Abstract

Calculations of direct climate forcing by anthropogenic aerosols commonly use radiative transfer parameters, including asymmetry parameter g. One method of obtaining the asymmetry parameter of a particle population is to convert measured values of the hemispheric-to-total-scatter ratio (backscatter ratio b) into their corresponding g values. We compare a conversion derived from Mie calculations with one derived from the Henyey–Greenstein (HG) phase function to show that the HG method systematically overestimates g for typical size distributions of accumulation-mode aerosols. A delta-Eddington radiative transfer calculation is used to show that a 10% overestimation of g can systematically reduce climate forcing as a result of aerosols by 12% or more. Mie computations are used to derive an empirical relationship between backscatter ratio and asymmetry parameter for log-normal accumulation-mode aerosols. This relationship can be used to convert the backscatter ratio to the asymmetry parameter, independent of geometric mean diameter Dgv or complex refractive index m, but the conversion requires knowledge of the breadth σg of the size distribution.

© 1995 Optical Society of America

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References

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  1. S. Twomey, “Pollution and the planetary albedo,” Atmos. Environ. 8, 1251–1256 (1974).
    [CrossRef]
  2. 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 aerosols,” Science 255, 423–430 (1992).
    [CrossRef] [PubMed]
  3. J. T. Kiehl, B. P. Briegleb, “The relative roles of sulfate aerosols and greenhouse gases in climate forcing,” Science 260, 311–314 (1993).
    [CrossRef] [PubMed]
  4. J. Hansen, W. Rossow, I. Fung, “The missing data on global climate change,” Issues Sci. Technol. 7, 62–69 (1990).
  5. J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The delta-Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2458 (1976).
    [CrossRef]
  6. R. J. Charlson, W. M. Porch, A. P. Waggoner, N. C. Ahlquist, “Background aerosol light scattering characteristics: nephelometric observations at Mauna Loa Observatory compared with results at other remote locations,” Tellus 26, 345–360 (1974).
    [CrossRef]
  7. P. K. Quinn, S. F. Marshall, T. S. Bates, D. S. Covert, V. N. Kapustin, “Comparison of measured and calculated aerosol properties relevant to the direct radiative forcing of tropospheric sulfate aerosol on climate,” J. Geophys. Res. 100, 8977–8992 (1995).
    [CrossRef]
  8. A. P. Waggoner, R. E. Weiss, N. C. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, “Optical characteristics of atmospheric aerosols,” Atmos. Environ. 15, 1891–1909 (1981).
    [CrossRef]
  9. W. J. Wiscombe, G. W. Grams, “The backscattered fraction in two-stream approximations,” J. Atmos. Sci. 33, 2240–2451 (1976).
    [CrossRef]
  10. H. W. Barker, “A parameterization and generalization of backscatter functions for two-stream approximations,” Contrib. Atmos. Phys. 67, 195–199 (1994).
  11. R. M. Welch, W. G. Zdunkowitz, “Backscattering approximations and their influence on Eddington-type solar flux calculations,” Contrib. Atmos. Phys. 55, 28–42 (1982).
  12. J. Hansen, “Exact and approximate solutions for multiple scattering by cloudy and hazy planetary atmospheres,” J. Atmos. Sci. 26, 478–487 (1969).
    [CrossRef]
  13. M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observations,” Appl. Opt. 33, 7206–7225 (1994).
    [CrossRef] [PubMed]
  14. See figure 16 in J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
    [CrossRef]
  15. S. F. Marshall, “Measurement-derived radiative transfer parameters for the aerosol climate forcing problem,” M.S. thesis (University of Washington, Seattle, Wash., 1994).
  16. G. S. Kent, G. K. Yue, U. O. Farrukh, A. Deepak, “Modeling atmospheric aerosol backscatter at CO2 wavelengths: I. Aerosol properties, modeling techniques, and associated problems,” Appl. Opt. 22, 1655–1665 (1983).
    [CrossRef] [PubMed]
  17. G. Hänel, “Optical properties of atmospheric particles: complete parameter sets obtained through polar photometry and an improved inversion technique,” Appl. Opt. 33, 7187–7199 (1994).
    [CrossRef] [PubMed]
  18. K. T. Whitby, “The physical characteristics of sulfur aerosols,” Atmos. Environ. 12, 135–159 (1978).
    [CrossRef]
  19. W. A. Hoppel, G. M. Frick, “Submicron aerosol size distributions measured over the tropical and south Pacific,” Atmos. Environ. 24, 645–659 (1990).
    [CrossRef]
  20. J. L. Gras, G. P. Ayers, “Marine aerosol at southern mid-latitudes,” J. Geophys. Res. 88, 10661–10666 (1983).
    [CrossRef]
  21. W. R. Leaitch, G. A. Isaac, “Tropospheric aerosol size distributions from 1982 to 1988 over eastern North America,” Atmos. Environ. 25, 601–619 (1991).
    [CrossRef]
  22. B. P. Briegleb, “Delta-Eddington approximation for solar radiation in the NCAR community climate model,” J. Geophys. Res. 97, 7603–7612 (1992).
    [CrossRef]
  23. R. G. Ellingson, J. Ellis, S. Fels, “The intercomparison of radiation codes used in climate models: long wave results,” J. Geophys. Res. 96, 8929–8953 (1991).
    [CrossRef]
  24. The tendency of the curves in Fig. 1 indicates that another one-to-one relationship between b and g may exist for particles with Dgv greater than a few micrometers. This relationship is not addressed because such large particles have a relatively small radiative effect compared with smaller particles—see Ref. 15.

1995

P. K. Quinn, S. F. Marshall, T. S. Bates, D. S. Covert, V. N. Kapustin, “Comparison of measured and calculated aerosol properties relevant to the direct radiative forcing of tropospheric sulfate aerosol on climate,” J. Geophys. Res. 100, 8977–8992 (1995).
[CrossRef]

1994

1993

J. T. Kiehl, B. P. Briegleb, “The relative roles of sulfate aerosols and greenhouse gases in climate forcing,” Science 260, 311–314 (1993).
[CrossRef] [PubMed]

1992

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 aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

B. P. Briegleb, “Delta-Eddington approximation for solar radiation in the NCAR community climate model,” J. Geophys. Res. 97, 7603–7612 (1992).
[CrossRef]

1991

R. G. Ellingson, J. Ellis, S. Fels, “The intercomparison of radiation codes used in climate models: long wave results,” J. Geophys. Res. 96, 8929–8953 (1991).
[CrossRef]

W. R. Leaitch, G. A. Isaac, “Tropospheric aerosol size distributions from 1982 to 1988 over eastern North America,” Atmos. Environ. 25, 601–619 (1991).
[CrossRef]

1990

W. A. Hoppel, G. M. Frick, “Submicron aerosol size distributions measured over the tropical and south Pacific,” Atmos. Environ. 24, 645–659 (1990).
[CrossRef]

J. Hansen, W. Rossow, I. Fung, “The missing data on global climate change,” Issues Sci. Technol. 7, 62–69 (1990).

1983

1982

R. M. Welch, W. G. Zdunkowitz, “Backscattering approximations and their influence on Eddington-type solar flux calculations,” Contrib. Atmos. Phys. 55, 28–42 (1982).

1981

A. P. Waggoner, R. E. Weiss, N. C. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, “Optical characteristics of atmospheric aerosols,” Atmos. Environ. 15, 1891–1909 (1981).
[CrossRef]

1978

K. T. Whitby, “The physical characteristics of sulfur aerosols,” Atmos. Environ. 12, 135–159 (1978).
[CrossRef]

1976

W. J. Wiscombe, G. W. Grams, “The backscattered fraction in two-stream approximations,” J. Atmos. Sci. 33, 2240–2451 (1976).
[CrossRef]

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The delta-Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2458 (1976).
[CrossRef]

1974

R. J. Charlson, W. M. Porch, A. P. Waggoner, N. C. Ahlquist, “Background aerosol light scattering characteristics: nephelometric observations at Mauna Loa Observatory compared with results at other remote locations,” Tellus 26, 345–360 (1974).
[CrossRef]

S. Twomey, “Pollution and the planetary albedo,” Atmos. Environ. 8, 1251–1256 (1974).
[CrossRef]

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

1969

J. Hansen, “Exact and approximate solutions for multiple scattering by cloudy and hazy planetary atmospheres,” J. Atmos. Sci. 26, 478–487 (1969).
[CrossRef]

Ahlquist, N. C.

A. P. Waggoner, R. E. Weiss, N. C. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, “Optical characteristics of atmospheric aerosols,” Atmos. Environ. 15, 1891–1909 (1981).
[CrossRef]

R. J. Charlson, W. M. Porch, A. P. Waggoner, N. C. Ahlquist, “Background aerosol light scattering characteristics: nephelometric observations at Mauna Loa Observatory compared with results at other remote locations,” Tellus 26, 345–360 (1974).
[CrossRef]

Ayers, G. P.

J. L. Gras, G. P. Ayers, “Marine aerosol at southern mid-latitudes,” J. Geophys. Res. 88, 10661–10666 (1983).
[CrossRef]

Barker, H. W.

H. W. Barker, “A parameterization and generalization of backscatter functions for two-stream approximations,” Contrib. Atmos. Phys. 67, 195–199 (1994).

Bates, T. S.

P. K. Quinn, S. F. Marshall, T. S. Bates, D. S. Covert, V. N. Kapustin, “Comparison of measured and calculated aerosol properties relevant to the direct radiative forcing of tropospheric sulfate aerosol on climate,” J. Geophys. Res. 100, 8977–8992 (1995).
[CrossRef]

Briegleb, B. P.

J. T. Kiehl, B. P. Briegleb, “The relative roles of sulfate aerosols and greenhouse gases in climate forcing,” Science 260, 311–314 (1993).
[CrossRef] [PubMed]

B. P. Briegleb, “Delta-Eddington approximation for solar radiation in the NCAR community climate model,” J. Geophys. Res. 97, 7603–7612 (1992).
[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 aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

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 aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

A. P. Waggoner, R. E. Weiss, N. C. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, “Optical characteristics of atmospheric aerosols,” Atmos. Environ. 15, 1891–1909 (1981).
[CrossRef]

R. J. Charlson, W. M. Porch, A. P. Waggoner, N. C. Ahlquist, “Background aerosol light scattering characteristics: nephelometric observations at Mauna Loa Observatory compared with results at other remote locations,” Tellus 26, 345–360 (1974).
[CrossRef]

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 aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

Covert, D. S.

P. K. Quinn, S. F. Marshall, T. S. Bates, D. S. Covert, V. N. Kapustin, “Comparison of measured and calculated aerosol properties relevant to the direct radiative forcing of tropospheric sulfate aerosol on climate,” J. Geophys. Res. 100, 8977–8992 (1995).
[CrossRef]

A. P. Waggoner, R. E. Weiss, N. C. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, “Optical characteristics of atmospheric aerosols,” Atmos. Environ. 15, 1891–1909 (1981).
[CrossRef]

Deepak, A.

Ellingson, R. G.

R. G. Ellingson, J. Ellis, S. Fels, “The intercomparison of radiation codes used in climate models: long wave results,” J. Geophys. Res. 96, 8929–8953 (1991).
[CrossRef]

Ellis, J.

R. G. Ellingson, J. Ellis, S. Fels, “The intercomparison of radiation codes used in climate models: long wave results,” J. Geophys. Res. 96, 8929–8953 (1991).
[CrossRef]

Farrukh, U. O.

Fels, S.

R. G. Ellingson, J. Ellis, S. Fels, “The intercomparison of radiation codes used in climate models: long wave results,” J. Geophys. Res. 96, 8929–8953 (1991).
[CrossRef]

Frick, G. M.

W. A. Hoppel, G. M. Frick, “Submicron aerosol size distributions measured over the tropical and south Pacific,” Atmos. Environ. 24, 645–659 (1990).
[CrossRef]

Fung, I.

J. Hansen, W. Rossow, I. Fung, “The missing data on global climate change,” Issues Sci. Technol. 7, 62–69 (1990).

Grams, G. W.

W. J. Wiscombe, G. W. Grams, “The backscattered fraction in two-stream approximations,” J. Atmos. Sci. 33, 2240–2451 (1976).
[CrossRef]

Gras, J. L.

J. L. Gras, G. P. Ayers, “Marine aerosol at southern mid-latitudes,” J. Geophys. Res. 88, 10661–10666 (1983).
[CrossRef]

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 aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

Hänel, G.

Hansen, J.

J. Hansen, W. Rossow, I. Fung, “The missing data on global climate change,” Issues Sci. Technol. 7, 62–69 (1990).

J. Hansen, “Exact and approximate solutions for multiple scattering by cloudy and hazy planetary atmospheres,” J. Atmos. Sci. 26, 478–487 (1969).
[CrossRef]

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 aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

See figure 16 in J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[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 aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

Hoppel, W. A.

W. A. Hoppel, G. M. Frick, “Submicron aerosol size distributions measured over the tropical and south Pacific,” Atmos. Environ. 24, 645–659 (1990).
[CrossRef]

Isaac, G. A.

W. R. Leaitch, G. A. Isaac, “Tropospheric aerosol size distributions from 1982 to 1988 over eastern North America,” Atmos. Environ. 25, 601–619 (1991).
[CrossRef]

Joseph, J. H.

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The delta-Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2458 (1976).
[CrossRef]

Kapustin, V. N.

P. K. Quinn, S. F. Marshall, T. S. Bates, D. S. Covert, V. N. Kapustin, “Comparison of measured and calculated aerosol properties relevant to the direct radiative forcing of tropospheric sulfate aerosol on climate,” J. Geophys. Res. 100, 8977–8992 (1995).
[CrossRef]

Kent, G. S.

Kiehl, J. T.

J. T. Kiehl, B. P. Briegleb, “The relative roles of sulfate aerosols and greenhouse gases in climate forcing,” Science 260, 311–314 (1993).
[CrossRef] [PubMed]

Leaitch, W. R.

W. R. Leaitch, G. A. Isaac, “Tropospheric aerosol size distributions from 1982 to 1988 over eastern North America,” Atmos. Environ. 25, 601–619 (1991).
[CrossRef]

Marshall, S. F.

P. K. Quinn, S. F. Marshall, T. S. Bates, D. S. Covert, V. N. Kapustin, “Comparison of measured and calculated aerosol properties relevant to the direct radiative forcing of tropospheric sulfate aerosol on climate,” J. Geophys. Res. 100, 8977–8992 (1995).
[CrossRef]

S. F. Marshall, “Measurement-derived radiative transfer parameters for the aerosol climate forcing problem,” M.S. thesis (University of Washington, Seattle, Wash., 1994).

Mishchenko, M. I.

Porch, W. M.

R. J. Charlson, W. M. Porch, A. P. Waggoner, N. C. Ahlquist, “Background aerosol light scattering characteristics: nephelometric observations at Mauna Loa Observatory compared with results at other remote locations,” Tellus 26, 345–360 (1974).
[CrossRef]

Quinn, P. K.

P. K. Quinn, S. F. Marshall, T. S. Bates, D. S. Covert, V. N. Kapustin, “Comparison of measured and calculated aerosol properties relevant to the direct radiative forcing of tropospheric sulfate aerosol on climate,” J. Geophys. Res. 100, 8977–8992 (1995).
[CrossRef]

Rossow, W.

J. Hansen, W. Rossow, I. Fung, “The missing data on global climate change,” Issues Sci. Technol. 7, 62–69 (1990).

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 aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

Travis, L. D.

Twomey, S.

S. Twomey, “Pollution and the planetary albedo,” Atmos. Environ. 8, 1251–1256 (1974).
[CrossRef]

Waggoner, A. P.

A. P. Waggoner, R. E. Weiss, N. C. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, “Optical characteristics of atmospheric aerosols,” Atmos. Environ. 15, 1891–1909 (1981).
[CrossRef]

R. J. Charlson, W. M. Porch, A. P. Waggoner, N. C. Ahlquist, “Background aerosol light scattering characteristics: nephelometric observations at Mauna Loa Observatory compared with results at other remote locations,” Tellus 26, 345–360 (1974).
[CrossRef]

Weinman, J. A.

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The delta-Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2458 (1976).
[CrossRef]

Weiss, R. E.

A. P. Waggoner, R. E. Weiss, N. C. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, “Optical characteristics of atmospheric aerosols,” Atmos. Environ. 15, 1891–1909 (1981).
[CrossRef]

Welch, R. M.

R. M. Welch, W. G. Zdunkowitz, “Backscattering approximations and their influence on Eddington-type solar flux calculations,” Contrib. Atmos. Phys. 55, 28–42 (1982).

Whitby, K. T.

K. T. Whitby, “The physical characteristics of sulfur aerosols,” Atmos. Environ. 12, 135–159 (1978).
[CrossRef]

Will, S.

A. P. Waggoner, R. E. Weiss, N. C. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, “Optical characteristics of atmospheric aerosols,” Atmos. Environ. 15, 1891–1909 (1981).
[CrossRef]

Wiscombe, W. J.

W. J. Wiscombe, G. W. Grams, “The backscattered fraction in two-stream approximations,” J. Atmos. Sci. 33, 2240–2451 (1976).
[CrossRef]

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The delta-Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2458 (1976).
[CrossRef]

Yue, G. K.

Zdunkowitz, W. G.

R. M. Welch, W. G. Zdunkowitz, “Backscattering approximations and their influence on Eddington-type solar flux calculations,” Contrib. Atmos. Phys. 55, 28–42 (1982).

Appl. Opt.

Atmos. Environ.

S. Twomey, “Pollution and the planetary albedo,” Atmos. Environ. 8, 1251–1256 (1974).
[CrossRef]

A. P. Waggoner, R. E. Weiss, N. C. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, “Optical characteristics of atmospheric aerosols,” Atmos. Environ. 15, 1891–1909 (1981).
[CrossRef]

K. T. Whitby, “The physical characteristics of sulfur aerosols,” Atmos. Environ. 12, 135–159 (1978).
[CrossRef]

W. A. Hoppel, G. M. Frick, “Submicron aerosol size distributions measured over the tropical and south Pacific,” Atmos. Environ. 24, 645–659 (1990).
[CrossRef]

W. R. Leaitch, G. A. Isaac, “Tropospheric aerosol size distributions from 1982 to 1988 over eastern North America,” Atmos. Environ. 25, 601–619 (1991).
[CrossRef]

Contrib. Atmos. Phys.

H. W. Barker, “A parameterization and generalization of backscatter functions for two-stream approximations,” Contrib. Atmos. Phys. 67, 195–199 (1994).

R. M. Welch, W. G. Zdunkowitz, “Backscattering approximations and their influence on Eddington-type solar flux calculations,” Contrib. Atmos. Phys. 55, 28–42 (1982).

Issues Sci. Technol.

J. Hansen, W. Rossow, I. Fung, “The missing data on global climate change,” Issues Sci. Technol. 7, 62–69 (1990).

J. Atmos. Sci.

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The delta-Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2458 (1976).
[CrossRef]

J. Hansen, “Exact and approximate solutions for multiple scattering by cloudy and hazy planetary atmospheres,” J. Atmos. Sci. 26, 478–487 (1969).
[CrossRef]

W. J. Wiscombe, G. W. Grams, “The backscattered fraction in two-stream approximations,” J. Atmos. Sci. 33, 2240–2451 (1976).
[CrossRef]

J. Geophys. Res.

J. L. Gras, G. P. Ayers, “Marine aerosol at southern mid-latitudes,” J. Geophys. Res. 88, 10661–10666 (1983).
[CrossRef]

B. P. Briegleb, “Delta-Eddington approximation for solar radiation in the NCAR community climate model,” J. Geophys. Res. 97, 7603–7612 (1992).
[CrossRef]

R. G. Ellingson, J. Ellis, S. Fels, “The intercomparison of radiation codes used in climate models: long wave results,” J. Geophys. Res. 96, 8929–8953 (1991).
[CrossRef]

P. K. Quinn, S. F. Marshall, T. S. Bates, D. S. Covert, V. N. Kapustin, “Comparison of measured and calculated aerosol properties relevant to the direct radiative forcing of tropospheric sulfate aerosol on climate,” J. Geophys. Res. 100, 8977–8992 (1995).
[CrossRef]

Science

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 aerosols,” Science 255, 423–430 (1992).
[CrossRef] [PubMed]

J. T. Kiehl, B. P. Briegleb, “The relative roles of sulfate aerosols and greenhouse gases in climate forcing,” Science 260, 311–314 (1993).
[CrossRef] [PubMed]

Space Sci. Rev.

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

Tellus

R. J. Charlson, W. M. Porch, A. P. Waggoner, N. C. Ahlquist, “Background aerosol light scattering characteristics: nephelometric observations at Mauna Loa Observatory compared with results at other remote locations,” Tellus 26, 345–360 (1974).
[CrossRef]

Other

S. F. Marshall, “Measurement-derived radiative transfer parameters for the aerosol climate forcing problem,” M.S. thesis (University of Washington, Seattle, Wash., 1994).

The tendency of the curves in Fig. 1 indicates that another one-to-one relationship between b and g may exist for particles with Dgv greater than a few micrometers. This relationship is not addressed because such large particles have a relatively small radiative effect compared with smaller particles—see Ref. 15.

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Figures (3)

Fig. 1
Fig. 1

Asymmetry parameter g as a function of backscatter ratio b. Mie calculations for unimodal log-normal size distributions at a wavelength of 550 nm, three refractive indices (real parts 1.33, 1.45, and 1.60, with the imaginary part always equal to 0) and 2 standard deviations (σg = 1.4 and 2.0) are compared with the relation for the Henyey–Greenstein (HG) phase function. The Dgv values used in the Mie calculations progress from smaller values in the lower right corner to larger values in the upper left. The Dgv values for n = 1.45, indicated with arrows, vary with assumed wavelength; for λ = 700 nm, multiply by 700/550 = 1.27. The one-to-one relationship between b and g exhibited by the HG phase function does not exist for the Mie calculations. Even if the standard deviation and refractive index are known, a single value of b can imply as many as three values of g.

Fig. 2
Fig. 2

Relationship between asymmetry parameter and backscatter ratio for unimodal log-normal distributions representative of accumulation-mode aerosols. For a fixed wavelength of 550 nm, 2 standard deviations (σg = 1.4 and 2.0) and two complex refractive indices (m = 1.40 − 0.16i and 1.50 − 0i) are used. Calculations for m = 1.40 − 0i and m = 1.55 − 0.16i are not shown, but are barely distinguishable from the m = 1.40 − 0.16i calculations. Dgv is increased from 0.1 μm in the lower right to 0.45 μm in the upper left of each curve. The Mie calculations give a range of g values for a given b value that is mainly determined by the variation in σg. For b = 0.1, g ranges from 0.605 to 0.64. The Henyey–Greenstein (HG) phase-function approximation systematically overpredicts the Mie calculations by 2–9%, becoming less accurate as σg decreases. The relationships between b and g found in the literature are shown as diamonds. The b value of 0.15 used by Charlson et al.2 corresponds to an asymmetry parameter of 0.54 when the HG relationship is used but gives a g value of 0.52 if the size distribution of Kiehl and Briegleb (Dgv = 0.42 μm, σg = 2.0, m = 1.43 − 0i at λ = 550 nm) is used.3 The g value of 0.69 used by Kiehl and Briegleb corresponds to b = 0.088 for the case of a HG phase function. The Mie-calculated backscatter ratio for the Kiehl and Briegleb size distribution was reported in round figures as 0.10, but reproduction of their calculations in this paper yielded a b value of 0.082.

Fig. 3
Fig. 3

Comparison of polynomial fit for Mie calculations with Henyey–Greenstein relation for the asymmetry parameter and the backscatter ratio. The Mie calculations were performed at 6 real refractive indices (1.33 ≤ n ≤ 1.6), 3 imaginary refractive indices (k = 0, 0.02, and 0.16), 7 standard deviations (1.4 ≤ σg ≤ 2.0), and 14 mean volume diameters (0.1 ≤ Dgv ≤ 0.45 μm at λ = 550 nm). Agreement between the polynomial fit and the Mie calculations is worst for particles with extreme values of Dgv (0.125 and 0.45 μm), narrow (σg = 1.4) size distributions, and large real refractive indices.

Tables (2)

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Table 1 Percent Change in Climate Forcing by Aerosols when Asymmetry Parametergis Changed from 0.6 to 0.66a

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Table 2 Coefficients Cl,mfor the Polynomial Fit of g(b, σg)a

Equations (7)

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P ( θ , x , m ) = I ( θ , x , m ) 0 π I ( θ , x , m ) sin θ d θ .
0 2 π 0 π P ( θ ) sin θ d θ d ϕ = 4 π .
g 1 2 0 π cos θ I ( θ ) sin θ d θ 0 π I ( θ ) sin θ d θ = 1 2 0 π cos θ P ( θ ) sin θ d θ .
b = π P ( θ ) sin θ d θ 0 π P ( θ ) sin θ d θ .
P HG ( θ ) 1 g 2 ( 1 + g 2 2 g cos θ ) 3 / 2 .
g ( b , σ g ) = l = 0 3 A l ( σ g ) b l .
A l ( σ g ) = m = 0 3 C l , m ( σ g ) m .

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