Abstract

Inversion of solar almucantar data is a simple and practical method of obtaining aerosol size distributions. In this paper, we have inverted a number of sets of simulated data, using the standard single scattering approximation, to test the errors involved in ignoring multiple scattering. We have also inverted the data using two techniques: one, a modification of the method proposed by Deirmendjian and Sekera; and the other that of McPeters and Green. Inversion results strongly suggest that the accuracy of the retrieved size distribution can be significantly improved by use of our modified Deirmendjian-Sekera approach, in which multiple scattering by molecules is included along with single scattering by molecules and aerosols.

© 1979 Optical Society of America

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References

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  1. M. A. Box, A. Deepak, Appl. Opt. 17, 3794 (1978).
    [CrossRef] [PubMed]
  2. A. E. S. Green, A. Deepak, B. J. Lipofsky, Appl. Opt. 10, 1263 (1971).
    [CrossRef] [PubMed]
  3. A. E. S. Green et al., J. Colloid Interface Sci. 39, 520 (1972).
    [CrossRef]
  4. R. D. McPeters, A. E. S. Green, Appl. Opt. 15, 2457 (1976).
    [CrossRef] [PubMed]
  5. J. T. Twitty, J. Atmos. Sci. 32, 584 (1975).
    [CrossRef]
  6. A. Deepak, “Inversion of Solar Aureole Measurements for Determining Aerosol Characteristics,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed. (Academic, New York, 1977), p 297–323.
  7. E. Raschke, Ed., “Terminology and Units of Radiation Quantities and Measurements,” IAMAP Radiation Commission Report (IAMAP, P.O. Box 3000, Boulder, Colo., 1978).
  8. B. H. Herman, S. R. Browning, J. Atmos. Sci. 22, 559 (1965).
    [CrossRef]
  9. J. V. Dave, “Development of Programs for Computing Characteristics of U.V. Radiation,” NASA contract 5-21680 (1972).
  10. A. Deepak, G. P. Box, “Analytic Modeling of Atmospheric Aerosol Size Distributions,” NASA report (1978).
  11. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersion (Elsevier, New York, 1969).
  12. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  13. Z. Sekera, Adv. Geophys. 3, 43 (1956).
    [CrossRef]
  14. D. Deirmendjian, Annales de Géophysique 13, 286 (1957).
  15. D. Deirmendjian, Annales de Géophysique 15, 218 (1959).
  16. D. Deirmendjian, “Use of Scattering Techniques in Cloud Microphysics Research. I. The Aureole Method,” Rand Corp. report R-590-PR (1970).
  17. H. L. Malchow, C. K. Whitney, “Inversion of Scattered Radiance Horizon Profiles for Gaseous Concentrations and Aerosol Parameters,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed. (Academic, New York, 1977), pp. 217–264.
  18. K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (U. California Press, Berkeley, 1960).

1978

1976

1975

J. T. Twitty, J. Atmos. Sci. 32, 584 (1975).
[CrossRef]

1972

J. V. Dave, “Development of Programs for Computing Characteristics of U.V. Radiation,” NASA contract 5-21680 (1972).

A. E. S. Green et al., J. Colloid Interface Sci. 39, 520 (1972).
[CrossRef]

1971

1965

B. H. Herman, S. R. Browning, J. Atmos. Sci. 22, 559 (1965).
[CrossRef]

1959

D. Deirmendjian, Annales de Géophysique 15, 218 (1959).

1957

D. Deirmendjian, Annales de Géophysique 13, 286 (1957).

1956

Z. Sekera, Adv. Geophys. 3, 43 (1956).
[CrossRef]

Box, G. P.

A. Deepak, G. P. Box, “Analytic Modeling of Atmospheric Aerosol Size Distributions,” NASA report (1978).

Box, M. A.

Browning, S. R.

B. H. Herman, S. R. Browning, J. Atmos. Sci. 22, 559 (1965).
[CrossRef]

Coulson, K. L.

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (U. California Press, Berkeley, 1960).

Dave, J. V.

J. V. Dave, “Development of Programs for Computing Characteristics of U.V. Radiation,” NASA contract 5-21680 (1972).

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (U. California Press, Berkeley, 1960).

Deepak, A.

M. A. Box, A. Deepak, Appl. Opt. 17, 3794 (1978).
[CrossRef] [PubMed]

A. E. S. Green, A. Deepak, B. J. Lipofsky, Appl. Opt. 10, 1263 (1971).
[CrossRef] [PubMed]

A. Deepak, “Inversion of Solar Aureole Measurements for Determining Aerosol Characteristics,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed. (Academic, New York, 1977), p 297–323.

A. Deepak, G. P. Box, “Analytic Modeling of Atmospheric Aerosol Size Distributions,” NASA report (1978).

Deirmendjian, D.

D. Deirmendjian, Annales de Géophysique 15, 218 (1959).

D. Deirmendjian, Annales de Géophysique 13, 286 (1957).

D. Deirmendjian, “Use of Scattering Techniques in Cloud Microphysics Research. I. The Aureole Method,” Rand Corp. report R-590-PR (1970).

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

Green, A. E. S.

Herman, B. H.

B. H. Herman, S. R. Browning, J. Atmos. Sci. 22, 559 (1965).
[CrossRef]

Lipofsky, B. J.

Malchow, H. L.

H. L. Malchow, C. K. Whitney, “Inversion of Scattered Radiance Horizon Profiles for Gaseous Concentrations and Aerosol Parameters,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed. (Academic, New York, 1977), pp. 217–264.

McPeters, R. D.

Sekera, Z.

Z. Sekera, Adv. Geophys. 3, 43 (1956).
[CrossRef]

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (U. California Press, Berkeley, 1960).

Twitty, J. T.

J. T. Twitty, J. Atmos. Sci. 32, 584 (1975).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Whitney, C. K.

H. L. Malchow, C. K. Whitney, “Inversion of Scattered Radiance Horizon Profiles for Gaseous Concentrations and Aerosol Parameters,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed. (Academic, New York, 1977), pp. 217–264.

Adv. Geophys.

Z. Sekera, Adv. Geophys. 3, 43 (1956).
[CrossRef]

Annales de Géophysique

D. Deirmendjian, Annales de Géophysique 13, 286 (1957).

D. Deirmendjian, Annales de Géophysique 15, 218 (1959).

Appl. Opt.

J. Atmos. Sci.

J. T. Twitty, J. Atmos. Sci. 32, 584 (1975).
[CrossRef]

B. H. Herman, S. R. Browning, J. Atmos. Sci. 22, 559 (1965).
[CrossRef]

J. Colloid Interface Sci.

A. E. S. Green et al., J. Colloid Interface Sci. 39, 520 (1972).
[CrossRef]

NASA contract 5-21680

J. V. Dave, “Development of Programs for Computing Characteristics of U.V. Radiation,” NASA contract 5-21680 (1972).

Other

A. Deepak, G. P. Box, “Analytic Modeling of Atmospheric Aerosol Size Distributions,” NASA report (1978).

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

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

D. Deirmendjian, “Use of Scattering Techniques in Cloud Microphysics Research. I. The Aureole Method,” Rand Corp. report R-590-PR (1970).

H. L. Malchow, C. K. Whitney, “Inversion of Scattered Radiance Horizon Profiles for Gaseous Concentrations and Aerosol Parameters,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed. (Academic, New York, 1977), pp. 217–264.

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (U. California Press, Berkeley, 1960).

A. Deepak, “Inversion of Solar Aureole Measurements for Determining Aerosol Characteristics,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed. (Academic, New York, 1977), p 297–323.

E. Raschke, Ed., “Terminology and Units of Radiation Quantities and Measurements,” IAMAP Radiation Commission Report (IAMAP, P.O. Box 3000, Boulder, Colo., 1978).

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Figures (1)

Fig. 1
Fig. 1

Illustrations of almucantar radiance and corresponding columnar scattering functions computed from radiative transfer code and single scattering approximations.

Tables (3)

Tables Icon

Table I Retrieved Size Distribution Parameters a and b Using the Single Scattering Approximation

Tables Icon

Table II Effective Optical Thicknesses Used In the Modified Deirmendjian-Sekera a and McPeters-Green b Inversions

Tables Icon

Table III Retrieved Size Distribution Parameters a and b Using Modified Deirmendjian-Sekera and McPeters-Green Approximations

Equations (18)

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n ( r ) = a r 2 exp ( - b r ) ( 0.03 μ m r 2.0 μ m ) .
L SS = Φ 0 sec θ exp ( - τ sec θ ) [ τ M P M ( ψ ) + τ P P P ( ψ ) ] / 4 π ,
cos ψ = cos 2 θ + sin 2 θ cos ϕ ,
F P ( ψ ) = L RT 4 π exp ( τ sec θ ) cos θ / Φ 0 - τ M P M ( ψ ) ,
F P ( ψ ) = λ 2 / 2 π 0 0 η ( r , y ) ( i 1 + i 2 ) d r d y ,
μ L ( τ , ξ ) τ = L - Φ 0 exp ( - τ / μ 0 ) P tot ( τ ; ξ , ξ 0 ) / 4 π - Ω L ( τ , ξ ) P tot ( τ ; ξ , ξ ) d ξ / 4 π ,
P tot ( τ ) = ( σ M P M + σ P P P ) / σ tot ,
σ i = - ( τ i ) / ( z ) , i = M , P , tot .
P tot ( τ ) = P M + f ( τ ) P D ,
P D = P P - P M ,
f ( τ ) = σ p / σ tot
L ( τ , ξ ) = L M ( τ , ξ ) + L D ( τ , ξ ) ,
μ L D ( τ , ξ ) τ = L D ( τ , ξ ) - Φ 0 exp ( - τ / μ 0 ) f ( τ ) P D ( τ ; ξ , ξ 0 ) / 4 π - Ω P M ( ξ , ξ ) L D ( τ , ξ ) d ξ / 4 π - f ( τ ) Ω P D ( L M + L D ) d ξ / 4 π .
L D S S = Φ 0 sec θ 0 exp ( - τ sec θ 0 P D f ( τ ) d τ / 4 π ,
L D SS = Φ 0 sec θ 0 exp ( - τ sec θ 0 ) τ P ( P P - P M ) / 4 π .
L MG = Φ 0 sec θ 0 exp ( - τ sec θ 0 ) ( d MG P M + τ P P P ) / 4 π ,
L R = Φ 0 sec θ 0 exp ( - τ sec θ 0 ) d D S P M / 4 π ,
L D S = Φ 0 sec θ 0 exp ( - τ sec θ 0 ) [ d D S P M + τ P ( P P - P M ) ] / 4 π = Φ 0 sec θ 0 exp ( - τ sec θ 0 ) [ ( d D S - τ P ) P M + τ P P P ] / 4 π .

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