Abstract

An approximate analytical expression is developed for the attenuation of middle ultraviolet radiation along slant paths through the atmosphere. The independent variables are wavelength, altitude of source (the detector is assumed to be above the atmosphere), angle of path with respect to zenith, and three parameters which characterize the ozone distribution. An approximate analytical expression is also developed for the scattered solar radiance seen by a satellite. Here the independent variables are the wavelength, the look angle and the sun angle with respect to the zenith, the scattering angle, and again three parameters which characterize the ozone distribution. The results based upon the formula are compared with previous studies and an experimental measurement.

© 1964 Optical Society of America

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References

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  1. A. E. S. Green, M. Griggs, Appl. Opt. 2, 561 (163).
  2. H. U. Dütsch, Arch. Meteorol. Geophys. Bioklimatol. Ser. A11, 240 (1959).
  3. A. E. S. Green, C. E. Porter, D. S. Saxon, eds., Proceedings of the International Conference on the Nuclear Optical Model (Florida State University Studies, 1959).
  4. R. Hofstadter, F. Bumiller, M. R. Yearian, Rev. Mod. Phys. 30, 482 (1958).
    [Crossref]
  5. A. E. S. Green, Phys. Today 15, (1), 41 (1962).
  6. T. L. Altshuler, Fig. 18, Document No. 61SD199, December1961, General Electric M. S. V. D.Philadelphia, Pa.
  7. S. Chapman, Proc. Phys. Soc. (London) 43, 483 (1931).
    [Crossref]
  8. AFCRL, Handbook of Geophysics (Macmillan, New York, 1960).
  9. Geophysics Corporation of American Report 61-35-A, AF 19(604)-7412, 1July1961.
  10. L. M. Biberman, unpublished note.
  11. E. Mayfield, private communication.

1962 (1)

A. E. S. Green, Phys. Today 15, (1), 41 (1962).

1959 (1)

H. U. Dütsch, Arch. Meteorol. Geophys. Bioklimatol. Ser. A11, 240 (1959).

1958 (1)

R. Hofstadter, F. Bumiller, M. R. Yearian, Rev. Mod. Phys. 30, 482 (1958).
[Crossref]

1931 (1)

S. Chapman, Proc. Phys. Soc. (London) 43, 483 (1931).
[Crossref]

Altshuler, T. L.

T. L. Altshuler, Fig. 18, Document No. 61SD199, December1961, General Electric M. S. V. D.Philadelphia, Pa.

Biberman, L. M.

L. M. Biberman, unpublished note.

Bumiller, F.

R. Hofstadter, F. Bumiller, M. R. Yearian, Rev. Mod. Phys. 30, 482 (1958).
[Crossref]

Chapman, S.

S. Chapman, Proc. Phys. Soc. (London) 43, 483 (1931).
[Crossref]

Dütsch, H. U.

H. U. Dütsch, Arch. Meteorol. Geophys. Bioklimatol. Ser. A11, 240 (1959).

Green, A. E. S.

A. E. S. Green, Phys. Today 15, (1), 41 (1962).

A. E. S. Green, M. Griggs, Appl. Opt. 2, 561 (163).

Griggs, M.

Hofstadter, R.

R. Hofstadter, F. Bumiller, M. R. Yearian, Rev. Mod. Phys. 30, 482 (1958).
[Crossref]

Mayfield, E.

E. Mayfield, private communication.

Yearian, M. R.

R. Hofstadter, F. Bumiller, M. R. Yearian, Rev. Mod. Phys. 30, 482 (1958).
[Crossref]

Appl. Opt. (1)

Arch. Meteorol. Geophys. Bioklimatol. (1)

H. U. Dütsch, Arch. Meteorol. Geophys. Bioklimatol. Ser. A11, 240 (1959).

Phys. Today (1)

A. E. S. Green, Phys. Today 15, (1), 41 (1962).

Proc. Phys. Soc. (London) (1)

S. Chapman, Proc. Phys. Soc. (London) 43, 483 (1931).
[Crossref]

Rev. Mod. Phys. (1)

R. Hofstadter, F. Bumiller, M. R. Yearian, Rev. Mod. Phys. 30, 482 (1958).
[Crossref]

Other (6)

AFCRL, Handbook of Geophysics (Macmillan, New York, 1960).

Geophysics Corporation of American Report 61-35-A, AF 19(604)-7412, 1July1961.

L. M. Biberman, unpublished note.

E. Mayfield, private communication.

T. L. Altshuler, Fig. 18, Document No. 61SD199, December1961, General Electric M. S. V. D.Philadelphia, Pa.

A. E. S. Green, C. E. Porter, D. S. Saxon, eds., Proceedings of the International Conference on the Nuclear Optical Model (Florida State University Studies, 1959).

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Figures (7)

Fig. 1
Fig. 1

Monthly means of vertical ozone distribution. In parentheses are number of single cases included in the means.

Fig. 2
Fig. 2

A “standard” density distribution for ozone. The solid curve shows a “standard” density for ozone proposed by Altshuler. It corresponds to 0.229 atm-cm of ozone in a vertical column. The dashed curve represents the analytical fit with the parameter wp = 0.218, yp = 23.25, and h = 4.63.

Fig. 3
Fig. 3

Integrated vertical paths of ozone for the “standard” distribution. The dashed curve was obtained by a planimeter integration of the standard distribution of Fig. 2. The solid curve corresponds to the analytical fit. The curve marked wa represents the effective thickness of air above a particular altitude

Fig. 4
Fig. 4

The functions H(λ), k(λ), and ks (λ) and their analytical fit.

Fig. 5
Fig. 5

Diagram illustrating the angles involved in albedo calculation. θ = zenith angle of sun, ϕ is zenith angle of satellite, and ψ is the angle of scattering.

Fig. 6
Fig. 6

The scattered solar irradiance as a function of wavelength looking downward with satellite and sun at the zenith.

Fig. 7
Fig. 7

The angular function β(θ,Φ,ψ) for a series of scattering angle values and for the standard ozone distribution (ν = 0.666). The results near θ = 90° and Φ = 90° must be viewed with care since the secant function fails.

Tables (2)

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Table I Dimensionless Ozone Distribution Functions

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Table II Solar Scattered Radiation Parameters

Equations (27)

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w = w 0 e y / h ,
w = w p { 1 + exp [ ( y y p ) / h ] } 1 ,
ρ = d w d y = w p h exp ( y y p ) / h [ 1 + exp ( y y p ) / h ] 2 .
w = w p e ( y y p ) / h .
w = w p f ( θ , x ) / [ 1 + exp ( y y p ) / h ] ,
T = exp { k ( λ ) w p f ( θ , x ) 1 + exp [ ( y y p ) / h ] } ,
k ( λ ) = 300 exp ( λ 2540 250 ) 2 cm 1 .
H ( λ ) = 1.00 × 10 2 exp ( λ 2540 250 ) watts cm 2 μ .
k a ( λ ) = 0.315 ( 2540 λ ) 4 km 1 ,
w a = w a p exp ( y y p h a ) ,
Δ t = d w d y Δ y = w a h a Δ y .
Δ M = w a h a R 2 Δ Ω Δ y sec ϕ ,
σ ( λ, ψ ) Δ Ω = 3 16 π ( 1 + cos 2 ψ ) σ ( λ ) Δ Ω ,
B = 3 16 π ( 1 + cos 2 ψ ) H ( λ ) k a ( λ ) w a p I sec ϕ .
I = e y p / h a 0 e y / h a [ exp w p k ( λ ) ( sec θ + sec ϕ ) 1 + e y p / h e y / h ] d y h a .
α = 600 w p [ exp ( λ 2540 250 ) 2 ] [ sec θ + sec ϕ 2 ] ,
v = h / h a ,
δ = e y p / h ,
I ( α , ν , δ ) = 1 δ ν 0 e x exp ( α 1 + δ e x / ν ) d x .
I ( α , ν , δ ) = ν λ ν γ ( ν , λ 1 + δ ) + ν ( ν + 1 ) 2 λ ν + 2 γ ( ν + 2 , λ 1 + δ ) + ,
λ = α ν 1 = α ( 1 ν + 1 α ) ,
γ ( ν , z ) Γ ( ν ) z v 1 e z [ 1 + O ( 1 z ) + ]
I = Γ ( ν + 1 ) α ν + ν Γ ( ν + 2 ) α ν + 1 + ν ( ν + 1 ) Γ ( ν + 2 ) 2 α ν + 2 ν 2 ( 1 + δ ) 2 e ( α / 1 + δ ) α δ ν + 1 .
B = 3.75 × 10 6 [ 100 w a p Γ ( ν + 1 ) ( 600 w p ) ν ] f β ( λ ) β ( θ , ϕ , ψ ) ,
β ( λ ) = exp ( λ 2540 250 ) [ exp ( λ 2540 250 ) 2 ] ν ( 2540 λ ) 4
β ( θ , ϕ , ψ ) = 1 + cos 2 ( ψ ) 2 1 ν ( sec θ + sec ϕ ) ν sec ϕ ,
B c = 3.5 × 10 6 W / cm 2 sr μ .

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