Abstract

A Monte Carlo model has been developed which simulates the multiple-scattering of middle-uv radiation in the lower atmosphere. The source of radiation is assumed to be monochromatic and located at a point. The physical effects taken into account in the model are Rayleigh and Mie scattering, pure absorption by particulates and trace atmospheric gases, and ground albedo. The model output consists of the multiply scattered radiance as a function of look-angle of a detector located within the atmosphere. Several examples are discussed, and comparisons are made with direct-source and single-scattered contributions to the signal received by the detector.

© 1978 Optical Society of America

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References

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  1. L. L. House, L. W. Avery, J. Quant. Spectrosc. Radiat. Transfer 9, 1579 (1969).
    [Crossref]
  2. R. R. Meier, J.-S. Lee, Astrophys. J. 219, 262 (1978).
    [Crossref]
  3. L. G. Henyey, J. L. Greenstein, Astrophys. J. 93, 70 (1941).
    [Crossref]
  4. L.-S. Lee, Astrophys. J. 217, 857 (1977).
    [Crossref]
  5. D. G. Collins, M. B. Wells, Radiation Research Assoc. Tech. Rept. ECOM-00240-F, Fort Worth, Texas (1965).
  6. R. L. Lucke, Thesis; Johns Hopkins U. (1975).
  7. R. L. Lucke, R. C. Henry, W. G. Fastie, Astron. J. 81, 1162 (1976).
    [Crossref]

1978 (1)

R. R. Meier, J.-S. Lee, Astrophys. J. 219, 262 (1978).
[Crossref]

1977 (1)

L.-S. Lee, Astrophys. J. 217, 857 (1977).
[Crossref]

1976 (1)

R. L. Lucke, R. C. Henry, W. G. Fastie, Astron. J. 81, 1162 (1976).
[Crossref]

1969 (1)

L. L. House, L. W. Avery, J. Quant. Spectrosc. Radiat. Transfer 9, 1579 (1969).
[Crossref]

1941 (1)

L. G. Henyey, J. L. Greenstein, Astrophys. J. 93, 70 (1941).
[Crossref]

Avery, L. W.

L. L. House, L. W. Avery, J. Quant. Spectrosc. Radiat. Transfer 9, 1579 (1969).
[Crossref]

Collins, D. G.

D. G. Collins, M. B. Wells, Radiation Research Assoc. Tech. Rept. ECOM-00240-F, Fort Worth, Texas (1965).

Fastie, W. G.

R. L. Lucke, R. C. Henry, W. G. Fastie, Astron. J. 81, 1162 (1976).
[Crossref]

Greenstein, J. L.

L. G. Henyey, J. L. Greenstein, Astrophys. J. 93, 70 (1941).
[Crossref]

Henry, R. C.

R. L. Lucke, R. C. Henry, W. G. Fastie, Astron. J. 81, 1162 (1976).
[Crossref]

Henyey, L. G.

L. G. Henyey, J. L. Greenstein, Astrophys. J. 93, 70 (1941).
[Crossref]

House, L. L.

L. L. House, L. W. Avery, J. Quant. Spectrosc. Radiat. Transfer 9, 1579 (1969).
[Crossref]

Lee, J.-S.

R. R. Meier, J.-S. Lee, Astrophys. J. 219, 262 (1978).
[Crossref]

Lee, L.-S.

L.-S. Lee, Astrophys. J. 217, 857 (1977).
[Crossref]

Lucke, R. L.

R. L. Lucke, R. C. Henry, W. G. Fastie, Astron. J. 81, 1162 (1976).
[Crossref]

R. L. Lucke, Thesis; Johns Hopkins U. (1975).

Meier, R. R.

R. R. Meier, J.-S. Lee, Astrophys. J. 219, 262 (1978).
[Crossref]

Wells, M. B.

D. G. Collins, M. B. Wells, Radiation Research Assoc. Tech. Rept. ECOM-00240-F, Fort Worth, Texas (1965).

Astron. J. (1)

R. L. Lucke, R. C. Henry, W. G. Fastie, Astron. J. 81, 1162 (1976).
[Crossref]

Astrophys. J. (3)

R. R. Meier, J.-S. Lee, Astrophys. J. 219, 262 (1978).
[Crossref]

L. G. Henyey, J. L. Greenstein, Astrophys. J. 93, 70 (1941).
[Crossref]

L.-S. Lee, Astrophys. J. 217, 857 (1977).
[Crossref]

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

L. L. House, L. W. Avery, J. Quant. Spectrosc. Radiat. Transfer 9, 1579 (1969).
[Crossref]

Other (2)

D. G. Collins, M. B. Wells, Radiation Research Assoc. Tech. Rept. ECOM-00240-F, Fort Worth, Texas (1965).

R. L. Lucke, Thesis; Johns Hopkins U. (1975).

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Figures (9)

Fig. 1
Fig. 1

Simulation model geometry.

Fig. 2
Fig. 2

Detector configuration showing referencing of scattering to detectors located in the plane containing the source and the scattering point. The angular bins of the detector are also indicated. For the models in this report Δα = 15°.

Fig. 3
Fig. 3

Ground reflection geometry for specular scattering showing a plane of scattering.

Fig. 4
Fig. 4

Top view of detector ring showing the effect of a finite number of detectors.

Fig. 5
Fig. 5

Geometric parameters of model conditions (see Table I for numerical values). Note that α is measured from nadir toward the source.

Fig. 6
Fig. 6

Radiance (left scale) at 2537 Å as a function of line-of-sight angle from nadir for the first three entries in Table I. The irradiance directly from the source is indicated for the two geometries by the circled symbols (use scale on right). The multiply scattered irradiance in a 0.0535 sr field of view can be found by referring the symbols to the right scale. No Mie scattering is included here. Symbols are used in place of histograms for clarity.

Fig. 7
Fig. 7

Radiances or irradiances at 2537 Å for the fourth, fifth, and sixth entries in Table I. Mie scattering is included (see Fig. 6 caption).

Fig. 8
Fig. 8

Radiances and irradiances at 2800 Å for the last three entries in Table II. No Mie scattering is included (see Fig. 6 caption).

Fig. 9
Fig. 9

Phase function for single scattering of unpolarized incident light. Results are shown for varying degrees of asymmetry, characterized by the first moment g, of the phase function.

Tables (1)

Tables Icon

Table I Model Parameters

Equations (37)

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σ R = 4.8 × 10 37 ( m ¯ 1 ) 2 / λ 4 ,
θ s = cos 1 ( 2 r 1 1 ) ,
ϕ s = 2 π r 2 ,
τ = ln r 3 .
x = x + τ u , y = y + τ υ , z = z + τ w ,
u = sin θ sin ϕ , υ = sin θ cos ϕ , w = cos θ .
x 2 + y 2 d 1 2
τ 1 = ( x + h s ) / cos θ ; τ 2 = τ τ 1 ,
x g = x + τ 1 sin θ sin ϕ , y g = y + τ 1 sin θ cos ϕ , z g = h s .
x = x g + τ 2 sin θ sin ϕ , y = y g + τ 2 sin θ cos ϕ , z = z g τ 2 cos θ .
f a = ( σ a n a ) / ( σ R n R + σ M n M ) ,
w = w exp ( f a τ ) ,
w = w ( 1 A g ) exp ( f a τ )
P i = w i p ( γ i ) d Ω i exp [ ( 1 + f a ) R i ] ,
Δ ω = β Δ α = [ ( 2 π ) / k ] Δ α .
Σ P i = Σ w i p ( γ i ) d Ω i exp [ ( 1 + f a ) R i ] .
I j = ( Σ P i / k ) / ( d A N Δ ω ) ,
I j = [ Σ w i p ( γ i ) exp [ ( 1 + f a ) R i ] / R i 2 ] / [ 2 π N ( σ R n R + σ n n M ) Δ α ] ,
I j = { Σ w i p ( γ i ) exp [ ( 1 + f a ) R i ] / R i 2 } / [ 8 π 2 N ( σ R n R + σ M n M ) 2 Δ α ]
p R ( γ i ) = 3 ( 1 + cos 2 γ i ) / 16 π ,
p M ( γ i ) = ( 1 g 2 ) / 4 π ( 1 + g 2 2 g cos γ i ) 3 / 2 ,
η = 2 π r 5 .
cos γ = { ( 1 + g 2 ) [ ( 1 g 2 ) / ( 1 g + 2 g r 6 ) 2 ] } / 2 g .
u 1 = sin γ sin η , υ 1 = sin γ cos η , w 1 = cos γ .
u = u 1 cos ϕ + ( υ 1 cos θ + w 1 sin θ ) sin ϕ , υ = u 1 sin ϕ + ( υ 1 cos θ + w 1 sin θ ) cos ϕ , w = υ 1 sin θ + w 1 cos θ ,
cos θ = w , cos ϕ = υ / sin θ , sin ϕ = u / sin θ .
x = x + τ u , y = y + τ υ , z = z + τ w .
F D S = exp [ ( 1 + f a ) τ D S ] / 4 π r D S 2 ,
g = 0 2 π 1 + 1 cos γ p ( γ ) d ( cos γ ) d ϕ .
p ( γ ) = ( 1 g 2 ) / 4 π ( 1 2 g cos γ + g 2 ) 3 / 2 ,
I = 0 ( r ) exp [ τ ( 1 + f a ) ] d s ,
( r ) = j ( r ) p ( γ ) ,
j ( r ) = F ( r ) σ n ,
f ( r ) Δ A = [ J / ( 4 π ) Δ Ω exp [ τ ( 1 + f a ) ] ,
F ( r ) = J 4 π r 2 exp [ τ ( 1 + f a ) ] .
I = J σ n 4 π 0 p ( γ ) r 2 exp [ ( τ + τ ) ( 1 + f a ) ] d s .
I = 3 32 π 2 J ( σ n ) 2 exp [ τ D S ( 1 + f a ) ] τ D S E 2 [ 2 τ D S ( 1 + f a ) ] ,

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