Novosibirsk, Russia, 1978), pp. 60–68.
  25. S. V. Samoilova, Yu. S. Balin, M. M. Krekova, “Accounting for the effects of multiple scattering in reconstruction of optical parameters of clouds from spaceborne sounding data,” Atm. Oceanic Opt. 11, 55–60 (1998).
  26. 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]

1998 (3)

G. M. Krekov, M. M. Krekova, “Structure of spaceborne lidar signal reflected by upper-level clouds. II. Optically inhomogeneous clouds,” Atm. Oceanic Opt. 11, 51–54 (1998).

G. M. Krekov, M. M. Krekova, V. S. Shamanaev, “Laser sensing of a subsurface oceanic layer. I. Effect of atmosphere and wind-driven sea waves,” Appl. Opt. 37, 1589–1595 (1998).
[CrossRef]

S. V. Samoilova, Yu. S. Balin, M. M. Krekova, “Accounting for the effects of multiple scattering in reconstruction of optical parameters of clouds from spaceborne sounding data,” Atm. Oceanic Opt. 11, 55–60 (1998).

1997 (1)

G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering of lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Beitr. Phys. Atmos. 70, 93–105 (1997).

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]

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B 60, 345–353 (1995).
[CrossRef]

1993 (2)

M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
[CrossRef]

V. A. Kovalev, “Lidar measurements of the vertical aerosol extinction profiles with range-dependent backscatter-to-extinction ratios,” Appl. Opt. 32, 6053–6065 (1993).
[CrossRef] [PubMed]

1989 (1)

Yo. Takano, K.-N. Liou, “Solar radiation transfer in cirrus clouds. 1. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

1988 (1)

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. V. Samokhvalov, S. V. Samoilova, “On laser sounding of clouds and underlying surface from space,” Atmos. Opt. 1, 93–99 (1988).

1987 (1)

1986 (1)

G. M. Krekov, M. M. Krekova, I. V. Samokhvalov, “Spaceborne lidar signals in stratus sounding,” Earth Res. Space 6, 77–83 (1986).

1985 (1)

1983 (1)

Yu. S. Balin, I. V. Samokhvalov, “Statistical characteristics of the back scattering vertical structure in the lower troposphere,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 19, 937–943 (1983).

1979 (1)

Arsenin, V. A.

A. N. Tikhonov, V. A. Arsenin, Methods for Solution of Incorrect Problems (Nauka, Moscow, 1974).

Arshinov, Yu.

B. Kaul, Yu. Arshinov, D. Romashov, I. Samokhvalov, Ch. Werner, J. Streicher, H. Herrmann, U. Oppel, H. Krasting, Crystal Clouds (Spektr, Tomsk, Russia), Chap. 4, pp. 48–77 (1997).

Balin, Yu. S.

S. V. Samoilova, Yu. S. Balin, M. M. Krekova, “Accounting for the effects of multiple scattering in reconstruction of optical parameters of clouds from spaceborne sounding data,” Atm. Oceanic Opt. 11, 55–60 (1998).

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. V. Samokhvalov, S. V. Samoilova, “On laser sounding of clouds and underlying surface from space,” Atmos. Opt. 1, 93–99 (1988).

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. A. Razenkov, “Noise-proof inversion of lidar equation,” Opt. Lett. 12, 13–15 (1987).
[CrossRef] [PubMed]

Yu. S. Balin, I. V. Samokhvalov, “Statistical characteristics of the back scattering vertical structure in the lower troposphere,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 19, 937–943 (1983).

Benayahu, Y.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Bissonnette, L. R.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[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]

Browell, E. V.

M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
[CrossRef]

Bruscaglioni, P.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Coakley, J. A.

M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
[CrossRef]

Cohen, A.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Darbinyan, R. A.

C. I. Marchuk, G. M. Mikhailov, T. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, E. P. Elepov, “Monte Carlo algorithms for solving nonstationary problems on propagation of narrow light beams in the atmosphere and ocean,” in Monte-Carlo Methods in Atmospheric Optics, G. I. Marchuk, ed. (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

Egert, S.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Elepov, E. P.

C. I. Marchuk, G. M. Mikhailov, T. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, E. P. Elepov, “Monte Carlo algorithms for solving nonstationary problems on propagation of narrow light beams in the atmosphere and ocean,” in Monte-Carlo Methods in Atmospheric Optics, G. I. Marchuk, ed. (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

Flesia, C.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

A. V. Starkov, C. Flesia, “Correction of spaceborne lidar signal for multiple scattering from high clouds,” in Nineteenth International Laser Radar Conference, U. N. Singh, S. Ismail, G. K. Schwemmer, eds., NASA/CP-1998-207671/PT 2 (NASA, Washington, D.C., 1998), pp. 967–969.

Gargner, C. S.

M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
[CrossRef]

Herrmann, H.

B. Kaul, Yu. Arshinov, D. Romashov, I. Samokhvalov, Ch. Werner, J. Streicher, H. Herrmann, U. Oppel, H. Krasting, Crystal Clouds (Spektr, Tomsk, Russia), Chap. 4, pp. 48–77 (1997).

Hoff, R. M.

M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
[CrossRef]

Hutt, D. L.

Ismaelli, A.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Jinhuan, Qiu

Qiu Jinhuan, H. Quenzel, M. Wenger, Parameterized Multiple-Scatter Lidar Equation and Its Application (Institute of Atmospheric Optics, Tomsk, Russia, 1990), P. I, pp. 345–348.

Kargin, B. A.

C. I. Marchuk, G. M. Mikhailov, T. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, E. P. Elepov, “Monte Carlo algorithms for solving nonstationary problems on propagation of narrow light beams in the atmosphere and ocean,” in Monte-Carlo Methods in Atmospheric Optics, G. I. Marchuk, ed. (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

Katsev, I. L.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B 60, 345–353 (1995).
[CrossRef]

Kaul, B.

B. Kaul, Yu. Arshinov, D. Romashov, I. Samokhvalov, Ch. Werner, J. Streicher, H. Herrmann, U. Oppel, H. Krasting, Crystal Clouds (Spektr, Tomsk, Russia), Chap. 4, pp. 48–77 (1997).

Kaul, B. V.

V. E. Zuev, G. O. Zadde, S. I. Kavkyanov, B. V. Kaul, “Interpretation of lidar return signals from the regions of large optical depths,” in Remote Sensing of the Atmosphere, V. Zuev, ed. (Nauka, Novosibirsk, Russia, 1978), pp. 60–68.

Kavkyanov, S. I.

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. V. Samokhvalov, S. V. Samoilova, “On laser sounding of clouds and underlying surface from space,” Atmos. Opt. 1, 93–99 (1988).

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. A. Razenkov, “Noise-proof inversion of lidar equation,” Opt. Lett. 12, 13–15 (1987).
[CrossRef] [PubMed]

V. E. Zuev, G. O. Zadde, S. I. Kavkyanov, B. V. Kaul, “Interpretation of lidar return signals from the regions of large optical depths,” in Remote Sensing of the Atmosphere, V. Zuev, ed. (Nauka, Novosibirsk, Russia, 1978), pp. 60–68.

Kent, G. S.

M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
[CrossRef]

Kerscher, M.

G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering of lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Beitr. Phys. Atmos. 70, 93–105 (1997).

Kiemle, C.

W. Renger, C. Kiemle, H.-G. Schreiber, M. Wirth, P. Moerl, “Airborne backscatter lidar measurements at 3 wavelengths during ELITE,” in ELITE-94, The European ‘LITE’ Correlative Measurement Campaign, P. Fletcher, F. Lodge, E. Attema, eds., esaWPP-107 (European Space Agency/European Space Telecommunication, Postbus 299 AG Noordwijk, The Netherlands, 1995), pp. 15–30.

Kiemle, Ch.

M. Wiegner, U. Oppel, H. Krasting, W. Renger, Ch. Kiemle, M. Wirth, “Cirrus measurements from a spaceborne lidar: influence of multiple scattering,” in Advances in Atmospheric Remote Sensing with Lidar, Selected papers of the 18th International Laser Radar Conference, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1997), pp. 189–192.

Kleiman, M.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Klett, J. D.

Kovalev, V. A.

Krasting, H.

M. Wiegner, U. Oppel, H. Krasting, W. Renger, Ch. Kiemle, M. Wirth, “Cirrus measurements from a spaceborne lidar: influence of multiple scattering,” in Advances in Atmospheric Remote Sensing with Lidar, Selected papers of the 18th International Laser Radar Conference, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1997), pp. 189–192.

B. Kaul, Yu. Arshinov, D. Romashov, I. Samokhvalov, Ch. Werner, J. Streicher, H. Herrmann, U. Oppel, H. Krasting, Crystal Clouds (Spektr, Tomsk, Russia), Chap. 4, pp. 48–77 (1997).

Krekov, G. M.

G. M. Krekov, M. M. Krekova, “Structure of spaceborne lidar signal reflected by upper-level clouds. II. Optically inhomogeneous clouds,” Atm. Oceanic Opt. 11, 51–54 (1998).

G. M. Krekov, M. M. Krekova, V. S. Shamanaev, “Laser sensing of a subsurface oceanic layer. I. Effect of atmosphere and wind-driven sea waves,” Appl. Opt. 37, 1589–1595 (1998).
[CrossRef]

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. V. Samokhvalov, S. V. Samoilova, “On laser sounding of clouds and underlying surface from space,” Atmos. Opt. 1, 93–99 (1988).

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. A. Razenkov, “Noise-proof inversion of lidar equation,” Opt. Lett. 12, 13–15 (1987).
[CrossRef] [PubMed]

G. M. Krekov, M. M. Krekova, I. V. Samokhvalov, “Spaceborne lidar signals in stratus sounding,” Earth Res. Space 6, 77–83 (1986).

Krekova, M. M.

G. M. Krekov, M. M. Krekova, “Structure of spaceborne lidar signal reflected by upper-level clouds. II. Optically inhomogeneous clouds,” Atm. Oceanic Opt. 11, 51–54 (1998).

G. M. Krekov, M. M. Krekova, V. S. Shamanaev, “Laser sensing of a subsurface oceanic layer. I. Effect of atmosphere and wind-driven sea waves,” Appl. Opt. 37, 1589–1595 (1998).
[CrossRef]

S. V. Samoilova, Yu. S. Balin, M. M. Krekova, “Accounting for the effects of multiple scattering in reconstruction of optical parameters of clouds from spaceborne sounding data,” Atm. Oceanic Opt. 11, 55–60 (1998).

G. M. Krekov, M. M. Krekova, I. V. Samokhvalov, “Spaceborne lidar signals in stratus sounding,” Earth Res. Space 6, 77–83 (1986).

Liou, K.-N.

Yo. Takano, K.-N. Liou, “Solar radiation transfer in cirrus clouds. 1. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Marchuk, C. I.

C. I. Marchuk, G. M. Mikhailov, T. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, E. P. Elepov, “Monte Carlo algorithms for solving nonstationary problems on propagation of narrow light beams in the atmosphere and ocean,” in Monte-Carlo Methods in Atmospheric Optics, G. I. Marchuk, ed. (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

McCormic, M. P.

M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
[CrossRef]

Melfi, S. H.

M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
[CrossRef]

Menzies, R. T.

M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
[CrossRef]

Mikhailov, G. M.

C. I. Marchuk, G. M. Mikhailov, T. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, E. P. Elepov, “Monte Carlo algorithms for solving nonstationary problems on propagation of narrow light beams in the atmosphere and ocean,” in Monte-Carlo Methods in Atmospheric Optics, G. I. Marchuk, ed. (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

Moerl, P.

W. Renger, C. Kiemle, H.-G. Schreiber, M. Wirth, P. Moerl, “Airborne backscatter lidar measurements at 3 wavelengths during ELITE,” in ELITE-94, The European ‘LITE’ Correlative Measurement Campaign, P. Fletcher, F. Lodge, E. Attema, eds., esaWPP-107 (European Space Agency/European Space Telecommunication, Postbus 299 AG Noordwijk, The Netherlands, 1995), pp. 15–30.

Nazaraliev, T. A.

C. I. Marchuk, G. M. Mikhailov, T. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, E. P. Elepov, “Monte Carlo algorithms for solving nonstationary problems on propagation of narrow light beams in the atmosphere and ocean,” in Monte-Carlo Methods in Atmospheric Optics, G. I. Marchuk, ed. (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

Noormohammadian, M.

G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering of lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Beitr. Phys. Atmos. 70, 93–105 (1997).

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Oppel, U.

B. Kaul, Yu. Arshinov, D. Romashov, I. Samokhvalov, Ch. Werner, J. Streicher, H. Herrmann, U. Oppel, H. Krasting, Crystal Clouds (Spektr, Tomsk, Russia), Chap. 4, pp. 48–77 (1997).

M. Wiegner, U. Oppel, H. Krasting, W. Renger, Ch. Kiemle, M. Wirth, “Cirrus measurements from a spaceborne lidar: influence of multiple scattering,” in Advances in Atmospheric Remote Sensing with Lidar, Selected papers of the 18th International Laser Radar Conference, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1997), pp. 189–192.

Oppel, U. G.

G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering of lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Beitr. Phys. Atmos. 70, 93–105 (1997).

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Platt, C. M. R.

M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
[CrossRef]

Polonsky, I. N.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B 60, 345–353 (1995).
[CrossRef]

Quenzel, H.

Qiu Jinhuan, H. Quenzel, M. Wenger, Parameterized Multiple-Scatter Lidar Equation and Its Application (Institute of Atmospheric Optics, Tomsk, Russia, 1990), P. I, pp. 345–348.

Randall, D. A.

M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
[CrossRef]

Razenkov, I. A.

Reagan, J. A.

M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
[CrossRef]

Renger, W.

G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering of lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Beitr. Phys. Atmos. 70, 93–105 (1997).

W. Renger, C. Kiemle, H.-G. Schreiber, M. Wirth, P. Moerl, “Airborne backscatter lidar measurements at 3 wavelengths during ELITE,” in ELITE-94, The European ‘LITE’ Correlative Measurement Campaign, P. Fletcher, F. Lodge, E. Attema, eds., esaWPP-107 (European Space Agency/European Space Telecommunication, Postbus 299 AG Noordwijk, The Netherlands, 1995), pp. 15–30.

M. Wiegner, U. Oppel, H. Krasting, W. Renger, Ch. Kiemle, M. Wirth, “Cirrus measurements from a spaceborne lidar: influence of multiple scattering,” in Advances in Atmospheric Remote Sensing with Lidar, Selected papers of the 18th International Laser Radar Conference, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1997), pp. 189–192.

Romashov, D.

B. Kaul, Yu. Arshinov, D. Romashov, I. Samokhvalov, Ch. Werner, J. Streicher, H. Herrmann, U. Oppel, H. Krasting, Crystal Clouds (Spektr, Tomsk, Russia), Chap. 4, pp. 48–77 (1997).

Ruppersberg, G. H.

G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering of lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Beitr. Phys. Atmos. 70, 93–105 (1997).

Samoilova, S. V.

S. V. Samoilova, Yu. S. Balin, M. M. Krekova, “Accounting for the effects of multiple scattering in reconstruction of optical parameters of clouds from spaceborne sounding data,” Atm. Oceanic Opt. 11, 55–60 (1998).

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. V. Samokhvalov, S. V. Samoilova, “On laser sounding of clouds and underlying surface from space,” Atmos. Opt. 1, 93–99 (1988).

Samokhvalov, I.

B. Kaul, Yu. Arshinov, D. Romashov, I. Samokhvalov, Ch. Werner, J. Streicher, H. Herrmann, U. Oppel, H. Krasting, Crystal Clouds (Spektr, Tomsk, Russia), Chap. 4, pp. 48–77 (1997).

Samokhvalov, I. V.

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. V. Samokhvalov, S. V. Samoilova, “On laser sounding of clouds and underlying surface from space,” Atmos. Opt. 1, 93–99 (1988).

G. M. Krekov, M. M. Krekova, I. V. Samokhvalov, “Spaceborne lidar signals in stratus sounding,” Earth Res. Space 6, 77–83 (1986).

Yu. S. Balin, I. V. Samokhvalov, “Statistical characteristics of the back scattering vertical structure in the lower troposphere,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 19, 937–943 (1983).

I. V. Samokhvalov, “Double scattering approximation of lidar equation for inhomogeneous atmosphere,” Opt. Lett. 4, 12–14 (1979).
[CrossRef]

Schreiber, H.-G.

W. Renger, C. Kiemle, H.-G. Schreiber, M. Wirth, P. Moerl, “Airborne backscatter lidar measurements at 3 wavelengths during ELITE,” in ELITE-94, The European ‘LITE’ Correlative Measurement Campaign, P. Fletcher, F. Lodge, E. Attema, eds., esaWPP-107 (European Space Agency/European Space Telecommunication, Postbus 299 AG Noordwijk, The Netherlands, 1995), pp. 15–30.

Schwendimann, P.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Shamanaev, V. S.

Starkov, A. V.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

A. V. Starkov, C. Flesia, “Correction of spaceborne lidar signal for multiple scattering from high clouds,” in Nineteenth International Laser Radar Conference, U. N. Singh, S. Ismail, G. K. Schwemmer, eds., NASA/CP-1998-207671/PT 2 (NASA, Washington, D.C., 1998), pp. 967–969.

Streicher, J.

B. Kaul, Yu. Arshinov, D. Romashov, I. Samokhvalov, Ch. Werner, J. Streicher, H. Herrmann, U. Oppel, H. Krasting, Crystal Clouds (Spektr, Tomsk, Russia), Chap. 4, pp. 48–77 (1997).

Takano, Yo.

Yo. Takano, K.-N. Liou, “Solar radiation transfer in cirrus clouds. 1. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Tikhonov, A. N.

A. N. Tikhonov, V. A. Arsenin, Methods for Solution of Incorrect Problems (Nauka, Moscow, 1974).

Wenger, M.

Qiu Jinhuan, H. Quenzel, M. Wenger, Parameterized Multiple-Scatter Lidar Equation and Its Application (Institute of Atmospheric Optics, Tomsk, Russia, 1990), P. I, pp. 345–348.

Werner, Ch.

B. Kaul, Yu. Arshinov, D. Romashov, I. Samokhvalov, Ch. Werner, J. Streicher, H. Herrmann, U. Oppel, H. Krasting, Crystal Clouds (Spektr, Tomsk, Russia), Chap. 4, pp. 48–77 (1997).

Wiegner, M.

M. Wiegner, U. Oppel, H. Krasting, W. Renger, Ch. Kiemle, M. Wirth, “Cirrus measurements from a spaceborne lidar: influence of multiple scattering,” in Advances in Atmospheric Remote Sensing with Lidar, Selected papers of the 18th International Laser Radar Conference, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1997), pp. 189–192.

Winker, D. M.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
[CrossRef]

D. M. Winker, “Simulation and modeling of multiple scattering effects observed in LITE data,” in Advances in Atmospheric Remote Sensing with Lidar, Selected papers of the 18th International Laser Radar Conference, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1997), pp. 185–188.

Wirth, M.

M. Wiegner, U. Oppel, H. Krasting, W. Renger, Ch. Kiemle, M. Wirth, “Cirrus measurements from a spaceborne lidar: influence of multiple scattering,” in Advances in Atmospheric Remote Sensing with Lidar, Selected papers of the 18th International Laser Radar Conference, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1997), pp. 189–192.

W. Renger, C. Kiemle, H.-G. Schreiber, M. Wirth, P. Moerl, “Airborne backscatter lidar measurements at 3 wavelengths during ELITE,” in ELITE-94, The European ‘LITE’ Correlative Measurement Campaign, P. Fletcher, F. Lodge, E. Attema, eds., esaWPP-107 (European Space Agency/European Space Telecommunication, Postbus 299 AG Noordwijk, The Netherlands, 1995), pp. 15–30.

Zaccanti, G.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Zadde, G. O.

V. E. Zuev, G. O. Zadde, S. I. Kavkyanov, B. V. Kaul, “Interpretation of lidar return signals from the regions of large optical depths,” in Remote Sensing of the Atmosphere, V. Zuev, ed. (Nauka, Novosibirsk, Russia, 1978), pp. 60–68.

Zege, E. P.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B 60, 345–353 (1995).
[CrossRef]

Zuev, V. E.

V. E. Zuev, G. O. Zadde, S. I. Kavkyanov, B. V. Kaul, “Interpretation of lidar return signals from the regions of large optical depths,” in Remote Sensing of the Atmosphere, V. Zuev, ed. (Nauka, Novosibirsk, Russia, 1978), pp. 60–68.

Appl. Opt. (4)

Appl. Phys. B (2)

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

E. P. Zege, I. L. Katsev, I. N. Polonsky, “Analytical solution to LIDAR return signals from clouds with regard to multiple scattering,” Appl. Phys. B 60, 345–353 (1995).
[CrossRef]

Atm. Oceanic Opt. (2)

G. M. Krekov, M. M. Krekova, “Structure of spaceborne lidar signal reflected by upper-level clouds. II. Optically inhomogeneous clouds,” Atm. Oceanic Opt. 11, 51–54 (1998).

S. V. Samoilova, Yu. S. Balin, M. M. Krekova, “Accounting for the effects of multiple scattering in reconstruction of optical parameters of clouds from spaceborne sounding data,” Atm. Oceanic Opt. 11, 55–60 (1998).

Atmos. Opt. (1)

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. V. Samokhvalov, S. V. Samoilova, “On laser sounding of clouds and underlying surface from space,” Atmos. Opt. 1, 93–99 (1988).

Beitr. Phys. Atmos. (1)

G. H. Ruppersberg, M. Kerscher, M. Noormohammadian, U. G. Oppel, W. Renger, “The influence of multiple scattering of lidar returns by cirrus clouds and an effective inversion algorithm for the extinction coefficient,” Beitr. Phys. Atmos. 70, 93–105 (1997).

Bull. Am. Meteorol. Soc. (1)

M. P. McCormic, D. M. Winker, E. V. Browell, J. A. Coakley, C. S. Gargner, R. M. Hoff, G. S. Kent, S. H. Melfi, R. T. Menzies, C. M. R. Platt, D. A. Randall, J. A. Reagan, “Scientific investigations planned for the lidar in-space technology experiment (LITE),” Bull. Am. Meteorol. Soc. 74, 205–214 (1993).
[CrossRef]

Earth Res. Space (1)

G. M. Krekov, M. M. Krekova, I. V. Samokhvalov, “Spaceborne lidar signals in stratus sounding,” Earth Res. Space 6, 77–83 (1986).

Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana (1)

Yu. S. Balin, I. V. Samokhvalov, “Statistical characteristics of the back scattering vertical structure in the lower troposphere,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 19, 937–943 (1983).

J. Atmos. Sci. (1)

Yo. Takano, K.-N. Liou, “Solar radiation transfer in cirrus clouds. 1. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Opt. Lett. (2)

Other (10)

W. Renger, C. Kiemle, H.-G. Schreiber, M. Wirth, P. Moerl, “Airborne backscatter lidar measurements at 3 wavelengths during ELITE,” in ELITE-94, The European ‘LITE’ Correlative Measurement Campaign, P. Fletcher, F. Lodge, E. Attema, eds., esaWPP-107 (European Space Agency/European Space Telecommunication, Postbus 299 AG Noordwijk, The Netherlands, 1995), pp. 15–30.

C. I. Marchuk, G. M. Mikhailov, T. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, E. P. Elepov, “Monte Carlo algorithms for solving nonstationary problems on propagation of narrow light beams in the atmosphere and ocean,” in Monte-Carlo Methods in Atmospheric Optics, G. I. Marchuk, ed. (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

A. N. Tikhonov, V. A. Arsenin, Methods for Solution of Incorrect Problems (Nauka, Moscow, 1974).

D. M. Winker, “Simulation and modeling of multiple scattering effects observed in LITE data,” in Advances in Atmospheric Remote Sensing with Lidar, Selected papers of the 18th International Laser Radar Conference, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1997), pp. 185–188.

M. Wiegner, U. Oppel, H. Krasting, W. Renger, Ch. Kiemle, M. Wirth, “Cirrus measurements from a spaceborne lidar: influence of multiple scattering,” in Advances in Atmospheric Remote Sensing with Lidar, Selected papers of the 18th International Laser Radar Conference, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1997), pp. 189–192.

A. V. Starkov, C. Flesia, “Correction of spaceborne lidar signal for multiple scattering from high clouds,” in Nineteenth International Laser Radar Conference, U. N. Singh, S. Ismail, G. K. Schwemmer, eds., NASA/CP-1998-207671/PT 2 (NASA, Washington, D.C., 1998), pp. 967–969.

B. Kaul, Yu. Arshinov, D. Romashov, I. Samokhvalov, Ch. Werner, J. Streicher, H. Herrmann, U. Oppel, H. Krasting, Crystal Clouds (Spektr, Tomsk, Russia), Chap. 4, pp. 48–77 (1997).

V. E. Zuev, G. O. Zadde, S. I. Kavkyanov, B. V. Kaul, “Interpretation of lidar return signals from the regions of large optical depths,” in Remote Sensing of the Atmosphere, V. Zuev, ed. (Nauka, Novosibirsk, Russia, 1978), pp. 60–68.

Qiu Jinhuan, H. Quenzel, M. Wenger, Parameterized Multiple-Scatter Lidar Equation and Its Application (Institute of Atmospheric Optics, Tomsk, Russia, 1990), P. I, pp. 345–348.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

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Figures (9)

Fig. 1
Fig. 1

Ratio of signals that are due to the first and the second orders of MS δ(z) for water-droplet (Model1) and cirrus (Model2) clouds. Curves 1, model profiles of the scattering coefficient; curves 2, δ(z) that correspond to these profiles.

Fig. 2
Fig. 2

Comparison of the methods of calculating returns for a spaceborne lidar by use of low orders of MS. (a) Monte Carlo method. (b) Method using an estimate of MS distribution: Σ, total signal; curves 1–5, signals that are due to first through fifth orders of scattering. Model profiles β(z) correspond to those in Fig. 1.

Fig. 3
Fig. 3

Comparison of the methods of calculating returns for an airborne lidar by use of low orders of MS. (a) Monte Carlo method: left, data from Ref. 4; right, our calculations. (b) Method using an estimate of MS distribution: Σ, total signal; curves 1–5, signals that are due to first through fifth orders of scattering.

Fig. 4
Fig. 4

Comparison among methods of reconstructing scattering coefficients from the returns calculated by the Monte Carlo method: 1, the exact profile of β(z); 2, the profile reconstructed without MS taken into account; 3, the profile obtained after 10 iterations at a priori (a) known and (b) unknown τε [profiles P(z) correspond to curves from Fig. 2(a)].

Fig. 5
Fig. 5

Retrieval of scattering coefficient values of cirrus clouds from data of synchronously flown airborne and spaceborne lidars on 14 September 1994 (orbit number 79): (a) lidar A returns, (b) lidar L returns, (c) scattering coefficient retrieved from A data, (d) scattering coefficient retrieved from L data. Here and in Figs. 6, 8, and 9, rel. un. means relative units.

Fig. 6
Fig. 6

Retrieval of scattering coefficient values of altostratus clouds from data of synchronously flown airborne and spaceborne lidars on 14 September 1994 (orbit number 79): (a) lidar A returns, (b) lidar L returns, (c) scattering coefficient retrieved from A data, (d) scattering coefficient retrieved from L data.

Fig. 7
Fig. 7

Comparison of optical parameters of different clouds obtained by use of data from the spaceborne and airborne lidars.

Fig. 8
Fig. 8

Comparison of scattering coefficients of cirrus clouds reconstructed by different methods for the regions shown in Figs. 5 and 7: (a) S(z) profiles, A data (curves 1) and L data (curves 2). (b) The corresponding β(z) profiles for A (curves 1) and L (curves 2) present the data obtained with MS taken into account after the fifth iteration and (curves 3) without accounting for MS.

Fig. 9
Fig. 9

Comparison of the scattering coefficients of altostratus clouds reconstructed by different methods for the regions shown in Figs. 6 and 7: (a) S(z) profiles, A data (curves 1) and L data (curves 2). (b) The corresponding β(z) profiles for A (curves 1) and L (curves 2) present the data obtained with for MS taken into account after the fifth iteration and (curves 3) without accounting for MS.

Equations (22)

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

P1z=Aγπzβzexp-2 z0z βzdzz2=AγπzβzT2z0, z/z2,
P2z=δzP1z,
δz=2πz2βz, πφxsinφR βx, φβx, π-φdxdφ,
R=Rz, x, φ=z2-2z-xx sin2φ/2
x=xz, x, φ=x+zz-xz-x sin2φ/2
δz=2πz2γπ1βz0α1 Γφz0zβxβxRdxdφ+1βzα1α2 Γφx1zβxβxRdxdφ+1βzα2α3 Γφx2zβxβxRdxdφ+α3π Γφz0zβxx2dxdφ,
Γφ=γφγπ-φsinφ, α1=2 arctanz tanφ0/2z-z0, α2=2 arctan2z-z01+cosφ0z0 sinφ0, α3=π-arccosz-z0z-z0+2Δz, x1=x1φ=z1-tanφ0/2cotφ/2, x2=x2φ=z1-z-z0z0cotφ/2;
P˜iz=δixP˜i-1z, δiz=δzi-1,
P˜Σz=i=1n P˜iz=P1zexpδz=P1zΔP˜z.
βz=P˜1zz22εΨz0, z*+2Ψz, z*,
P˜1z=P˜1βz, γφ, z=Pz/ΔP˜z, Ψz1, z2=z1z2 P˜1zz2dz;
ε=ετε, z*=1exp2τz0, z*-1
β¯j=βj-1;
P1,j=P˜1β¯j, γ;
βj=βετ*, P1,j.
Φβεz=z0zmaxβεz-βcz2dz,
Φβz, τε=βmaxτεj,k-βmaxτεj,k-12,
τεj,0=0.5zmax-zeβmax=0.5zmax-zeP˜1,jzeze2zezmax P˜1,jzz2dz,
Pz=P1zMz,
βz=P1zMzz22ε z0zmax P1zMzz2dz+2 zzmax P1zMzz2dz.
βz=P1zMzz22εMz1z0zmax P1zz2dz+2Mz2zzmax P1zz2dz
MzMz2βzβ0zMzMz1, z0z MzdzMz2τzτ0zz0z MzdzMz11.

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