Abstract

Depth profiles and polarization characteristics of airborne lidar return signals have been calculated by the Monte Carlo method. We analyze some peculiarities of depth profiles of lidar return signals for a rough air–water interface. The distorting effect of the atmosphere on the lidar return signal structure is evaluated as a function of the geometry of the observations. Calculated results are compared with the data of airborne lidar measurements for λ = 0.53 μm.

© 1998 Optical Society of America

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  1. M. F. Penny, R. H. Abbot, D. M. Phillips, B. Billard, D. Rees, D. W. Faulkner, D. G. Cartwright, B. Woodcock, G. J. Perry, P. J. Wilsen, T. R. Adams, J. Richards, “Airborne laser hydrography in Australia,” Appl. Opt. 25, 2046–2058 (1986).
    [CrossRef] [PubMed]
  2. B. Billard, “Estimation of mean sea surface reference in the WRELADS airborne depth sounder,” Appl. Opt. 25, 2067–2073 (1986).
    [CrossRef] [PubMed]
  3. F. E. Hoge, C. W. Wright, C. W. Krabill, R. R. Buntzen, G. D. Gilbert, R. N. Swift, J. K. Yungel, E. Berry, “Airborne lidar detection of subsurface oceanic scattering layers,” Appl. Opt. 27, 3969–3977 (1988).
    [CrossRef] [PubMed]
  4. I. E. Penner, I. V. Samokhvalov, V. S. Shamanaev, “Optical sensing of the marine frontal zone,” Atmos. Opt. 1, 60–66 (1988).
  5. V. M. Orlov, I. V. Samokhvalov, M. L. Belov, V. S. Shamanaev, V. M. Klimkin, A. V. Belokhvostikov, I. E. Penner, R. G. Safin, A. B. Yudovskii, Remote Control of the Upper Layer of the Ocean (Nauka, Novosibirsk, Russian Federation, 1991).
  6. H. R. Gordon, “Ship perturbation of irradiance measurements at sea. I. Monte Carlo simulations,” Appl. Opt. 24, 4172–4182 (1985).
    [CrossRef] [PubMed]
  7. M. M. Krekova, G. M. Krekov, I. V. Samokhvalov, V. S. Shamanaev, “Numerical evaluation of the possibilities of remote laser sensing of fish schools,” Appl. Opt. 33, 5715–5720 (1994).
    [CrossRef] [PubMed]
  8. H. R. Gordon, “Interpretation of airborne oceanic lidar effects of multiple scattering,” Appl. Opt. 21, 2996–3002 (1982).
    [CrossRef] [PubMed]
  9. G. I. Marchuk, G. M. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, B. S. Elexov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, Berlin, 1980), Chap. 5.
    [CrossRef]
  10. G. M. Krekov, G. A. Mikhailov, B. A. Kargin, “On algorithms for statistical simulation of diffusion in a medium with a reflecting surface,” Izv. Vyssh. Uchebn. Zaved. Fiz. 9, 99–105 (1968).
  11. G. M. Krekov, G. A. Mikhailov, B. A. Kargin, “On Monte Carlo algorithms for solving problems of the theory of the narrow light beam propagation,” Izv. Vyssh. Uchebn. Zaved. Fiz. 5, 55–59 (1968).
  12. A. S. Monin, V. P. Krasnitskii, Phenomena on the Ocean Surface (Gidrometeoizdat, Leningrad, 1985).
  13. C. Cox, W. Munk, “Measurements of the roughness of the sea surface from photographs of the Sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
    [CrossRef]
  14. B. A. Kargin, S. M. Prigarin, “Simulation of the sea surface roughness and study of its optical properties by the Monte Carlo method,” Atmos. Oceanic Opt. 5, 186–190 (1992).
  15. O. E. Dzhetybaev, B. A. Kargin, “Application of statistical simulation to a solution of problems of optical sensing of the atmosphere–ocean system,” in Current Problems of Applied Mathematics and Mathematical Simulation, A. S. Alekseev, ed. (Nauka, Novosibirsk, Russian Federation, 1982), pp. 83–91.
  16. V. E. Zuev, G. M. Krekov, Optical Models of the Atmosphere (Gigrometeoizdat, Leningrad, 1986).
  17. K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).
  18. O. V. Kopelevich, K. S. Shifrin, “Modern concept of the optical properties of sea water,” in Atmospheric and Ocean Optics (Nauka, Moscow, 1981), pp. 4–49.
  19. V. I. Man’kovskii, “Extreme phase functions of light scattering by sea water,” Mar. Hydrophys. Invest. 3, 100–108 (1973).
  20. O. V. Kopelevich, “Experimental data on the optical properties of sea water in ocean optics,” in Ocean Optics, A. S. Monin, ed. (Nauka, Moscow, 1983), Vol. 1, pp. 166–201.
  21. V. E. Zuev, G. M. Krekov, M. M. Krekova, “Theoretical aspects of the problem of laser sensing of clouds,” in Problems of Laser Sensing of the Atmosphere (Nauka, Novosibirsk, Russian Federation, 1976), pp. 3–33.
  22. G. M. Krekov, M. M. Krekova, V. I. Samokhvalov, “Estimation of the signals of spaceborne lidars in sensing of stratified clouds,” Issled. Zemli iz Kosmosa 6, 77–83 (1986).
  23. F. E. Hoge, R. N. Swift, E. B. Frederik, “Water depth measurements using an airborne pulsed neon laser system,” Appl. Opt. 19, 871–883 (1988).
    [CrossRef]
  24. I. M. Levin, V. I. Feigel, “A limitation on the maximum sounding depth due to radiation backscattering in the atmosphere,” in Optics of the Sea and the Atmosphere (Academic, Krasnoyarsk, Russian Federation, 1990), pp. 64–65.
  25. G. M. Krekov, M. M. Krekova, V. S. Shamanaev, “Numerical estimates of the atmospheric influence on the signal shape in sensing of sea water,” Atmos. Oceanic Opt. 5, 777–779 (1992).

1994 (1)

1992 (2)

B. A. Kargin, S. M. Prigarin, “Simulation of the sea surface roughness and study of its optical properties by the Monte Carlo method,” Atmos. Oceanic Opt. 5, 186–190 (1992).

G. M. Krekov, M. M. Krekova, V. S. Shamanaev, “Numerical estimates of the atmospheric influence on the signal shape in sensing of sea water,” Atmos. Oceanic Opt. 5, 777–779 (1992).

1988 (3)

1986 (3)

1985 (1)

1982 (1)

1973 (1)

V. I. Man’kovskii, “Extreme phase functions of light scattering by sea water,” Mar. Hydrophys. Invest. 3, 100–108 (1973).

1968 (2)

G. M. Krekov, G. A. Mikhailov, B. A. Kargin, “On algorithms for statistical simulation of diffusion in a medium with a reflecting surface,” Izv. Vyssh. Uchebn. Zaved. Fiz. 9, 99–105 (1968).

G. M. Krekov, G. A. Mikhailov, B. A. Kargin, “On Monte Carlo algorithms for solving problems of the theory of the narrow light beam propagation,” Izv. Vyssh. Uchebn. Zaved. Fiz. 5, 55–59 (1968).

1954 (1)

Abbot, R. H.

Adams, T. R.

Belokhvostikov, A. V.

V. M. Orlov, I. V. Samokhvalov, M. L. Belov, V. S. Shamanaev, V. M. Klimkin, A. V. Belokhvostikov, I. E. Penner, R. G. Safin, A. B. Yudovskii, Remote Control of the Upper Layer of the Ocean (Nauka, Novosibirsk, Russian Federation, 1991).

Belov, M. L.

V. M. Orlov, I. V. Samokhvalov, M. L. Belov, V. S. Shamanaev, V. M. Klimkin, A. V. Belokhvostikov, I. E. Penner, R. G. Safin, A. B. Yudovskii, Remote Control of the Upper Layer of the Ocean (Nauka, Novosibirsk, Russian Federation, 1991).

Berry, E.

Billard, B.

Buntzen, R. R.

Cartwright, D. G.

Cox, C.

Darbinyan, R. A.

G. I. Marchuk, G. M. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, B. S. Elexov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

Dzhetybaev, O. E.

O. E. Dzhetybaev, B. A. Kargin, “Application of statistical simulation to a solution of problems of optical sensing of the atmosphere–ocean system,” in Current Problems of Applied Mathematics and Mathematical Simulation, A. S. Alekseev, ed. (Nauka, Novosibirsk, Russian Federation, 1982), pp. 83–91.

Elexov, B. S.

G. I. Marchuk, G. M. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, B. S. Elexov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

Faulkner, D. W.

Feigel, V. I.

I. M. Levin, V. I. Feigel, “A limitation on the maximum sounding depth due to radiation backscattering in the atmosphere,” in Optics of the Sea and the Atmosphere (Academic, Krasnoyarsk, Russian Federation, 1990), pp. 64–65.

Frederik, E. B.

Gilbert, G. D.

Gordon, H. R.

Hoge, F. E.

Kargin, B. A.

B. A. Kargin, S. M. Prigarin, “Simulation of the sea surface roughness and study of its optical properties by the Monte Carlo method,” Atmos. Oceanic Opt. 5, 186–190 (1992).

G. M. Krekov, G. A. Mikhailov, B. A. Kargin, “On Monte Carlo algorithms for solving problems of the theory of the narrow light beam propagation,” Izv. Vyssh. Uchebn. Zaved. Fiz. 5, 55–59 (1968).

G. M. Krekov, G. A. Mikhailov, B. A. Kargin, “On algorithms for statistical simulation of diffusion in a medium with a reflecting surface,” Izv. Vyssh. Uchebn. Zaved. Fiz. 9, 99–105 (1968).

G. I. Marchuk, G. M. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, B. S. Elexov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

O. E. Dzhetybaev, B. A. Kargin, “Application of statistical simulation to a solution of problems of optical sensing of the atmosphere–ocean system,” in Current Problems of Applied Mathematics and Mathematical Simulation, A. S. Alekseev, ed. (Nauka, Novosibirsk, Russian Federation, 1982), pp. 83–91.

Klimkin, V. M.

V. M. Orlov, I. V. Samokhvalov, M. L. Belov, V. S. Shamanaev, V. M. Klimkin, A. V. Belokhvostikov, I. E. Penner, R. G. Safin, A. B. Yudovskii, Remote Control of the Upper Layer of the Ocean (Nauka, Novosibirsk, Russian Federation, 1991).

Kopelevich, O. V.

O. V. Kopelevich, “Experimental data on the optical properties of sea water in ocean optics,” in Ocean Optics, A. S. Monin, ed. (Nauka, Moscow, 1983), Vol. 1, pp. 166–201.

O. V. Kopelevich, K. S. Shifrin, “Modern concept of the optical properties of sea water,” in Atmospheric and Ocean Optics (Nauka, Moscow, 1981), pp. 4–49.

Krabill, C. W.

Krasnitskii, V. P.

A. S. Monin, V. P. Krasnitskii, Phenomena on the Ocean Surface (Gidrometeoizdat, Leningrad, 1985).

Krekov, G. M.

M. M. Krekova, G. M. Krekov, I. V. Samokhvalov, V. S. Shamanaev, “Numerical evaluation of the possibilities of remote laser sensing of fish schools,” Appl. Opt. 33, 5715–5720 (1994).
[CrossRef] [PubMed]

G. M. Krekov, M. M. Krekova, V. S. Shamanaev, “Numerical estimates of the atmospheric influence on the signal shape in sensing of sea water,” Atmos. Oceanic Opt. 5, 777–779 (1992).

G. M. Krekov, M. M. Krekova, V. I. Samokhvalov, “Estimation of the signals of spaceborne lidars in sensing of stratified clouds,” Issled. Zemli iz Kosmosa 6, 77–83 (1986).

G. M. Krekov, G. A. Mikhailov, B. A. Kargin, “On Monte Carlo algorithms for solving problems of the theory of the narrow light beam propagation,” Izv. Vyssh. Uchebn. Zaved. Fiz. 5, 55–59 (1968).

G. M. Krekov, G. A. Mikhailov, B. A. Kargin, “On algorithms for statistical simulation of diffusion in a medium with a reflecting surface,” Izv. Vyssh. Uchebn. Zaved. Fiz. 9, 99–105 (1968).

V. E. Zuev, G. M. Krekov, M. M. Krekova, “Theoretical aspects of the problem of laser sensing of clouds,” in Problems of Laser Sensing of the Atmosphere (Nauka, Novosibirsk, Russian Federation, 1976), pp. 3–33.

V. E. Zuev, G. M. Krekov, Optical Models of the Atmosphere (Gigrometeoizdat, Leningrad, 1986).

Krekova, M. M.

M. M. Krekova, G. M. Krekov, I. V. Samokhvalov, V. S. Shamanaev, “Numerical evaluation of the possibilities of remote laser sensing of fish schools,” Appl. Opt. 33, 5715–5720 (1994).
[CrossRef] [PubMed]

G. M. Krekov, M. M. Krekova, V. S. Shamanaev, “Numerical estimates of the atmospheric influence on the signal shape in sensing of sea water,” Atmos. Oceanic Opt. 5, 777–779 (1992).

G. M. Krekov, M. M. Krekova, V. I. Samokhvalov, “Estimation of the signals of spaceborne lidars in sensing of stratified clouds,” Issled. Zemli iz Kosmosa 6, 77–83 (1986).

V. E. Zuev, G. M. Krekov, M. M. Krekova, “Theoretical aspects of the problem of laser sensing of clouds,” in Problems of Laser Sensing of the Atmosphere (Nauka, Novosibirsk, Russian Federation, 1976), pp. 3–33.

Levin, I. M.

I. M. Levin, V. I. Feigel, “A limitation on the maximum sounding depth due to radiation backscattering in the atmosphere,” in Optics of the Sea and the Atmosphere (Academic, Krasnoyarsk, Russian Federation, 1990), pp. 64–65.

Man’kovskii, V. I.

V. I. Man’kovskii, “Extreme phase functions of light scattering by sea water,” Mar. Hydrophys. Invest. 3, 100–108 (1973).

Marchuk, G. I.

G. I. Marchuk, G. M. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, B. S. Elexov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

Mikhailov, G. A.

G. M. Krekov, G. A. Mikhailov, B. A. Kargin, “On algorithms for statistical simulation of diffusion in a medium with a reflecting surface,” Izv. Vyssh. Uchebn. Zaved. Fiz. 9, 99–105 (1968).

G. M. Krekov, G. A. Mikhailov, B. A. Kargin, “On Monte Carlo algorithms for solving problems of the theory of the narrow light beam propagation,” Izv. Vyssh. Uchebn. Zaved. Fiz. 5, 55–59 (1968).

Mikhailov, G. M.

G. I. Marchuk, G. M. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, B. S. Elexov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

Monin, A. S.

A. S. Monin, V. P. Krasnitskii, Phenomena on the Ocean Surface (Gidrometeoizdat, Leningrad, 1985).

Munk, W.

Nazaraliev, M. A.

G. I. Marchuk, G. M. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, B. S. Elexov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

Orlov, V. M.

V. M. Orlov, I. V. Samokhvalov, M. L. Belov, V. S. Shamanaev, V. M. Klimkin, A. V. Belokhvostikov, I. E. Penner, R. G. Safin, A. B. Yudovskii, Remote Control of the Upper Layer of the Ocean (Nauka, Novosibirsk, Russian Federation, 1991).

Penner, I. E.

I. E. Penner, I. V. Samokhvalov, V. S. Shamanaev, “Optical sensing of the marine frontal zone,” Atmos. Opt. 1, 60–66 (1988).

V. M. Orlov, I. V. Samokhvalov, M. L. Belov, V. S. Shamanaev, V. M. Klimkin, A. V. Belokhvostikov, I. E. Penner, R. G. Safin, A. B. Yudovskii, Remote Control of the Upper Layer of the Ocean (Nauka, Novosibirsk, Russian Federation, 1991).

Penny, M. F.

Perry, G. J.

Phillips, D. M.

Prigarin, S. M.

B. A. Kargin, S. M. Prigarin, “Simulation of the sea surface roughness and study of its optical properties by the Monte Carlo method,” Atmos. Oceanic Opt. 5, 186–190 (1992).

Rees, D.

Richards, J.

Safin, R. G.

V. M. Orlov, I. V. Samokhvalov, M. L. Belov, V. S. Shamanaev, V. M. Klimkin, A. V. Belokhvostikov, I. E. Penner, R. G. Safin, A. B. Yudovskii, Remote Control of the Upper Layer of the Ocean (Nauka, Novosibirsk, Russian Federation, 1991).

Samokhvalov, I. V.

M. M. Krekova, G. M. Krekov, I. V. Samokhvalov, V. S. Shamanaev, “Numerical evaluation of the possibilities of remote laser sensing of fish schools,” Appl. Opt. 33, 5715–5720 (1994).
[CrossRef] [PubMed]

I. E. Penner, I. V. Samokhvalov, V. S. Shamanaev, “Optical sensing of the marine frontal zone,” Atmos. Opt. 1, 60–66 (1988).

V. M. Orlov, I. V. Samokhvalov, M. L. Belov, V. S. Shamanaev, V. M. Klimkin, A. V. Belokhvostikov, I. E. Penner, R. G. Safin, A. B. Yudovskii, Remote Control of the Upper Layer of the Ocean (Nauka, Novosibirsk, Russian Federation, 1991).

Samokhvalov, V. I.

G. M. Krekov, M. M. Krekova, V. I. Samokhvalov, “Estimation of the signals of spaceborne lidars in sensing of stratified clouds,” Issled. Zemli iz Kosmosa 6, 77–83 (1986).

Shamanaev, V. S.

M. M. Krekova, G. M. Krekov, I. V. Samokhvalov, V. S. Shamanaev, “Numerical evaluation of the possibilities of remote laser sensing of fish schools,” Appl. Opt. 33, 5715–5720 (1994).
[CrossRef] [PubMed]

G. M. Krekov, M. M. Krekova, V. S. Shamanaev, “Numerical estimates of the atmospheric influence on the signal shape in sensing of sea water,” Atmos. Oceanic Opt. 5, 777–779 (1992).

I. E. Penner, I. V. Samokhvalov, V. S. Shamanaev, “Optical sensing of the marine frontal zone,” Atmos. Opt. 1, 60–66 (1988).

V. M. Orlov, I. V. Samokhvalov, M. L. Belov, V. S. Shamanaev, V. M. Klimkin, A. V. Belokhvostikov, I. E. Penner, R. G. Safin, A. B. Yudovskii, Remote Control of the Upper Layer of the Ocean (Nauka, Novosibirsk, Russian Federation, 1991).

Shifrin, K. S.

O. V. Kopelevich, K. S. Shifrin, “Modern concept of the optical properties of sea water,” in Atmospheric and Ocean Optics (Nauka, Moscow, 1981), pp. 4–49.

K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).

Swift, R. N.

Wilsen, P. J.

Woodcock, B.

Wright, C. W.

Yudovskii, A. B.

V. M. Orlov, I. V. Samokhvalov, M. L. Belov, V. S. Shamanaev, V. M. Klimkin, A. V. Belokhvostikov, I. E. Penner, R. G. Safin, A. B. Yudovskii, Remote Control of the Upper Layer of the Ocean (Nauka, Novosibirsk, Russian Federation, 1991).

Yungel, J. K.

Zuev, V. E.

V. E. Zuev, G. M. Krekov, M. M. Krekova, “Theoretical aspects of the problem of laser sensing of clouds,” in Problems of Laser Sensing of the Atmosphere (Nauka, Novosibirsk, Russian Federation, 1976), pp. 3–33.

V. E. Zuev, G. M. Krekov, Optical Models of the Atmosphere (Gigrometeoizdat, Leningrad, 1986).

Appl. Opt. (7)

Atmos. Oceanic Opt. (2)

G. M. Krekov, M. M. Krekova, V. S. Shamanaev, “Numerical estimates of the atmospheric influence on the signal shape in sensing of sea water,” Atmos. Oceanic Opt. 5, 777–779 (1992).

B. A. Kargin, S. M. Prigarin, “Simulation of the sea surface roughness and study of its optical properties by the Monte Carlo method,” Atmos. Oceanic Opt. 5, 186–190 (1992).

Atmos. Opt. (1)

I. E. Penner, I. V. Samokhvalov, V. S. Shamanaev, “Optical sensing of the marine frontal zone,” Atmos. Opt. 1, 60–66 (1988).

Issled. Zemli iz Kosmosa (1)

G. M. Krekov, M. M. Krekova, V. I. Samokhvalov, “Estimation of the signals of spaceborne lidars in sensing of stratified clouds,” Issled. Zemli iz Kosmosa 6, 77–83 (1986).

Izv. Vyssh. Uchebn. Zaved. Fiz. (2)

G. M. Krekov, G. A. Mikhailov, B. A. Kargin, “On algorithms for statistical simulation of diffusion in a medium with a reflecting surface,” Izv. Vyssh. Uchebn. Zaved. Fiz. 9, 99–105 (1968).

G. M. Krekov, G. A. Mikhailov, B. A. Kargin, “On Monte Carlo algorithms for solving problems of the theory of the narrow light beam propagation,” Izv. Vyssh. Uchebn. Zaved. Fiz. 5, 55–59 (1968).

J. Opt. Soc. Am. (1)

Mar. Hydrophys. Invest. (1)

V. I. Man’kovskii, “Extreme phase functions of light scattering by sea water,” Mar. Hydrophys. Invest. 3, 100–108 (1973).

Other (10)

O. V. Kopelevich, “Experimental data on the optical properties of sea water in ocean optics,” in Ocean Optics, A. S. Monin, ed. (Nauka, Moscow, 1983), Vol. 1, pp. 166–201.

V. E. Zuev, G. M. Krekov, M. M. Krekova, “Theoretical aspects of the problem of laser sensing of clouds,” in Problems of Laser Sensing of the Atmosphere (Nauka, Novosibirsk, Russian Federation, 1976), pp. 3–33.

A. S. Monin, V. P. Krasnitskii, Phenomena on the Ocean Surface (Gidrometeoizdat, Leningrad, 1985).

O. E. Dzhetybaev, B. A. Kargin, “Application of statistical simulation to a solution of problems of optical sensing of the atmosphere–ocean system,” in Current Problems of Applied Mathematics and Mathematical Simulation, A. S. Alekseev, ed. (Nauka, Novosibirsk, Russian Federation, 1982), pp. 83–91.

V. E. Zuev, G. M. Krekov, Optical Models of the Atmosphere (Gigrometeoizdat, Leningrad, 1986).

K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).

O. V. Kopelevich, K. S. Shifrin, “Modern concept of the optical properties of sea water,” in Atmospheric and Ocean Optics (Nauka, Moscow, 1981), pp. 4–49.

V. M. Orlov, I. V. Samokhvalov, M. L. Belov, V. S. Shamanaev, V. M. Klimkin, A. V. Belokhvostikov, I. E. Penner, R. G. Safin, A. B. Yudovskii, Remote Control of the Upper Layer of the Ocean (Nauka, Novosibirsk, Russian Federation, 1991).

G. I. Marchuk, G. M. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, B. S. Elexov, Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

I. M. Levin, V. I. Feigel, “A limitation on the maximum sounding depth due to radiation backscattering in the atmosphere,” in Optics of the Sea and the Atmosphere (Academic, Krasnoyarsk, Russian Federation, 1990), pp. 64–65.

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Figures (8)

Fig. 1
Fig. 1

Vertical profiles of the aerosol extinction coefficients σ a (z) in the atmospheric boundary layer above the ocean as functions of the driving wind velocity W = 3 (curve1), 7 (curve2), and15m/ s (curve3).

Fig. 2
Fig. 2

Model scattering phase functions g 1(θ) … g 4(θ) indicated by the number adjacent to the curves.

Fig. 3
Fig. 3

Depth profiles of the lidar return signal intensities I(h) as functions of the parameters η and the optical state of the atmosphere. Calculations with σ a = 0.2 (curves 1–3) and 0.5 km-1 (curves 4 and 5), η = 0.08 (curves 1–4) and 0.68 (curve 5). Curves 3 and 5 are for the intensity of the singly scattered signal I (1)(h).

Fig. 4
Fig. 4

Sensing of hydrosol inversion: 1, I(h) calculated with σ w = 600 km-1 in the inversion layer at depths of 10 ≤ h ≤ 15 m and 200 km-1 outside this layer; the scattering phase function g 4(θ) remained unchanged with depth; 2, I(h) calculated with σ w (h) = 200 km-1; the scattering phase function was g 2(θ) in the layer and g 4(θ) below this layer. In both cases η = 0.68.

Fig. 5
Fig. 5

Lidar return signal power for interactions of different multiplicities at φ d = 7 mrad and W = 1 (curves 1–4) and 3 m/s (curves 1′–4′). The curves with or without a prime represent scattering multiplicity.

Fig. 6
Fig. 6

Depth profiles of the lidar return signal power P(h) as functions of the driving wind velocity W = 1 (curve 1), 3 (curve 2), 5 (curve 3), and 7 m/s (curve 4) at φ d = 22 mrad, σ w (h) = 200 km-1, Λ w = 0.813, and Λ b = 0.2.

Fig. 7
Fig. 7

Depth profiles of the components of the lidar return signal power P w (h) (curves 1–3) and P a (h) (curves 1′–3′) at W = 1 m/s and φ d = 0.035 (curves 1 and 1′), 0.175 (curves 2 and 2′), and 0.35 rad (curves 3 and 3′). The lidar was at altitude H s = 200 m above the water surface.

Fig. 8
Fig. 8

Total lidar return signal powers P(h) (curves 3 and 6) and its components P a (h) (curves 2 and 5) and P w (h) (curves 1 and 4) at φ d = 1.6 (curves 1–3) and 3.5 mrad (curves 4–6).

Tables (3)

Tables Icon

Table 1 Dependence of k = Ibg/I on Parameter η and Scattering Phase Function g(θ) (%)

Tables Icon

Table 2 Ratios E/Ef (%) as Functions of the Driving Wind Velocity W and the Field-of-View Angle of the Detector φd

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Table 3 Dependence of the Average Energy of a Singly Scattered Signal E(1), in Relative Units, on the Driving Wind Velocity W and the Field-of-View Angle of Detector φ d

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P t = P a t + P s t + P w t + P b t ,
φ ω j ,   r j ω * ,   r * = exp - τ r j ,   r * g θ 2 π | r j - r * | 2   Δ Ω m * Δ t i ,
ξ n = j = 1 N j   q j φ ω j ,   r j ω * ,   r * ,
φ ω j ,   r j ω * ,   r * = φ ω j ,   r j l ,   r ω * ,   r * × p l 1 - R ω j ,   l / n 2 .

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