Abstract

Atmospheric precipitation, similar to turbulence (and together with it), causes significant intensity fluctuations (σ32). They also result in characteristic peculiarities of the intensity fluctuation spectrum [W(f)]. The measurements were carried out along the 130–1310-m path. The He–Ne laser generated at λ = 0.6328 μm. The beam diffraction parameter Ω=kα02/L(k=2π/λ) is the wavenumber, α0 is the effective beam radius). The measurements were made in collimated, divergent, and focused beams. The receiver’s diameter was 0.1 mm. It was noticed that, in precipitation (snowfall, rain) regardless of the laser beam parameters, the turbulence properties are mainly observed in the low-frequency region and those of precipitation in the high-frequency region. In weak precipitation the spectrum had two maxima, and at heavy precipitation it had its hydrometeoric maximum at frequency fr in the range of several kilohertz. In heavy rains in the region of low frequencies f < fr the spectrum was described by the dependence W(f) ~ f with satisfactory accuracy. In rain at f > fr the spectrum decreased as W(f) ~ fα. In snowfall at f > fr the following dependence was observed: W(f) ~ lβf. The theoretical conclusion fr ~ V/d, where V is the terminal rate and d is the mean particle size, was quantitatively verified. On the 130-m path the experimental values of the normalized variance (σ32) are described by the dependence σ32=A+Nτ, where τ is the optical depth of precipitation. The coefficient N in the divergent beam depends on the particle sizes and increases from 0.3 to 0.8 when increasing the maximum size of particles from 0.1 to 3 cm, respectively. The estimates of turbulence σT2 and snowfall σc2 contributions to the measured variance σ32 were made assuming that they are additive (i.e., σ32=σT2+σc2). When the maximum diameter of the snowfall particles was <5 mm and τ = 0.4–0.5, the empirical dependence σc2=0.07+0.37logΩ for Ω values of 0.3–30 was obtained. Measurements of the scattered radiation in the snowfall (Ω = 54, L = 130 m) were carried out at the receiver’s angular distance 10−4 rad from the beam axis; σ32 at τ > 0.2 was saturated at the leve of ~0.85. Here W(f) had its maximum in the region of a few kilohertz. We concluded that the high-frequency region of the intensity fluctuation spectrum in the divergent laser beam had the largest information content. A focused beam was preferable for studying the turbulence in precipitation.

© 1988 Optical Society of America

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References

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  1. V. E. Zuev, M. V. Kabanov, B. A. Saveliev, “Propagation of Laser Beams in Scattering Media,” Appl. Opt. 8, 137 (1969).
    [CrossRef] [PubMed]
  2. V. E. Zuev, V. I. Peresypkin, V. Ya. Fadeev, G. A. Koloshin, P. S. Konstantinov, Laser Devices for Providing for Navigation (Nauka, Novosibirsk, 1985).
  3. B. Crosignani, P. di Porto, M. Bertolotti, Statistical Properties of Scattered Light (Academic, New York, 1975).
  4. M. Francon, La cranularite laser (speckle) et ses applications en optique (Masson, Paris, 1978).
  5. A. G. Borovoy, M. V. Kabanov, B. A. Saveliev, “Intensity Fluctuations of Optical Radiation in Scattering Media,” Appl. Opt. 14, 2731 (1975).
    [CrossRef] [PubMed]
  6. D. Raymond, K. Wilson, J. Appl. Meteorol. 13, 180 (1974).
    [CrossRef]
  7. T. Wang, S. F. Clifford, “Use of Rainfall-Induced Optical Scintillations to Measure Path-Averaged Rain Parameters,” J. Opt. Soc. Am. 65, 927 (1975).
    [CrossRef]
  8. N. A. Vostretsov, A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 20, 581 (1984).
  9. T. Wang, R. Lataitis, R. S. Lawrence, G. R. Ochs, J. Appl. Meteorol. 21, 1747 (1982).
    [CrossRef]
  10. A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 21, 147 (1985).
  11. N. A. Vostretsov, A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, “Statistical Characteristics of Laser-Beam Intensity Fluctuations in Snowfall,” Preprint N13, Siberian Branch of the U.S.S.R.Academy of Sciences, Tomsk (1982).

1985 (1)

A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 21, 147 (1985).

1984 (1)

N. A. Vostretsov, A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 20, 581 (1984).

1982 (1)

T. Wang, R. Lataitis, R. S. Lawrence, G. R. Ochs, J. Appl. Meteorol. 21, 1747 (1982).
[CrossRef]

1975 (2)

1974 (1)

D. Raymond, K. Wilson, J. Appl. Meteorol. 13, 180 (1974).
[CrossRef]

1969 (1)

Bertolotti, M.

B. Crosignani, P. di Porto, M. Bertolotti, Statistical Properties of Scattered Light (Academic, New York, 1975).

Borovoy, A. G.

Clifford, S. F.

Crosignani, B.

B. Crosignani, P. di Porto, M. Bertolotti, Statistical Properties of Scattered Light (Academic, New York, 1975).

di Porto, P.

B. Crosignani, P. di Porto, M. Bertolotti, Statistical Properties of Scattered Light (Academic, New York, 1975).

Fadeev, V. Ya.

V. E. Zuev, V. I. Peresypkin, V. Ya. Fadeev, G. A. Koloshin, P. S. Konstantinov, Laser Devices for Providing for Navigation (Nauka, Novosibirsk, 1985).

Francon, M.

M. Francon, La cranularite laser (speckle) et ses applications en optique (Masson, Paris, 1978).

Kabanov, M. V.

A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 21, 147 (1985).

N. A. Vostretsov, A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 20, 581 (1984).

A. G. Borovoy, M. V. Kabanov, B. A. Saveliev, “Intensity Fluctuations of Optical Radiation in Scattering Media,” Appl. Opt. 14, 2731 (1975).
[CrossRef] [PubMed]

V. E. Zuev, M. V. Kabanov, B. A. Saveliev, “Propagation of Laser Beams in Scattering Media,” Appl. Opt. 8, 137 (1969).
[CrossRef] [PubMed]

N. A. Vostretsov, A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, “Statistical Characteristics of Laser-Beam Intensity Fluctuations in Snowfall,” Preprint N13, Siberian Branch of the U.S.S.R.Academy of Sciences, Tomsk (1982).

Koloshin, G. A.

V. E. Zuev, V. I. Peresypkin, V. Ya. Fadeev, G. A. Koloshin, P. S. Konstantinov, Laser Devices for Providing for Navigation (Nauka, Novosibirsk, 1985).

Konstantinov, P. S.

V. E. Zuev, V. I. Peresypkin, V. Ya. Fadeev, G. A. Koloshin, P. S. Konstantinov, Laser Devices for Providing for Navigation (Nauka, Novosibirsk, 1985).

Lataitis, R.

T. Wang, R. Lataitis, R. S. Lawrence, G. R. Ochs, J. Appl. Meteorol. 21, 1747 (1982).
[CrossRef]

Lawrence, R. S.

T. Wang, R. Lataitis, R. S. Lawrence, G. R. Ochs, J. Appl. Meteorol. 21, 1747 (1982).
[CrossRef]

Ochs, G. R.

T. Wang, R. Lataitis, R. S. Lawrence, G. R. Ochs, J. Appl. Meteorol. 21, 1747 (1982).
[CrossRef]

Peresypkin, V. I.

V. E. Zuev, V. I. Peresypkin, V. Ya. Fadeev, G. A. Koloshin, P. S. Konstantinov, Laser Devices for Providing for Navigation (Nauka, Novosibirsk, 1985).

Raymond, D.

D. Raymond, K. Wilson, J. Appl. Meteorol. 13, 180 (1974).
[CrossRef]

Saveliev, B. A.

Tsvyk, R. Sh.

A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 21, 147 (1985).

N. A. Vostretsov, A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 20, 581 (1984).

N. A. Vostretsov, A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, “Statistical Characteristics of Laser-Beam Intensity Fluctuations in Snowfall,” Preprint N13, Siberian Branch of the U.S.S.R.Academy of Sciences, Tomsk (1982).

Vostretsov, N. A.

N. A. Vostretsov, A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 20, 581 (1984).

N. A. Vostretsov, A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, “Statistical Characteristics of Laser-Beam Intensity Fluctuations in Snowfall,” Preprint N13, Siberian Branch of the U.S.S.R.Academy of Sciences, Tomsk (1982).

Wang, T.

Wilson, K.

D. Raymond, K. Wilson, J. Appl. Meteorol. 13, 180 (1974).
[CrossRef]

Zhukov, A. F.

A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 21, 147 (1985).

N. A. Vostretsov, A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 20, 581 (1984).

N. A. Vostretsov, A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, “Statistical Characteristics of Laser-Beam Intensity Fluctuations in Snowfall,” Preprint N13, Siberian Branch of the U.S.S.R.Academy of Sciences, Tomsk (1982).

Zuev, V. E.

V. E. Zuev, M. V. Kabanov, B. A. Saveliev, “Propagation of Laser Beams in Scattering Media,” Appl. Opt. 8, 137 (1969).
[CrossRef] [PubMed]

V. E. Zuev, V. I. Peresypkin, V. Ya. Fadeev, G. A. Koloshin, P. S. Konstantinov, Laser Devices for Providing for Navigation (Nauka, Novosibirsk, 1985).

Appl. Opt. (2)

Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana (2)

A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 21, 147 (1985).

N. A. Vostretsov, A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 20, 581 (1984).

J. Appl. Meteorol. (2)

T. Wang, R. Lataitis, R. S. Lawrence, G. R. Ochs, J. Appl. Meteorol. 21, 1747 (1982).
[CrossRef]

D. Raymond, K. Wilson, J. Appl. Meteorol. 13, 180 (1974).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (4)

N. A. Vostretsov, A. F. Zhukov, M. V. Kabanov, R. Sh. Tsvyk, “Statistical Characteristics of Laser-Beam Intensity Fluctuations in Snowfall,” Preprint N13, Siberian Branch of the U.S.S.R.Academy of Sciences, Tomsk (1982).

V. E. Zuev, V. I. Peresypkin, V. Ya. Fadeev, G. A. Koloshin, P. S. Konstantinov, Laser Devices for Providing for Navigation (Nauka, Novosibirsk, 1985).

B. Crosignani, P. di Porto, M. Bertolotti, Statistical Properties of Scattered Light (Academic, New York, 1975).

M. Francon, La cranularite laser (speckle) et ses applications en optique (Masson, Paris, 1978).

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Figures (7)

Fig. 1
Fig. 1

Schematic of the laser optical system: 1–6, plane reflecting mirrors; 7, shield; 8, neutral light filter; 9, 0.1-mm diam diaphragm; 10, interference light filter.

Fig. 2
Fig. 2

Frequency spectrum of the laser beam intensity fluctuations (Ω = 54, L = 130) at different optical depths of snowfall: 1, τ < 0.02; 2, τ = 0.02; 3, τ = 0.05; 4, τ = 0.2.

Fig. 3
Fig. 3

Frequency spectrum of the laser beam intensity fluctuations in rain (τ = 0.1) at different beam parameters: 1, a focused beam (F/L = 1, Ω = 54); 2, a collimated beam (Ω = 54); 3, a divergent beam (Ω = 0.075); 4, a divergent beam, no precipitation (Ω = 0.075).

Fig. 4
Fig. 4

Dependence of the laser beam intensity fluctuation variance on the snowfall optical depth (L = 130): (a) Ω = 54; (b) Ω = 0.075; (c) Ω = 54; (d) Ω = 0.075.

Fig. 5
Fig. 5

Dependence σ 3 2 = f ( τ ) along the path L = 390 m for Ω = 5.5: 1, d < 0.5 cm; 2, tapioca snow; 3, flakes.

Fig. 6
Fig. 6

Frequency spectrum of the focused beam scattered radiation intensity (Ω = 54, L = 130 m, L/F = 1 at different optical depths): 1, τ = 0.41; 2, τ = 0.33; 3, τ = 0.20; 4, τ = 0.12. The receiver diameter is 0.1 mm. The receiver is placed at an angular distance 10−4 rad from the beam axis in the focal plane.

Fig. 7
Fig. 7

Dependence of variance of the scattered radiation intensity fluctuations on precipitation rate (L = 130, Ω = 54, L/F = 1).

Tables (1)

Tables Icon

Table I Dependence of Measured Variance ( σ 3 2 ) , Turbulence ( σ T 2 ) , and Snowfall ( σ c 2 ) Contributions on Ω (τ = 0.4–0.5, d ≤ 5 mm)

Equations (2)

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U ( f ) = { A 1 e b f for snowfall , A 2 f c for rain .
U ( f ) f , f < f r .

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