Abstract

We propose a new method of particle size retrieval for mixed-phase and ice crystal clouds. The method enables us to identify each component of a bicomponent cloud composed of water droplets and ice crystals and to retrieve a size distribution separately for each cloud component. We explore the method’s capability by using sythetic multiangular data of scattered-light intensity. We model cloud microphysical characteristics by assuming two noninteracting cloud components, such as liquid or supercooled droplets and cubic or hexagonal ice crystals, with regular simple geometrical shapes as first approximation. The sensitivity of the method is tested for different relative concentrations of the cloud components that are varied over a wide range. First, we investigate the applicability limit of the single-component cloud approximation in retrieving particle size distributions of a bicomponent cloud. Second, we test the method to retrieve size distributions simultaneously for both components in mixed-phase clouds, and we discuss the conditions of its applicability.

© 1997 Optical Society of America

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    [CrossRef]

1995 (4)

1994 (1)

K. L. Liou, Y. Takano, “Light scattering by nonspherical particles: remote sensing and climatic implications,” Atmos. Res. 31, 271–298 (1994).
[CrossRef]

1993 (2)

S. L. Oshchepkov, O. V. Dubovik, “1993c: Specific features of the method of laser diffraction spectrometry in the condition of anomalous diffraction,” J. Phys. D 26, 728–732 (1993).
[CrossRef]

A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
[CrossRef] [PubMed]

1989 (1)

1985 (1)

D. J. Brown, P. G. Felton, “Direct measurement of concentration and size for particles of different shapes using laser light diffraction,” J. Chem. Eng. Des. 63, 125–132 (1985).

1984 (1)

1983 (1)

1979 (1)

1973 (1)

1970 (1)

K. S. Shifrin, V. A. Punina, “Conditions of corona observations in polydispersed clouds,” Izv. Atmos. Ocean. Phys. 6, 112–118 (1970).

1968 (1)

1966 (1)

1962 (1)

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

Brown, D. J.

D. J. Brown, P. G. Felton, “Direct measurement of concentration and size for particles of different shapes using laser light diffraction,” J. Chem. Eng. Des. 63, 125–132 (1985).

Chahine, M. T.

Cox, S. K.

R. M. Welch, S. K. Cox, J. M. Davis, Solar Radiation and Clouds, Meteor Monographs (American Meteorological Society, Dallas, Texas, 1980).

Crepel, O

O Crepel, J. F. Gayet, J. F. Fournol, S Oshchepkov, “A new polar nephelometer for the measurements of optical and microphysical cloud properties. II: preliminary tests,” Ann. Geophys. (to be published).

Davis, J. M.

R. M. Welch, S. K. Cox, J. M. Davis, Solar Radiation and Clouds, Meteor Monographs (American Meteorological Society, Dallas, Texas, 1980).

Dobbins, R. A.

Dubovik, O. V.

O. V. Dubovik, T. V. Lapyonok, S. L. Oshchepkov, “Improved technique for data inversion: optical sizing of multicomponent aerosols,” Appl. Opt. 34, 8422–8435 (1995).
[CrossRef] [PubMed]

S. L. Oshchepkov, O. V. Dubovik, “1993c: Specific features of the method of laser diffraction spectrometry in the condition of anomalous diffraction,” J. Phys. D 26, 728–732 (1993).
[CrossRef]

S. L. Oshchepkov, O. V. Dubovik, T. V. Lapyonok, “A method of numerical solution of linear inverse problems at the log normal noise distribution. The estimation of aerosol size distributions,” in IRS’92: Current Problems in Atmospheric Radiation, Proceedings of the International Radiation Symposium, S. Keevallik, O. Kärner, eds. (A. Deepak, Hampton, Va., 1993), pp. 334–337.

S. L. Oshchepkov, O. V. Dubovik, “The improvement of an airborne nephelometer,” Note 121 (Observatoire de Physique de Globe de Clermont–Ferrand, Laboratoire de Meteorologie Physique, Clermont–Ferrand, France, 1993).

Felton, P. G.

D. J. Brown, P. G. Felton, “Direct measurement of concentration and size for particles of different shapes using laser light diffraction,” J. Chem. Eng. Des. 63, 125–132 (1985).

Fournol, J. F.

O Crepel, J. F. Gayet, J. F. Fournol, S Oshchepkov, “A new polar nephelometer for the measurements of optical and microphysical cloud properties. II: preliminary tests,” Ann. Geophys. (to be published).

Fraser, A. B.

Gayet, J. F.

O Crepel, J. F. Gayet, J. F. Fournol, S Oshchepkov, “A new polar nephelometer for the measurements of optical and microphysical cloud properties. II: preliminary tests,” Ann. Geophys. (to be published).

Halle, G. M.

Herman, M.

Iaquinta, J.

J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet-rosette ice crystals,” J. Atmos. Sci. 42, 1401–1413 (1995).
[CrossRef]

Isaka, H.

J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet-rosette ice crystals,” J. Atmos. Sci. 42, 1401–1413 (1995).
[CrossRef]

Jizmagian, G. S.

Klett, J. D.

J. D. Klett, “Orientation model for particles in turbulence,” J. Atmos. Sci. 52, 2276–2285 (1995).
[CrossRef]

H. R. Pruppacher, J. D. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1978).
[CrossRef]

Lapyonok, T. V.

O. V. Dubovik, T. V. Lapyonok, S. L. Oshchepkov, “Improved technique for data inversion: optical sizing of multicomponent aerosols,” Appl. Opt. 34, 8422–8435 (1995).
[CrossRef] [PubMed]

S. L. Oshchepkov, O. V. Dubovik, T. V. Lapyonok, “A method of numerical solution of linear inverse problems at the log normal noise distribution. The estimation of aerosol size distributions,” in IRS’92: Current Problems in Atmospheric Radiation, Proceedings of the International Radiation Symposium, S. Keevallik, O. Kärner, eds. (A. Deepak, Hampton, Va., 1993), pp. 334–337.

Liou, K. L.

K. L. Liou, Y. Takano, “Light scattering by nonspherical particles: remote sensing and climatic implications,” Atmos. Res. 31, 271–298 (1994).
[CrossRef]

Macke, A.

Mazin, P

P Mazin, A. N. Nevzorov, On the Microstructure of the Clouds, Problems of Cloud Physics (n.p., 1987), pp. 37–49.

Muinonen, K.

Nevzorov, A. N.

P Mazin, A. N. Nevzorov, On the Microstructure of the Clouds, Problems of Cloud Physics (n.p., 1987), pp. 37–49.

Oshchepkov, S

O Crepel, J. F. Gayet, J. F. Fournol, S Oshchepkov, “A new polar nephelometer for the measurements of optical and microphysical cloud properties. II: preliminary tests,” Ann. Geophys. (to be published).

Oshchepkov, S. L.

O. V. Dubovik, T. V. Lapyonok, S. L. Oshchepkov, “Improved technique for data inversion: optical sizing of multicomponent aerosols,” Appl. Opt. 34, 8422–8435 (1995).
[CrossRef] [PubMed]

S. L. Oshchepkov, O. V. Dubovik, “1993c: Specific features of the method of laser diffraction spectrometry in the condition of anomalous diffraction,” J. Phys. D 26, 728–732 (1993).
[CrossRef]

S. L. Oshchepkov, O. V. Dubovik, “The improvement of an airborne nephelometer,” Note 121 (Observatoire de Physique de Globe de Clermont–Ferrand, Laboratoire de Meteorologie Physique, Clermont–Ferrand, France, 1993).

S. L. Oshchepkov, O. V. Dubovik, T. V. Lapyonok, “A method of numerical solution of linear inverse problems at the log normal noise distribution. The estimation of aerosol size distributions,” in IRS’92: Current Problems in Atmospheric Radiation, Proceedings of the International Radiation Symposium, S. Keevallik, O. Kärner, eds. (A. Deepak, Hampton, Va., 1993), pp. 334–337.

Personne, P.

J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet-rosette ice crystals,” J. Atmos. Sci. 42, 1401–1413 (1995).
[CrossRef]

Phillips, B. L.

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

Pruppacher, H. R.

H. R. Pruppacher, J. D. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1978).
[CrossRef]

Punina, V. A.

K. S. Shifrin, V. A. Punina, “Conditions of corona observations in polydispersed clouds,” Izv. Atmos. Ocean. Phys. 6, 112–118 (1970).

Querry, M. R.

Santer, R.

Shifrin, K. S.

K. S. Shifrin, V. A. Punina, “Conditions of corona observations in polydispersed clouds,” Izv. Atmos. Ocean. Phys. 6, 112–118 (1970).

Takano, Y.

K. L. Liou, Y. Takano, “Light scattering by nonspherical particles: remote sensing and climatic implications,” Atmos. Res. 31, 271–298 (1994).
[CrossRef]

Warren, S. G.

Welch, R. M.

R. M. Welch, S. K. Cox, J. M. Davis, Solar Radiation and Clouds, Meteor Monographs (American Meteorological Society, Dallas, Texas, 1980).

Xu, L.

Zang, J.

Appl. Opt. (7)

Atmos. Res. (1)

K. L. Liou, Y. Takano, “Light scattering by nonspherical particles: remote sensing and climatic implications,” Atmos. Res. 31, 271–298 (1994).
[CrossRef]

Izv. Atmos. Ocean. Phys. (1)

K. S. Shifrin, V. A. Punina, “Conditions of corona observations in polydispersed clouds,” Izv. Atmos. Ocean. Phys. 6, 112–118 (1970).

J. Assoc. Comput. Mach. (1)

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

J. Atmos. Sci. (2)

J. D. Klett, “Orientation model for particles in turbulence,” J. Atmos. Sci. 52, 2276–2285 (1995).
[CrossRef]

J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet-rosette ice crystals,” J. Atmos. Sci. 42, 1401–1413 (1995).
[CrossRef]

J. Chem. Eng. Des. (1)

D. J. Brown, P. G. Felton, “Direct measurement of concentration and size for particles of different shapes using laser light diffraction,” J. Chem. Eng. Des. 63, 125–132 (1985).

J. Opt. Soc. Am. (3)

J. Phys. D (1)

S. L. Oshchepkov, O. V. Dubovik, “1993c: Specific features of the method of laser diffraction spectrometry in the condition of anomalous diffraction,” J. Phys. D 26, 728–732 (1993).
[CrossRef]

Other (6)

S. L. Oshchepkov, O. V. Dubovik, T. V. Lapyonok, “A method of numerical solution of linear inverse problems at the log normal noise distribution. The estimation of aerosol size distributions,” in IRS’92: Current Problems in Atmospheric Radiation, Proceedings of the International Radiation Symposium, S. Keevallik, O. Kärner, eds. (A. Deepak, Hampton, Va., 1993), pp. 334–337.

P Mazin, A. N. Nevzorov, On the Microstructure of the Clouds, Problems of Cloud Physics (n.p., 1987), pp. 37–49.

R. M. Welch, S. K. Cox, J. M. Davis, Solar Radiation and Clouds, Meteor Monographs (American Meteorological Society, Dallas, Texas, 1980).

H. R. Pruppacher, J. D. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1978).
[CrossRef]

O Crepel, J. F. Gayet, J. F. Fournol, S Oshchepkov, “A new polar nephelometer for the measurements of optical and microphysical cloud properties. II: preliminary tests,” Ann. Geophys. (to be published).

S. L. Oshchepkov, O. V. Dubovik, “The improvement of an airborne nephelometer,” Note 121 (Observatoire de Physique de Globe de Clermont–Ferrand, Laboratoire de Meteorologie Physique, Clermont–Ferrand, France, 1993).

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Figures (4)

Fig. 1
Fig. 1

Particle size distributions of a multicomponent cloud retrieved under the assumption of a single-component cloud. Initial multicomponent clouds: (a) hexagonal/cubic ice crystal cloud with the same volume content, (b) spherical/hexagonal/cubic ice crystal cloud with the same volume content. Retrieved size distributions: curve A, spherical particle cloud; curve B, hexagonal ice crystal cloud; curve C, cubic ice crystal cloud.

Fig. 2
Fig. 2

Sensitivity of the retrieved single-component size distributions to the ratio of volume contents of different cloud components. Initial multicomponent clouds: water droplet/hexagonal ice crystal cloud with a volume-content ratio (ice/water) of (a) 0.1, (b) 1.0, and (c) 10; water droplet/cubic ice crystal cloud with a volume-content ratio (ice/water) of (a′) 0.1, (b′) 1.0, and (c′) 10. Retrieved size distribution for (a), (a′), (b), and (b′): water droplet cloud. Retrieved size distributions for (c) and (c′): curve A, spherical particle cloud; curve B, hexagonal ice crystal cloud; curve C, cubic ice crystal cloud.

Fig. 3
Fig. 3

Volume scattering phase functions for individual cloud components.

Fig. 4
Fig. 4

Sensitivity of the size distributions of different cloud components, retrieved simultaneously under the assumption of a multi-component cloud, to the ratio of volume contents of different cloud components. Initial multicomponent clouds: water droplet/hexagonal ice crystal cloud with a volume-content ratio (ice/water) of (a) 0.1, (b) 1.0, and (c) 10; hexagonal/cubic ice crystal cloud with a volume-content ratio (hexagonal ice/cubic ice) of (a′) 0.1, (b′) 1.0, and (c′) 10. The estimated volume content and effective radius and their corresponding retrieval errors ɛ0 are listed for each of the components in Table 1.

Tables (1)

Tables Icon

Table 1 True Values and Errors in Retrieved Particle Volume Content and Effective Size of Both Components for Different Cloud Compositiona

Equations (20)

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d N d R = d N 1 d R + d N 2 d R + d N 3 d R .
d N s d R = N s Γ ( μ s + 1 ) ( R 0 s μ s ) μ s + 1 R μ s exp ( - μ s R R 0 s ) ,
σ ( Θ j ) = 3 4 s = 1 2 - Q ( k R , m s , Θ j ) R v s ( ln R ) d ln R .
σ = 2 π 0 π σ ( Θ ) sin Θ d Θ ,
v s ( ln R ) = d V s d ln R = 4 3 π R 3 d N s d ln R ,
C s = - + v s ( ln R ) d ln R ,
C cub = ( π 6 ) 1 / 2 C ,             C hex = 6 π 1 / 2 β ( 3 + 8 β ) 3 / 2 C .
σ * = [ K 1 K 2 ] [ ϕ 1 ϕ 2 ] + Δ ,
f * = f ( a 1 , a 2 ) + ξ
{ f * } = ln { σ * } j             ( j = 1 , 2 , , J ) , { a * } = ln { ϕ * } i s             ( i s = 1 , 2 , , E s ) , { f ( a 1 , a 2 ) } j = ln s = 1 2 i s = 1 E s K j i s exp { a s } i s             ( j = 1 , 2 , , J ; i s = 1 , 2 , , E s )
[ a 1 a 2 ] q + 1 = [ a 1 a 2 ] 1 - H q { [ U 1 q U 2 q ] ( f q - f * ) + [ γ 1 Ω 1 0 0 γ 2 Ω 2 ] [ a 1 a 2 ] q } ,
{ H q } i s i s = ( i s = 1 E 1 + E 2 | { [ U 1 q U 2 q ] T [ U 1 q U 2 q ] + [ γ 1 Ω 1 0 0 γ 2 Ω 2 ] } i s i s | ) - 1 δ i s i s , { U s q } j i s = f j a i s | a 1 q , a 2 q .
R s = - + v s ( ln R ) d ln R - + R - 1 v s ( ln R ) d ln R .
ɛ 0 2 = 1 J j = 1 J ( ln σ j - ln s = 1 2 i s = 1 E s K j i s { ϕ s } i s ) 2 ,
[ a 1 a 2 ] a ,             [ U 1 q U 2 q ] U q ,             [ γ 1 Ω 1 0 0 γ 2 Ω 2 ] γ Ω ,
v ( ln R ) = v 1 ( ln R ) + v 2 ( ln R ) .
( PhRMSD ) 2 = ( 1 / J ) lim q { [ f ( a q ) - f * ] T [ f ( a q ) - f * ] } ,
C = C ^ s - C s C s ,             δ R = R ^ s - R s R s ,
PhRMSD ɛ 0
Θ 1.84 ( λ / 2 π R ) .

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