Abstract

Unlike other errors in the lidar equation solution for the two-component atmosphere, the error of the measured aerosol extinction coefficient caused by inaccuracies in the assumed aerosol backscatter-to-extinction ratios significantly depends on the aerosol spatial inhomogeneity. In a slightly nonhomogeneous atmosphere, an incorrect value in the assumed aerosol backscatter-to-extinction ratio does not significantly corrupt the measurement result, whereas in an atmosphere with a large monotonic change of the aerosol extinction [e.g., in the lower troposphere], the incorrect value yields a large distortion of the retrieved extinction-coefficient profile. In the latter case, even the far-end solution can produce a large error in the retrieved extinction coefficient. The analytical formulas for the determination of the range errors, obtained for the Klett and the optical-depth solutions, show that these errors significantly depend on the method of the boundary-condition determination. Distortions of the retrieved aerosol extinction profiles are, in general, larger if the assumed aerosol backscatter-to-extinction ratio is underestimated in relation to the real value.

© 1995 Optical Society of America

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References

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  1. V. A. Kovalev, H. Moosmüller, “Distortion of particulate extinction profiles measured with lidar in a two-component atmosphere,” Appl. Opt. 33, 6499–6507 (1994).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  11. V. E. Zuev, G. M. Krekov, Optical Models of the Atmosphere (Gidrometeoizdat, Leningrad, 1986), Chap. 5, pp. 145–157.

1994

1993

1991

V. A. Kovalev, E. E. Rybakov, V. M. Ignatenko, “Retrieving the profile of attenuation factor from data of one-angle lidar sensing,” Atmos. Opt. 4, 588–592 (1991).

1989

1988

1987

1985

1984

Balin, Yu. S.

Browell, E. V.

Ignatenko, V. M.

V. A. Kovalev, E. E. Rybakov, V. M. Ignatenko, “Retrieving the profile of attenuation factor from data of one-angle lidar sensing,” Atmos. Opt. 4, 588–592 (1991).

Ismail, S.

Kavkyanov, S. I.

Klett, J. D.

Kovalev, V. A.

Krekov, G. M.

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

V. E. Zuev, G. M. Krekov, Optical Models of the Atmosphere (Gidrometeoizdat, Leningrad, 1986), Chap. 5, pp. 145–157.

Moosmüller, H.

Nakane, H.

Rasenkov, I. A.

Rybakov, E. E.

V. A. Kovalev, E. E. Rybakov, V. M. Ignatenko, “Retrieving the profile of attenuation factor from data of one-angle lidar sensing,” Atmos. Opt. 4, 588–592 (1991).

Sasano, Y.

Shipley, S. T.

Weinman, J. A.

Zuev, V. E.

V. E. Zuev, G. M. Krekov, Optical Models of the Atmosphere (Gidrometeoizdat, Leningrad, 1986), Chap. 5, pp. 145–157.

Appl. Opt.

Atmos. Opt.

V. A. Kovalev, E. E. Rybakov, V. M. Ignatenko, “Retrieving the profile of attenuation factor from data of one-angle lidar sensing,” Atmos. Opt. 4, 588–592 (1991).

Opt. Lett.

Other

V. E. Zuev, G. M. Krekov, Optical Models of the Atmosphere (Gidrometeoizdat, Leningrad, 1986), Chap. 5, pp. 145–157.

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Figures (7)

Fig. 1
Fig. 1

Dependence of the retrieved σ a (r) profiles on assumed aerosol backscatter-to-extinction ratios. The model σ a (r) profile is shown as curve 1. Curves 2–5 show the σ a (r) profiles retrieved with P π, a = 0.015 sr−1, P π, a = 0.02 sr−1, P π, a = 0.04 sr−1, and P π, a = 0.05 sr−1, respectively. The correct boundary value of σ a (r b ) is specified at r b = 2 km.

Fig. 2
Fig. 2

Conditions are the same as in Fig. 1, except that the model σ a (r) profile changes monotonically within the range from 0.5 to 1.3 km.

Fig. 3
Fig. 3

σ a (r) and σ m (r) vertical profiles (curves 1 and 2, respectively) used for the numerical experiments shown in Figs. 4 and 5, below.

Fig. 4
Fig. 4

σ a (r) profiles retrieved with incorrect P π, a values. The model σ a (r) and σ m (r) vertical profiles are shown in Fig. 3. The numerical experiment is made for a ground-based up-looking lidar, and the correct boundary value of σ a (r b ) is specified at the altitude of 2.5 km.

Fig. 5
Fig. 5

Conditions are the same as in Fig. 4, but with the numerical experiment performed for an airborne down-looking lidar. The plane altitude is 3 km, and the correct boundary value of σ a (r b ) is specified near the ground.

Fig. 6
Fig. 6

σ a (r) profiles retrieved with the optical-depth solution. The model σ a (r) profile (curve 1) and the retrieving conditions are the same as in Fig. 4.

Fig. 7
Fig. 7

σ a (r) profiles retrieved with the optical-depth solution. The model σ a (r) profile (curve 1) and retrieving conditions are the same as in Fig. 5.

Equations (17)

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S ( r ) = C u ( r ) exp [ - 2 r 0 r u ( r ) d r ] ,
u ( r ) = σ m ( r ) [ a ( r ) + R ( r ) ] ,
R ( r ) = σ a ( r ) σ m ( r ) ,
a ( r ) = P π , m P π , a ( r ) ;
u ( r ) = 0.5 S ( r ) I b - r b r S ( r ) d r ,
I b = 0.5 S ( r b ) u ( r b ) .
I b = r 0 r m S ( r ) d r 1 - T 2 ( r 0 , r m ) exp { - 2 r 0 r m σ m ( r ) [ a ( r ) - 1 ] d r } .
Y ( r ) = C 1 a as ( r ) exp { - 2 r 0 r [ a as ( r ) - 1 ] σ m ( r ) d r } .
S ( r ) = C 2 D ( r ) u est ( r ) exp [ - 2 r 0 r u est ( r ) d r ] .
u est ( r ) = σ m ( r ) [ a as ( r ) + R ( r ) ] .
D ( r ) = 1 + R ( r ) a ( r ) 1 + R ( r ) a ( r ) [ P π , a ( r ) ] as P π , a ( r ) .
u ( r ) u est ( r ) = D ( r ) V c 2 ( r b , r ) D ( r b ) - 2 r b r D ( r ) u est ( r ) V c 2 ( r b , r ) d r ,
V c 2 ( r b , r ) = exp { - 2 r b r σ m ( r ) [ a as ( r ) + R ( r ) ] d r } .
δ σ a ( r ) = [ 1 + a as ( r ) R ( r ) ] [ u ( r ) u est ( r ) - 1 ] .
u ( r ) u est ( r ) = D ( r ) V c 2 ( r 0 , r ) 2 1 - V c 2 ( r 0 , r m ) r 0 r m D ( r ) u est ( r ) V c 2 ( r 0 , r ) d r - 2 r 0 r D ( r ) u est ( r ) V c 2 ( r 0 , r ) d r ,
Δ a ( r ) a ( r ) = - Δ P π , a ( r ) P π , a ( r ) + Δ P π , a ( r ) .
D ( r ) P π , a ( r ) [ P π , a ( r ) ] as ,

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