Abstract

Predictions concerning the scattering and absorption characteristics of electromagnetic radiation interacting with nonspherical particles are obtained by suppression of particle resonances (surface waves) in classical Mie scattering theory. The importance of the particle resonance phenomenon and thus the nonspherical corrections is related to the three classical variables ni, nr, and x, the imaginary and real components of the index of refraction and the size parameter, respectively. The resonance phenomenon becomes increasingly restricted to small values of x as nr increases. For solar wavelengths and cloud size particles resonance phenomenon may be neglected for nr ≳ 2. As nr decreases the effect of nonsphericity becomes increasingly significant to both scattering and absorption. For nr ≲ 2.0 and ni ≃ 10−5, suppression of particle resonances in Mie theory predicts increases in absorption efficiency of several orders of magnitude in the region of the absorption peak.

© 1978 Optical Society of America

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References

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    [CrossRef]
  2. SMIC Report, Study of Man’s Impact on Climate (MIT Press, Cambridge, Mass., 1971).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  23. W. J. Wiscombe, J. Atmos. Sci. 34, 1408 (1977).
    [CrossRef]
  24. J. Joseph, W. J. Wiscombe, J. A. Weinman, J. Atmos. Sci. 33, 2452 (1976).
    [CrossRef]
  25. J. R. Probert-Jones, “Surface Waves Associated with the Backscattering of Microwave Radiation by Large Ice Spheres,” in Electromagnetic Waves, M. Kerker, Ed. (Macmillan, New York, 1963), pp. 237–250.
  26. H. Inada, Appl. Opt. 13, 1928 (1974).
    [CrossRef] [PubMed]
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    [CrossRef]
  28. P. S. Ray, Appl. Opt. 11, 1836 (1972).
    [CrossRef] [PubMed]
  29. H. R. Pruppacher, R. L. Pitter, J. Atmos. Sci. 28, 86 (1971).
    [CrossRef]
  30. H. K. Weickmann, Die eisphase in der atmosphere, Library Trans. 273 (Royal Aircraft Establishment, Farnborough, 1947), 96 pp.
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  32. K. Ya. Kondratyev, R. M. Welch, O. B. Vasilyev, V. F. Zhvalev, L. S. Ivlev, V. F. Radionov, “Calculations of Free Atmospheric Shortwave Spectral Characteristics over the Desert” (from the CAENEX-70 data), submitted for publication to Tellus (1978).

1978 (1)

1977 (3)

1976 (7)

J. Joseph, W. J. Wiscombe, J. A. Weinman, J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

E. M. Patterson, D. A. Gillette, G. W. Grams, J. Appl. Meteorol. 15, 470 (1976).
[CrossRef]

R. M. Welch, J. F. Geleyn, W. G. Zdunkowski, G. Korb, Beitr. Phys. 49, 128 (1976).

R. H. Zerull, Beitr. Atmos. 49, 168 (1976).

R. G. Pinnick, D. E. Carrol, D. J. Hofman, Appl. Opt. 15, 384 (1976).
[CrossRef] [PubMed]

P. Chylek, J. Opt. Soc. Am. 66, 285 (1976).
[CrossRef]

P. Chylek, G. W. Grams, R. G. Pinnick, Science 193, 480 (1976).
[CrossRef]

1975 (2)

A. Heymsfield, J. Atmos. Sci. 31, 799 (1975).
[CrossRef]

D. Deirmendjian, J. Appl. Meteorol. 14, 1584 (1975).
[CrossRef]

1974 (4)

K. N. Liou, J. Atmos. Sci. 31, 522 (1974).
[CrossRef]

S. B. Idso, Science 186, 50 (1974).
[CrossRef] [PubMed]

H. Inada, Appl. Opt. 13, 1928 (1974).
[CrossRef] [PubMed]

P. S. Ray, J. J. Stephens, Radio Sci. 9, 43 (1974).
[CrossRef]

1972 (2)

1971 (4)

H. Jacobowitz, J. Quant. Spectrosc. Radiat Transfer 11, 691 (1971).
[CrossRef]

J. M. Mitchell, J. Appl. Meteorol. 10, 703 (1971).
[CrossRef]

S. I. Rasool, S. H. Schneider, Science 173, 138 (1971).
[CrossRef] [PubMed]

H. R. Pruppacher, R. L. Pitter, J. Atmos. Sci. 28, 86 (1971).
[CrossRef]

1970 (1)

1967 (1)

Bennett, H. S.

Carrol, D. E.

Chylek, P.

Cox, S. K.

K. T. Griffith, S. K. Cox, “Infrared Radiative Properties of Tropical Cirrus Clouds Inferred from Broadband Measurements,” Atmospheric Science Paper 269 (Colorado State U., Fort Collins, 1977).

R. M. Welch, S. K. Cox, “Absorption of Solar Radiation in Clouds,” submitted for publication, AMS Monograph Series (1978).

Deirmendjian, D.

D. Deirmendjian, J. Appl. Meteorol. 14, 1584 (1975).
[CrossRef]

Draper, J. S.

Gagné, G.

Geleyn, J. F.

R. M. Welch, J. F. Geleyn, W. G. Zdunkowski, G. Korb, Beitr. Phys. 49, 128 (1976).

Giese, R. H.

Gillette, D. A.

E. M. Patterson, D. A. Gillette, G. W. Grams, J. Appl. Meteorol. 15, 470 (1976).
[CrossRef]

Grams, G. W.

E. M. Patterson, D. A. Gillette, G. W. Grams, J. Appl. Meteorol. 15, 470 (1976).
[CrossRef]

P. Chylek, G. W. Grams, R. G. Pinnick, Science 193, 480 (1976).
[CrossRef]

Griffith, K. T.

K. T. Griffith, S. K. Cox, “Infrared Radiative Properties of Tropical Cirrus Clouds Inferred from Broadband Measurements,” Atmospheric Science Paper 269 (Colorado State U., Fort Collins, 1977).

Heymsfield, A.

A. Heymsfield, J. Atmos. Sci. 31, 799 (1975).
[CrossRef]

Hofman, D. J.

Holland, A. C.

Idso, S. B.

S. B. Idso, Science 186, 50 (1974).
[CrossRef] [PubMed]

Inada, H.

Ivlev, L. S.

K. Ya. Kondratyev, R. M. Welch, O. B. Vasilyev, V. F. Zhvalev, L. S. Ivlev, V. F. Radionov, “Calculations of Free Atmospheric Shortwave Spectral Characteristics over the Desert” (from the CAENEX-70 data), submitted for publication to Tellus (1978).

Jacobowitz, H.

H. Jacobowitz, J. Quant. Spectrosc. Radiat Transfer 11, 691 (1971).
[CrossRef]

Joseph, J.

J. Joseph, W. J. Wiscombe, J. A. Weinman, J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

Kondratyev, K. Ya.

K. Ya. Kondratyev, R. M. Welch, O. B. Vasilyev, V. F. Zhvalev, L. S. Ivlev, V. F. Radionov, “Calculations of Free Atmospheric Shortwave Spectral Characteristics over the Desert” (from the CAENEX-70 data), submitted for publication to Tellus (1978).

Korb, G.

R. M. Welch, J. F. Geleyn, W. G. Zdunkowski, G. Korb, Beitr. Phys. 49, 128 (1976).

Liou, K. N.

Mitchell, J. M.

J. M. Mitchell, J. Appl. Meteorol. 10, 703 (1971).
[CrossRef]

Patterson, E. M.

E. M. Patterson, D. A. Gillette, G. W. Grams, J. Appl. Meteorol. 15, 470 (1976).
[CrossRef]

Pinnick, R. G.

Pitter, R. L.

H. R. Pruppacher, R. L. Pitter, J. Atmos. Sci. 28, 86 (1971).
[CrossRef]

Probert-Jones, J. R.

J. R. Probert-Jones, “Surface Waves Associated with the Backscattering of Microwave Radiation by Large Ice Spheres,” in Electromagnetic Waves, M. Kerker, Ed. (Macmillan, New York, 1963), pp. 237–250.

Pruppacher, H. R.

H. R. Pruppacher, R. L. Pitter, J. Atmos. Sci. 28, 86 (1971).
[CrossRef]

Radionov, V. F.

K. Ya. Kondratyev, R. M. Welch, O. B. Vasilyev, V. F. Zhvalev, L. S. Ivlev, V. F. Radionov, “Calculations of Free Atmospheric Shortwave Spectral Characteristics over the Desert” (from the CAENEX-70 data), submitted for publication to Tellus (1978).

Rasool, S. I.

S. I. Rasool, S. H. Schneider, Science 173, 138 (1971).
[CrossRef] [PubMed]

Ray, P. S.

P. S. Ray, J. J. Stephens, Radio Sci. 9, 43 (1974).
[CrossRef]

P. S. Ray, Appl. Opt. 11, 1836 (1972).
[CrossRef] [PubMed]

Rosasco, G. J.

Schneider, S. H.

S. I. Rasool, S. H. Schneider, Science 173, 138 (1971).
[CrossRef] [PubMed]

Stephens, J. J.

P. S. Ray, J. J. Stephens, Radio Sci. 9, 43 (1974).
[CrossRef]

Van de Hulst, H. C.

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

Vasilyev, O. B.

K. Ya. Kondratyev, R. M. Welch, O. B. Vasilyev, V. F. Zhvalev, L. S. Ivlev, V. F. Radionov, “Calculations of Free Atmospheric Shortwave Spectral Characteristics over the Desert” (from the CAENEX-70 data), submitted for publication to Tellus (1978).

Weickmann, H. K.

H. K. Weickmann, Die eisphase in der atmosphere, Library Trans. 273 (Royal Aircraft Establishment, Farnborough, 1947), 96 pp.

Weinman, J. A.

J. Joseph, W. J. Wiscombe, J. A. Weinman, J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

Weiss, K.

Welch, R. M.

R. M. Welch, J. F. Geleyn, W. G. Zdunkowski, G. Korb, Beitr. Phys. 49, 128 (1976).

K. Ya. Kondratyev, R. M. Welch, O. B. Vasilyev, V. F. Zhvalev, L. S. Ivlev, V. F. Radionov, “Calculations of Free Atmospheric Shortwave Spectral Characteristics over the Desert” (from the CAENEX-70 data), submitted for publication to Tellus (1978).

R. M. Welch, S. K. Cox, “Absorption of Solar Radiation in Clouds,” submitted for publication, AMS Monograph Series (1978).

Wiscombe, W. J.

W. J. Wiscombe, J. Atmos. Sci. 34, 1408 (1977).
[CrossRef]

J. Joseph, W. J. Wiscombe, J. A. Weinman, J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

Zdunkowski, W. G.

R. M. Welch, J. F. Geleyn, W. G. Zdunkowski, G. Korb, Beitr. Phys. 49, 128 (1976).

Zerull, R. H.

R. H. Zerull, Beitr. Atmos. 49, 168 (1976).

Zerull, R. M.

Zhvalev, V. F.

K. Ya. Kondratyev, R. M. Welch, O. B. Vasilyev, V. F. Zhvalev, L. S. Ivlev, V. F. Radionov, “Calculations of Free Atmospheric Shortwave Spectral Characteristics over the Desert” (from the CAENEX-70 data), submitted for publication to Tellus (1978).

Appl. Opt. (8)

Beitr. Atmos. (1)

R. H. Zerull, Beitr. Atmos. 49, 168 (1976).

Beitr. Phys. (1)

R. M. Welch, J. F. Geleyn, W. G. Zdunkowski, G. Korb, Beitr. Phys. 49, 128 (1976).

J. Appl. Meteorol. (3)

J. M. Mitchell, J. Appl. Meteorol. 10, 703 (1971).
[CrossRef]

E. M. Patterson, D. A. Gillette, G. W. Grams, J. Appl. Meteorol. 15, 470 (1976).
[CrossRef]

D. Deirmendjian, J. Appl. Meteorol. 14, 1584 (1975).
[CrossRef]

J. Atmos. Sci. (5)

W. J. Wiscombe, J. Atmos. Sci. 34, 1408 (1977).
[CrossRef]

J. Joseph, W. J. Wiscombe, J. A. Weinman, J. Atmos. Sci. 33, 2452 (1976).
[CrossRef]

A. Heymsfield, J. Atmos. Sci. 31, 799 (1975).
[CrossRef]

H. R. Pruppacher, R. L. Pitter, J. Atmos. Sci. 28, 86 (1971).
[CrossRef]

K. N. Liou, J. Atmos. Sci. 31, 522 (1974).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Quant. Spectrosc. Radiat Transfer (1)

H. Jacobowitz, J. Quant. Spectrosc. Radiat Transfer 11, 691 (1971).
[CrossRef]

Radio Sci. (1)

P. S. Ray, J. J. Stephens, Radio Sci. 9, 43 (1974).
[CrossRef]

Science (3)

S. I. Rasool, S. H. Schneider, Science 173, 138 (1971).
[CrossRef] [PubMed]

S. B. Idso, Science 186, 50 (1974).
[CrossRef] [PubMed]

P. Chylek, G. W. Grams, R. G. Pinnick, Science 193, 480 (1976).
[CrossRef]

Other (7)

R. M. Welch, S. K. Cox, “Absorption of Solar Radiation in Clouds,” submitted for publication, AMS Monograph Series (1978).

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

SMIC Report, Study of Man’s Impact on Climate (MIT Press, Cambridge, Mass., 1971).

J. R. Probert-Jones, “Surface Waves Associated with the Backscattering of Microwave Radiation by Large Ice Spheres,” in Electromagnetic Waves, M. Kerker, Ed. (Macmillan, New York, 1963), pp. 237–250.

H. K. Weickmann, Die eisphase in der atmosphere, Library Trans. 273 (Royal Aircraft Establishment, Farnborough, 1947), 96 pp.

K. T. Griffith, S. K. Cox, “Infrared Radiative Properties of Tropical Cirrus Clouds Inferred from Broadband Measurements,” Atmospheric Science Paper 269 (Colorado State U., Fort Collins, 1977).

K. Ya. Kondratyev, R. M. Welch, O. B. Vasilyev, V. F. Zhvalev, L. S. Ivlev, V. F. Radionov, “Calculations of Free Atmospheric Shortwave Spectral Characteristics over the Desert” (from the CAENEX-70 data), submitted for publication to Tellus (1978).

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Figures (5)

Fig. 1
Fig. 1

Mie extinction (QE), scattering (QS), and absorption (QA) efficiencies for spherical particles as a function of size parameter (x) for several values of the complex index of refraction (m = nrini). nr = (1.3, 1.5, and 1.7) for columns (1–3), respectively. ni = (10−1, - - -; 10−3, – –; 10−5, —).

Fig. 2
Fig. 2

Mie extinction (QE), scattering (QS), and absorption (QA) efficiencies for nonspherical particles as a function of size parameter (x) for several values of the complex index of refraction (m = nrini). nr = (1.3, 1.5, and 1.7) for columns (1–3), respectively. ni = (10−1, - - -; 10−3, – –; 10−5, —).

Fig. 3
Fig. 3

Mie scattering (QS) and absorption (QA) efficiencies for spherical and nonspherical particles as a function of size parameter (x) for several values of the complex index of refraction (m = nrini). ni = (10−1, 10−3, and 10−5) for columns (1–3), respectively. nr = (1.3, - - - -; 1.5, – –; 1.7 —). Calculations for spherical particles are shown in the upper two rows with corresponding calculations for nonspherical particles in the lower two rows. Note that the ordinate in (l) is plotted on a logarithmic scale.

Fig. 4
Fig. 4

Mie scattering (QS) and absorption (QA) efficiencies for spherical and nonspherical particles as a function of size parameter (x) for several values of the complex index of refraction (m = nrini). nr = (2, 2.5, and 3) in columns (1–3), respectively, ni = (1, - - -; 10−2, – –; 10−4, —). Calculations for spherical particles are shown in the upper two rows with corresponding calculations for nonspherical particles in the lower two rows.

Fig. 5
Fig. 5

Mie extinction (QE), scattering (QS), and absorption (QA) efficiencies for spherical (column 1) and nonspherical (column 2) particles as a function of size parameter (x) for several values of the complex index of refraction (m = nrini). ni = 1. nr = (9, - - - -; 7, – –; 5, —).

Equations (4)

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β e = r 1 r 2 π r 2 n ( r ) Q E ( r ) d r ,
β s = r 1 r 2 π r 2 n ( r ) Q S ( r ) d r ,
β a = r 1 r 2 π r 2 n ( r ) Q A ( r ) d r ,
P ( cos θ ) = l = 0 N a l P l ( cos θ ) ,

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