Abstract

An examination of the haze regime, used in the sense of diminished surface meteorological range, shows that the lower and upper limits can be defined by meteorological ranges 1.2 km and 15 km, respectively. In order to develop relationships between surface haze and vertical attenuation, eight meteorological ranges are selected from within these limits; then, vertical aerosol attenuation parameters are computed by deriving an aerosol scale height for each meteorological range. A sample tabulation for one of twenty wavelengths in the uv, visible, and ir is presented and combined with previously published attenuation parameters (aerosols, molecules, and ozone) to the 50-km altitude.

© 1970 Optical Society of America

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References

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  1. H. Koschmieder, Beitr. Phys. Atmos. 12, 33, 171 (1924).
  2. L. Foitzik, Wiss. Abh. Reich. Wetterdienst, Berlin 4: No. 5 (1938).
  3. M. Neiburger, C. W. Chien, Physics of Precipitation, Geophys. Monogr. No. 5 (Amer. Geophys. Union, Washington, D.C., 1960), p. 191.
    [CrossRef]
  4. K. Bullrich, Z. Angew. Math. Phys. 14, 434 (1963).
    [CrossRef]
  5. O. W. Goes, Beitr. Phys. Atmos. 36, 127 (1963).
  6. R. G. Eldridge, Bull. Amer. Meteorol. Soc. 50, 422 (1969).
  7. E. O. Hulbert, J. Opt. Soc. Amer. 31, 467 (1941).
    [CrossRef]
  8. J. S. Curcio, G. L. Knestrick, T. H. Cosden, “Atmospheric Scattering in the Visible and Infrared,” NRL Rep. 5567. U.S. Naval Research Laboratory, Washington, D.C. (1961).
  9. L. Elterman, “UV, Visible and IR Attenuation to 50 km,” Rep. AFCRL 68-1053, AFCRL, Bedford, Mass. (1968).
  10. L. Elterman, “Vertical Attenuation Model with Eight Surface Meteorological Ranges 2–13 km,” Rep. AFCRL-70-0200, AFCRL, Bedford, Mass. (1970).
  11. H. Siedentopf, “Light in the Troposphere,” Transl. D. Krans, Rep. AFCRL-TN-55-210. AFCRL, Bedford, Mass. (1955).
  12. R. Penndorf, “The Vertical Distribution of Mie Particles in the Troposphere,” Geophysics Research Paper No. 25, AFCRL, Bedford, Mass. (1954).
  13. J. M. Rosen, “Simultaneous Dust and Ozone Soundings over North and Central America,” Final Rep. Contr. No. NONR-710 (22), University of Minnesota (1960).
  14. L. Elterman, R. Wexler, D. T. Chang, Appl. Opt. 8, 893 (1969).
    [CrossRef] [PubMed]
  15. I. H. Blifford, L. D. Renger, J. Atmos. Sci. 26, 716 (1969).
    [CrossRef]
  16. G. P. Faraponova, Izv., Atmos. Oceanic Phys. Soc. 1, No. 6, 607 (1965); transl. P. A. Keehn.
  17. K. Ya. Kondratiev, Radiation in the Atmosphere, International Geophysics Series, J. Van Miegham, Ed. (Academic Press, New York, 1969), Vol. 12, p. 291.

1969 (3)

R. G. Eldridge, Bull. Amer. Meteorol. Soc. 50, 422 (1969).

I. H. Blifford, L. D. Renger, J. Atmos. Sci. 26, 716 (1969).
[CrossRef]

L. Elterman, R. Wexler, D. T. Chang, Appl. Opt. 8, 893 (1969).
[CrossRef] [PubMed]

1965 (1)

G. P. Faraponova, Izv., Atmos. Oceanic Phys. Soc. 1, No. 6, 607 (1965); transl. P. A. Keehn.

1963 (2)

K. Bullrich, Z. Angew. Math. Phys. 14, 434 (1963).
[CrossRef]

O. W. Goes, Beitr. Phys. Atmos. 36, 127 (1963).

1941 (1)

E. O. Hulbert, J. Opt. Soc. Amer. 31, 467 (1941).
[CrossRef]

1924 (1)

H. Koschmieder, Beitr. Phys. Atmos. 12, 33, 171 (1924).

Blifford, I. H.

I. H. Blifford, L. D. Renger, J. Atmos. Sci. 26, 716 (1969).
[CrossRef]

Bullrich, K.

K. Bullrich, Z. Angew. Math. Phys. 14, 434 (1963).
[CrossRef]

Chang, D. T.

Chien, C. W.

M. Neiburger, C. W. Chien, Physics of Precipitation, Geophys. Monogr. No. 5 (Amer. Geophys. Union, Washington, D.C., 1960), p. 191.
[CrossRef]

Cosden, T. H.

J. S. Curcio, G. L. Knestrick, T. H. Cosden, “Atmospheric Scattering in the Visible and Infrared,” NRL Rep. 5567. U.S. Naval Research Laboratory, Washington, D.C. (1961).

Curcio, J. S.

J. S. Curcio, G. L. Knestrick, T. H. Cosden, “Atmospheric Scattering in the Visible and Infrared,” NRL Rep. 5567. U.S. Naval Research Laboratory, Washington, D.C. (1961).

Eldridge, R. G.

R. G. Eldridge, Bull. Amer. Meteorol. Soc. 50, 422 (1969).

Elterman, L.

L. Elterman, R. Wexler, D. T. Chang, Appl. Opt. 8, 893 (1969).
[CrossRef] [PubMed]

L. Elterman, “Vertical Attenuation Model with Eight Surface Meteorological Ranges 2–13 km,” Rep. AFCRL-70-0200, AFCRL, Bedford, Mass. (1970).

L. Elterman, “UV, Visible and IR Attenuation to 50 km,” Rep. AFCRL 68-1053, AFCRL, Bedford, Mass. (1968).

Faraponova, G. P.

G. P. Faraponova, Izv., Atmos. Oceanic Phys. Soc. 1, No. 6, 607 (1965); transl. P. A. Keehn.

Foitzik, L.

L. Foitzik, Wiss. Abh. Reich. Wetterdienst, Berlin 4: No. 5 (1938).

Goes, O. W.

O. W. Goes, Beitr. Phys. Atmos. 36, 127 (1963).

Hulbert, E. O.

E. O. Hulbert, J. Opt. Soc. Amer. 31, 467 (1941).
[CrossRef]

Knestrick, G. L.

J. S. Curcio, G. L. Knestrick, T. H. Cosden, “Atmospheric Scattering in the Visible and Infrared,” NRL Rep. 5567. U.S. Naval Research Laboratory, Washington, D.C. (1961).

Kondratiev, K. Ya.

K. Ya. Kondratiev, Radiation in the Atmosphere, International Geophysics Series, J. Van Miegham, Ed. (Academic Press, New York, 1969), Vol. 12, p. 291.

Koschmieder, H.

H. Koschmieder, Beitr. Phys. Atmos. 12, 33, 171 (1924).

Neiburger, M.

M. Neiburger, C. W. Chien, Physics of Precipitation, Geophys. Monogr. No. 5 (Amer. Geophys. Union, Washington, D.C., 1960), p. 191.
[CrossRef]

Penndorf, R.

R. Penndorf, “The Vertical Distribution of Mie Particles in the Troposphere,” Geophysics Research Paper No. 25, AFCRL, Bedford, Mass. (1954).

Renger, L. D.

I. H. Blifford, L. D. Renger, J. Atmos. Sci. 26, 716 (1969).
[CrossRef]

Rosen, J. M.

J. M. Rosen, “Simultaneous Dust and Ozone Soundings over North and Central America,” Final Rep. Contr. No. NONR-710 (22), University of Minnesota (1960).

Siedentopf, H.

H. Siedentopf, “Light in the Troposphere,” Transl. D. Krans, Rep. AFCRL-TN-55-210. AFCRL, Bedford, Mass. (1955).

Wexler, R.

Appl. Opt. (1)

Beitr. Phys. Atmos. (2)

H. Koschmieder, Beitr. Phys. Atmos. 12, 33, 171 (1924).

O. W. Goes, Beitr. Phys. Atmos. 36, 127 (1963).

Bull. Amer. Meteorol. Soc. (1)

R. G. Eldridge, Bull. Amer. Meteorol. Soc. 50, 422 (1969).

Izv., Atmos. Oceanic Phys. Soc. (1)

G. P. Faraponova, Izv., Atmos. Oceanic Phys. Soc. 1, No. 6, 607 (1965); transl. P. A. Keehn.

J. Atmos. Sci. (1)

I. H. Blifford, L. D. Renger, J. Atmos. Sci. 26, 716 (1969).
[CrossRef]

J. Opt. Soc. Amer. (1)

E. O. Hulbert, J. Opt. Soc. Amer. 31, 467 (1941).
[CrossRef]

Z. Angew. Math. Phys. (1)

K. Bullrich, Z. Angew. Math. Phys. 14, 434 (1963).
[CrossRef]

Other (9)

L. Foitzik, Wiss. Abh. Reich. Wetterdienst, Berlin 4: No. 5 (1938).

M. Neiburger, C. W. Chien, Physics of Precipitation, Geophys. Monogr. No. 5 (Amer. Geophys. Union, Washington, D.C., 1960), p. 191.
[CrossRef]

K. Ya. Kondratiev, Radiation in the Atmosphere, International Geophysics Series, J. Van Miegham, Ed. (Academic Press, New York, 1969), Vol. 12, p. 291.

J. S. Curcio, G. L. Knestrick, T. H. Cosden, “Atmospheric Scattering in the Visible and Infrared,” NRL Rep. 5567. U.S. Naval Research Laboratory, Washington, D.C. (1961).

L. Elterman, “UV, Visible and IR Attenuation to 50 km,” Rep. AFCRL 68-1053, AFCRL, Bedford, Mass. (1968).

L. Elterman, “Vertical Attenuation Model with Eight Surface Meteorological Ranges 2–13 km,” Rep. AFCRL-70-0200, AFCRL, Bedford, Mass. (1970).

H. Siedentopf, “Light in the Troposphere,” Transl. D. Krans, Rep. AFCRL-TN-55-210. AFCRL, Bedford, Mass. (1955).

R. Penndorf, “The Vertical Distribution of Mie Particles in the Troposphere,” Geophysics Research Paper No. 25, AFCRL, Bedford, Mass. (1954).

J. M. Rosen, “Simultaneous Dust and Ozone Soundings over North and Central America,” Final Rep. Contr. No. NONR-710 (22), University of Minnesota (1960).

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Figures (4)

Fig. 1
Fig. 1

Defined limits of the haze regime. Arrows designate the meteorological ranges selected for developing attenuation parameters. Also shown is the Rayleigh limit which corresponds to the Rayleigh attenuation coefficient βr = 1.162 × 10−2 km−1 and the related meteorological range 336 km; λ = 0.55 μ represents the photopic region.

Fig. 2
Fig. 2

Wavelength distributions of the surface aerosol attenuation coefficient for Vη = 6 km and Vη = 10 km derived from Vη = 4 km using Eq. (2). The Vη = 4 km curve is obtained from measurements by Curcio et al.,8 which included the wavelength region 0.40 μ ≤ λ ≤ 2.17 μ. An extrapolation (dashed lines) to 0.27 μ permits computations for an over-all twenty selected wavelengths, 0.27 μ ≤ λ ≤ 2.17 μ, and eight meteorological ranges 2 km ≤ Vη ≤ 13 km.

Fig. 3
Fig. 3

Relationships of four aerosol scale heights (Hp) with meteorological ranges (Vη), aerosol attenuation coefficients (βp), and aerosol mixing layer altitude (0–5 km). The aerosol scale height family was computed using λ = 0.55 μ. The dashed lines represent values of βp(h) above 5 km (Ref. 9).

Fig. 4
Fig. 4

Comparison of vertical optical thickness and transmission for ±σ (standard deviation) and a mean aerosol attenuation coefficient βp(h5, λ0.55) at the top of an aerosol mixing layer having 5 km depth. T and τ, transmission and optical thickness based on βp(h50.55) = 5.0 × 10−3km−1, the mean of 79 measurements. T1 and τ1, transmission and optical thickness based on βp(h50.55) − σ, where τ = 3.4 × 10−3. T2 and τ2, transmission and optical thickness based on βp(h50.55) + σ.

Tables (3)

Tables Icon

Table I Surface Meteorological Ranges and Corresponding Parametersa

Tables Icon

Table II Surface Aerosol Attenuation Coefficients (Fig. 2) Based on Koschmieder1 and Eq. (2)

Tables Icon

Table III Parameters at 0.30 μ

Equations (17)

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V η = 3.91 / β ext ,
β ext = β p + β r .
β p ( V η , λ ) = β p ( V 4 , λ ) · [ ( 3.91 / V η ) β r ( λ 0.55 ) ] [ ( 3.91 / V 4 ) β r ( λ 0.55 ) ,
β p ( m , r , λ ) = r 1 r 2 σ p ( m , r , λ ) n ( r ) d r ,
n ( r ) = N 0 ( V η ) ψ ( r )
β p ( r , λ , V η ) = N 0 ( V η ) r 1 r 2 σ p ( r , λ ) ψ ( r ) d r .
β p ( h , λ ) / β r ( h , λ ) = [ σ p ( λ ) / σ r ( λ ) ] · [ N p ( h ) / N r ( h ) ] ,
β p ( h 5 , λ 0.55 ) = β p ( h 0 , λ 0.55 ) exp ( h / H p ) .
τ p ( h , λ , V η ) = 0 h β p ( h , λ , V η ) d h .
β p ( h , λ , V η ) = β p ( h 0 , λ , V η ) exp [ h / H p ( V η ) ] .
τ p ( h , λ , V η ) = H p ( V η ) · β p ( h 0 , λ , V η ) H p ( V η ) { β p ( h 0 , λ , V η ) · exp [ h / H p ( V η ) ] } .
τ p ( h , λ , V η ) = H p ( V η ) [ β p ( h 0 , λ , V η ) β p ( h , λ , V η ) ] .
β ext ( h , λ , V η ) = β r ( h , λ ) + β 3 ( h , λ ) + β p ( h , λ , V η ) .
T h ( h , λ , V η ) = exp [ β ext ( h , λ , V η ) · d ] .
T 0 h ( h , λ , V η ) = exp [ τ ext ( h , λ , V η ) · sec θ ] .
T Δ h ( h , λ , V η ) = exp [ τ ext ( h 2 , λ , V η ) τ ext ( h 1 , λ , V η ) ] sec θ .
T h ( h , λ , V η ) = exp [ τ ext ( h , λ , V η ) sec θ ] .

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