Abstract

The problem of the disagreement between cirrus crystal sizes determined remotely and by in situ measurements is shown to be due to inappropriate application of Mie theory. We retrieved the absorption optical depth at 8.3 and 11.1 μm from 11 tropical anvil cirrus clouds, using data from the High Resolution Infrared Radiation Sounder (HIRS). We related the absorption optical depth ratio between the two wavelengths to crystal size (the size was defined in terms of the crystal median mass dimension) by assuming Mie theory applied to ice spheres and anomalous diffraction theory (ADT) applied to hexagonal columns, hexagonal plates, bullet rosettes, and aggregates (polycrystals). The application of Mie theory to retrievals yielded crystal sizes approximately one third those obtained with ADT. The retrievals of crystal size by use of HIRS data are compared with measurements of habit and crystal size obtained from in situ measurements of tropical anvil cirrus particles. The results of the comparison show that ADT provides the more realistic retrieval. Moreover, we demonstrate that at infrared wavelengths retrieval of crystal size depends on assumed habit. The reason why Mie theory predicts smaller sizes than ADT is shown to result from particle geometry and enhanced absorption owing to the capture of photons from above the edge of the particle (tunneling). The contribution of particle geometry to absorption is three times greater than from tunneling, but this process enhances absorption by a further 35%. The complex angular momentum and T-matrix methods are used to show that the contribution to absorption by tunneling is diminished as the asphericity of spheroidal particles is increased. At an aspect ratio of 6 the contribution to the absorption that is due to tunneling is substantially reduced for oblate particles, whereas for prolate particles the tunneling contribution is reduced by 50% relative to the sphere.

© 1998 Optical Society of America

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  3. Y. Takano, K. N. Liou, “Light scattering by irregularly shaped ice crystals: climatic implications,” in Proceedings of the Eighth Conference on Atmospheric Radiation (Deepak, Hampton, Va., 1994), pp. 440–442.
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    [CrossRef]
  5. A. J. Heymsfield, G. M. McFarquhar, “High albedos of cirrus in the tropical pacific warm pool: microphysical interpretations from CEPEX and from Kwajalein, Marshall Islands,” J. Atmos. Sci. 53, 2424–2451 (1996).
    [CrossRef]
  6. G. M. McFarquhar, A. J. Heymsfield, “Microphysical characteristics of three anvils sampled during the Central Equatorial Pacific Experiment,” J. Atmos. Sci. 53, 2401–2423 (1996).
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  7. R. G. Knollenberg, K. Kelly, J. C. Wilson, “Measurements of high number densities of ice crystals in the tops of tropical cumulonimbus,” J. Geophys. Res. 98, 8639–8664 (1993).
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  8. W. P. Arnott, Y. Ya. Dong, J. Hallett, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
    [CrossRef]
  9. A. J. Heymsfield, C. M. R. Platt, “A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content,” J. Atmos. Sci. 41, 846–855 (1984).
    [CrossRef]
  10. A. J. Heymsfield, L. M. Miloshevich, “Relative humidity and temperature influences on cirrus formation and evolution: observations from wave clouds and FIRE II,” J. Atmos. Sci. 52, 4302–4326 (1995).
    [CrossRef]
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    [CrossRef]
  13. K. I. Strabala, S. A. Ackerman, W. P. Menzel, “Cloud properties inferred from 8–12 μm data,” J. Appl. Meteorol. 33, 212–229 (1994).
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  14. S. A. Ackerman, W. L. Smith, A. D. Collard, X. L. Ma, H. E. Revercomb, R. O. Knuteson, S. C. Lee, “Cirrus cloud properties derived from high spectral resolution infrared spectrometry during FIRE II. II. Aircraft HIS results,” J. Atmos. Sci. 52, 4246–4263 (1995).
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  15. P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, S. Zhian, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
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  23. S. C. Ou, K. N. Liou, W. M. Gooch, Y. Takano, “Remote sensing of cirrus cloud parameters using advanced very-high-resolution radiometer 3.7 and 10.9 μm channels,” Appl. Opt. 32, 2171–2180 (1993).
    [CrossRef] [PubMed]
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  28. W. P. Arnott, Ya. Y. Dong, J. Hallett, “Extinction efficiency in the IR (2 μm–18 μm) of laboratory ice clouds: observations of scattering minima in the Christiansen bands of ice,” Appl. Opt. 34, 541–551 (1995).
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    [CrossRef]
  32. F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969).
    [CrossRef]
  33. D. L. Mitchell, W. P. Arnott, “Model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. II. Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
    [CrossRef]
  34. V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948).
    [CrossRef]
  35. A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
    [CrossRef]
  36. D. L. Mitchell, “Evolution of snow-size spectra in cyclonic storms. II. Deviations from the exponential form,” J. Atmos. Sci. 48, 1885–1899 (1991).
    [CrossRef]
  37. H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1493 (1980).
    [CrossRef]
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    [CrossRef] [PubMed]
  39. P. N. Francis, “Infrared radiative properties of clouds,” Ph.D. dissertation (University of Oxford, Oxford, 1991).
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1996

A. J. Heymsfield, G. M. McFarquhar, “High albedos of cirrus in the tropical pacific warm pool: microphysical interpretations from CEPEX and from Kwajalein, Marshall Islands,” J. Atmos. Sci. 53, 2424–2451 (1996).
[CrossRef]

G. M. McFarquhar, A. J. Heymsfield, “Microphysical characteristics of three anvils sampled during the Central Equatorial Pacific Experiment,” J. Atmos. Sci. 53, 2401–2423 (1996).
[CrossRef]

D. L. Mitchell, A. Macke, Y. Liu, “Modelling cirrus clouds. II. Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (1996).
[CrossRef]

1995

S. A. Ackerman, W. L. Smith, A. D. Collard, X. L. Ma, H. E. Revercomb, R. O. Knuteson, S. C. Lee, “Cirrus cloud properties derived from high spectral resolution infrared spectrometry during FIRE II. II. Aircraft HIS results,” J. Atmos. Sci. 52, 4246–4263 (1995).
[CrossRef]

A. J. Heymsfield, L. M. Miloshevich, “Relative humidity and temperature influences on cirrus formation and evolution: observations from wave clouds and FIRE II,” J. Atmos. Sci. 52, 4302–4326 (1995).
[CrossRef]

S. Zhian, K. P. Shine, “Parameterization of ice cloud radiative properties and its application to the potential climatic importance of mixed phase clouds,” J. Clim. 8, 1874–1888 (1995).
[CrossRef]

A. Macke, M. I. Mishchenko, K. Muinonen, B. E. Carlson, “Scattering of light by large nonspherical particles: ray tracing approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995).
[CrossRef] [PubMed]

W. P. Arnott, Ya. Y. Dong, J. Hallett, “Extinction efficiency in the IR (2 μm–18 μm) of laboratory ice clouds: observations of scattering minima in the Christiansen bands of ice,” Appl. Opt. 34, 541–551 (1995).
[CrossRef] [PubMed]

1994

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

W. P. Arnott, Y. Ya. Dong, J. Hallett, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, S. Zhian, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

K. I. Strabala, S. A. Ackerman, W. P. Menzel, “Cloud properties inferred from 8–12 μm data,” J. Appl. Meteorol. 33, 212–229 (1994).
[CrossRef]

D. L. Mitchell, W. P. Arnott, “Model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. II. Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
[CrossRef]

1993

R. G. Knollenberg, K. Kelly, J. C. Wilson, “Measurements of high number densities of ice crystals in the tops of tropical cumulonimbus,” J. Geophys. Res. 98, 8639–8664 (1993).
[CrossRef]

S. C. Ou, K. N. Liou, W. M. Gooch, Y. Takano, “Remote sensing of cirrus cloud parameters using advanced very-high-resolution radiometer 3.7 and 10.9 μm channels,” Appl. Opt. 32, 2171–2180 (1993).
[CrossRef] [PubMed]

1992

Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

L. G. Guimaraes, H. M. Nussenzvieg, “The theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
[CrossRef]

1991

D. L. Mitchell, “Evolution of snow-size spectra in cyclonic storms. II. Deviations from the exponential form,” J. Atmos. Sci. 48, 1885–1899 (1991).
[CrossRef]

1990

J. D. Spinhirne, W. D. Hart, “Cirrus structure and radiative parameters from airborne lidar and spectral radiometer observations: the 28 October 1986 FIRE study,” Mon. Weather Rev. 118, 2329–2343 (1990).
[CrossRef]

S. A. Ackerman, W. L. Smith, J. D. Spinhirne, H. E. Revercomb, “The 27–28 October 1986 FIRE IFO cirrus case study: spectral properties of cirrus clouds in the 8–12 μm window,” Mon. Weather Rev. 118, 2377–2388 (1990).
[CrossRef]

1989

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. I. Single scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–20 (1989).
[CrossRef]

1988

H. M. Nussenzveig, “Uniform approximation in scattering by spheres,” J. Phys. A 21, 81–109 (1988).
[CrossRef]

1986

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

1984

A. J. Heymsfield, C. M. R. Platt, “A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

S. G. Warren, “Optical constants of ice for the ultraviolet and microwave,” Appl. Opt. 23, 1206–1225 (1984).
[CrossRef] [PubMed]

1981

G. L. Stephens, P. J. Webster, “Clouds and climate: sensitivity of simple systems,” J. Atmos. Sci. 38, 235–247 (1981).
[CrossRef]

1980

S. Asano, M. Sato, “Light scattering by randomly oriented spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
[CrossRef] [PubMed]

H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1493 (1980).
[CrossRef]

1970

A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

1969

F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969).
[CrossRef]

1948

V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948).
[CrossRef]

Ackerman, S. A.

S. A. Ackerman, W. L. Smith, A. D. Collard, X. L. Ma, H. E. Revercomb, R. O. Knuteson, S. C. Lee, “Cirrus cloud properties derived from high spectral resolution infrared spectrometry during FIRE II. II. Aircraft HIS results,” J. Atmos. Sci. 52, 4246–4263 (1995).
[CrossRef]

K. I. Strabala, S. A. Ackerman, W. P. Menzel, “Cloud properties inferred from 8–12 μm data,” J. Appl. Meteorol. 33, 212–229 (1994).
[CrossRef]

S. A. Ackerman, W. L. Smith, J. D. Spinhirne, H. E. Revercomb, “The 27–28 October 1986 FIRE IFO cirrus case study: spectral properties of cirrus clouds in the 8–12 μm window,” Mon. Weather Rev. 118, 2377–2388 (1990).
[CrossRef]

Arnott, W. P.

W. P. Arnott, Ya. Y. Dong, J. Hallett, “Extinction efficiency in the IR (2 μm–18 μm) of laboratory ice clouds: observations of scattering minima in the Christiansen bands of ice,” Appl. Opt. 34, 541–551 (1995).
[CrossRef] [PubMed]

W. P. Arnott, Y. Ya. Dong, J. Hallett, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

D. L. Mitchell, W. P. Arnott, “Model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. II. Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
[CrossRef]

Asano, S.

Ashkin, A.

P. Chylek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1979).

Auer, A. H.

A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Bevan, A.

D. E. Parker, C. K. Folland, A. Bevan, M. N. Ward, M. Jackson, K. Maskell, “Marine surface data for analysis of climatic fluctuations on interannual to century timescales,” in Natural Climate Variability On Decade-to-Century Timescales, D. G. Martinson, K. Bryan, M. Ghil, M. N. Hall, T. R. Karl, E. S. Sarachik, S. Sorooshian, L. D. Talley, eds. (National Academy of Sciences, Washington, D.C., 1994), p. 29.

Bryant, F. D.

F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969).
[CrossRef]

Carlson, B. E.

Chylek, P.

P. Chylek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1979).

P. Chylek, J. D. Klett, R. A. Sutherland, “Scattering cross sections of nonspherical particles in WKB and anomalous diffraction approximation,” in Seventh Conference on Atmospheric Radiation (Deepak, Hampton, Va., 1990), pp. 381–384.

Collard, A. D.

S. A. Ackerman, W. L. Smith, A. D. Collard, X. L. Ma, H. E. Revercomb, R. O. Knuteson, S. C. Lee, “Cirrus cloud properties derived from high spectral resolution infrared spectrometry during FIRE II. II. Aircraft HIS results,” J. Atmos. Sci. 52, 4246–4263 (1995).
[CrossRef]

Dong, Y. Ya.

W. P. Arnott, Y. Ya. Dong, J. Hallett, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

Dong, Ya. Y.

Folland, C. K.

D. E. Parker, C. K. Folland, A. Bevan, M. N. Ward, M. Jackson, K. Maskell, “Marine surface data for analysis of climatic fluctuations on interannual to century timescales,” in Natural Climate Variability On Decade-to-Century Timescales, D. G. Martinson, K. Bryan, M. Ghil, M. N. Hall, T. R. Karl, E. S. Sarachik, S. Sorooshian, L. D. Talley, eds. (National Academy of Sciences, Washington, D.C., 1994), p. 29.

Francis, P. N.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, S. Zhian, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

P. N. Francis, “Infrared radiative properties of clouds,” Ph.D. dissertation (University of Oxford, Oxford, 1991).

Giese, R. H.

R. H. Zerull, R. H. Giese, S. Schwill, K. Weiss, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1979).

Gooch, W. M.

Guimaraes, L. G.

L. G. Guimaraes, H. M. Nussenzvieg, “The theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
[CrossRef]

Hallett, J.

W. P. Arnott, Ya. Y. Dong, J. Hallett, “Extinction efficiency in the IR (2 μm–18 μm) of laboratory ice clouds: observations of scattering minima in the Christiansen bands of ice,” Appl. Opt. 34, 541–551 (1995).
[CrossRef] [PubMed]

W. P. Arnott, Y. Ya. Dong, J. Hallett, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

Hart, W. D.

J. D. Spinhirne, W. D. Hart, “Cirrus structure and radiative parameters from airborne lidar and spectral radiometer observations: the 28 October 1986 FIRE study,” Mon. Weather Rev. 118, 2329–2343 (1990).
[CrossRef]

Heymsfield, A. J.

A. J. Heymsfield, G. M. McFarquhar, “High albedos of cirrus in the tropical pacific warm pool: microphysical interpretations from CEPEX and from Kwajalein, Marshall Islands,” J. Atmos. Sci. 53, 2424–2451 (1996).
[CrossRef]

G. M. McFarquhar, A. J. Heymsfield, “Microphysical characteristics of three anvils sampled during the Central Equatorial Pacific Experiment,” J. Atmos. Sci. 53, 2401–2423 (1996).
[CrossRef]

A. J. Heymsfield, L. M. Miloshevich, “Relative humidity and temperature influences on cirrus formation and evolution: observations from wave clouds and FIRE II,” J. Atmos. Sci. 52, 4302–4326 (1995).
[CrossRef]

A. J. Heymsfield, C. M. R. Platt, “A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

Jackson, M.

D. E. Parker, C. K. Folland, A. Bevan, M. N. Ward, M. Jackson, K. Maskell, “Marine surface data for analysis of climatic fluctuations on interannual to century timescales,” in Natural Climate Variability On Decade-to-Century Timescales, D. G. Martinson, K. Bryan, M. Ghil, M. N. Hall, T. R. Karl, E. S. Sarachik, S. Sorooshian, L. D. Talley, eds. (National Academy of Sciences, Washington, D.C., 1994), p. 29.

Jones, A.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, S. Zhian, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Kelly, K.

R. G. Knollenberg, K. Kelly, J. C. Wilson, “Measurements of high number densities of ice crystals in the tops of tropical cumulonimbus,” J. Geophys. Res. 98, 8639–8664 (1993).
[CrossRef]

Kiehl, J. T.

P. Chylek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1979).

Klett, J. D.

P. Chylek, J. D. Klett, R. A. Sutherland, “Scattering cross sections of nonspherical particles in WKB and anomalous diffraction approximation,” in Seventh Conference on Atmospheric Radiation (Deepak, Hampton, Va., 1990), pp. 381–384.

Knollenberg, R. G.

R. G. Knollenberg, K. Kelly, J. C. Wilson, “Measurements of high number densities of ice crystals in the tops of tropical cumulonimbus,” J. Geophys. Res. 98, 8639–8664 (1993).
[CrossRef]

Knuteson, R. O.

S. A. Ackerman, W. L. Smith, A. D. Collard, X. L. Ma, H. E. Revercomb, R. O. Knuteson, S. C. Lee, “Cirrus cloud properties derived from high spectral resolution infrared spectrometry during FIRE II. II. Aircraft HIS results,” J. Atmos. Sci. 52, 4246–4263 (1995).
[CrossRef]

Ko, M. K. W.

P. Chylek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1979).

Latimer, P.

F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969).
[CrossRef]

Lee, S. C.

S. A. Ackerman, W. L. Smith, A. D. Collard, X. L. Ma, H. E. Revercomb, R. O. Knuteson, S. C. Lee, “Cirrus cloud properties derived from high spectral resolution infrared spectrometry during FIRE II. II. Aircraft HIS results,” J. Atmos. Sci. 52, 4246–4263 (1995).
[CrossRef]

Liou, K. N.

S. C. Ou, K. N. Liou, W. M. Gooch, Y. Takano, “Remote sensing of cirrus cloud parameters using advanced very-high-resolution radiometer 3.7 and 10.9 μm channels,” Appl. Opt. 32, 2171–2180 (1993).
[CrossRef] [PubMed]

Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. I. Single scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–20 (1989).
[CrossRef]

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

Y. Takano, K. N. Liou, “Light scattering by irregularly shaped ice crystals: climatic implications,” in Proceedings of the Eighth Conference on Atmospheric Radiation (Deepak, Hampton, Va., 1994), pp. 440–442.

Liu, Y.

D. L. Mitchell, A. Macke, Y. Liu, “Modelling cirrus clouds. II. Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (1996).
[CrossRef]

Ma, X. L.

S. A. Ackerman, W. L. Smith, A. D. Collard, X. L. Ma, H. E. Revercomb, R. O. Knuteson, S. C. Lee, “Cirrus cloud properties derived from high spectral resolution infrared spectrometry during FIRE II. II. Aircraft HIS results,” J. Atmos. Sci. 52, 4246–4263 (1995).
[CrossRef]

Macke, A.

D. L. Mitchell, A. Macke, Y. Liu, “Modelling cirrus clouds. II. Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (1996).
[CrossRef]

A. Macke, M. I. Mishchenko, K. Muinonen, B. E. Carlson, “Scattering of light by large nonspherical particles: ray tracing approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995).
[CrossRef] [PubMed]

D. L. Mitchell, A. Macke, “A new treatment of cirrus cloud radiative properties,” in IRS’96: Current Problems in Atmospheric Radiation (Deepak, Hampton, Va., 1997), pp. 163–166.

Maskell, K.

D. E. Parker, C. K. Folland, A. Bevan, M. N. Ward, M. Jackson, K. Maskell, “Marine surface data for analysis of climatic fluctuations on interannual to century timescales,” in Natural Climate Variability On Decade-to-Century Timescales, D. G. Martinson, K. Bryan, M. Ghil, M. N. Hall, T. R. Karl, E. S. Sarachik, S. Sorooshian, L. D. Talley, eds. (National Academy of Sciences, Washington, D.C., 1994), p. 29.

McFarquhar, G. M.

A. J. Heymsfield, G. M. McFarquhar, “High albedos of cirrus in the tropical pacific warm pool: microphysical interpretations from CEPEX and from Kwajalein, Marshall Islands,” J. Atmos. Sci. 53, 2424–2451 (1996).
[CrossRef]

G. M. McFarquhar, A. J. Heymsfield, “Microphysical characteristics of three anvils sampled during the Central Equatorial Pacific Experiment,” J. Atmos. Sci. 53, 2401–2423 (1996).
[CrossRef]

Menzel, W. P.

K. I. Strabala, S. A. Ackerman, W. P. Menzel, “Cloud properties inferred from 8–12 μm data,” J. Appl. Meteorol. 33, 212–229 (1994).
[CrossRef]

Miloshevich, L. M.

A. J. Heymsfield, L. M. Miloshevich, “Relative humidity and temperature influences on cirrus formation and evolution: observations from wave clouds and FIRE II,” J. Atmos. Sci. 52, 4302–4326 (1995).
[CrossRef]

Minnis, P.

Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

Mishchenko, M. I.

Mitchell, D. L.

D. L. Mitchell, A. Macke, Y. Liu, “Modelling cirrus clouds. II. Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (1996).
[CrossRef]

D. L. Mitchell, W. P. Arnott, “Model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. II. Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
[CrossRef]

D. L. Mitchell, “Evolution of snow-size spectra in cyclonic storms. II. Deviations from the exponential form,” J. Atmos. Sci. 48, 1885–1899 (1991).
[CrossRef]

D. L. Mitchell, A. Macke, “A new treatment of cirrus cloud radiative properties,” in IRS’96: Current Problems in Atmospheric Radiation (Deepak, Hampton, Va., 1997), pp. 163–166.

Muinonen, K.

Nussenzveig, H. M.

H. M. Nussenzveig, “Uniform approximation in scattering by spheres,” J. Phys. A 21, 81–109 (1988).
[CrossRef]

H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1493 (1980).
[CrossRef]

H. M. Nussenzveig, Causality and Dispersion Relations (Academic, New York, 1972).

Nussenzvieg, H. M.

L. G. Guimaraes, H. M. Nussenzvieg, “The theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
[CrossRef]

Ou, S. C.

Parker, D. E.

D. E. Parker, C. K. Folland, A. Bevan, M. N. Ward, M. Jackson, K. Maskell, “Marine surface data for analysis of climatic fluctuations on interannual to century timescales,” in Natural Climate Variability On Decade-to-Century Timescales, D. G. Martinson, K. Bryan, M. Ghil, M. N. Hall, T. R. Karl, E. S. Sarachik, S. Sorooshian, L. D. Talley, eds. (National Academy of Sciences, Washington, D.C., 1994), p. 29.

Platt, C. M. R.

A. J. Heymsfield, C. M. R. Platt, “A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

Revercomb, H. E.

S. A. Ackerman, W. L. Smith, A. D. Collard, X. L. Ma, H. E. Revercomb, R. O. Knuteson, S. C. Lee, “Cirrus cloud properties derived from high spectral resolution infrared spectrometry during FIRE II. II. Aircraft HIS results,” J. Atmos. Sci. 52, 4246–4263 (1995).
[CrossRef]

S. A. Ackerman, W. L. Smith, J. D. Spinhirne, H. E. Revercomb, “The 27–28 October 1986 FIRE IFO cirrus case study: spectral properties of cirrus clouds in the 8–12 μm window,” Mon. Weather Rev. 118, 2377–2388 (1990).
[CrossRef]

Sato, M.

Saunders, R. W.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, S. Zhian, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Schwill, S.

R. H. Zerull, R. H. Giese, S. Schwill, K. Weiss, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1979).

Shine, K. P.

S. Zhian, K. P. Shine, “Parameterization of ice cloud radiative properties and its application to the potential climatic importance of mixed phase clouds,” J. Clim. 8, 1874–1888 (1995).
[CrossRef]

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, S. Zhian, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Slingo, A.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, S. Zhian, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Smith, W. L.

S. A. Ackerman, W. L. Smith, A. D. Collard, X. L. Ma, H. E. Revercomb, R. O. Knuteson, S. C. Lee, “Cirrus cloud properties derived from high spectral resolution infrared spectrometry during FIRE II. II. Aircraft HIS results,” J. Atmos. Sci. 52, 4246–4263 (1995).
[CrossRef]

S. A. Ackerman, W. L. Smith, J. D. Spinhirne, H. E. Revercomb, “The 27–28 October 1986 FIRE IFO cirrus case study: spectral properties of cirrus clouds in the 8–12 μm window,” Mon. Weather Rev. 118, 2377–2388 (1990).
[CrossRef]

Spinhirne, J. D.

S. A. Ackerman, W. L. Smith, J. D. Spinhirne, H. E. Revercomb, “The 27–28 October 1986 FIRE IFO cirrus case study: spectral properties of cirrus clouds in the 8–12 μm window,” Mon. Weather Rev. 118, 2377–2388 (1990).
[CrossRef]

J. D. Spinhirne, W. D. Hart, “Cirrus structure and radiative parameters from airborne lidar and spectral radiometer observations: the 28 October 1986 FIRE study,” Mon. Weather Rev. 118, 2329–2343 (1990).
[CrossRef]

Stephens, G. L.

G. L. Stephens, P. J. Webster, “Clouds and climate: sensitivity of simple systems,” J. Atmos. Sci. 38, 235–247 (1981).
[CrossRef]

G. L. Stephens, Remote Sensing of the Lower Atmosphere. An Introduction (Oxford U. Press, Oxford, 1994).

Strabala, K. I.

K. I. Strabala, S. A. Ackerman, W. P. Menzel, “Cloud properties inferred from 8–12 μm data,” J. Appl. Meteorol. 33, 212–229 (1994).
[CrossRef]

Sutherland, R. A.

P. Chylek, J. D. Klett, R. A. Sutherland, “Scattering cross sections of nonspherical particles in WKB and anomalous diffraction approximation,” in Seventh Conference on Atmospheric Radiation (Deepak, Hampton, Va., 1990), pp. 381–384.

Takano, Y.

S. C. Ou, K. N. Liou, W. M. Gooch, Y. Takano, “Remote sensing of cirrus cloud parameters using advanced very-high-resolution radiometer 3.7 and 10.9 μm channels,” Appl. Opt. 32, 2171–2180 (1993).
[CrossRef] [PubMed]

Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. I. Single scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–20 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Light scattering by irregularly shaped ice crystals: climatic implications,” in Proceedings of the Eighth Conference on Atmospheric Radiation (Deepak, Hampton, Va., 1994), pp. 440–442.

Travis, L. D.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Veal, D. L.

A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Vouk, V.

V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948).
[CrossRef]

Ward, M. N.

D. E. Parker, C. K. Folland, A. Bevan, M. N. Ward, M. Jackson, K. Maskell, “Marine surface data for analysis of climatic fluctuations on interannual to century timescales,” in Natural Climate Variability On Decade-to-Century Timescales, D. G. Martinson, K. Bryan, M. Ghil, M. N. Hall, T. R. Karl, E. S. Sarachik, S. Sorooshian, L. D. Talley, eds. (National Academy of Sciences, Washington, D.C., 1994), p. 29.

Warren, S. G.

Webster, P. J.

G. L. Stephens, P. J. Webster, “Clouds and climate: sensitivity of simple systems,” J. Atmos. Sci. 38, 235–247 (1981).
[CrossRef]

Weiss, K.

R. H. Zerull, R. H. Giese, S. Schwill, K. Weiss, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1979).

Wilson, J. C.

R. G. Knollenberg, K. Kelly, J. C. Wilson, “Measurements of high number densities of ice crystals in the tops of tropical cumulonimbus,” J. Geophys. Res. 98, 8639–8664 (1993).
[CrossRef]

Wiscombe, W. J.

H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1493 (1980).
[CrossRef]

Zerull, R. H.

R. H. Zerull, R. H. Giese, S. Schwill, K. Weiss, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1979).

Zhian, S.

S. Zhian, K. P. Shine, “Parameterization of ice cloud radiative properties and its application to the potential climatic importance of mixed phase clouds,” J. Clim. 8, 1874–1888 (1995).
[CrossRef]

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, S. Zhian, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Appl. Opt.

J. Appl. Meteorol.

K. I. Strabala, S. A. Ackerman, W. P. Menzel, “Cloud properties inferred from 8–12 μm data,” J. Appl. Meteorol. 33, 212–229 (1994).
[CrossRef]

J. Atmos. Sci.

S. A. Ackerman, W. L. Smith, A. D. Collard, X. L. Ma, H. E. Revercomb, R. O. Knuteson, S. C. Lee, “Cirrus cloud properties derived from high spectral resolution infrared spectrometry during FIRE II. II. Aircraft HIS results,” J. Atmos. Sci. 52, 4246–4263 (1995).
[CrossRef]

G. L. Stephens, P. J. Webster, “Clouds and climate: sensitivity of simple systems,” J. Atmos. Sci. 38, 235–247 (1981).
[CrossRef]

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. I. Single scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–20 (1989).
[CrossRef]

A. J. Heymsfield, G. M. McFarquhar, “High albedos of cirrus in the tropical pacific warm pool: microphysical interpretations from CEPEX and from Kwajalein, Marshall Islands,” J. Atmos. Sci. 53, 2424–2451 (1996).
[CrossRef]

G. M. McFarquhar, A. J. Heymsfield, “Microphysical characteristics of three anvils sampled during the Central Equatorial Pacific Experiment,” J. Atmos. Sci. 53, 2401–2423 (1996).
[CrossRef]

A. J. Heymsfield, C. M. R. Platt, “A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

A. J. Heymsfield, L. M. Miloshevich, “Relative humidity and temperature influences on cirrus formation and evolution: observations from wave clouds and FIRE II,” J. Atmos. Sci. 52, 4302–4326 (1995).
[CrossRef]

A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

D. L. Mitchell, “Evolution of snow-size spectra in cyclonic storms. II. Deviations from the exponential form,” J. Atmos. Sci. 48, 1885–1899 (1991).
[CrossRef]

D. L. Mitchell, A. Macke, Y. Liu, “Modelling cirrus clouds. II. Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (1996).
[CrossRef]

D. L. Mitchell, W. P. Arnott, “Model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. II. Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
[CrossRef]

Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

J. Clim.

S. Zhian, K. P. Shine, “Parameterization of ice cloud radiative properties and its application to the potential climatic importance of mixed phase clouds,” J. Clim. 8, 1874–1888 (1995).
[CrossRef]

J. Colloid Interface Sci.

F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969).
[CrossRef]

J. Geophys. Res.

R. G. Knollenberg, K. Kelly, J. C. Wilson, “Measurements of high number densities of ice crystals in the tops of tropical cumulonimbus,” J. Geophys. Res. 98, 8639–8664 (1993).
[CrossRef]

W. P. Arnott, Y. Ya. Dong, J. Hallett, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

J. Phys. A

H. M. Nussenzveig, “Uniform approximation in scattering by spheres,” J. Phys. A 21, 81–109 (1988).
[CrossRef]

Mon. Weather Rev.

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

J. D. Spinhirne, W. D. Hart, “Cirrus structure and radiative parameters from airborne lidar and spectral radiometer observations: the 28 October 1986 FIRE study,” Mon. Weather Rev. 118, 2329–2343 (1990).
[CrossRef]

S. A. Ackerman, W. L. Smith, J. D. Spinhirne, H. E. Revercomb, “The 27–28 October 1986 FIRE IFO cirrus case study: spectral properties of cirrus clouds in the 8–12 μm window,” Mon. Weather Rev. 118, 2377–2388 (1990).
[CrossRef]

Nature (London)

V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948).
[CrossRef]

Opt. Commun.

L. G. Guimaraes, H. M. Nussenzvieg, “The theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1493 (1980).
[CrossRef]

Q. J. R. Meteorol. Soc.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, S. Zhian, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Other

Y. Takano, K. N. Liou, “Light scattering by irregularly shaped ice crystals: climatic implications,” in Proceedings of the Eighth Conference on Atmospheric Radiation (Deepak, Hampton, Va., 1994), pp. 440–442.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

P. Chylek, J. D. Klett, R. A. Sutherland, “Scattering cross sections of nonspherical particles in WKB and anomalous diffraction approximation,” in Seventh Conference on Atmospheric Radiation (Deepak, Hampton, Va., 1990), pp. 381–384.

D. L. Mitchell, A. Macke, “A new treatment of cirrus cloud radiative properties,” in IRS’96: Current Problems in Atmospheric Radiation (Deepak, Hampton, Va., 1997), pp. 163–166.

H. M. Nussenzveig, Causality and Dispersion Relations (Academic, New York, 1972).

P. Chylek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1979).

R. H. Zerull, R. H. Giese, S. Schwill, K. Weiss, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1979).

P. N. Francis, “Infrared radiative properties of clouds,” Ph.D. dissertation (University of Oxford, Oxford, 1991).

G. L. Stephens, Remote Sensing of the Lower Atmosphere. An Introduction (Oxford U. Press, Oxford, 1994).

D. E. Parker, C. K. Folland, A. Bevan, M. N. Ward, M. Jackson, K. Maskell, “Marine surface data for analysis of climatic fluctuations on interannual to century timescales,” in Natural Climate Variability On Decade-to-Century Timescales, D. G. Martinson, K. Bryan, M. Ghil, M. N. Hall, T. R. Karl, E. S. Sarachik, S. Sorooshian, L. D. Talley, eds. (National Academy of Sciences, Washington, D.C., 1994), p. 29.

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Figures (5)

Fig. 1
Fig. 1

Absorption efficiency Q abs plotted against d e calculated from CAM and ADT. The geometric optics contribution (GO) is shown by the crosses, and the edge (above and below) and the above-edge contributions are shown by the diamonds and the asterisks, respectively. The straight line indicates Q abs = 1.

Fig. 2
Fig. 2

Calculations of absorption efficiency as a function of d e from CAM, T matrix (curves a–c) and ADT. The T-matrix calculations are for (a) oblate and (b) prolate spheroids with aspect ratios R of 2 (curve a), 4 (curve b), and 6 (curve c). The straight line indicates Q abs = 1.

Fig. 3
Fig. 3

Calculation of absorption efficiency as a function of d e for (a) oblate spheroids and (b) prolate spheroids, both with an aspect ratio of 6. The crosses represent the result of adding (a) the geometric optics contribution and (b) the geometric optics plus 50% of the above-edge contribution from the sphere to ADT.

Fig. 4
Fig. 4

Emissivity at 8.3 and 11.1 μm with Mie theory and ADT applied for mean maximum dimensions of 10, 20, 30, 50, 100, and 200 μm. (a) Mie theory applied to ice spheres (i.e., including tunneling), (b) ADT applied to ice spheres (excluding tunneling), (c) ADT applied to polycrystals.

Fig. 5
Fig. 5

Retrievals of crystal mass dimension (D m ) plotted against measured brightness temperature, assuming different habits and treatments of absorption. Dashed lines, the CEPEX in situ measurements of mass dimension. Mie theory applied to ice spheres (triangles); ADT applied to columns (squares), to polycrystals (diamonds), to plates (pluses), and to bullet rosettes (crosses).

Equations (12)

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

Q abs = 1 P     1 - exp - 4 π n i d 1 λ d P ,
Q abs = 1 - exp - 4 π n i d e λ .
β abs = 0   PQ abs n D d D .
n D = N 0 D ν exp - Λ D .
D ¯ = 1 / Λ .
τ abs = β abs Z ,
D m = β + 0.67 Λ .
Q abs = Q abs F + Q abs ae + Q abs be .
μ   d I τ ,   μ ,   θ d τ = I τ ,   μ ,   θ - S τ ,   μ ,   θ .
I λ 0 ,   μ ,   θ = I λ clear τ ,   μ ,   θ exp - τ / μ + 0 τ exp - t / μ S λ t ,   μ ,   θ d t μ ,
I λ = I λ clear   exp - τ abs μ + 1 - exp - τ abs μ B λ T c ,
τ abs = - μ   ln B λ T c - I λ B λ T c - I λ clear .

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