Abstract

The terminology of light scattering pertinent to a simple form of the lidar equation and the approximate analytical solution of the lidar equation are reviewed without specific restriction on the nature of the cloud scatterers. A boundary value of the volume backscattering coefficient and the relationship between extinction and backscattering are required for the solution. Given the boundary value of the backscattering coefficient and the total transmittance through a cloud, it is possible to derive (by successive approximation) an extinction/backscatter ratio empirically. Application of the method to the ruby lidar return from a cirrus cloud led to a ratio of 28 sr, and to reasonable profiles of the backscatter coefficient and the transmittance through the cloud.

© 1969 Optical Society of America

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References

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  1. R. Penndorf, J. Opt. Soc. Amer. 52, 402 (1962).
    [CrossRef]
  2. L. Elterman, “UV, Visible, and IR Attenuation for Altitudes to 50 km, 1968,” Rep. AFCRL–68–0153, Air Force Cambridge Research Laboratories1968).
  3. W. E. Evans, “Remote Probing of High Cloud Cover via Satellite-Borne Lidar,” Final Rep. NASr–49(27), Stanford Research Institute, Menlo Park, California (1968).
  4. W. Hitschfeld, J. Bordan, J. Meteorol. 11, 58 (1954).
    [CrossRef]
  5. E. W. Barrett, O. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
    [CrossRef]
  6. E. E. Uthe, Stanford Research Institute (1968); unpublished notes.
  7. S. Twomey, H. B. Howell, Appl. Opt. 4, 501 (1965).
    [CrossRef]
  8. J. A. Curcio, G. L. Knestrick, J. Opt. Soc. Amer. 48, 686 (1958).
    [CrossRef]
  9. W. Viezee, E. E. Uthe, R. T. H. Collis, J. Appl. Meteorol. 8, 274 (1969).
    [CrossRef]

1969 (1)

W. Viezee, E. E. Uthe, R. T. H. Collis, J. Appl. Meteorol. 8, 274 (1969).
[CrossRef]

1967 (1)

E. W. Barrett, O. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
[CrossRef]

1965 (1)

1962 (1)

R. Penndorf, J. Opt. Soc. Amer. 52, 402 (1962).
[CrossRef]

1958 (1)

J. A. Curcio, G. L. Knestrick, J. Opt. Soc. Amer. 48, 686 (1958).
[CrossRef]

1954 (1)

W. Hitschfeld, J. Bordan, J. Meteorol. 11, 58 (1954).
[CrossRef]

Barrett, E. W.

E. W. Barrett, O. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
[CrossRef]

Ben-Dov, O.

E. W. Barrett, O. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
[CrossRef]

Bordan, J.

W. Hitschfeld, J. Bordan, J. Meteorol. 11, 58 (1954).
[CrossRef]

Collis, R. T. H.

W. Viezee, E. E. Uthe, R. T. H. Collis, J. Appl. Meteorol. 8, 274 (1969).
[CrossRef]

Curcio, J. A.

J. A. Curcio, G. L. Knestrick, J. Opt. Soc. Amer. 48, 686 (1958).
[CrossRef]

Elterman, L.

L. Elterman, “UV, Visible, and IR Attenuation for Altitudes to 50 km, 1968,” Rep. AFCRL–68–0153, Air Force Cambridge Research Laboratories1968).

Evans, W. E.

W. E. Evans, “Remote Probing of High Cloud Cover via Satellite-Borne Lidar,” Final Rep. NASr–49(27), Stanford Research Institute, Menlo Park, California (1968).

Hitschfeld, W.

W. Hitschfeld, J. Bordan, J. Meteorol. 11, 58 (1954).
[CrossRef]

Howell, H. B.

Knestrick, G. L.

J. A. Curcio, G. L. Knestrick, J. Opt. Soc. Amer. 48, 686 (1958).
[CrossRef]

Penndorf, R.

R. Penndorf, J. Opt. Soc. Amer. 52, 402 (1962).
[CrossRef]

Twomey, S.

Uthe, E. E.

W. Viezee, E. E. Uthe, R. T. H. Collis, J. Appl. Meteorol. 8, 274 (1969).
[CrossRef]

E. E. Uthe, Stanford Research Institute (1968); unpublished notes.

Viezee, W.

W. Viezee, E. E. Uthe, R. T. H. Collis, J. Appl. Meteorol. 8, 274 (1969).
[CrossRef]

Appl. Opt. (1)

J. Appl. Meteorol. (2)

W. Viezee, E. E. Uthe, R. T. H. Collis, J. Appl. Meteorol. 8, 274 (1969).
[CrossRef]

E. W. Barrett, O. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967).
[CrossRef]

J. Meteorol. (1)

W. Hitschfeld, J. Bordan, J. Meteorol. 11, 58 (1954).
[CrossRef]

J. Opt. Soc. Amer. (2)

J. A. Curcio, G. L. Knestrick, J. Opt. Soc. Amer. 48, 686 (1958).
[CrossRef]

R. Penndorf, J. Opt. Soc. Amer. 52, 402 (1962).
[CrossRef]

Other (3)

L. Elterman, “UV, Visible, and IR Attenuation for Altitudes to 50 km, 1968,” Rep. AFCRL–68–0153, Air Force Cambridge Research Laboratories1968).

W. E. Evans, “Remote Probing of High Cloud Cover via Satellite-Borne Lidar,” Final Rep. NASr–49(27), Stanford Research Institute, Menlo Park, California (1968).

E. E. Uthe, Stanford Research Institute (1968); unpublished notes.

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Figures (2)

Fig. 1
Fig. 1

Oscilloscope traces of lidar return from cirrus cloud at 2130 PST, 21 February 1968, Menlo Park.

Fig. 2
Fig. 2

Backscattering and transmittance profiles derived from lidar observation of cirrus cloud.

Equations (18)

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G = geometric cross section at normal incidence ( m 2 ) , q θ = angular scattering efficiency ( sr 1 ) = [ energy scattered in unit time into unit solid angle in direction θ ] [ enregy incident in unit time on G ] , Q s = total scattered efficiency ( nondimensional ) = 0 4 π q θ d ω .
β θ = angular volume scattering coefficient ( cm 1 sr 1 ) = [ energy scattered in unit time from unit volume into unit solid angel in direction θ ] [ enregy incident in unit time on unit geometric cross section of V ] β = total volume scattering coefficient ( cm 1 ) = 0 4 π β θ d ω .
j = index denoting j th set of identical particles , β θ = j ( q θ G N ) j = j ( f θ Q s G N ) j , β = j ( Q s G N ) j , where Q s 2 for large scatterers .
β θ = f ¯ θ β ,
f ¯ θ = j ( f θ Q s G N ) j / j ( Q s G N ) j .
P R ( r ) r 2 = A R L P T T 2 a β π ( r ) exp ( 2 r c r γ d r ) ,
S ( r ) = 10 log { [ P R ( r ) r 2 ] / [ P R ( r 1 ) r 1 2 ] } .
0.23 S ( r ) = ln [ β π ( r ) / β π ( r 1 ) ] 2 r 1 r γ d r ,
β π ( r 1 ) = β π ( r M ) [ P R ( r 1 ) r 1 2 / ] [ P R ( r M ) r M 2 ] .
0.23 d S d r = d ln β π d r 2 γ .
γ = ( g / f ¯ π ) β π = b β π .
( d ψ / d r ) + 0.23 ( d S / d r ) ψ + 2 b = 0.
β π ( r ) = exp [ 0.23 S ( r ) ] { ψ 1 2 b r 1 r exp [ 0.23 S ( h ) ] d h } 1 ,
γ = a + b β π ,
β π ( r ) = exp [ 0.23 S ( r ) + 2 a ( r r 1 ) ] { ψ 1 2 b × r 1 r exp [ 0.23 S ( h ) + 2 a ( h r 1 ) ] d h } 1 ,
γ = b C ( r ) β π ,
β π ( r ) = exp [ 0.23 S ( r ) ] { ψ 1 2 b × r 1 r C ( h ) exp [ 0.23 S ( h ) ] d h } 1 .
d ln β π d r = 1 d ln γ k d r ,

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