Abstract

Inversions have been performed separately on spectral solar beam extinction data (0.4–1.0 μm) and on solar aureole scattering data (scattering angle ≲13°) to derive aerosol size distributions over the radius range of sensitivity appropriate to each inversion methodology. The bimodal size distributions derived from the two optical data types were normally found to be consistent in the region of overlapping radius. In one example, however, the presence of an independent absorber was postulated to bring the extinction and the scattering results into agreement. The derived aerosol particle size distributions were substituted into a Mie code to compute a scattering phase function which was then used in a radiative transfer model (discrete ordinate method) in order to compare calculations of sky radiance at large angles from the sun with radiometer field data. Data analysis illustrates the importance of the small-particle modal feature and of atmopsheric absorption to obtain consistency between extinction, aureole, and sky radiance data.

© 1984 Optical Society of America

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References

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  1. N. T. O’Neill, J. R. Miller, “Combined Solar Aureole and Solar Beam Extinction Measurements. 1: Calibration Considerations,” Appl. Opt. 23, 0000 (1984), this issue.
    [CrossRef]
  2. S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York, 1977).
  3. G. Yamamoto, M. Tanaka, “Determination of Aerosol Size Distribution from Spectral Attenuation Measurements,” Appl. Opt. 8, 447 (1969).
    [CrossRef] [PubMed]
  4. J. T. Twitty, “The Inversion of Aureole Measurements to Derive Aerosol Size Distributions,” J. Atmos. Sci., 32, 584 (1975).
    [CrossRef]
  5. G. E. Shaw, “Inversion of Optical Scattering and Spectral Extinction Measurements to Recover Aerosol Size Spectra, Appl. Opt. 18, 988 (1979).
    [CrossRef] [PubMed]
  6. N. T. O’Neill, J. R. Miller, “Constrained Linear Inversion of Optical Scattering Data for Particle Size Spectra: an Approach to Angular Optimization,” Appl. Opt. 21, 1231 (1982).
    [CrossRef]
  7. S. Twomey, H. B. Howell, “Some Aspects of the Optical Estimation of Microstructure in Fog and Cloud,” Appl. Opt. 6, 2125 (1967).
    [CrossRef] [PubMed]
  8. K. T. Whitby, R. B. Husar, B. Y. Liu, “The Aerosol Size Distribution of the Los Angeles Smog,” J. Colloid Interface Sci. 39, 177 (1972).
    [CrossRef]
  9. K. Willeke, K. T. Whitby, W. E. Clark, V. A. Marple, “Size Distribution of Denver Aerosols: A Comparison of Two Sites,” Atmos. Environ. 8, 609 (1974).
    [CrossRef] [PubMed]
  10. W. G. Egan, C. E. Shaw, “Effects of Aerosols on Optically Remotely Sensed Data,” in Proceedings, Fifteenth International Symposium on Remote Sensing (Environmental Research Institute of Michigan, Ann Arbor, 1981).
  11. A. Angstrom, “The Parameter of Atmospheric Turbidity,” Tellus 14, 64 (1964).
  12. C. Tomasi, “Weak Absorption by Atmospheric Water Vapour in the Visible and Near Infrared Region,” Nuovo Cimento C 2C, Ser. 1, 511 (1979).
    [CrossRef]
  13. H. Rosen, a. D. Hansen, L. Gundel, T. Novakov, “Identification of the Optically Absorbing Component in Urban Aerosols,” Appl. Opt. 17, 3859 (1978).
    [CrossRef] [PubMed]
  14. G. N. Plass, “Mie Scattering and Absorption Cross Sections for Absorbing Particles,” Appl. Opt. 5, 279 (1966).
    [CrossRef] [PubMed]
  15. R. W. Bergstrom, “Comments on the Estimation of Aerosol Absorption Coefficients in the Atmosphere,” Contrib. Atmos. Phys. 46, 198 (1973).
  16. M. A. Box, A. Deepak, “Multiple Scattering Corrections to the Aureole,” in Proceedings, Third Conference on Atmospheric Radiation, 28–30 June 1978 (American Meteorological Society, Boston, 1978).
  17. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  18. K. N. Liou, “A Numerical Experiment on Chandrasekhar’s Discrete Ordinate Method for Radiative Transfer: Applications to Cloudy and Hazy Atmospheres,” J. Atmos. Sci. 30, 1303 (1973).
    [CrossRef]
  19. K. Stamnes, R. A. Swanson, “A New Look at the Discrete Ordinate Method for Radiative Transfer Calculations in Anisotropically Scattering Atmospheres,” J. Atmos. Sci. 38, 387 (1981).
    [CrossRef]
  20. J. V. Dave, “Extensive Datasets of the Diffuse Radiation in Realistic Atmospheric Models with Aerosols and Common Absorbing Gases,” Sol. Energy 21, 361 (1978).
    [CrossRef]
  21. G. A. Kharitonova, in Atmospheric Optics, N. B. Divari, Ed. (Consultants Bureau, New York, 1970).
  22. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969).

1984 (1)

N. T. O’Neill, J. R. Miller, “Combined Solar Aureole and Solar Beam Extinction Measurements. 1: Calibration Considerations,” Appl. Opt. 23, 0000 (1984), this issue.
[CrossRef]

1982 (1)

1981 (1)

K. Stamnes, R. A. Swanson, “A New Look at the Discrete Ordinate Method for Radiative Transfer Calculations in Anisotropically Scattering Atmospheres,” J. Atmos. Sci. 38, 387 (1981).
[CrossRef]

1979 (2)

C. Tomasi, “Weak Absorption by Atmospheric Water Vapour in the Visible and Near Infrared Region,” Nuovo Cimento C 2C, Ser. 1, 511 (1979).
[CrossRef]

G. E. Shaw, “Inversion of Optical Scattering and Spectral Extinction Measurements to Recover Aerosol Size Spectra, Appl. Opt. 18, 988 (1979).
[CrossRef] [PubMed]

1978 (2)

H. Rosen, a. D. Hansen, L. Gundel, T. Novakov, “Identification of the Optically Absorbing Component in Urban Aerosols,” Appl. Opt. 17, 3859 (1978).
[CrossRef] [PubMed]

J. V. Dave, “Extensive Datasets of the Diffuse Radiation in Realistic Atmospheric Models with Aerosols and Common Absorbing Gases,” Sol. Energy 21, 361 (1978).
[CrossRef]

1975 (1)

J. T. Twitty, “The Inversion of Aureole Measurements to Derive Aerosol Size Distributions,” J. Atmos. Sci., 32, 584 (1975).
[CrossRef]

1974 (1)

K. Willeke, K. T. Whitby, W. E. Clark, V. A. Marple, “Size Distribution of Denver Aerosols: A Comparison of Two Sites,” Atmos. Environ. 8, 609 (1974).
[CrossRef] [PubMed]

1973 (2)

R. W. Bergstrom, “Comments on the Estimation of Aerosol Absorption Coefficients in the Atmosphere,” Contrib. Atmos. Phys. 46, 198 (1973).

K. N. Liou, “A Numerical Experiment on Chandrasekhar’s Discrete Ordinate Method for Radiative Transfer: Applications to Cloudy and Hazy Atmospheres,” J. Atmos. Sci. 30, 1303 (1973).
[CrossRef]

1972 (1)

K. T. Whitby, R. B. Husar, B. Y. Liu, “The Aerosol Size Distribution of the Los Angeles Smog,” J. Colloid Interface Sci. 39, 177 (1972).
[CrossRef]

1969 (1)

1967 (1)

1966 (1)

1964 (1)

A. Angstrom, “The Parameter of Atmospheric Turbidity,” Tellus 14, 64 (1964).

Angstrom, A.

A. Angstrom, “The Parameter of Atmospheric Turbidity,” Tellus 14, 64 (1964).

Bergstrom, R. W.

R. W. Bergstrom, “Comments on the Estimation of Aerosol Absorption Coefficients in the Atmosphere,” Contrib. Atmos. Phys. 46, 198 (1973).

Box, M. A.

M. A. Box, A. Deepak, “Multiple Scattering Corrections to the Aureole,” in Proceedings, Third Conference on Atmospheric Radiation, 28–30 June 1978 (American Meteorological Society, Boston, 1978).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Clark, W. E.

K. Willeke, K. T. Whitby, W. E. Clark, V. A. Marple, “Size Distribution of Denver Aerosols: A Comparison of Two Sites,” Atmos. Environ. 8, 609 (1974).
[CrossRef] [PubMed]

Dave, J. V.

J. V. Dave, “Extensive Datasets of the Diffuse Radiation in Realistic Atmospheric Models with Aerosols and Common Absorbing Gases,” Sol. Energy 21, 361 (1978).
[CrossRef]

Deepak, A.

M. A. Box, A. Deepak, “Multiple Scattering Corrections to the Aureole,” in Proceedings, Third Conference on Atmospheric Radiation, 28–30 June 1978 (American Meteorological Society, Boston, 1978).

Deirmendjian, D.

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

Egan, W. G.

W. G. Egan, C. E. Shaw, “Effects of Aerosols on Optically Remotely Sensed Data,” in Proceedings, Fifteenth International Symposium on Remote Sensing (Environmental Research Institute of Michigan, Ann Arbor, 1981).

Gundel, L.

Hansen, a. D.

Howell, H. B.

Husar, R. B.

K. T. Whitby, R. B. Husar, B. Y. Liu, “The Aerosol Size Distribution of the Los Angeles Smog,” J. Colloid Interface Sci. 39, 177 (1972).
[CrossRef]

Kharitonova, G. A.

G. A. Kharitonova, in Atmospheric Optics, N. B. Divari, Ed. (Consultants Bureau, New York, 1970).

Liou, K. N.

K. N. Liou, “A Numerical Experiment on Chandrasekhar’s Discrete Ordinate Method for Radiative Transfer: Applications to Cloudy and Hazy Atmospheres,” J. Atmos. Sci. 30, 1303 (1973).
[CrossRef]

Liu, B. Y.

K. T. Whitby, R. B. Husar, B. Y. Liu, “The Aerosol Size Distribution of the Los Angeles Smog,” J. Colloid Interface Sci. 39, 177 (1972).
[CrossRef]

Marple, V. A.

K. Willeke, K. T. Whitby, W. E. Clark, V. A. Marple, “Size Distribution of Denver Aerosols: A Comparison of Two Sites,” Atmos. Environ. 8, 609 (1974).
[CrossRef] [PubMed]

Miller, J. R.

N. T. O’Neill, J. R. Miller, “Combined Solar Aureole and Solar Beam Extinction Measurements. 1: Calibration Considerations,” Appl. Opt. 23, 0000 (1984), this issue.
[CrossRef]

N. T. O’Neill, J. R. Miller, “Constrained Linear Inversion of Optical Scattering Data for Particle Size Spectra: an Approach to Angular Optimization,” Appl. Opt. 21, 1231 (1982).
[CrossRef]

Novakov, T.

O’Neill, N. T.

N. T. O’Neill, J. R. Miller, “Combined Solar Aureole and Solar Beam Extinction Measurements. 1: Calibration Considerations,” Appl. Opt. 23, 0000 (1984), this issue.
[CrossRef]

N. T. O’Neill, J. R. Miller, “Constrained Linear Inversion of Optical Scattering Data for Particle Size Spectra: an Approach to Angular Optimization,” Appl. Opt. 21, 1231 (1982).
[CrossRef]

Plass, G. N.

Rosen, H.

Shaw, C. E.

W. G. Egan, C. E. Shaw, “Effects of Aerosols on Optically Remotely Sensed Data,” in Proceedings, Fifteenth International Symposium on Remote Sensing (Environmental Research Institute of Michigan, Ann Arbor, 1981).

Shaw, G. E.

Stamnes, K.

K. Stamnes, R. A. Swanson, “A New Look at the Discrete Ordinate Method for Radiative Transfer Calculations in Anisotropically Scattering Atmospheres,” J. Atmos. Sci. 38, 387 (1981).
[CrossRef]

Swanson, R. A.

K. Stamnes, R. A. Swanson, “A New Look at the Discrete Ordinate Method for Radiative Transfer Calculations in Anisotropically Scattering Atmospheres,” J. Atmos. Sci. 38, 387 (1981).
[CrossRef]

Tanaka, M.

Tomasi, C.

C. Tomasi, “Weak Absorption by Atmospheric Water Vapour in the Visible and Near Infrared Region,” Nuovo Cimento C 2C, Ser. 1, 511 (1979).
[CrossRef]

Twitty, J. T.

J. T. Twitty, “The Inversion of Aureole Measurements to Derive Aerosol Size Distributions,” J. Atmos. Sci., 32, 584 (1975).
[CrossRef]

Twomey, S.

S. Twomey, H. B. Howell, “Some Aspects of the Optical Estimation of Microstructure in Fog and Cloud,” Appl. Opt. 6, 2125 (1967).
[CrossRef] [PubMed]

S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York, 1977).

Whitby, K. T.

K. Willeke, K. T. Whitby, W. E. Clark, V. A. Marple, “Size Distribution of Denver Aerosols: A Comparison of Two Sites,” Atmos. Environ. 8, 609 (1974).
[CrossRef] [PubMed]

K. T. Whitby, R. B. Husar, B. Y. Liu, “The Aerosol Size Distribution of the Los Angeles Smog,” J. Colloid Interface Sci. 39, 177 (1972).
[CrossRef]

Willeke, K.

K. Willeke, K. T. Whitby, W. E. Clark, V. A. Marple, “Size Distribution of Denver Aerosols: A Comparison of Two Sites,” Atmos. Environ. 8, 609 (1974).
[CrossRef] [PubMed]

Yamamoto, G.

Appl. Opt. (7)

Atmos. Environ. (1)

K. Willeke, K. T. Whitby, W. E. Clark, V. A. Marple, “Size Distribution of Denver Aerosols: A Comparison of Two Sites,” Atmos. Environ. 8, 609 (1974).
[CrossRef] [PubMed]

Contrib. Atmos. Phys. (1)

R. W. Bergstrom, “Comments on the Estimation of Aerosol Absorption Coefficients in the Atmosphere,” Contrib. Atmos. Phys. 46, 198 (1973).

J. Atmos. Sci. (3)

J. T. Twitty, “The Inversion of Aureole Measurements to Derive Aerosol Size Distributions,” J. Atmos. Sci., 32, 584 (1975).
[CrossRef]

K. N. Liou, “A Numerical Experiment on Chandrasekhar’s Discrete Ordinate Method for Radiative Transfer: Applications to Cloudy and Hazy Atmospheres,” J. Atmos. Sci. 30, 1303 (1973).
[CrossRef]

K. Stamnes, R. A. Swanson, “A New Look at the Discrete Ordinate Method for Radiative Transfer Calculations in Anisotropically Scattering Atmospheres,” J. Atmos. Sci. 38, 387 (1981).
[CrossRef]

J. Colloid Interface Sci. (1)

K. T. Whitby, R. B. Husar, B. Y. Liu, “The Aerosol Size Distribution of the Los Angeles Smog,” J. Colloid Interface Sci. 39, 177 (1972).
[CrossRef]

Nuovo Cimento C (1)

C. Tomasi, “Weak Absorption by Atmospheric Water Vapour in the Visible and Near Infrared Region,” Nuovo Cimento C 2C, Ser. 1, 511 (1979).
[CrossRef]

Sol. Energy (1)

J. V. Dave, “Extensive Datasets of the Diffuse Radiation in Realistic Atmospheric Models with Aerosols and Common Absorbing Gases,” Sol. Energy 21, 361 (1978).
[CrossRef]

Tellus (1)

A. Angstrom, “The Parameter of Atmospheric Turbidity,” Tellus 14, 64 (1964).

Other (6)

W. G. Egan, C. E. Shaw, “Effects of Aerosols on Optically Remotely Sensed Data,” in Proceedings, Fifteenth International Symposium on Remote Sensing (Environmental Research Institute of Michigan, Ann Arbor, 1981).

S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York, 1977).

G. A. Kharitonova, in Atmospheric Optics, N. B. Divari, Ed. (Consultants Bureau, New York, 1970).

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

M. A. Box, A. Deepak, “Multiple Scattering Corrections to the Aureole,” in Proceedings, Third Conference on Atmospheric Radiation, 28–30 June 1978 (American Meteorological Society, Boston, 1978).

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

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Figures (8)

Fig. 1
Fig. 1

Variation of scattering and extinction-derived particle size distributions on 12 Nov. 1981.

Fig. 2
Fig. 2

Comparison of the log–linear parameter γ obtained from scattering data [Eq. (7)] and extinction data [Eq. (5)] for a number of measuring days.

Fig. 3
Fig. 3

Optical data and corresponding particle size distribution for 4 Nov. 1981. Solid lines in (a) and (b) represent calculations of the optical vectors using the separate size distribution shown as solid lines in (c), obtained by inversion of the optical data in (a) and (b). Dashed lines correspond to a distribution selected for its consistency with both scattering and extinction data.

Fig. 4
Fig. 4

Optical data and corresponding particle size distribution for 14 Nov. 1981. Key same as Fig. 3.

Fig. 5
Fig. 5

DOM computations with twenty-four streams (circles) compared to Dave’s model 4, Haze L data (solid curves) for an almucantar scan (θv = θ0).

Fig. 6
Fig. 6

Discrete ordinate method calculations showing the approach to convergence as the number of streams is increased. Input parameters are those of Dave (model 3, Haze L θv = θ0 = 60°).

Fig. 7
Fig. 7

Multiple scattering calculations for 4 Nov. 1981 based on the inversion data of Fig. 3. The error bars on the computed (solid) lines are uncertainty estimates dependent on the number of streams used in the discrete ordinate method.

Fig. 8
Fig. 8

Multiple scattering calculations for 8 Nov. 1981 based on the inversion data of Fig. 4.

Equations (9)

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τ λ = 0 π r 2 Q ( α ) a ( r ) d r ,
τ λ [ p ( cos χ ) - 1 ] = 0 π r 2 Q ( α ) [ p ( α , cos χ ) - 1 ] a ( r ) d r ,
f ( r ) = r 4 a ( r ) .
f i C ˜ i ɛ r G ˜ ,
f i f i ( min ) = ɛ r G ˜ / C ˜ i ,
τ A = b λ - α
α = γ - 3.
P A ( cos χ ) = b χ - α ,
α = [ 0.24 , 1.16 ] by γ = 3.7 / α 0.226 .

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