Abstract

In this study we attempt to determine the aerosol complex index of refraction and size distribution from scattering measurements of polarized light. We illustrate that the scattering matrix elements M2 (100°) and D21 (150°) can be selected as an optimum set of matrix elements for determination of the complex index of refraction. We also illustrate that errors increase if we include insensitive scattering matrix elements in the determination of the complex index of refraction. A method is developed for the simultaneous determination of the complex index of refraction and the size distribution. In our method, we selected two sets of matrix elements, M2 (100°) and D21 (150°), for the determination of the complex index of refraction and others, which are much less sensitive to the complex index of refraction than M2 (100°) and D21 (150°), for the determination of the size distribution, based on their sensitivity analyses. A modified inversion library algorithm is adopted to solve the coupled system. Numerical experiments show that both the complex index of refraction and the size distribution can be determined with reasonable accuracy when we apply our method to scattering measurements of polarized light.

© 1997 Optical Society of America

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  1. J. A. Coakley, R. D. Cess, F. B. Yurevich, “The effect of tropospheric aerosol on the earth’s radiation budget: a parametrization for climate models,” J. Atmos. Sci. 40, 116–138 (1983).
    [Crossref]
  2. S. Twomey, “The influence of pollution on the shortwave albedo of cloud,” J. Atmos. Sci. 34, 1149–1152 (1977).
    [Crossref]
  3. S. Twomey, M. Piepgrass, T. L. Wolfe, “An assessment of the impact of pollution on the global albedo,” Tellus 36b, 356–366 (1984).
    [Crossref]
  4. R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic sulfate aerosols,” Science 255, 423–430 (1992).
    [Crossref] [PubMed]
  5. F-S. Zhao, G-Y. Shi, “One dimensional analyses of aerosol climate effects,” Atmos. Sci. Suppl. 18, 902–909 (1994), in Chinese.
  6. G. Yamamoto, M. Tanaka, “Increase of global albedo due to air pollution,” J. Atmos. Sci. 29, 1405–1412 (1972).
    [Crossref]
  7. R. Eiden, “The elliptical polarization of light scattered by a volume of atmospheric air,” Appl. Opt. 5, 569–575 (1966).
    [Crossref] [PubMed]
  8. G. Ward, K. M. Cushing, R. D. McPeters, A. E. S. Green, “Atmospheric aerosol index of refraction and size-altitude distribution from bistatic laser scattering and solar aureole measurements,” Appl. Opt. 12, 2585–2592 (1973).
    [Crossref] [PubMed]
  9. G. W. Grams, J. H. Blifford, D. A. Gillette, P. B. Russell, “Complex index of refraction of airborne soil particles,” J. Appl. Meteorol. 13, 459–471 (1974).
    [Crossref]
  10. M. Z. Hansen, “Atmospheric particle analysis using angular light scattering,” Appl. Opt. 19, 2534–2538 (1980).
    [Crossref]
  11. J. A. Reagon, D. M. Byrne, M. D. King, J. D. Spinhirne, B. H. Herman, “Determination of the complex refractive index and size distribution of atmospheric particulates from bistatic–monostatic lidar and solar radiometer measurements,” J. Geophys. Res. 85, 1591–1599 (1980).
    [Crossref]
  12. M. Tanaka, T. Nakajima, T. Takamura, “Simultaneous determination of the complex refractive index and size distribution of airborne and water suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60, 1259–1272 (1982).
  13. M. Tanaka, T. Takamura, T. Nakajima, “Refractive index and size distribution of aerosols as estimated from light scattering measurements,” J. Climate Appl. Meteorol. 22, 1253–1261 (1983).
    [Crossref]
  14. J-H. Qiu, X-J. Zhou, D-R. Lu, “Theoretical analysis of remote sensing method,” Sci. Sin. Ser. B) 28, 745–757 (1985).
  15. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 5, pp. 40–46.
  16. E. M. Patterson, D. A. Gillette, “Commonalties in measures size distributions for aerosols having a soil-derived component,” J. Geophys. Res. 82, 2074–2082 (1977).
    [Crossref]
  17. J-H. Qiu, X-J. Zhou, “Inversion of aerosol size distribution from aureole and extinction measurements,” Atmos. Sci. 7, 33–42 (1983), in Chinese.
  18. J. E. Hansen, L. D. Travis, “Light scattering in planetary atmosphere,” Space Sci. Rev. 16, 527–610 (1974).
    [Crossref]
  19. F-S. Zhao, “A method of the determination of the complex index of refraction and size distribution from the measurements of scattered light,” Ph.D. dissertation (Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, China, 1989).
  20. G. Yamamoto, M. Tanaka, “Determination of aerosol size distribution from spectral attenuation measurements,” Appl. Opt. 8, 447–453 (1969).
    [Crossref] [PubMed]
  21. M. D. King, M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distribution obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
    [Crossref]
  22. D. L. Phillips, “A technique for the numerical solution of certain integral equations of first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962).
    [Crossref]
  23. S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
    [Crossref]

1994 (1)

F-S. Zhao, G-Y. Shi, “One dimensional analyses of aerosol climate effects,” Atmos. Sci. Suppl. 18, 902–909 (1994), in Chinese.

1992 (1)

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic sulfate aerosols,” Science 255, 423–430 (1992).
[Crossref] [PubMed]

1985 (1)

J-H. Qiu, X-J. Zhou, D-R. Lu, “Theoretical analysis of remote sensing method,” Sci. Sin. Ser. B) 28, 745–757 (1985).

1984 (1)

S. Twomey, M. Piepgrass, T. L. Wolfe, “An assessment of the impact of pollution on the global albedo,” Tellus 36b, 356–366 (1984).
[Crossref]

1983 (3)

J. A. Coakley, R. D. Cess, F. B. Yurevich, “The effect of tropospheric aerosol on the earth’s radiation budget: a parametrization for climate models,” J. Atmos. Sci. 40, 116–138 (1983).
[Crossref]

J-H. Qiu, X-J. Zhou, “Inversion of aerosol size distribution from aureole and extinction measurements,” Atmos. Sci. 7, 33–42 (1983), in Chinese.

M. Tanaka, T. Takamura, T. Nakajima, “Refractive index and size distribution of aerosols as estimated from light scattering measurements,” J. Climate Appl. Meteorol. 22, 1253–1261 (1983).
[Crossref]

1982 (1)

M. Tanaka, T. Nakajima, T. Takamura, “Simultaneous determination of the complex refractive index and size distribution of airborne and water suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60, 1259–1272 (1982).

1980 (2)

M. Z. Hansen, “Atmospheric particle analysis using angular light scattering,” Appl. Opt. 19, 2534–2538 (1980).
[Crossref]

J. A. Reagon, D. M. Byrne, M. D. King, J. D. Spinhirne, B. H. Herman, “Determination of the complex refractive index and size distribution of atmospheric particulates from bistatic–monostatic lidar and solar radiometer measurements,” J. Geophys. Res. 85, 1591–1599 (1980).
[Crossref]

1978 (1)

M. D. King, M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distribution obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[Crossref]

1977 (2)

E. M. Patterson, D. A. Gillette, “Commonalties in measures size distributions for aerosols having a soil-derived component,” J. Geophys. Res. 82, 2074–2082 (1977).
[Crossref]

S. Twomey, “The influence of pollution on the shortwave albedo of cloud,” J. Atmos. Sci. 34, 1149–1152 (1977).
[Crossref]

1974 (2)

G. W. Grams, J. H. Blifford, D. A. Gillette, P. B. Russell, “Complex index of refraction of airborne soil particles,” J. Appl. Meteorol. 13, 459–471 (1974).
[Crossref]

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmosphere,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

1973 (1)

1972 (1)

G. Yamamoto, M. Tanaka, “Increase of global albedo due to air pollution,” J. Atmos. Sci. 29, 1405–1412 (1972).
[Crossref]

1969 (1)

1966 (1)

1963 (1)

S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
[Crossref]

1962 (1)

D. L. Phillips, “A technique for the numerical solution of certain integral equations of first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962).
[Crossref]

Blifford, J. H.

G. W. Grams, J. H. Blifford, D. A. Gillette, P. B. Russell, “Complex index of refraction of airborne soil particles,” J. Appl. Meteorol. 13, 459–471 (1974).
[Crossref]

Byrne, D. M.

J. A. Reagon, D. M. Byrne, M. D. King, J. D. Spinhirne, B. H. Herman, “Determination of the complex refractive index and size distribution of atmospheric particulates from bistatic–monostatic lidar and solar radiometer measurements,” J. Geophys. Res. 85, 1591–1599 (1980).
[Crossref]

Byrne, M.

M. D. King, M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distribution obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[Crossref]

Cess, R. D.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic sulfate aerosols,” Science 255, 423–430 (1992).
[Crossref] [PubMed]

J. A. Coakley, R. D. Cess, F. B. Yurevich, “The effect of tropospheric aerosol on the earth’s radiation budget: a parametrization for climate models,” J. Atmos. Sci. 40, 116–138 (1983).
[Crossref]

Charlson, R. J.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic sulfate aerosols,” Science 255, 423–430 (1992).
[Crossref] [PubMed]

Coakley, J. A.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic sulfate aerosols,” Science 255, 423–430 (1992).
[Crossref] [PubMed]

J. A. Coakley, R. D. Cess, F. B. Yurevich, “The effect of tropospheric aerosol on the earth’s radiation budget: a parametrization for climate models,” J. Atmos. Sci. 40, 116–138 (1983).
[Crossref]

Cushing, K. M.

Eiden, R.

Gillette, D. A.

E. M. Patterson, D. A. Gillette, “Commonalties in measures size distributions for aerosols having a soil-derived component,” J. Geophys. Res. 82, 2074–2082 (1977).
[Crossref]

G. W. Grams, J. H. Blifford, D. A. Gillette, P. B. Russell, “Complex index of refraction of airborne soil particles,” J. Appl. Meteorol. 13, 459–471 (1974).
[Crossref]

Grams, G. W.

G. W. Grams, J. H. Blifford, D. A. Gillette, P. B. Russell, “Complex index of refraction of airborne soil particles,” J. Appl. Meteorol. 13, 459–471 (1974).
[Crossref]

Green, A. E. S.

Hales, J. M.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic sulfate aerosols,” Science 255, 423–430 (1992).
[Crossref] [PubMed]

Hansen, J. E.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic sulfate aerosols,” Science 255, 423–430 (1992).
[Crossref] [PubMed]

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmosphere,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Hansen, M. Z.

M. Z. Hansen, “Atmospheric particle analysis using angular light scattering,” Appl. Opt. 19, 2534–2538 (1980).
[Crossref]

Herman, B. H.

J. A. Reagon, D. M. Byrne, M. D. King, J. D. Spinhirne, B. H. Herman, “Determination of the complex refractive index and size distribution of atmospheric particulates from bistatic–monostatic lidar and solar radiometer measurements,” J. Geophys. Res. 85, 1591–1599 (1980).
[Crossref]

Herman, B. M.

M. D. King, M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distribution obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[Crossref]

Hofmann, D. J.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic sulfate aerosols,” Science 255, 423–430 (1992).
[Crossref] [PubMed]

King, M. D.

J. A. Reagon, D. M. Byrne, M. D. King, J. D. Spinhirne, B. H. Herman, “Determination of the complex refractive index and size distribution of atmospheric particulates from bistatic–monostatic lidar and solar radiometer measurements,” J. Geophys. Res. 85, 1591–1599 (1980).
[Crossref]

M. D. King, M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distribution obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[Crossref]

Lu, D-R.

J-H. Qiu, X-J. Zhou, D-R. Lu, “Theoretical analysis of remote sensing method,” Sci. Sin. Ser. B) 28, 745–757 (1985).

McPeters, R. D.

Nakajima, T.

M. Tanaka, T. Takamura, T. Nakajima, “Refractive index and size distribution of aerosols as estimated from light scattering measurements,” J. Climate Appl. Meteorol. 22, 1253–1261 (1983).
[Crossref]

M. Tanaka, T. Nakajima, T. Takamura, “Simultaneous determination of the complex refractive index and size distribution of airborne and water suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60, 1259–1272 (1982).

Patterson, E. M.

E. M. Patterson, D. A. Gillette, “Commonalties in measures size distributions for aerosols having a soil-derived component,” J. Geophys. Res. 82, 2074–2082 (1977).
[Crossref]

Phillips, D. L.

D. L. Phillips, “A technique for the numerical solution of certain integral equations of first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962).
[Crossref]

Piepgrass, M.

S. Twomey, M. Piepgrass, T. L. Wolfe, “An assessment of the impact of pollution on the global albedo,” Tellus 36b, 356–366 (1984).
[Crossref]

Qiu, J-H.

J-H. Qiu, X-J. Zhou, D-R. Lu, “Theoretical analysis of remote sensing method,” Sci. Sin. Ser. B) 28, 745–757 (1985).

J-H. Qiu, X-J. Zhou, “Inversion of aerosol size distribution from aureole and extinction measurements,” Atmos. Sci. 7, 33–42 (1983), in Chinese.

Reagan, J. A.

M. D. King, M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distribution obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[Crossref]

Reagon, J. A.

J. A. Reagon, D. M. Byrne, M. D. King, J. D. Spinhirne, B. H. Herman, “Determination of the complex refractive index and size distribution of atmospheric particulates from bistatic–monostatic lidar and solar radiometer measurements,” J. Geophys. Res. 85, 1591–1599 (1980).
[Crossref]

Russell, P. B.

G. W. Grams, J. H. Blifford, D. A. Gillette, P. B. Russell, “Complex index of refraction of airborne soil particles,” J. Appl. Meteorol. 13, 459–471 (1974).
[Crossref]

Schwartz, S. E.

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic sulfate aerosols,” Science 255, 423–430 (1992).
[Crossref] [PubMed]

Shi, G-Y.

F-S. Zhao, G-Y. Shi, “One dimensional analyses of aerosol climate effects,” Atmos. Sci. Suppl. 18, 902–909 (1994), in Chinese.

Spinhirne, J. D.

J. A. Reagon, D. M. Byrne, M. D. King, J. D. Spinhirne, B. H. Herman, “Determination of the complex refractive index and size distribution of atmospheric particulates from bistatic–monostatic lidar and solar radiometer measurements,” J. Geophys. Res. 85, 1591–1599 (1980).
[Crossref]

Takamura, T.

M. Tanaka, T. Takamura, T. Nakajima, “Refractive index and size distribution of aerosols as estimated from light scattering measurements,” J. Climate Appl. Meteorol. 22, 1253–1261 (1983).
[Crossref]

M. Tanaka, T. Nakajima, T. Takamura, “Simultaneous determination of the complex refractive index and size distribution of airborne and water suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60, 1259–1272 (1982).

Tanaka, M.

M. Tanaka, T. Takamura, T. Nakajima, “Refractive index and size distribution of aerosols as estimated from light scattering measurements,” J. Climate Appl. Meteorol. 22, 1253–1261 (1983).
[Crossref]

M. Tanaka, T. Nakajima, T. Takamura, “Simultaneous determination of the complex refractive index and size distribution of airborne and water suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60, 1259–1272 (1982).

G. Yamamoto, M. Tanaka, “Increase of global albedo due to air pollution,” J. Atmos. Sci. 29, 1405–1412 (1972).
[Crossref]

G. Yamamoto, M. Tanaka, “Determination of aerosol size distribution from spectral attenuation measurements,” Appl. Opt. 8, 447–453 (1969).
[Crossref] [PubMed]

Travis, L. D.

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmosphere,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Twomey, S.

S. Twomey, M. Piepgrass, T. L. Wolfe, “An assessment of the impact of pollution on the global albedo,” Tellus 36b, 356–366 (1984).
[Crossref]

S. Twomey, “The influence of pollution on the shortwave albedo of cloud,” J. Atmos. Sci. 34, 1149–1152 (1977).
[Crossref]

S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
[Crossref]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 5, pp. 40–46.

Ward, G.

Wolfe, T. L.

S. Twomey, M. Piepgrass, T. L. Wolfe, “An assessment of the impact of pollution on the global albedo,” Tellus 36b, 356–366 (1984).
[Crossref]

Yamamoto, G.

G. Yamamoto, M. Tanaka, “Increase of global albedo due to air pollution,” J. Atmos. Sci. 29, 1405–1412 (1972).
[Crossref]

G. Yamamoto, M. Tanaka, “Determination of aerosol size distribution from spectral attenuation measurements,” Appl. Opt. 8, 447–453 (1969).
[Crossref] [PubMed]

Yurevich, F. B.

J. A. Coakley, R. D. Cess, F. B. Yurevich, “The effect of tropospheric aerosol on the earth’s radiation budget: a parametrization for climate models,” J. Atmos. Sci. 40, 116–138 (1983).
[Crossref]

Zhao, F-S.

F-S. Zhao, G-Y. Shi, “One dimensional analyses of aerosol climate effects,” Atmos. Sci. Suppl. 18, 902–909 (1994), in Chinese.

F-S. Zhao, “A method of the determination of the complex index of refraction and size distribution from the measurements of scattered light,” Ph.D. dissertation (Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, China, 1989).

Zhou, X-J.

J-H. Qiu, X-J. Zhou, D-R. Lu, “Theoretical analysis of remote sensing method,” Sci. Sin. Ser. B) 28, 745–757 (1985).

J-H. Qiu, X-J. Zhou, “Inversion of aerosol size distribution from aureole and extinction measurements,” Atmos. Sci. 7, 33–42 (1983), in Chinese.

Appl. Opt. (4)

Atmos. Sci. (1)

J-H. Qiu, X-J. Zhou, “Inversion of aerosol size distribution from aureole and extinction measurements,” Atmos. Sci. 7, 33–42 (1983), in Chinese.

Atmos. Sci. Suppl. (1)

F-S. Zhao, G-Y. Shi, “One dimensional analyses of aerosol climate effects,” Atmos. Sci. Suppl. 18, 902–909 (1994), in Chinese.

J. Appl. Meteorol. (1)

G. W. Grams, J. H. Blifford, D. A. Gillette, P. B. Russell, “Complex index of refraction of airborne soil particles,” J. Appl. Meteorol. 13, 459–471 (1974).
[Crossref]

J. Assoc. Comput. Mach. (2)

D. L. Phillips, “A technique for the numerical solution of certain integral equations of first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962).
[Crossref]

S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
[Crossref]

J. Atmos. Sci. (4)

G. Yamamoto, M. Tanaka, “Increase of global albedo due to air pollution,” J. Atmos. Sci. 29, 1405–1412 (1972).
[Crossref]

J. A. Coakley, R. D. Cess, F. B. Yurevich, “The effect of tropospheric aerosol on the earth’s radiation budget: a parametrization for climate models,” J. Atmos. Sci. 40, 116–138 (1983).
[Crossref]

S. Twomey, “The influence of pollution on the shortwave albedo of cloud,” J. Atmos. Sci. 34, 1149–1152 (1977).
[Crossref]

M. D. King, M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distribution obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[Crossref]

J. Climate Appl. Meteorol. (1)

M. Tanaka, T. Takamura, T. Nakajima, “Refractive index and size distribution of aerosols as estimated from light scattering measurements,” J. Climate Appl. Meteorol. 22, 1253–1261 (1983).
[Crossref]

J. Geophys. Res. (2)

E. M. Patterson, D. A. Gillette, “Commonalties in measures size distributions for aerosols having a soil-derived component,” J. Geophys. Res. 82, 2074–2082 (1977).
[Crossref]

J. A. Reagon, D. M. Byrne, M. D. King, J. D. Spinhirne, B. H. Herman, “Determination of the complex refractive index and size distribution of atmospheric particulates from bistatic–monostatic lidar and solar radiometer measurements,” J. Geophys. Res. 85, 1591–1599 (1980).
[Crossref]

J. Meteorol. Soc. Jpn. (1)

M. Tanaka, T. Nakajima, T. Takamura, “Simultaneous determination of the complex refractive index and size distribution of airborne and water suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60, 1259–1272 (1982).

Sci. Sin. Ser. B) (1)

J-H. Qiu, X-J. Zhou, D-R. Lu, “Theoretical analysis of remote sensing method,” Sci. Sin. Ser. B) 28, 745–757 (1985).

Science (1)

R. J. Charlson, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, D. J. Hofmann, “Climate forcing by anthropogenic sulfate aerosols,” Science 255, 423–430 (1992).
[Crossref] [PubMed]

Space Sci. Rev. (1)

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmosphere,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Tellus (1)

S. Twomey, M. Piepgrass, T. L. Wolfe, “An assessment of the impact of pollution on the global albedo,” Tellus 36b, 356–366 (1984).
[Crossref]

Other (2)

F-S. Zhao, “A method of the determination of the complex index of refraction and size distribution from the measurements of scattered light,” Ph.D. dissertation (Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, China, 1989).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 5, pp. 40–46.

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Figures (15)

Fig. 1
Fig. 1

Sensitivity functions of M1 to (a) nr and (b) ni. The size distributions used to calculate the sensitivity functions are listed in Table 1: m0 = 1.50–0.01i.

Fig. 2
Fig. 2

Same as Fig. 1 except for the scattering matrix element M2.

Fig. 3
Fig. 3

Same as Fig. 1 except for the scattering matrix element S21.

Fig. 4
Fig. 4

Same as Fig. 1 except for the scattering matrix element D21.

Fig. 5
Fig. 5

Sensitivity function of M1 to (a) nr and (b)ni: 1, n (r) = cr-(v* + 1), v* = 2, λ = 0.6328 µm, m0 = 1.45–0.005 i; 2, n(r) = cr- (v* + 1), v* = 4, λ = 0.6328 µm, m0 = 1.55–0.03i; 3, n(r) = cr-(v* + 1), v* = 3, λ = 0.4 µm, m0 = 1.50–0.01i; 4, n (r) = cr-(v* + 1), v* = 3, λ = 0.6328 µm, m0 = 1.50–0.01 i.

Fig. 6
Fig. 6

Same as Fig. 5 except for the scattering matrix element M2.

Fig. 7
Fig. 7

Same as Fig. 5 except for the scattering matrix element S21.

Fig. 8
Fig. 8

Same as Fig. 5 except for the scattering matrix element D21.

Fig. 9
Fig. 9

Projections of δ (in percent) hypersurfaces on the plane of the complex index of refraction obtained by use of the scattering matrix elements M2 (100°) and D21 (150°) for (a) mode 1 and (b) mode 3. The solid curves represent isolines of δ. m0 = 1.50–0.01 i.

Fig. 10
Fig. 10

Same as Fig. 9 except for the scattering matrix elements M1 (θ) and M2 (θ) with θ ∈ [7°, 170°].

Fig. 11
Fig. 11

Same as Fig. 9 except for the volume scattering function [(M1 + M2)/2] at scattering angles of 90°, 100°, 160°, and 170°.

Fig. 12
Fig. 12

Projection of the hypersurface of the standard deviation for M2 (100°) and D21 (150°) minus that for M2 (100°), D21 (150°), M2 (10°), and D21 (10°). m0 = 1.50–0.01 i. The size distribution used for the calculation was mode 3.

Fig. 13
Fig. 13

Isolines of the standard deviation δ (in percent) for (a) mode 1, (b) mode 3, (c) mode 5. The isolines were derived from the values of the standard deviation obtained from the library values of the complex index of refraction shown in Eq. (16). m0 = 1.50–0.01i.

Fig. 14
Fig. 14

Same as Fig. 13(b) except for the standard deviation δ1 (for the definition of δ1 see the text).

Fig. 15
Fig. 15

Retrieved aerosol size distributions for (a) mode 1, (b) mode 3, (c) mode 5. Solid curves and circles represent true and retrieved size distributions, respectively.

Tables (2)

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Table 1 Aerosol Size Distribution Used for the Sensitivity Analyses

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Table 2 Scattering Matrix Elements for the Determination of Aerosol Size Distribution

Equations (20)

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IsQsUsVs=λ24π2R2×12M2+M112M2-M10012M2-M112M2-M100S21-D2100D21S21IiQiUiVi,
M1=0 S1θ, m, xs1*θ, m, xnrdr,
M2=0 S2θ, m, xs2*θ, m, xnrdr,
S21=120s1θ, m, xs2*θ, m, x+s2θ, m, xs1*θ, m, xnrdr,
D21=120is2θ, m, xs1*θ, m, x-s1θ, m, xs2*θ, m, xnrdr,
δ=i=1N1N1-βim, θ, λ, nrβim21/2,
δ=12ε1- ln β1nrnr-nr0- ln β1nini-ni02+ε2- ln β2nrnr-nr0- ln β2nini-ni021/2,
ε1- ln β1nrnr-nr0- ln β1nini-ni0 ln β1nr+ε2- ln β2nrnr-nr0- ln β2nini-ni0× ln β2nr=0,
ε1- ln β1nrnr-nr0- ln β1nini-ni0 ln β1ni+ε2- ln β2nrnr-nr0- ln β2nini-ni0× ln β2ni=0.
Δnr=nr-nr0=ε1 ln β1nr+ε2 ln β2nr ln β1nr ln β1ni+ ln β2nr ln β2niε1 ln β1ni+ε2 ln β2ni  ln β1ni2+ ln β2ni2Dβm02,
Δni=ni-ni0= ln β1nr2+ ln β2nr2ε1 ln β1nr+ε2 ln β2nr ln β1nr ln β1ni+ ln β2nr ln β2niε1 ln β1ni+ε2 ln β2niDβm02,
Dβm0= ln β1nr ln β1ni ln β2nr ln β2ni
δ=i=12121-β1icm, θ, λ, nrβ1im21/2
β2im=rminrmaxk2im, θ, r, λnrdr+ε2i=j=1Nrjrj+1 k2im, θ, r, λnrdr+ε2i, i=1, 2, ,14,
nr=hrfr,
nr=1.400.05, 1.60, ni=0.005, 0.01, 0.02, 0.03, 0.05.
f=ATmAm+γH-1ATmβ2m,
Aij=rjrj+1 k2im, θ, rhrdr.
γ=10-4, 2×10-4,,4×10.
δ1=i=12121-β1icm, θ, λ, nrβ1im2+i=1141141-β2icm, θ, λ, nrβ2im21/2.

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