Abstract

A simplified physical model of cirrus cloud 8–13-μ radiance is derived, in an attempt to explain measured cloud radiance characteristics. Thermal emission and scattering of irradiance from the earth are considered separately. The scattering diagram for a 50-μ radius ice sphere, which is opaque at these wavelengths, is computed from diffraction theory and specular surface reflection. Thermal emission is found to exceed scattered radiance significantly for all zenith angles, and computed radiance values are found to match measured cloud radiance closely.

© 1968 Optical Society of America

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References

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  1. F. F. Hall, Appl. Opt. 7, 891 (1968).
    [CrossRef] [PubMed]
  2. Z. Sekera, “Radiative Transfer in a Planetary Atmosphere with Imperfect Scattering,” Rand Corp. R–413–PR, June1963 (AD 407 493).
  3. R. K. McDonald, R. W. Deltenre, J. Opt. Soc. Amer. 53, 860 (1963).
    [CrossRef]
  4. G. Yamamoto, M. Tanaka, K. Kamitani, J. Atmos. Sci. 23, 305 (1966).
    [CrossRef]
  5. H. Weickmann, Ber. Deut. Wetter. U. S. Zone 6, 61 (1949) (available from NASA as R&T 273).
  6. H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957), p. 111.
  7. W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).
    [CrossRef]
  8. D. Deirmendjian, R. Clasen, W. Viezee, J. Opt. Soc. Amer. 51, 620 (1961).
    [CrossRef]
  9. S. Twomey, Tables of Scattering and Extinction Efficiencies, unpublished computations by U. S. Weather Bureau, Washington, D. C. (1963).
  10. Ref. 6, p. 99.
  11. J. R. Hodkinson, in Electromagnetic Scattering, M. Kerker, Ed. (Pergamon Press, Inc., New York, 1963), pp. 87–100.
  12. F. F. Hall, Appl. Opt. 3, 781 (1964).
    [CrossRef]
  13. R. O. Gumprecht, C. M. Sliepevich, Phys. Chem. 57, 90 (1953).
    [CrossRef]
  14. P. J. Klass, Aviation Week & Space Technol. 88, 80 (1968).

1968 (3)

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).
[CrossRef]

P. J. Klass, Aviation Week & Space Technol. 88, 80 (1968).

F. F. Hall, Appl. Opt. 7, 891 (1968).
[CrossRef] [PubMed]

1966 (1)

G. Yamamoto, M. Tanaka, K. Kamitani, J. Atmos. Sci. 23, 305 (1966).
[CrossRef]

1964 (1)

1963 (1)

R. K. McDonald, R. W. Deltenre, J. Opt. Soc. Amer. 53, 860 (1963).
[CrossRef]

1961 (1)

D. Deirmendjian, R. Clasen, W. Viezee, J. Opt. Soc. Amer. 51, 620 (1961).
[CrossRef]

1953 (1)

R. O. Gumprecht, C. M. Sliepevich, Phys. Chem. 57, 90 (1953).
[CrossRef]

1949 (1)

H. Weickmann, Ber. Deut. Wetter. U. S. Zone 6, 61 (1949) (available from NASA as R&T 273).

Clasen, R.

D. Deirmendjian, R. Clasen, W. Viezee, J. Opt. Soc. Amer. 51, 620 (1961).
[CrossRef]

Deirmendjian, D.

D. Deirmendjian, R. Clasen, W. Viezee, J. Opt. Soc. Amer. 51, 620 (1961).
[CrossRef]

Deltenre, R. W.

R. K. McDonald, R. W. Deltenre, J. Opt. Soc. Amer. 53, 860 (1963).
[CrossRef]

Gumprecht, R. O.

R. O. Gumprecht, C. M. Sliepevich, Phys. Chem. 57, 90 (1953).
[CrossRef]

Hall, F. F.

Hodkinson, J. R.

J. R. Hodkinson, in Electromagnetic Scattering, M. Kerker, Ed. (Pergamon Press, Inc., New York, 1963), pp. 87–100.

Irvine, W. M.

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).
[CrossRef]

Kamitani, K.

G. Yamamoto, M. Tanaka, K. Kamitani, J. Atmos. Sci. 23, 305 (1966).
[CrossRef]

Klass, P. J.

P. J. Klass, Aviation Week & Space Technol. 88, 80 (1968).

McDonald, R. K.

R. K. McDonald, R. W. Deltenre, J. Opt. Soc. Amer. 53, 860 (1963).
[CrossRef]

Pollack, J. B.

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).
[CrossRef]

Sekera, Z.

Z. Sekera, “Radiative Transfer in a Planetary Atmosphere with Imperfect Scattering,” Rand Corp. R–413–PR, June1963 (AD 407 493).

Sliepevich, C. M.

R. O. Gumprecht, C. M. Sliepevich, Phys. Chem. 57, 90 (1953).
[CrossRef]

Tanaka, M.

G. Yamamoto, M. Tanaka, K. Kamitani, J. Atmos. Sci. 23, 305 (1966).
[CrossRef]

Twomey, S.

S. Twomey, Tables of Scattering and Extinction Efficiencies, unpublished computations by U. S. Weather Bureau, Washington, D. C. (1963).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957), p. 111.

Viezee, W.

D. Deirmendjian, R. Clasen, W. Viezee, J. Opt. Soc. Amer. 51, 620 (1961).
[CrossRef]

Weickmann, H.

H. Weickmann, Ber. Deut. Wetter. U. S. Zone 6, 61 (1949) (available from NASA as R&T 273).

Yamamoto, G.

G. Yamamoto, M. Tanaka, K. Kamitani, J. Atmos. Sci. 23, 305 (1966).
[CrossRef]

Appl. Opt. (2)

Aviation Week & Space Technol. (1)

P. J. Klass, Aviation Week & Space Technol. 88, 80 (1968).

Ber. Deut. Wetter. U. S. Zone (1)

H. Weickmann, Ber. Deut. Wetter. U. S. Zone 6, 61 (1949) (available from NASA as R&T 273).

Icarus (1)

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).
[CrossRef]

J. Atmos. Sci. (1)

G. Yamamoto, M. Tanaka, K. Kamitani, J. Atmos. Sci. 23, 305 (1966).
[CrossRef]

J. Opt. Soc. Amer. (2)

D. Deirmendjian, R. Clasen, W. Viezee, J. Opt. Soc. Amer. 51, 620 (1961).
[CrossRef]

R. K. McDonald, R. W. Deltenre, J. Opt. Soc. Amer. 53, 860 (1963).
[CrossRef]

Phys. Chem. (1)

R. O. Gumprecht, C. M. Sliepevich, Phys. Chem. 57, 90 (1953).
[CrossRef]

Other (5)

Z. Sekera, “Radiative Transfer in a Planetary Atmosphere with Imperfect Scattering,” Rand Corp. R–413–PR, June1963 (AD 407 493).

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957), p. 111.

S. Twomey, Tables of Scattering and Extinction Efficiencies, unpublished computations by U. S. Weather Bureau, Washington, D. C. (1963).

Ref. 6, p. 99.

J. R. Hodkinson, in Electromagnetic Scattering, M. Kerker, Ed. (Pergamon Press, Inc., New York, 1963), pp. 87–100.

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Figures (7)

Fig. 1
Fig. 1

Optical constants of ice.

Fig. 2
Fig. 2

Scattering diagram for 50-μ radius ice spheres.

Fig. 3
Fig. 3

Scattering geometry where the earth is the source of irradiance.

Fig. 4
Fig. 4

Infrared radiance of a cirrus cloud at 8–13.5 μ.

Fig. 5
Fig. 5

Infrared radiance of a cirrus haze at 8–13.5 μ.

Fig. 6
Fig. 6

Comparison of haze model radiance with measurements.

Fig. 7
Fig. 7

Comparison of cloud model radiance with measurements.

Equations (14)

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i 1 = π 2 a 2 ρ 1 / λ 2 , i 2 = π 2 a 2 ρ 2 / λ 2 .
τ a = π a 2 Q a n l ,
= ( 1 - e - τ a / ξ ) ( 1 - ω ) .
N E ( ζ ) = ( 1 - ω ) N B B ( T ) 8 - 13.5 [ 1 - exp ( - π a 2 Q a n l / ξ ) ] .
d N s ( ζ ) = λ 2 N n d l 8 π 2 ξ j ( i 1 + i 2 ) j Δ Ω j ,
β = 0 τ 1 exp ( - τ ξ - τ ξ ) d τ = ξ ξ ξ + ξ × { 1 - exp [ - τ 1 ( 1 ξ + 1 ξ ) ] } .
Q sca = Q diff + Q refl ,
τ s = π a 2 Q ref l n l .
τ x = τ a + τ s ,
N s ( ζ ) = λ 2 N n l 8 π 2 j ( i 1 + i 2 ) j Δ Ω j ξ j ξ j + ξ × { 1 - exp [ - τ x ( 1 ξ j + 1 ξ ) ] } ,
N c = N v + t ( N E + N s ) .
P = ( i 1 - i 2 ) / ( i 1 + i 2 ) = ( i - i ) / ( i + i ) .
P ( ζ ) = [ j ( i 1 ) j - j ( i 2 ) j ] / [ j ( i 1 ) j + j ( i 2 ) j ] ,
i 1 , 2 = i ( θ ) 1 , 2 cos 2 ψ + i ( θ ) 2 , 1 sin 2 ψ ,

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