Abstract

The reflected flux from a regular array of 2- and 3-D clouds has been computed to estimate the effect of fractional cloud cover on albedos and the solar flux available to heat the earth’s surface. The broken clouds are represented by a regular array of identical cuboids for the 3-D problem and equally spaced, infinitely long, bars for the 2-D problem. A diffusion approximation to the radiative transfer equation is used to compute the fluxes leaving each face of the cloud. Interaction between clouds is simulated by assuming diffuse exitance from the cloud faces and applying angle factors to obtain modified boundary conditions on each cloud face.

© 1982 Optical Society of America

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References

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  1. T. B. McKee, S. K. Cox, J. Atmos. Sci. 31, 1885 (1974).
    [CrossRef]
  2. R. Davies, J. Atmos. Sci. 35, 1712 (1978).
    [CrossRef]
  3. K. N. Liou, S. C. Ou, J. Atmos. Sci. 36, 1985 (1979).
    [CrossRef]
  4. Harshvardhan, J. A. Weinman, R. Davies, J. Atmos. Sci. 38, 2500 (1981).
    [CrossRef]
  5. M. Aida, J. Quant. Spectrosc. Radiat. Transfer 17, 303 (1977).
    [CrossRef]
  6. M. Gube, J. Schmetz, E. Raschke, Beitr. Phys. Atmos. 53, 24 (1980).
  7. S. G. Bradley, J. Atmos. Sci. 38, 2243 (1981).
    [CrossRef]
  8. Harshvardhan, J. A. Weinman, J. Atmos. Sci. 39, 431 (1982).
    [CrossRef]
  9. V. Plank, J. Appl. Meteorol. 8, 46 (1969).
    [CrossRef]
  10. E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (McGraw-Hill, New York, 1978).
  11. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

1982 (1)

Harshvardhan, J. A. Weinman, J. Atmos. Sci. 39, 431 (1982).
[CrossRef]

1981 (2)

Harshvardhan, J. A. Weinman, R. Davies, J. Atmos. Sci. 38, 2500 (1981).
[CrossRef]

S. G. Bradley, J. Atmos. Sci. 38, 2243 (1981).
[CrossRef]

1980 (1)

M. Gube, J. Schmetz, E. Raschke, Beitr. Phys. Atmos. 53, 24 (1980).

1979 (1)

K. N. Liou, S. C. Ou, J. Atmos. Sci. 36, 1985 (1979).
[CrossRef]

1978 (1)

R. Davies, J. Atmos. Sci. 35, 1712 (1978).
[CrossRef]

1977 (1)

M. Aida, J. Quant. Spectrosc. Radiat. Transfer 17, 303 (1977).
[CrossRef]

1974 (1)

T. B. McKee, S. K. Cox, J. Atmos. Sci. 31, 1885 (1974).
[CrossRef]

1969 (1)

V. Plank, J. Appl. Meteorol. 8, 46 (1969).
[CrossRef]

Aida, M.

M. Aida, J. Quant. Spectrosc. Radiat. Transfer 17, 303 (1977).
[CrossRef]

Bradley, S. G.

S. G. Bradley, J. Atmos. Sci. 38, 2243 (1981).
[CrossRef]

Cess, R. D.

E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (McGraw-Hill, New York, 1978).

Cox, S. K.

T. B. McKee, S. K. Cox, J. Atmos. Sci. 31, 1885 (1974).
[CrossRef]

Davies, R.

Harshvardhan, J. A. Weinman, R. Davies, J. Atmos. Sci. 38, 2500 (1981).
[CrossRef]

R. Davies, J. Atmos. Sci. 35, 1712 (1978).
[CrossRef]

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

Gube, M.

M. Gube, J. Schmetz, E. Raschke, Beitr. Phys. Atmos. 53, 24 (1980).

Harshvardhan,

Harshvardhan, J. A. Weinman, J. Atmos. Sci. 39, 431 (1982).
[CrossRef]

Harshvardhan, J. A. Weinman, R. Davies, J. Atmos. Sci. 38, 2500 (1981).
[CrossRef]

Liou, K. N.

K. N. Liou, S. C. Ou, J. Atmos. Sci. 36, 1985 (1979).
[CrossRef]

McKee, T. B.

T. B. McKee, S. K. Cox, J. Atmos. Sci. 31, 1885 (1974).
[CrossRef]

Ou, S. C.

K. N. Liou, S. C. Ou, J. Atmos. Sci. 36, 1985 (1979).
[CrossRef]

Plank, V.

V. Plank, J. Appl. Meteorol. 8, 46 (1969).
[CrossRef]

Raschke, E.

M. Gube, J. Schmetz, E. Raschke, Beitr. Phys. Atmos. 53, 24 (1980).

Schmetz, J.

M. Gube, J. Schmetz, E. Raschke, Beitr. Phys. Atmos. 53, 24 (1980).

Sparrow, E. M.

E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (McGraw-Hill, New York, 1978).

Weinman, J. A.

Harshvardhan, J. A. Weinman, J. Atmos. Sci. 39, 431 (1982).
[CrossRef]

Harshvardhan, J. A. Weinman, R. Davies, J. Atmos. Sci. 38, 2500 (1981).
[CrossRef]

Beitr. Phys. Atmos. (1)

M. Gube, J. Schmetz, E. Raschke, Beitr. Phys. Atmos. 53, 24 (1980).

J. Appl. Meteorol. (1)

V. Plank, J. Appl. Meteorol. 8, 46 (1969).
[CrossRef]

J. Atmos. Sci. (6)

S. G. Bradley, J. Atmos. Sci. 38, 2243 (1981).
[CrossRef]

Harshvardhan, J. A. Weinman, J. Atmos. Sci. 39, 431 (1982).
[CrossRef]

T. B. McKee, S. K. Cox, J. Atmos. Sci. 31, 1885 (1974).
[CrossRef]

R. Davies, J. Atmos. Sci. 35, 1712 (1978).
[CrossRef]

K. N. Liou, S. C. Ou, J. Atmos. Sci. 36, 1985 (1979).
[CrossRef]

Harshvardhan, J. A. Weinman, R. Davies, J. Atmos. Sci. 38, 2500 (1981).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

M. Aida, J. Quant. Spectrosc. Radiat. Transfer 17, 303 (1977).
[CrossRef]

Other (2)

E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (McGraw-Hill, New York, 1978).

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

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Figures (8)

Fig. 1
Fig. 1

Schematic showing regular array of cuboids.

Fig. 2
Fig. 2

Ratio of flux reflected by a cloud array to that reflected by an isolated cloud obtained from this study, ––, with the results obtained by Aida, ●. Model uses ω ˜ = 0.9999 and g = 0.86; vertical optical depth, τ* = 49.

Fig. 3
Fig. 3

(Ne/N) vs N for overhead sun. The cloud array consists of identical cubes of unit aspect ratio. Single-scattering albedos are marked on figures, g = 0.86; vertical optical depth is τ* = 100. These results are nearly identical to those applicable to the case when ϕ = 90° for θ0 = 30° and 60°.

Fig. 4
Fig. 4

Schematic showing regular array of infinitely long bars.

Fig. 5
Fig. 5

(Ne/N) vs N for overhead sun. The cloud array consists of identical infinitely long bars of unit aspect ratio. Single-scattering albedos are marked on figures, g = 0.86; vertical optical depth is τ* = 100.

Fig. 6
Fig. 6

As in Fig. 5 except at solar zenith angle θ0 = 30° and ϕ = 0°

Fig. 7
Fig. 7

As in Fig. 5 except at solar zenith angle θ0 = 60° and ϕ = 0°

Fig. 8
Fig. 8

Fractional flux transmitted through bar and stratiform clouds as a function of μ0 = cosθ0 and ϕ = 0° for cloud fractions N = 0.25, 0.50, and 0.75.

Tables (1)

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Table I Plane–parallel Albedos App

Equations (8)

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( F ) x = s / 2 = F ( F ) x = - s / 2 ,
( F ) x = s / 2 = ( F ) x = - s / 2 ,
F c = [ 1 + 2 a ( 1 + 0.15 N ) - 0.15 ( 1 - N ) ] N 1 + 2 a N ( 1 + 0.15 N ) .
F = N e F p p ( τ * ) ,
F b = ( 1 - N a N ) [ 1 + ( a N 1 - N ) 2 - 1 ] ,
F ¯ ( x = s / 2 ) = F 0 sin θ 0 { d z * cos θ 0 + cos θ 0 τ * [ 1 - exp ( z * - d cot θ 0 ) / cos θ 0 ] }
F ¯ ( x = s / 2 ) = F 0 sin θ 0 ,
N e N = 1 + ( 1 - N ) 2 N [ 1 + tan θ 0 - sec θ 0 ]

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