Abstract

The possibilities of cloud characteristics retrieval with multiple-field-of-view Raman lidar are considered. It has been shown that the Raman lidar return is sensitive to two cloud characteristics; the scattering coefficient and the effective droplet size. This sensitivity is studied and the optimal receiver fields-of-view (FOVs) for cloud sounding are recommended. The optimal FOV values are estimated to be approximately R/H (R, the collecting optics radius, H, the cloud altitude) to measure the scattering coefficient profiles, and 0.01z/H for the droplet size measurements (z, the cloud thickness). The algorithm based on the iterative scheme and singular value decomposition as a regularization procedure is presented and verified using computer simulation. The recommendations for profile retrieval with variable altitude resolution are given.

© 2007 Optical Society of America

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References

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  1. A. Arking, "The radiative effects of clouds and their impact on climate," Bull. Am. Meteorol. Soc. 72, 795-813 (1991).
    [CrossRef]
  2. Climate Change Science: An Analysis of Some Key Questions (National Academy Press, 2001) (http://books.nap.edu/).
  3. K. Sassen, "Polarization lidar for identifying indirect aerosol effects on clouds," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 184-186.
  4. D. P. Donovan and A. C. A. P. van Lammeren, "Cloud effective particle size and water content profile retrievals using combined lidar and radar observation. Part 1," J. Geophys. Res. 106, 27425-27448 (2001).
    [CrossRef]
  5. H. Sauvageot and J. Omar, "Radar reflectivity of cumulus clouds," J. Geophys. Res. C: Oceans Atmos. 4, 264-272 (1987).
  6. I. R. Paluch, C. A. Knight, and L. J. Miller, "Cloud liquid water and radar reflectivity of nonprecipitating cumulus clouds," J. Atmos. Sci. 53, 1587-1603 (1996).
    [CrossRef]
  7. E. J. O'Connor, A. J. Illingworth, and R. J. Hogan, "Remote sensing of stratocumulus using radar/lidar synergy," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 178-180.
  8. A. A. Kokhanovskii and E. P. Zege, "Parametrization of local optical characteristics of cloudy media," Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 33, 190-198 (1997).
  9. A. Ansmann, M. Reibesell, and C. Weitkamp, "Measurement of atmospheric aerosol extinction profiles with Raman lidar," Opt. Lett. 15, 746-748 (1990).
    [CrossRef] [PubMed]
  10. J. Reichardt, U. Wandinger, M. Serwazi, and C. Weitkamp, "Combined Raman lidar for aerosol, ozone, and moisture measurements," Opt. Eng. 35, 1457-1465 (1996).
    [CrossRef]
  11. L. Bissonnette and D. Hutt, "Multiple scattering lidar," Appl. Opt. 29, 5045-5046 (1990).
    [CrossRef] [PubMed]
  12. G. Roy, L. Bissonnette, C. Bastille, and G. Vallee, "Estimation of cloud droplet-size density distribution from multiple-field-of-view lidar returns," Opt. Eng. 36, 3404-3415 (1997).
    [CrossRef]
  13. L. R. Bissonnette, G. Roy, and N. Roy, "Multiple-scattering-based lidar retrieval: method and results of cloud probings," Appl. Opt. 44, 5565-5581 (2005).
    [CrossRef] [PubMed]
  14. L. R. Bissonnette, G. Roy, and G. Tremblay, "Lidar-based characterization of the geometry and structure of water clouds," J. Geophys. Res. C: Oceans Atmos. 24, 1364-1376 (2007).
  15. I. Polonskii, E. Zege, and I. L. Katsev, "Lidar sounding of warm clouds and determination of their microstructure parameters," Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 37, 624-632 (2001).
  16. I. Veselovskii, M. Korenskii, V. Griaznov, D. N. Whiteman, M. McGill, G. Roy, and L. Bissonnette, "Information content of data measured with a multiple-field-of-view lidar," Appl. Opt. 45, 6839-6848 (2006).
    [CrossRef] [PubMed]
  17. A. Malinka and E. Zege, "Using multiple scattering in Raman lidar sounding of warm clouds," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 297-299.
  18. A. Malinka, "Raman lidar remote sensing of geophysical media," in Light Scattering Reviews 2: Remote sensing and inverse problems, A. Kokhanovsky, ed. (Springer, 2007), pp. 125-155.
  19. A. V. Malinka and E. P. Zege, "Analytical modeling of Raman lidar return, including multiple scattering," Appl. Opt. 42, 1075-1081 (2003).
    [CrossRef] [PubMed]
  20. E. Zege, A. Ivanov, and I. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, 1991).
    [CrossRef]
  21. A. Kokhanovsky, Optics of Light Scattering Media: Problems and Solutions (Springer-Verlag, 2001).
  22. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).
  23. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, 1969).
  24. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing. 2nd ed. (Cambridge U. Press, 1992).

2007 (2)

L. R. Bissonnette, G. Roy, and G. Tremblay, "Lidar-based characterization of the geometry and structure of water clouds," J. Geophys. Res. C: Oceans Atmos. 24, 1364-1376 (2007).

A. Malinka, "Raman lidar remote sensing of geophysical media," in Light Scattering Reviews 2: Remote sensing and inverse problems, A. Kokhanovsky, ed. (Springer, 2007), pp. 125-155.

2006 (1)

2005 (1)

2003 (4)

A. Malinka and E. Zege, "Using multiple scattering in Raman lidar sounding of warm clouds," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 297-299.

A. V. Malinka and E. P. Zege, "Analytical modeling of Raman lidar return, including multiple scattering," Appl. Opt. 42, 1075-1081 (2003).
[CrossRef] [PubMed]

K. Sassen, "Polarization lidar for identifying indirect aerosol effects on clouds," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 184-186.

E. J. O'Connor, A. J. Illingworth, and R. J. Hogan, "Remote sensing of stratocumulus using radar/lidar synergy," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 178-180.

2001 (4)

D. P. Donovan and A. C. A. P. van Lammeren, "Cloud effective particle size and water content profile retrievals using combined lidar and radar observation. Part 1," J. Geophys. Res. 106, 27425-27448 (2001).
[CrossRef]

Climate Change Science: An Analysis of Some Key Questions (National Academy Press, 2001) (http://books.nap.edu/).

I. Polonskii, E. Zege, and I. L. Katsev, "Lidar sounding of warm clouds and determination of their microstructure parameters," Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 37, 624-632 (2001).

A. Kokhanovsky, Optics of Light Scattering Media: Problems and Solutions (Springer-Verlag, 2001).

1997 (2)

G. Roy, L. Bissonnette, C. Bastille, and G. Vallee, "Estimation of cloud droplet-size density distribution from multiple-field-of-view lidar returns," Opt. Eng. 36, 3404-3415 (1997).
[CrossRef]

A. A. Kokhanovskii and E. P. Zege, "Parametrization of local optical characteristics of cloudy media," Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 33, 190-198 (1997).

1996 (2)

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

I. R. Paluch, C. A. Knight, and L. J. Miller, "Cloud liquid water and radar reflectivity of nonprecipitating cumulus clouds," J. Atmos. Sci. 53, 1587-1603 (1996).
[CrossRef]

1992 (1)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing. 2nd ed. (Cambridge U. Press, 1992).

1991 (2)

E. Zege, A. Ivanov, and I. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, 1991).
[CrossRef]

A. Arking, "The radiative effects of clouds and their impact on climate," Bull. Am. Meteorol. Soc. 72, 795-813 (1991).
[CrossRef]

1990 (2)

1987 (1)

H. Sauvageot and J. Omar, "Radar reflectivity of cumulus clouds," J. Geophys. Res. C: Oceans Atmos. 4, 264-272 (1987).

1969 (1)

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

1957 (1)

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

Ansmann, A.

Arking, A.

A. Arking, "The radiative effects of clouds and their impact on climate," Bull. Am. Meteorol. Soc. 72, 795-813 (1991).
[CrossRef]

Bastille, C.

G. Roy, L. Bissonnette, C. Bastille, and G. Vallee, "Estimation of cloud droplet-size density distribution from multiple-field-of-view lidar returns," Opt. Eng. 36, 3404-3415 (1997).
[CrossRef]

Bissonnette, L.

Bissonnette, L. R.

L. R. Bissonnette, G. Roy, and G. Tremblay, "Lidar-based characterization of the geometry and structure of water clouds," J. Geophys. Res. C: Oceans Atmos. 24, 1364-1376 (2007).

L. R. Bissonnette, G. Roy, and N. Roy, "Multiple-scattering-based lidar retrieval: method and results of cloud probings," Appl. Opt. 44, 5565-5581 (2005).
[CrossRef] [PubMed]

Deirmendjian, D.

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

Donovan, D. P.

D. P. Donovan and A. C. A. P. van Lammeren, "Cloud effective particle size and water content profile retrievals using combined lidar and radar observation. Part 1," J. Geophys. Res. 106, 27425-27448 (2001).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing. 2nd ed. (Cambridge U. Press, 1992).

Griaznov, V.

Hogan, R. J.

E. J. O'Connor, A. J. Illingworth, and R. J. Hogan, "Remote sensing of stratocumulus using radar/lidar synergy," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 178-180.

Hutt, D.

Illingworth, A. J.

E. J. O'Connor, A. J. Illingworth, and R. J. Hogan, "Remote sensing of stratocumulus using radar/lidar synergy," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 178-180.

Ivanov, A.

E. Zege, A. Ivanov, and I. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, 1991).
[CrossRef]

Katsev, I.

E. Zege, A. Ivanov, and I. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, 1991).
[CrossRef]

Katsev, I. L.

I. Polonskii, E. Zege, and I. L. Katsev, "Lidar sounding of warm clouds and determination of their microstructure parameters," Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 37, 624-632 (2001).

Knight, C. A.

I. R. Paluch, C. A. Knight, and L. J. Miller, "Cloud liquid water and radar reflectivity of nonprecipitating cumulus clouds," J. Atmos. Sci. 53, 1587-1603 (1996).
[CrossRef]

Kokhanovskii, A. A.

A. A. Kokhanovskii and E. P. Zege, "Parametrization of local optical characteristics of cloudy media," Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 33, 190-198 (1997).

Kokhanovsky, A.

A. Kokhanovsky, Optics of Light Scattering Media: Problems and Solutions (Springer-Verlag, 2001).

Korenskii, M.

Malinka, A.

A. Malinka, "Raman lidar remote sensing of geophysical media," in Light Scattering Reviews 2: Remote sensing and inverse problems, A. Kokhanovsky, ed. (Springer, 2007), pp. 125-155.

A. Malinka and E. Zege, "Using multiple scattering in Raman lidar sounding of warm clouds," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 297-299.

Malinka, A. V.

McGill, M.

Miller, L. J.

I. R. Paluch, C. A. Knight, and L. J. Miller, "Cloud liquid water and radar reflectivity of nonprecipitating cumulus clouds," J. Atmos. Sci. 53, 1587-1603 (1996).
[CrossRef]

O'Connor, E. J.

E. J. O'Connor, A. J. Illingworth, and R. J. Hogan, "Remote sensing of stratocumulus using radar/lidar synergy," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 178-180.

Omar, J.

H. Sauvageot and J. Omar, "Radar reflectivity of cumulus clouds," J. Geophys. Res. C: Oceans Atmos. 4, 264-272 (1987).

Paluch, I. R.

I. R. Paluch, C. A. Knight, and L. J. Miller, "Cloud liquid water and radar reflectivity of nonprecipitating cumulus clouds," J. Atmos. Sci. 53, 1587-1603 (1996).
[CrossRef]

Polonskii, I.

I. Polonskii, E. Zege, and I. L. Katsev, "Lidar sounding of warm clouds and determination of their microstructure parameters," Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 37, 624-632 (2001).

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing. 2nd ed. (Cambridge U. Press, 1992).

Reibesell, M.

Reichardt, J.

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

Roy, G.

L. R. Bissonnette, G. Roy, and G. Tremblay, "Lidar-based characterization of the geometry and structure of water clouds," J. Geophys. Res. C: Oceans Atmos. 24, 1364-1376 (2007).

I. Veselovskii, M. Korenskii, V. Griaznov, D. N. Whiteman, M. McGill, G. Roy, and L. Bissonnette, "Information content of data measured with a multiple-field-of-view lidar," Appl. Opt. 45, 6839-6848 (2006).
[CrossRef] [PubMed]

L. R. Bissonnette, G. Roy, and N. Roy, "Multiple-scattering-based lidar retrieval: method and results of cloud probings," Appl. Opt. 44, 5565-5581 (2005).
[CrossRef] [PubMed]

G. Roy, L. Bissonnette, C. Bastille, and G. Vallee, "Estimation of cloud droplet-size density distribution from multiple-field-of-view lidar returns," Opt. Eng. 36, 3404-3415 (1997).
[CrossRef]

Roy, N.

Sassen, K.

K. Sassen, "Polarization lidar for identifying indirect aerosol effects on clouds," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 184-186.

Sauvageot, H.

H. Sauvageot and J. Omar, "Radar reflectivity of cumulus clouds," J. Geophys. Res. C: Oceans Atmos. 4, 264-272 (1987).

Serwazi, M.

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

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing. 2nd ed. (Cambridge U. Press, 1992).

Tremblay, G.

L. R. Bissonnette, G. Roy, and G. Tremblay, "Lidar-based characterization of the geometry and structure of water clouds," J. Geophys. Res. C: Oceans Atmos. 24, 1364-1376 (2007).

Vallee, G.

G. Roy, L. Bissonnette, C. Bastille, and G. Vallee, "Estimation of cloud droplet-size density distribution from multiple-field-of-view lidar returns," Opt. Eng. 36, 3404-3415 (1997).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

van Lammeren, A. C. A. P.

D. P. Donovan and A. C. A. P. van Lammeren, "Cloud effective particle size and water content profile retrievals using combined lidar and radar observation. Part 1," J. Geophys. Res. 106, 27425-27448 (2001).
[CrossRef]

Veselovskii, I.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing. 2nd ed. (Cambridge U. Press, 1992).

Wandinger, U.

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

Weitkamp, C.

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

A. Ansmann, M. Reibesell, and C. Weitkamp, "Measurement of atmospheric aerosol extinction profiles with Raman lidar," Opt. Lett. 15, 746-748 (1990).
[CrossRef] [PubMed]

Whiteman, D. N.

Zege, E.

A. Malinka and E. Zege, "Using multiple scattering in Raman lidar sounding of warm clouds," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 297-299.

I. Polonskii, E. Zege, and I. L. Katsev, "Lidar sounding of warm clouds and determination of their microstructure parameters," Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 37, 624-632 (2001).

E. Zege, A. Ivanov, and I. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, 1991).
[CrossRef]

Zege, E. P.

A. V. Malinka and E. P. Zege, "Analytical modeling of Raman lidar return, including multiple scattering," Appl. Opt. 42, 1075-1081 (2003).
[CrossRef] [PubMed]

A. A. Kokhanovskii and E. P. Zege, "Parametrization of local optical characteristics of cloudy media," Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 33, 190-198 (1997).

Appl. Opt. (4)

Bull. Am. Meteorol. Soc. (1)

A. Arking, "The radiative effects of clouds and their impact on climate," Bull. Am. Meteorol. Soc. 72, 795-813 (1991).
[CrossRef]

Izv. Acad. Sci. USSR Atmos. Oceanic Phys. (2)

A. A. Kokhanovskii and E. P. Zege, "Parametrization of local optical characteristics of cloudy media," Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 33, 190-198 (1997).

I. Polonskii, E. Zege, and I. L. Katsev, "Lidar sounding of warm clouds and determination of their microstructure parameters," Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 37, 624-632 (2001).

J. Atmos. Sci. (1)

I. R. Paluch, C. A. Knight, and L. J. Miller, "Cloud liquid water and radar reflectivity of nonprecipitating cumulus clouds," J. Atmos. Sci. 53, 1587-1603 (1996).
[CrossRef]

J. Geophys. Res. (3)

D. P. Donovan and A. C. A. P. van Lammeren, "Cloud effective particle size and water content profile retrievals using combined lidar and radar observation. Part 1," J. Geophys. Res. 106, 27425-27448 (2001).
[CrossRef]

H. Sauvageot and J. Omar, "Radar reflectivity of cumulus clouds," J. Geophys. Res. C: Oceans Atmos. 4, 264-272 (1987).

L. R. Bissonnette, G. Roy, and G. Tremblay, "Lidar-based characterization of the geometry and structure of water clouds," J. Geophys. Res. C: Oceans Atmos. 24, 1364-1376 (2007).

Opt. Eng. (2)

G. Roy, L. Bissonnette, C. Bastille, and G. Vallee, "Estimation of cloud droplet-size density distribution from multiple-field-of-view lidar returns," Opt. Eng. 36, 3404-3415 (1997).
[CrossRef]

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

Opt. Lett. (1)

Other (10)

E. J. O'Connor, A. J. Illingworth, and R. J. Hogan, "Remote sensing of stratocumulus using radar/lidar synergy," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 178-180.

Climate Change Science: An Analysis of Some Key Questions (National Academy Press, 2001) (http://books.nap.edu/).

K. Sassen, "Polarization lidar for identifying indirect aerosol effects on clouds," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 184-186.

A. Malinka and E. Zege, "Using multiple scattering in Raman lidar sounding of warm clouds," in Proceedings of the 6th International Symposium on Tropospheric Profiling: Needs and Technologies (ISTP, 2003), U. Wandinger, R. Engelmann, and K. Schmieder, eds. (Institute for Tropospheric Research, 2003), pp. 297-299.

A. Malinka, "Raman lidar remote sensing of geophysical media," in Light Scattering Reviews 2: Remote sensing and inverse problems, A. Kokhanovsky, ed. (Springer, 2007), pp. 125-155.

E. Zege, A. Ivanov, and I. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, 1991).
[CrossRef]

A. Kokhanovsky, Optics of Light Scattering Media: Problems and Solutions (Springer-Verlag, 2001).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

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

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing. 2nd ed. (Cambridge U. Press, 1992).

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Figures (7)

Fig. 1
Fig. 1

Sensitivity of the signal to drop size in the ith layer: (a) two-layered cloud and (b) ten-layered cloud. The cloud altitude is 2000 m, the cloud thickness is 400 m, the source divergence and the receiver FOV are 0.05 and 0.5   mrad , respectively, the source and receiver radii are 0.1 and 0.5 m, respectively, the scattering coefficient is 0.01 m 1 , ρ = 100 .

Fig. 2
Fig. 2

(a) Single scattering, multiple scattering, and total signal and (b) relative contribution of single scattering versus FOV. Vertical lines, the values of γ 1 and γ 2 ; sounding depth z = 100 ; other parameters are the same as in Fig. 1.

Fig. 3
Fig. 3

Signal sensitivity to the (a) extinction coefficient and to the (b) drop size. The abscissa is defined with Eq. (30). The optical depths are equal to 1, 2, 3, and 4.

Fig. 4
Fig. 4

Top plot—signals, measured (•) and calculated with retrieved profiles ( ) for the receiver FOVs of 0.25 and 1 mrad. Middle and bottom plots—the scattering coefficient and the drop size profiles, respectively, true (dashes) and retrieved (solid) values. Receiver spatial resolution is 15 m. The true cloud is homogeneous, the retrieved cloud profile is considered as five layered.

Fig. 5
Fig. 5

Same as Fig. 4, but the retrieved cloud profile is considered as 20 layered.

Fig. 6
Fig. 6

Same as Fig. 5, but the true cloud is thin.

Fig. 7
Fig. 7

Same as Fig. 5, but the true cloud is thick and has a complex profile. Retrieval is performed with variable sublayer thickness.

Equations (53)

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

z = c t 2 H ,
F ( γ r , z ) = C max ν d ν 2 π φ e f f ( ν ) exp ( 0 z [ ε e f f ( ξ ) σ e f f ( ξ ) P e f f f ( ξ , ν ( z ξ ) ) ] d ξ ) ,
φ e f f ( ν ) = 1 ( z + H ) 2 2 J 1 ( ν R s ) ν R s 2 J 1 [ ν ( z + H ) γ s ] ν γ s × 2 π R r J 1 ( ν R r ) ν 2 π γ r J 1 [ ν ( z + H ) γ r ] ν ,
ε e f f ( z ) = ε ( λ 0 , z ) + ε ( λ R , z ) ,
σ e f f ( z ) = σ ( λ 0 , z ) + σ ( λ R , z ) ,
P e f f f ( p ) = 1 2 0 P e f f f ( θ ) J 0 ( p θ ) θ d θ ,
P e f f f ( z , θ ) = σ ( λ 0 , z ) P f ( λ 0 , z , θ ) + σ ( λ R , z ) P f ( λ R , z , θ ) σ ( λ 0 , z ) + σ ( λ R , z ) .
ε ( λ 0 , z ) = ε ( λ R , z ) = σ ( λ 0 , z ) = σ ( λ R , z ) = σ ( z ) .
ρ ( z ) = π r 32 ( z ) ( 1 λ 0 + 1 λ R ) .
P e f f f ( z , θ ) = P f ( ρ ( z ) , θ ) ,
P e f f f ( z , p ) = P f ( ρ ( z ) , p ) .
F ( γ r , z ) = C max ν d ν 2 π φ e f f ( ν ) exp ( 2 0 z σ ( ξ ) × [ 1 P f ( ρ ( ξ ) , ν ( z ξ ) ) ] d ξ ) .
P ( ρ , θ ) = 1 2 ( ρ 2 P D ( ρ θ ) + P G O ( θ ) ) .
d p d r = r μ μ ! ( r 32 μ + 3 ) μ 1   exp ( μ + 3 r 32 r ) ,
P ( ρ , p ) = 1 2 ( P D ( p / ρ ) + P GO ( p ) ) .
F ( γ r , z ) = C max ν d ν 2 π φ e f f ( ν ) exp ( 2 τ + i = 1 N σ i z i - 1 z i [ P D ( z ξ ρ i ν ) + P GO ( ( z ξ ) ν ) ] d ξ ) ,
P D ( p < 0 ) = P GO ( p < 0 ) 0.
F ( γ r , z ) = C max ν d ν 2 π φ e f f ( ν ) exp ( 2 τ ) G D G GO ,
G D = exp ( i = 1 N σ i ρ i ν [ R D ( Δ z i ρ i ν ) R D ( Δ z i 1 ρ i ν ) ] ) ,
G GO = exp ( i = 1 N σ i ν [ R GO ( Δ z i ν ) R GO ( Δ z i 1 ν ) ] ) ,
R D ( p ) = 0 p P D ( x ) d x ,          R D ( p < 0 ) 0 ,
R GO ( p ) = 0 p P GO ( x ) d x , R GO ( p < 0 ) 0 ,
Δ z i = z z i ,
C i ρ ( γ r , z ) = ρ i F ( γ r , z ) F ( γ r , z ) ρ i .
C i ρ ( γ r , z ) = C max F ( γ r , z ) ν d ν 2 π φ e f f ( ν ) exp ( 2 τ ) ρ i G D ρ i G GO ,
ρ i G D G D ρ i = σ i ρ i ν [ R D ( Δ z i ρ i ν ) R D ( Δ z i 1 ρ i ν ) ] + σ i [ Δ z i P D ( Δ z i ρ i ν ) Δ z i 1 P D ( Δ z i 1 ρ i ν ) ] .
C i σ ( γ r , z ) = σ i F ( γ r , z ) F ( γ r , z ) σ i .
C i σ ( γ r , z ) = C max F ( γ r , z ) ν d ν 2 π φ e f f ( ν ) σ i D ,
D = 2 ( z i z i 1 ) ρ i ν [ R D ( Δ z i ρ i ν ) R D ( Δ z i 1 ρ i ν ) ] 1 ν [ R GO ( Δ z i ν ) R GO ( Δ z i 1 ν ) ] [ exp ( 2 τ ) G D G GO ] .
γ 1 = max { γ s , R r z + H , R s z + H } ,
γ 2 = γ s + R r z + H + R s z + H .
γ 1 < R r / H < γ 2 .
x = ρ γ r ( z + H ) z ,
γ r 0.01 z / H .
X = ( σ i , ρ i , C max ) .
F m = [ F m ( γ 1 , z n ) , F m ( γ 2 , z n ) ] .
F m = F ( X ) .
Δ F F = Δ X X C ,
C i n = [ C i σ ( γ 1 , z n ) C i σ ( γ 2 , z n ) C i ρ ( γ 1 , z n ) C i ρ ( γ 2 , z n ) 1 1 ] ,
X k + 1 = X k ( 1 + log ( F m / F ) C 1 ) ,
err X = 1 λ min 2 N + 1 err F ,
λ c r = 1 2 N + 1 ,
err i n i err .
err X 2 = δ x · δ x ˜ ¯ L ,
δ x i = Δ X i X i ,
δ f = δ x C ,
δ x = δ f C ˜ ( C C ˜ ) 1 .
e r r X 2 = 1 L δ f C ˜ ( C C ˜ ) 2 C δ f ˜ ¯ .
e r r X 2 = 1 L S p ( δ f ˜ δ f ¯ C ˜ ( C C ˜ ) 2 C ) ,
δ f k 2 ¯ = err F 2 .
err X 2 = err F 2 L S p ( ( C C ˜ ) 1 ) = err F 2 L k 1 λ k 2 ,
k 1 λ k 2 1 λ min 2 .
err X = err F λ min L .

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