Abstract

The reasons for instability of the lidar equation solution are investigated. An effective method of recovering the attenuation coefficient profile and transmittance of an optically thick atmosphere from the data of single-frequency laser sounding is suggested. The method enables one to obtain stable solutions of the lidar equation for sounding paths adjacent to the horizontal ones without the use of absolute calibration of the lidar. A comparison is made with the known algorithms of processing. The results of experimental tests of the method when sounding fogs in the boundary atmospheric layer are described.

© 1987 Optical Society of America

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References

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  1. V. E. Zuev, G. M. Krekov, M. M. Krekova, I. E. Naats, in Problems of Laser Sounding of the Atmosphere, V. E. Zuev, Ed. (Nauka, Novosibirsk, 1976), p. 3.
  2. V. E. Zuev, G. O. Zadde, S. I. Kavkyanov, B. V. Kaul, in Remote Sounding of the Atmosphere, V. E. Zuev, Ed. (Nauka, Novosibirsk, 1978), p. 60.
  3. S. I. Kavkyanov, G. M. Krekov, in Investigation of Atmospheric Aerosol by the Methods of Laser Sounding, M. V. Kabanov, Ed. (Nauka, Novosibirsk, 1980), p. 3.
  4. V. E. Zuev, S. I. Kavkyanov, G. M. Krekov. Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana 19, 255 (1983).
  5. J. D. Klett, Appl. Opt. 20, 211 (1981).
    [CrossRef] [PubMed]
  6. J. D. Klett, Appl. Opt. 22, 514 (1983).
    [CrossRef] [PubMed]
  7. Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. A. Razenkov, A.C. 1038839 (USSR), B.I. No. 32, 174 (1983).

1983 (3)

V. E. Zuev, S. I. Kavkyanov, G. M. Krekov. Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana 19, 255 (1983).

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. A. Razenkov, A.C. 1038839 (USSR), B.I. No. 32, 174 (1983).

J. D. Klett, Appl. Opt. 22, 514 (1983).
[CrossRef] [PubMed]

1981 (1)

Balin, Yu. S.

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. A. Razenkov, A.C. 1038839 (USSR), B.I. No. 32, 174 (1983).

Kaul, B. V.

V. E. Zuev, G. O. Zadde, S. I. Kavkyanov, B. V. Kaul, in Remote Sounding of the Atmosphere, V. E. Zuev, Ed. (Nauka, Novosibirsk, 1978), p. 60.

Kavkyanov, S. I.

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. A. Razenkov, A.C. 1038839 (USSR), B.I. No. 32, 174 (1983).

V. E. Zuev, S. I. Kavkyanov, G. M. Krekov. Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana 19, 255 (1983).

S. I. Kavkyanov, G. M. Krekov, in Investigation of Atmospheric Aerosol by the Methods of Laser Sounding, M. V. Kabanov, Ed. (Nauka, Novosibirsk, 1980), p. 3.

V. E. Zuev, G. O. Zadde, S. I. Kavkyanov, B. V. Kaul, in Remote Sounding of the Atmosphere, V. E. Zuev, Ed. (Nauka, Novosibirsk, 1978), p. 60.

Klett, J. D.

Krekov, G. M.

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. A. Razenkov, A.C. 1038839 (USSR), B.I. No. 32, 174 (1983).

V. E. Zuev, S. I. Kavkyanov, G. M. Krekov. Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana 19, 255 (1983).

V. E. Zuev, G. M. Krekov, M. M. Krekova, I. E. Naats, in Problems of Laser Sounding of the Atmosphere, V. E. Zuev, Ed. (Nauka, Novosibirsk, 1976), p. 3.

S. I. Kavkyanov, G. M. Krekov, in Investigation of Atmospheric Aerosol by the Methods of Laser Sounding, M. V. Kabanov, Ed. (Nauka, Novosibirsk, 1980), p. 3.

Krekova, M. M.

V. E. Zuev, G. M. Krekov, M. M. Krekova, I. E. Naats, in Problems of Laser Sounding of the Atmosphere, V. E. Zuev, Ed. (Nauka, Novosibirsk, 1976), p. 3.

Naats, I. E.

V. E. Zuev, G. M. Krekov, M. M. Krekova, I. E. Naats, in Problems of Laser Sounding of the Atmosphere, V. E. Zuev, Ed. (Nauka, Novosibirsk, 1976), p. 3.

Razenkov, I. A.

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. A. Razenkov, A.C. 1038839 (USSR), B.I. No. 32, 174 (1983).

Zadde, G. O.

V. E. Zuev, G. O. Zadde, S. I. Kavkyanov, B. V. Kaul, in Remote Sounding of the Atmosphere, V. E. Zuev, Ed. (Nauka, Novosibirsk, 1978), p. 60.

Zuev, V. E.

V. E. Zuev, S. I. Kavkyanov, G. M. Krekov. Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana 19, 255 (1983).

V. E. Zuev, G. M. Krekov, M. M. Krekova, I. E. Naats, in Problems of Laser Sounding of the Atmosphere, V. E. Zuev, Ed. (Nauka, Novosibirsk, 1976), p. 3.

V. E. Zuev, G. O. Zadde, S. I. Kavkyanov, B. V. Kaul, in Remote Sounding of the Atmosphere, V. E. Zuev, Ed. (Nauka, Novosibirsk, 1978), p. 60.

A.C. 1038839 (USSR) (1)

Yu. S. Balin, S. I. Kavkyanov, G. M. Krekov, I. A. Razenkov, A.C. 1038839 (USSR), B.I. No. 32, 174 (1983).

Appl. Opt. (2)

Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana (1)

V. E. Zuev, S. I. Kavkyanov, G. M. Krekov. Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana 19, 255 (1983).

Other (3)

V. E. Zuev, G. M. Krekov, M. M. Krekova, I. E. Naats, in Problems of Laser Sounding of the Atmosphere, V. E. Zuev, Ed. (Nauka, Novosibirsk, 1976), p. 3.

V. E. Zuev, G. O. Zadde, S. I. Kavkyanov, B. V. Kaul, in Remote Sounding of the Atmosphere, V. E. Zuev, Ed. (Nauka, Novosibirsk, 1978), p. 60.

S. I. Kavkyanov, G. M. Krekov, in Investigation of Atmospheric Aerosol by the Methods of Laser Sounding, M. V. Kabanov, Ed. (Nauka, Novosibirsk, 1980), p. 3.

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Figures (2)

Fig. 1
Fig. 1

Recovery of the homogeneous model profile for errors in determination of initial value σr0 of 10, 5, and 2.5% (curves 1, 2, 3) and −10, −5, and −2.5% (curves 1′, 2′, 3′). The dashed curve denotes the recovered profile sigma;r with an error in specifying the boundary value σrm of 50%.

Fig. 2
Fig. 2

Recovery of profiles σr in fogs using the algorithm of Eqs. (10), (12), and (17) (curves 1) and with photometer calibration at the beginning of the path (curves 2) and calibration at the end of the path using the logarithmic derivative method (curves 3).

Tables (1)

Tables Icon

Table 1 Comparison of Two Methods of Calibration When Inverting the Lidar Equation

Equations (14)

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P r = A r r - 2 β r T 0 r 2 = A r r - 2 β r exp ( - 2 0 r σ r d r )
ψ r = P r r 2 / ( A r g r T 0 r 0 2 ) = σ r exp ( - 2 r 0 r σ r d r ) ,
d σ r / d r - σ r d ln ψ r / d r = 2 σ r 2 ,
σ r = ψ r ( ψ r k / σ r k - 2 r k r ψ r d r ) - 1 .
T r o r 2 = ψ r k / σ r k - 2 r k r ψ r d r .
σ r = ψ r ( ψ r m / σ r m + 2 r r m ψ r d r ) - 1 .
σ r m = ψ r m ( 1 - 2 r 0 r m ψ r d r ) - 1 = P r m r m 2 ( A r g r T 0 r 0 2 - 2 r 0 r m P r r 2 d r ) - 1 ,
T r 0 r 2 = T r 0 r k 2 - 2 r k r ψ r d r ,
σ r = ψ r ( T r 0 r k 2 - 2 r k r ψ r d r ) . ⁻¹
k = ( T r 0 r k - 2 - 1 ) - 1 = [ exp ( 2 τ r 0 r k ) - 1 ] - 1
T r 0 r 2 = 1 - 1 1 + k r 0 r ψ r d r / r 0 r k ψ r d r ,
σ r = ψ r ( 2 k r 0 r k ψ r d r + 2 r r k ψ r d r ) - 1 .
T r 0 r m 2 = exp [ - 3 r 0 r m ( r - r 0 ) ln ψ r 0 ψ r d r / ( r m - r 0 ) 2 ] .
σ r m = - ln ( ψ r m / ψ r * ) / ( r m - r * ) / 2.

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