Abstract

A database management system has been realized that, by taking physical and chemical properties (the complex refractive index and the size distribution) of basic components as its starting point, allows the user to obtain optical properties of default as well as user-defined aerosol classes. Default classes are defined in accordance with the most widely known and used aerosol models. We obtain user-defined classes by varying the mixing ratio of components, creating new mixtures of default components, or by defining user components, thereby supplying the size distribution and the refractive index. The effect of relative humidity (RH) on the refractive index and the size distribution is properly accounted for up to RH = 99%. The two known mechanisms of obtaining classes from components are allowed (internal or external mixing).

© 1997 Optical Society of America

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References

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  1. S. Twomey, “The influence of pollution on the shortwave albedo of clouds,” J. Atmos. Sci. 34, 1149–1152 (1977).
    [CrossRef]
  2. E. P. Shettle, R. W. Fenn, “Models for the aerosol lower atmosphere and the effects of humidity variations on their optical properties,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).
  3. G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols. Global Climatology and Radiative Characteristics (Deepak, Hampton, Va.1991).
  4. O. B. Toon, J. B. Pollack, “A global average model of atmospheric aerosol for radiative transfer calculations,” J. Appl. Meteorol. 15, 225–246 (1976).
    [CrossRef]
  5. R. W. Fenn, “Aerosol-Verteilungen und atmospharisches Streulicht,” Beitr. Phys. Atmos. 37, 69–104 (1964).
  6. A. Deepak, H. E. Gerbers, eds., “Report of the experts’ meeting on aerosols and their climatic effects,” (World Climate Research Program, Geneva, 1983).
  7. World Meteorological Organization, “A preliminary cloudless standard atmosphere for radiation computation,” (World Climate Research Program, CAS, Radiation Commission of IAMAP, Boulder, Colo., 1986).
  8. M. Wang, H. R. Gordon, “Radiance reflected from the ocean-atmosphere system: synthesis from individual components of the aerosol size distribution,” Appl. Opt. 33, 7088–7095 (1994).
    [CrossRef] [PubMed]
  9. A. M. Ignatov, L. L. Stowe, S. M. Sakerin, G. K. Korotaev, “Validation of the NOAA/NESDIS satellite aerosol product over the North Atlantic in 1989,” J. Geophys. Res. 100, 5123–5132 (1995).
    [CrossRef]
  10. F. Dulac, D. Tanré, G. Bergametti, P. Buat-Ménard, M. Desbois, D. Sutton, “Assessment of the African airborne dust mass over the western Mediterranean Sea using Meteosat data,” J. Geophys. Res. 97, 2489–2506 (1992).
    [CrossRef]
  11. J. M. Haywood, K. P. Shine, “The effect of anthropogenic sulfate and soot aerosol on the clear sky planetary radiation budget,” Geophys. Res. Lett. 22, 603–606 (1995).
    [CrossRef]
  12. M. I. Mishchenko, A. A. Lacis, B. E. Carlson, L. D. Travis, “Nonsphericity of dustlike tropospheric aerosol: implication for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
    [CrossRef]
  13. F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwind, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the LOWTRAN 6 model,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).
  14. G. Häanel, “The properties of atmospheric aerosol particles as functions of the relative humidity at thermodynamic equilibrium with the surrounding moist air,” Adv. Geophys. 19, 73–188 (1976).
    [CrossRef]
  15. G. Häanel, “The physical chemistry of atmospheric particles,” in Hygroscopic Aerosol, L. H. Ruhnke, A. Deepak, eds. (Deepak, Hampton, Va., 1984), pp. 1–20.
  16. E. P. Shettle, Remote Sensing Division, U. S. Naval Research Laboratory, Washington, D.C. 20375 (personal communication, 1996).
  17. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), pp. 151–285.
  18. Yu. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and the North Atlantic,” J. Geophys. Res. 99, 20983–20988 (1994).
    [CrossRef]

1995 (3)

A. M. Ignatov, L. L. Stowe, S. M. Sakerin, G. K. Korotaev, “Validation of the NOAA/NESDIS satellite aerosol product over the North Atlantic in 1989,” J. Geophys. Res. 100, 5123–5132 (1995).
[CrossRef]

J. M. Haywood, K. P. Shine, “The effect of anthropogenic sulfate and soot aerosol on the clear sky planetary radiation budget,” Geophys. Res. Lett. 22, 603–606 (1995).
[CrossRef]

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, L. D. Travis, “Nonsphericity of dustlike tropospheric aerosol: implication for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

1994 (2)

M. Wang, H. R. Gordon, “Radiance reflected from the ocean-atmosphere system: synthesis from individual components of the aerosol size distribution,” Appl. Opt. 33, 7088–7095 (1994).
[CrossRef] [PubMed]

Yu. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and the North Atlantic,” J. Geophys. Res. 99, 20983–20988 (1994).
[CrossRef]

1992 (1)

F. Dulac, D. Tanré, G. Bergametti, P. Buat-Ménard, M. Desbois, D. Sutton, “Assessment of the African airborne dust mass over the western Mediterranean Sea using Meteosat data,” J. Geophys. Res. 97, 2489–2506 (1992).
[CrossRef]

1977 (1)

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

1976 (2)

O. B. Toon, J. B. Pollack, “A global average model of atmospheric aerosol for radiative transfer calculations,” J. Appl. Meteorol. 15, 225–246 (1976).
[CrossRef]

G. Häanel, “The properties of atmospheric aerosol particles as functions of the relative humidity at thermodynamic equilibrium with the surrounding moist air,” Adv. Geophys. 19, 73–188 (1976).
[CrossRef]

1964 (1)

R. W. Fenn, “Aerosol-Verteilungen und atmospharisches Streulicht,” Beitr. Phys. Atmos. 37, 69–104 (1964).

Abreu, L. W.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwind, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the LOWTRAN 6 model,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

Bergametti, G.

F. Dulac, D. Tanré, G. Bergametti, P. Buat-Ménard, M. Desbois, D. Sutton, “Assessment of the African airborne dust mass over the western Mediterranean Sea using Meteosat data,” J. Geophys. Res. 97, 2489–2506 (1992).
[CrossRef]

Buat-Ménard, P.

F. Dulac, D. Tanré, G. Bergametti, P. Buat-Ménard, M. Desbois, D. Sutton, “Assessment of the African airborne dust mass over the western Mediterranean Sea using Meteosat data,” J. Geophys. Res. 97, 2489–2506 (1992).
[CrossRef]

Carlson, B. E.

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, L. D. Travis, “Nonsphericity of dustlike tropospheric aerosol: implication for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

Chetwind, J. H.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwind, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the LOWTRAN 6 model,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

Clough, S. A.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwind, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the LOWTRAN 6 model,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

d’Almeida, G. A.

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols. Global Climatology and Radiative Characteristics (Deepak, Hampton, Va.1991).

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), pp. 151–285.

Desbois, M.

F. Dulac, D. Tanré, G. Bergametti, P. Buat-Ménard, M. Desbois, D. Sutton, “Assessment of the African airborne dust mass over the western Mediterranean Sea using Meteosat data,” J. Geophys. Res. 97, 2489–2506 (1992).
[CrossRef]

Dulac, F.

F. Dulac, D. Tanré, G. Bergametti, P. Buat-Ménard, M. Desbois, D. Sutton, “Assessment of the African airborne dust mass over the western Mediterranean Sea using Meteosat data,” J. Geophys. Res. 97, 2489–2506 (1992).
[CrossRef]

Fenn, R. W.

R. W. Fenn, “Aerosol-Verteilungen und atmospharisches Streulicht,” Beitr. Phys. Atmos. 37, 69–104 (1964).

E. P. Shettle, R. W. Fenn, “Models for the aerosol lower atmosphere and the effects of humidity variations on their optical properties,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwind, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the LOWTRAN 6 model,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

Gallery, W. O.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwind, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the LOWTRAN 6 model,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

Gordon, H. R.

Häanel, G.

G. Häanel, “The properties of atmospheric aerosol particles as functions of the relative humidity at thermodynamic equilibrium with the surrounding moist air,” Adv. Geophys. 19, 73–188 (1976).
[CrossRef]

G. Häanel, “The physical chemistry of atmospheric particles,” in Hygroscopic Aerosol, L. H. Ruhnke, A. Deepak, eds. (Deepak, Hampton, Va., 1984), pp. 1–20.

Haywood, J. M.

J. M. Haywood, K. P. Shine, “The effect of anthropogenic sulfate and soot aerosol on the clear sky planetary radiation budget,” Geophys. Res. Lett. 22, 603–606 (1995).
[CrossRef]

Ignatov, A. M.

A. M. Ignatov, L. L. Stowe, S. M. Sakerin, G. K. Korotaev, “Validation of the NOAA/NESDIS satellite aerosol product over the North Atlantic in 1989,” J. Geophys. Res. 100, 5123–5132 (1995).
[CrossRef]

Kneizys, F. X.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwind, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the LOWTRAN 6 model,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

Koepke, P.

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols. Global Climatology and Radiative Characteristics (Deepak, Hampton, Va.1991).

Korotaev, G. K.

A. M. Ignatov, L. L. Stowe, S. M. Sakerin, G. K. Korotaev, “Validation of the NOAA/NESDIS satellite aerosol product over the North Atlantic in 1989,” J. Geophys. Res. 100, 5123–5132 (1995).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, L. D. Travis, “Nonsphericity of dustlike tropospheric aerosol: implication for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, L. D. Travis, “Nonsphericity of dustlike tropospheric aerosol: implication for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

O’Neill, N. T.

Yu. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and the North Atlantic,” J. Geophys. Res. 99, 20983–20988 (1994).
[CrossRef]

Pollack, J. B.

O. B. Toon, J. B. Pollack, “A global average model of atmospheric aerosol for radiative transfer calculations,” J. Appl. Meteorol. 15, 225–246 (1976).
[CrossRef]

Sakerin, S. M.

A. M. Ignatov, L. L. Stowe, S. M. Sakerin, G. K. Korotaev, “Validation of the NOAA/NESDIS satellite aerosol product over the North Atlantic in 1989,” J. Geophys. Res. 100, 5123–5132 (1995).
[CrossRef]

Selby, J. E. A.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwind, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the LOWTRAN 6 model,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

Shettle, E. P.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwind, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the LOWTRAN 6 model,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

E. P. Shettle, R. W. Fenn, “Models for the aerosol lower atmosphere and the effects of humidity variations on their optical properties,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols. Global Climatology and Radiative Characteristics (Deepak, Hampton, Va.1991).

E. P. Shettle, Remote Sensing Division, U. S. Naval Research Laboratory, Washington, D.C. 20375 (personal communication, 1996).

Shine, K. P.

J. M. Haywood, K. P. Shine, “The effect of anthropogenic sulfate and soot aerosol on the clear sky planetary radiation budget,” Geophys. Res. Lett. 22, 603–606 (1995).
[CrossRef]

Smirnov, A. V.

Yu. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and the North Atlantic,” J. Geophys. Res. 99, 20983–20988 (1994).
[CrossRef]

Smyshlyaev, S. P.

Yu. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and the North Atlantic,” J. Geophys. Res. 99, 20983–20988 (1994).
[CrossRef]

Stowe, L. L.

A. M. Ignatov, L. L. Stowe, S. M. Sakerin, G. K. Korotaev, “Validation of the NOAA/NESDIS satellite aerosol product over the North Atlantic in 1989,” J. Geophys. Res. 100, 5123–5132 (1995).
[CrossRef]

Sutton, D.

F. Dulac, D. Tanré, G. Bergametti, P. Buat-Ménard, M. Desbois, D. Sutton, “Assessment of the African airborne dust mass over the western Mediterranean Sea using Meteosat data,” J. Geophys. Res. 97, 2489–2506 (1992).
[CrossRef]

Tanré, D.

F. Dulac, D. Tanré, G. Bergametti, P. Buat-Ménard, M. Desbois, D. Sutton, “Assessment of the African airborne dust mass over the western Mediterranean Sea using Meteosat data,” J. Geophys. Res. 97, 2489–2506 (1992).
[CrossRef]

Toon, O. B.

O. B. Toon, J. B. Pollack, “A global average model of atmospheric aerosol for radiative transfer calculations,” J. Appl. Meteorol. 15, 225–246 (1976).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, L. D. Travis, “Nonsphericity of dustlike tropospheric aerosol: implication for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

Twomey, S.

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

Villevalde, Yu. V.

Yu. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and the North Atlantic,” J. Geophys. Res. 99, 20983–20988 (1994).
[CrossRef]

Wang, M.

Yakovlev, V. V.

Yu. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and the North Atlantic,” J. Geophys. Res. 99, 20983–20988 (1994).
[CrossRef]

Adv. Geophys. (1)

G. Häanel, “The properties of atmospheric aerosol particles as functions of the relative humidity at thermodynamic equilibrium with the surrounding moist air,” Adv. Geophys. 19, 73–188 (1976).
[CrossRef]

Appl. Opt. (1)

Beitr. Phys. Atmos. (1)

R. W. Fenn, “Aerosol-Verteilungen und atmospharisches Streulicht,” Beitr. Phys. Atmos. 37, 69–104 (1964).

Geophys. Res. Lett. (2)

J. M. Haywood, K. P. Shine, “The effect of anthropogenic sulfate and soot aerosol on the clear sky planetary radiation budget,” Geophys. Res. Lett. 22, 603–606 (1995).
[CrossRef]

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, L. D. Travis, “Nonsphericity of dustlike tropospheric aerosol: implication for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

J. Appl. Meteorol. (1)

O. B. Toon, J. B. Pollack, “A global average model of atmospheric aerosol for radiative transfer calculations,” J. Appl. Meteorol. 15, 225–246 (1976).
[CrossRef]

J. Atmos. Sci. (1)

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

J. Geophys. Res. (3)

A. M. Ignatov, L. L. Stowe, S. M. Sakerin, G. K. Korotaev, “Validation of the NOAA/NESDIS satellite aerosol product over the North Atlantic in 1989,” J. Geophys. Res. 100, 5123–5132 (1995).
[CrossRef]

F. Dulac, D. Tanré, G. Bergametti, P. Buat-Ménard, M. Desbois, D. Sutton, “Assessment of the African airborne dust mass over the western Mediterranean Sea using Meteosat data,” J. Geophys. Res. 97, 2489–2506 (1992).
[CrossRef]

Yu. V. Villevalde, A. V. Smirnov, N. T. O’Neill, S. P. Smyshlyaev, V. V. Yakovlev, “Measurement of aerosol optical depth in the Pacific Ocean and the North Atlantic,” J. Geophys. Res. 99, 20983–20988 (1994).
[CrossRef]

Other (8)

G. Häanel, “The physical chemistry of atmospheric particles,” in Hygroscopic Aerosol, L. H. Ruhnke, A. Deepak, eds. (Deepak, Hampton, Va., 1984), pp. 1–20.

E. P. Shettle, Remote Sensing Division, U. S. Naval Research Laboratory, Washington, D.C. 20375 (personal communication, 1996).

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), pp. 151–285.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwind, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: the LOWTRAN 6 model,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

E. P. Shettle, R. W. Fenn, “Models for the aerosol lower atmosphere and the effects of humidity variations on their optical properties,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols. Global Climatology and Radiative Characteristics (Deepak, Hampton, Va.1991).

A. Deepak, H. E. Gerbers, eds., “Report of the experts’ meeting on aerosols and their climatic effects,” (World Climate Research Program, Geneva, 1983).

World Meteorological Organization, “A preliminary cloudless standard atmosphere for radiation computation,” (World Climate Research Program, CAS, Radiation Commission of IAMAP, Boulder, Colo., 1986).

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Figures (6)

Fig. 1
Fig. 1

Database structure, with input-output details.

Fig. 2
Fig. 2

Internal and external mixing logic flows.

Fig. 3
Fig. 3

Comparison of measured and calculated optical depth spectra. Vertical bars represent the fitting tolerance limits. VILL, input values of Villevalde et al.18

Fig. 4
Fig. 4

Left: spectral extinction coefficients (at 1 particle/cm3) of externally and internally mixed aerosol classes. Right: spectral percentage differences between the two quantities.

Fig. 5
Fig. 5

Left: spectral single-scattering albedo values of externally and internally mixed aerosol classes. Right: spectral percentage differences between the two quantities.

Fig. 6
Fig. 6

Examined aerosol dry components. Left: spectral extinction coefficients (at 1 particle/cm3). Right: spectral single-scattering albedo values. WS1, water soluble 1; WS2, water soluble 2; D–L, dustlike; Soo, soot; Oce, oceanic.

Tables (7)

Tables Icon

Table 1 Relevant Information on Aerosol Component Size Distributions and Refractive Indicesa

Tables Icon

Table 2 Default Aerosol Classesa

Tables Icon

Table 3 Comparisons with Other Databasesa

Tables Icon

Table 4 Parameters of Size Distributions and Aerosol Abundances Employed in Fitting Measurements by Villevalde et al.18

Tables Icon

Table 5 Spectral Refractive Indices of the Examined Aerosol Componentsa

Tables Icon

Table 6 Spectral Refractive Indices for Examined Internally Mixed Aerosol Classes

Tables Icon

Table 7 Examined Aerosol-Class Input Data

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

dNdr=Cr ln10σ2πexp-logr/rm22σ2,
dNdr=Arα exp-brγ,
m=mw+m0-mwr0/r3,
kn2+2=kwnw2+2+k0n02+2-kwnw2+2r0r3,
dNr/drr2<cutoff value  r>rmax,  r>rmin,
τAλ=Kextλ km-1 cm3A μm-2×103,
A=Af+Ac, nf=Af/A, nc=Ac/A,
Kext,sca,abs=jnjKjext,sca,absj nj
ω0=jnjKjextω0jjnjKjext
Pγ=jnjKjscaPjγj njKjsca,
m=j vjmjj vj,
vj=4/3πnj0r3dN/drdr=4/3πnjrmj3×exp92σjloge2.

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