Abstract

A solution of the single-scattering lidar equation requires a relationship between the coefficients of backscatter β(r) and extinction σ(r) to be of the formβ(r) = C2σ(r)k, where C2 and k are parameters independent of range r. The sensitivity of a particular lidar inversion algorithm to uncertainties in C2 and k is investigated using a measured lidar return which indicated the atmosphere to be essentially horizontally homogeneous during a reduced visibility condition. Starting with the measured power returned as a function of range, extinction coefficients and average visibilities are calculated using the inversion algorithm for different values of C2 and k and compared with those inferred from the lidar return using the slope method. The calculated extinction coefficients (and visibilities) were found to be extremely sensitive to uncertainties in C2. This questions the usefulness of the lidar inversion algorithm for aerosol extinction applications when the air mass characteristics change along the measurement path.

© 1985 Optical Society of America

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References

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  1. J. D. Klett, “Stable Analytical Inversion Solution for Processing Lidar Returns,” Appl. Opt. 20, 211 (1981).
    [CrossRef] [PubMed]
  2. J. A. Ferguson, D. H. Stephens, “Algorithm for Inverting Lidar Returns,” Appl. Opt. 22, 3673 (1983).
    [CrossRef] [PubMed]
  3. J. M. Mulders, “Algorithm for Inverting Lidar Returns: Comment,” Appl. Opt. 23, 2855 (1984).
    [CrossRef] [PubMed]
  4. R. H. Kohl, “Discussion of the Interpretation Problem Encountered in Single-Wavelength Lidar Transmissometers,” J. Appl. Meteorol. 17, 1034 (1978).
    [CrossRef]
  5. O. D. Barteneva, “Scattering Functions of Light in the Atmospheric Boundary Layer,” Bull. Acad. Sci. USSR Geophys. Ser. 12, 32–1244 (1960).
  6. J. W. Fitzgerald, “Effect of Relative Humidity on the Aerosol Backscattering Coefficient at 0.694- and 10.6-μm Wavelengths,” Appl. Opt. 23, 411 (1984).
    [CrossRef] [PubMed]
  7. W. J. Lentz, “The Visioceilometer: A Portable Visibility and Cloud Ceiling Height Lidar,” ASL TR 0105 (1982).

1984 (2)

1983 (1)

1981 (1)

1978 (1)

R. H. Kohl, “Discussion of the Interpretation Problem Encountered in Single-Wavelength Lidar Transmissometers,” J. Appl. Meteorol. 17, 1034 (1978).
[CrossRef]

1960 (1)

O. D. Barteneva, “Scattering Functions of Light in the Atmospheric Boundary Layer,” Bull. Acad. Sci. USSR Geophys. Ser. 12, 32–1244 (1960).

Barteneva, O. D.

O. D. Barteneva, “Scattering Functions of Light in the Atmospheric Boundary Layer,” Bull. Acad. Sci. USSR Geophys. Ser. 12, 32–1244 (1960).

Ferguson, J. A.

Fitzgerald, J. W.

Klett, J. D.

Kohl, R. H.

R. H. Kohl, “Discussion of the Interpretation Problem Encountered in Single-Wavelength Lidar Transmissometers,” J. Appl. Meteorol. 17, 1034 (1978).
[CrossRef]

Lentz, W. J.

W. J. Lentz, “The Visioceilometer: A Portable Visibility and Cloud Ceiling Height Lidar,” ASL TR 0105 (1982).

Mulders, J. M.

Stephens, D. H.

Appl. Opt. (4)

Bull. Acad. Sci. USSR Geophys. Ser. 12 (1)

O. D. Barteneva, “Scattering Functions of Light in the Atmospheric Boundary Layer,” Bull. Acad. Sci. USSR Geophys. Ser. 12, 32–1244 (1960).

J. Appl. Meteorol. (1)

R. H. Kohl, “Discussion of the Interpretation Problem Encountered in Single-Wavelength Lidar Transmissometers,” J. Appl. Meteorol. 17, 1034 (1978).
[CrossRef]

Other (1)

W. J. Lentz, “The Visioceilometer: A Portable Visibility and Cloud Ceiling Height Lidar,” ASL TR 0105 (1982).

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Figures (5)

Fig. 1
Fig. 1

S(r) vs range determined from a lidar return.

Fig. 2
Fig. 2

Changes in the parameter In C 1 C 2 with changes in the value of C2 appropriate for Eq. (7).

Fig. 3
Fig. 3

Calculated values of extinction coefficient σ(r) as a function of range for different values of the parameter ln ( C 1 C 2 ).

Fig. 4
Fig. 4

Calculated visibilities for relative changes in C2 for differing values of k.

Fig. 5
Fig. 5

σ(r) vs range for relative changes in C2 determined from Eq. (16).

Equations (18)

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S ( r ) ln [ P ( r ) r 2 ] = ln ( C 1 C 2 ) + k ln σ ( r ) 2 0 r σ ( r ) d r .
β ( r ) = C 2 σ ( r ) k .
d S ( r ) d r = k σ ( r ) d σ ( r ) d r 2 σ ( r ) ,
σ ( r ) = exp { [ S ( r ) S ( r 0 ) ] / k } σ ( r 0 ) 1 2 k r 0 r exp { [ S ( r ) S ( r 0 ) ] / k } d r ,
σ ( r ) = exp { [ S ( r ) S ( r f ) ] / k } σ ( r f ) 1 + 2 k r r f exp { [ S ( r ) S ( r f ) ] / k } d r ,
σ ( r f ) = { exp [ S m ( r f ) + 2 I 0 ln ( C 1 C 2 ) k ] 2 k r 0 r f exp [ S m ( r ) S m ( r f ) k ] d r } 1 .
k ln σ ( r 0 ) = S m ( r 0 ) + 2 r 0 σ ( r 0 ) ln ( C 1 C 2 )
½ d S ( r ) d r .
S ( r ) = 1.68 r 4.98
ln ( C 1 C 2 ) = 4.8.
ln ( C 1 C 2 ) = ln ( C 2 / C 2 ) 4.8 ,
VIS = 3.912 ( r f r 0 ) , r 0 r f σ ( r ) d r ,
k ln σ ( r 0 ) = S m ( r 0 ) + 2 r 0 σ ( r 0 ) ln ( C 1 C 2 ) .
k ln χ = ln ( C 2 C 2 ) + 2 r 0 σ ( r 0 ) ( 1 1 χ ) ,
χ = σ ( r 0 ) σ ( r 0 ) .
σ ( r f ) = σ 0 1 + [ ( C 2 / C 2 ) 1 ] exp [ 2 σ 0 ( r f r f ) ] .
σ ( r f ) = σ 0 1 + [ ( C 2 / C 2 ) 1 ] exp 2 σ 0 ( r r 0 ) ] .
r = r 0 1 2 σ 0 ln [ 1 ( C 2 / C 2 ) ] .

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