Abstract

Spectral light from 550 to 650  nm reflected from the surface of an ice cloud produced in a temperature-controlled column is measured at seven different angles between 16.7° and 29.9°. Cloud optical depth (τ) is determined from the extinction of a 670  nm laser and is corrected for forward scattering using a Monte Carlo ray-tracing algorithm. Reflection measurements are compared to expectations from a plane-parallel radiative transfer model with input parameters based on the measured τ and a phase function for the observed ice crystal types. The plane-parallel radiative transfer model can be used to interpret the measured reflection for τ less than about 0.4 for this particular experiment, ideal for providing a validation data set to assist with the development of satellite bidirectional remote sensing.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2002 (2)

K. N. Liou and Y. Takano, "Interpretation of cirrus cloud polarization measurements from radiative transfer theory," Geophys. Res. Lett. 29, doi: (2002).
[CrossRef]

L. Wind and W. W. Szymanski, "Quantification of scattering corrections to the Beer-Lambert law for transmittance measurements in turbid media," Meas. Sci. Technol. 13, 270-275 (2002).
[CrossRef]

2001 (1)

M. B. Meyers and J. Hallett, "Micrometer-sized hygroscopic particles in the atmosphere: aircraft measurement in the Arctic," J. Geophys. Res. [Atmos.] 106, 34067-34080 (2001).
[CrossRef]

2000 (2)

B. Barkey, K. N. Liou, Y. Takano, and W. Gellerman, "Experimental and theoretical spectral reflection properties of ice clouds generated in a laboratory chamber," Appl. Opt. 39, 3561-3564 (2000).
[CrossRef]

P. Rolland, K. N. Liou, M. D. King, S. C. Tsay, and G. M. McFarquhar, "Remote sensing of optical and microphysical properties of cirrus clouds using Moderate Resolution Imaging Spectrometer channels: Methodology and sensitivity to physical assumptions," J. Geophys. Res. [Atmos.] 105, 11721-11738 (2000).
[CrossRef]

1998 (2)

H. Chepfer, G. Brogniez, and Y. Fouquart, "Cirrus clouds' microphysical properties deduced from POLDER observations," J. Quant. Spectrosc. Radiat. Transfer 60, 375-390 (1998).
[CrossRef]

P. Yang and K. N. Liou, "Single scattering properties of complex ice crystals in terrestrial atmosphere," Contrib. Atmos. Phys. 71, 223-248 (1998).

1996 (1)

M. I. Mishchenko, W. B. Rossow, A. Macke, and A. A. Lacis, "Sensitivity of cirrus cloud albedo, bidirectional reflectance, and optical thickness retrieval accuracy to ice particle shape," J. Geophys. Res. [Atmos.] 101, 16973-16986 (1996).
[CrossRef]

1995 (3)

S. C. Ou, K. N. Liou, Y. Takano, N. X. Rao, Q. Fu, A. J. Heymsfield, L. M. Miloshevich, B. Baum, and S. A. Kinne, "Remote sounding of cirrus cloud optical depths and ice crystal sizes from AVHRR data: verification using FIRE II IFO measurements," J. Atmos. Sci. 52, 4143-4158 (1995).
[CrossRef]

B. C. Gao and Y. J. Kaufman, "Selection of the 1.375-µm MODIS channel for remote sensing of cirrus clouds and stratospheric aerosols from space," J. Atmos. Sci. 52, 4231-4237 (1995).
[CrossRef]

Y. Takano and K. N. Liou, "Radiative transfer in cirrus clouds. Part III: Light scattering by irregular ice crystals," J. Atmos. Sci. 52, 818-837 (1995).
[CrossRef]

1994 (1)

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

1993 (1)

1991 (1)

K. F. Evans and G. L. Stephens, "A new polarized atmospheric radiative transfer model," J. Quant. Spectrosc. Radiat. Transfer 46, 413-423 (1991).
[CrossRef]

1989 (3)

Y. Takano and K. N. Liou, "Solar radiative transfer in cirrus clouds. Part II: Theory and computation of multiple scattering in an isotropic medium," J. Atmos. Sci. 46, 20-36 (1989).
[CrossRef]

Y. Takano and K. N. Liou, "Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals," J. Atmos. Sci. 46, 3-19 (1989).
[CrossRef]

S. Kinne and K. N. Liou, "The effects of the nonsphericity and size distribution of ice crystals on the radiative properties of cirrus clouds," Atmos. Res. 24, 273-284 (1989).
[CrossRef]

1985 (1)

1982 (1)

1980 (1)

1978 (1)

1973 (1)

1968 (2)

G. N. Plass and G. W. Kattawar, "Monte Carlo calculations of light scattering from clouds," Appl. Opt. 7, 415-419 (1968).
[CrossRef] [PubMed]

R. Zander, "Additional details on the near-infrared reflectivity of laboratory ice clouds," J. Geophys. Res. 73, 6581-6584 (1968).
[CrossRef]

1966 (1)

R. Zander, "Spectral properties of ice clouds and hoarfrost," J. Geophys. Res. 71, 375-378 (1966).

1953 (1)

R. O. Gumprecht and C. M. Sliepcevich, "Scattering of light by large spherical particles," J. Phys. Chem. 57, 90-95 (1953).
[CrossRef]

Arnott, W. P.

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

Barkey, B.

Baum, B.

S. C. Ou, K. N. Liou, Y. Takano, N. X. Rao, Q. Fu, A. J. Heymsfield, L. M. Miloshevich, B. Baum, and S. A. Kinne, "Remote sounding of cirrus cloud optical depths and ice crystal sizes from AVHRR data: verification using FIRE II IFO measurements," J. Atmos. Sci. 52, 4143-4158 (1995).
[CrossRef]

Bohren, C. F.

Box, M. A.

Brogniez, G.

H. Chepfer, G. Brogniez, and Y. Fouquart, "Cirrus clouds' microphysical properties deduced from POLDER observations," J. Quant. Spectrosc. Radiat. Transfer 60, 375-390 (1998).
[CrossRef]

Bucher, E. A.

Chepfer, H.

H. Chepfer, G. Brogniez, and Y. Fouquart, "Cirrus clouds' microphysical properties deduced from POLDER observations," J. Quant. Spectrosc. Radiat. Transfer 60, 375-390 (1998).
[CrossRef]

Deepak, A.

Evans, K. F.

K. F. Evans and G. L. Stephens, "A new polarized atmospheric radiative transfer model," J. Quant. Spectrosc. Radiat. Transfer 46, 413-423 (1991).
[CrossRef]

Fouquart, Y.

H. Chepfer, G. Brogniez, and Y. Fouquart, "Cirrus clouds' microphysical properties deduced from POLDER observations," J. Quant. Spectrosc. Radiat. Transfer 60, 375-390 (1998).
[CrossRef]

Fu, Q.

S. C. Ou, K. N. Liou, Y. Takano, N. X. Rao, Q. Fu, A. J. Heymsfield, L. M. Miloshevich, B. Baum, and S. A. Kinne, "Remote sounding of cirrus cloud optical depths and ice crystal sizes from AVHRR data: verification using FIRE II IFO measurements," J. Atmos. Sci. 52, 4143-4158 (1995).
[CrossRef]

Gao, B. C.

B. C. Gao and Y. J. Kaufman, "Selection of the 1.375-µm MODIS channel for remote sensing of cirrus clouds and stratospheric aerosols from space," J. Atmos. Sci. 52, 4231-4237 (1995).
[CrossRef]

Gellerman, W.

Gumprecht, R. O.

R. O. Gumprecht and C. M. Sliepcevich, "Scattering of light by large spherical particles," J. Phys. Chem. 57, 90-95 (1953).
[CrossRef]

Hallett, J.

M. B. Meyers and J. Hallett, "Micrometer-sized hygroscopic particles in the atmosphere: aircraft measurement in the Arctic," J. Geophys. Res. [Atmos.] 106, 34067-34080 (2001).
[CrossRef]

Heymsfield, A. J.

S. C. Ou, K. N. Liou, Y. Takano, N. X. Rao, Q. Fu, A. J. Heymsfield, L. M. Miloshevich, B. Baum, and S. A. Kinne, "Remote sounding of cirrus cloud optical depths and ice crystal sizes from AVHRR data: verification using FIRE II IFO measurements," J. Atmos. Sci. 52, 4143-4158 (1995).
[CrossRef]

Kattawar, G. W.

Kaufman, Y. J.

B. C. Gao and Y. J. Kaufman, "Selection of the 1.375-µm MODIS channel for remote sensing of cirrus clouds and stratospheric aerosols from space," J. Atmos. Sci. 52, 4231-4237 (1995).
[CrossRef]

King, M. D.

P. Rolland, K. N. Liou, M. D. King, S. C. Tsay, and G. M. McFarquhar, "Remote sensing of optical and microphysical properties of cirrus clouds using Moderate Resolution Imaging Spectrometer channels: Methodology and sensitivity to physical assumptions," J. Geophys. Res. [Atmos.] 105, 11721-11738 (2000).
[CrossRef]

Kinne, S.

S. Kinne and K. N. Liou, "The effects of the nonsphericity and size distribution of ice crystals on the radiative properties of cirrus clouds," Atmos. Res. 24, 273-284 (1989).
[CrossRef]

Kinne, S. A.

S. C. Ou, K. N. Liou, Y. Takano, N. X. Rao, Q. Fu, A. J. Heymsfield, L. M. Miloshevich, B. Baum, and S. A. Kinne, "Remote sounding of cirrus cloud optical depths and ice crystal sizes from AVHRR data: verification using FIRE II IFO measurements," J. Atmos. Sci. 52, 4143-4158 (1995).
[CrossRef]

Koh, G.

Lacis, A. A.

M. I. Mishchenko, W. B. Rossow, A. Macke, and A. A. Lacis, "Sensitivity of cirrus cloud albedo, bidirectional reflectance, and optical thickness retrieval accuracy to ice particle shape," J. Geophys. Res. [Atmos.] 101, 16973-16986 (1996).
[CrossRef]

Langmuir, I.

I. Langmuir, "Mathematical investigation of water droplet trajectories," in The Collected Works of Irving Langmuir, C.G.Suits, ed. (Pergamon, 1961).

Liou, K. N.

K. N. Liou and Y. Takano, "Interpretation of cirrus cloud polarization measurements from radiative transfer theory," Geophys. Res. Lett. 29, doi: (2002).
[CrossRef]

P. Rolland, K. N. Liou, M. D. King, S. C. Tsay, and G. M. McFarquhar, "Remote sensing of optical and microphysical properties of cirrus clouds using Moderate Resolution Imaging Spectrometer channels: Methodology and sensitivity to physical assumptions," J. Geophys. Res. [Atmos.] 105, 11721-11738 (2000).
[CrossRef]

B. Barkey, K. N. Liou, Y. Takano, and W. Gellerman, "Experimental and theoretical spectral reflection properties of ice clouds generated in a laboratory chamber," Appl. Opt. 39, 3561-3564 (2000).
[CrossRef]

P. Yang and K. N. Liou, "Single scattering properties of complex ice crystals in terrestrial atmosphere," Contrib. Atmos. Phys. 71, 223-248 (1998).

Y. Takano and K. N. Liou, "Radiative transfer in cirrus clouds. Part III: Light scattering by irregular ice crystals," J. Atmos. Sci. 52, 818-837 (1995).
[CrossRef]

S. C. Ou, K. N. Liou, Y. Takano, N. X. Rao, Q. Fu, A. J. Heymsfield, L. M. Miloshevich, B. Baum, and S. A. Kinne, "Remote sounding of cirrus cloud optical depths and ice crystal sizes from AVHRR data: verification using FIRE II IFO measurements," J. Atmos. Sci. 52, 4143-4158 (1995).
[CrossRef]

S. Kinne and K. N. Liou, "The effects of the nonsphericity and size distribution of ice crystals on the radiative properties of cirrus clouds," Atmos. Res. 24, 273-284 (1989).
[CrossRef]

Y. Takano and K. N. Liou, "Solar radiative transfer in cirrus clouds. Part II: Theory and computation of multiple scattering in an isotropic medium," J. Atmos. Sci. 46, 20-36 (1989).
[CrossRef]

Y. Takano and K. N. Liou, "Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals," J. Atmos. Sci. 46, 3-19 (1989).
[CrossRef]

K. N. Liou, Y. Takano, and P. Yang, "Light scattering-and radiative transfer in ice crystal clouds: Applications to climate research," in Light Scattering by Nonspherical Particles, M.I.Mishchenko, J.W.Hovenier, and L.D.Travis, eds. (Academic, 2000), pp. 417-449.
[CrossRef]

Macke, A.

M. I. Mishchenko, W. B. Rossow, A. Macke, and A. A. Lacis, "Sensitivity of cirrus cloud albedo, bidirectional reflectance, and optical thickness retrieval accuracy to ice particle shape," J. Geophys. Res. [Atmos.] 101, 16973-16986 (1996).
[CrossRef]

McFarquhar, G. M.

P. Rolland, K. N. Liou, M. D. King, S. C. Tsay, and G. M. McFarquhar, "Remote sensing of optical and microphysical properties of cirrus clouds using Moderate Resolution Imaging Spectrometer channels: Methodology and sensitivity to physical assumptions," J. Geophys. Res. [Atmos.] 105, 11721-11738 (2000).
[CrossRef]

Meyers, M. B.

M. B. Meyers and J. Hallett, "Micrometer-sized hygroscopic particles in the atmosphere: aircraft measurement in the Arctic," J. Geophys. Res. [Atmos.] 106, 34067-34080 (2001).
[CrossRef]

Miloshevich, L. M.

S. C. Ou, K. N. Liou, Y. Takano, N. X. Rao, Q. Fu, A. J. Heymsfield, L. M. Miloshevich, B. Baum, and S. A. Kinne, "Remote sounding of cirrus cloud optical depths and ice crystal sizes from AVHRR data: verification using FIRE II IFO measurements," J. Atmos. Sci. 52, 4143-4158 (1995).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, W. B. Rossow, A. Macke, and A. A. Lacis, "Sensitivity of cirrus cloud albedo, bidirectional reflectance, and optical thickness retrieval accuracy to ice particle shape," J. Geophys. Res. [Atmos.] 101, 16973-16986 (1996).
[CrossRef]

Mitchell, D. L.

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

Nakaya, U.

U. Nakaya, Snow Crystals (Harvard U. Press, 1954).

Ou, S. C.

S. C. Ou, K. N. Liou, Y. Takano, N. X. Rao, Q. Fu, A. J. Heymsfield, L. M. Miloshevich, B. Baum, and S. A. Kinne, "Remote sounding of cirrus cloud optical depths and ice crystal sizes from AVHRR data: verification using FIRE II IFO measurements," J. Atmos. Sci. 52, 4143-4158 (1995).
[CrossRef]

Plass, G. N.

Rao, N. X.

S. C. Ou, K. N. Liou, Y. Takano, N. X. Rao, Q. Fu, A. J. Heymsfield, L. M. Miloshevich, B. Baum, and S. A. Kinne, "Remote sounding of cirrus cloud optical depths and ice crystal sizes from AVHRR data: verification using FIRE II IFO measurements," J. Atmos. Sci. 52, 4143-4158 (1995).
[CrossRef]

Rolland, P.

P. Rolland, K. N. Liou, M. D. King, S. C. Tsay, and G. M. McFarquhar, "Remote sensing of optical and microphysical properties of cirrus clouds using Moderate Resolution Imaging Spectrometer channels: Methodology and sensitivity to physical assumptions," J. Geophys. Res. [Atmos.] 105, 11721-11738 (2000).
[CrossRef]

Rossow, W. B.

M. I. Mishchenko, W. B. Rossow, A. Macke, and A. A. Lacis, "Sensitivity of cirrus cloud albedo, bidirectional reflectance, and optical thickness retrieval accuracy to ice particle shape," J. Geophys. Res. [Atmos.] 101, 16973-16986 (1996).
[CrossRef]

Sliepcevich, C. M.

R. O. Gumprecht and C. M. Sliepcevich, "Scattering of light by large spherical particles," J. Phys. Chem. 57, 90-95 (1953).
[CrossRef]

Stephens, G. L.

K. F. Evans and G. L. Stephens, "A new polarized atmospheric radiative transfer model," J. Quant. Spectrosc. Radiat. Transfer 46, 413-423 (1991).
[CrossRef]

Szymanski, W. W.

L. Wind and W. W. Szymanski, "Quantification of scattering corrections to the Beer-Lambert law for transmittance measurements in turbid media," Meas. Sci. Technol. 13, 270-275 (2002).
[CrossRef]

Takano, Y.

K. N. Liou and Y. Takano, "Interpretation of cirrus cloud polarization measurements from radiative transfer theory," Geophys. Res. Lett. 29, doi: (2002).
[CrossRef]

B. Barkey, K. N. Liou, Y. Takano, and W. Gellerman, "Experimental and theoretical spectral reflection properties of ice clouds generated in a laboratory chamber," Appl. Opt. 39, 3561-3564 (2000).
[CrossRef]

Y. Takano and K. N. Liou, "Radiative transfer in cirrus clouds. Part III: Light scattering by irregular ice crystals," J. Atmos. Sci. 52, 818-837 (1995).
[CrossRef]

S. C. Ou, K. N. Liou, Y. Takano, N. X. Rao, Q. Fu, A. J. Heymsfield, L. M. Miloshevich, B. Baum, and S. A. Kinne, "Remote sounding of cirrus cloud optical depths and ice crystal sizes from AVHRR data: verification using FIRE II IFO measurements," J. Atmos. Sci. 52, 4143-4158 (1995).
[CrossRef]

Y. Takano and K. N. Liou, "Solar radiative transfer in cirrus clouds. Part II: Theory and computation of multiple scattering in an isotropic medium," J. Atmos. Sci. 46, 20-36 (1989).
[CrossRef]

Y. Takano and K. N. Liou, "Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals," J. Atmos. Sci. 46, 3-19 (1989).
[CrossRef]

K. N. Liou, Y. Takano, and P. Yang, "Light scattering-and radiative transfer in ice crystal clouds: Applications to climate research," in Light Scattering by Nonspherical Particles, M.I.Mishchenko, J.W.Hovenier, and L.D.Travis, eds. (Academic, 2000), pp. 417-449.
[CrossRef]

Tam, W. G.

Tsay, S. C.

P. Rolland, K. N. Liou, M. D. King, S. C. Tsay, and G. M. McFarquhar, "Remote sensing of optical and microphysical properties of cirrus clouds using Moderate Resolution Imaging Spectrometer channels: Methodology and sensitivity to physical assumptions," J. Geophys. Res. [Atmos.] 105, 11721-11738 (2000).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

Walker, P. L.

Wind, L.

L. Wind and W. W. Szymanski, "Quantification of scattering corrections to the Beer-Lambert law for transmittance measurements in turbid media," Meas. Sci. Technol. 13, 270-275 (2002).
[CrossRef]

Yang, P.

P. Yang and K. N. Liou, "Single scattering properties of complex ice crystals in terrestrial atmosphere," Contrib. Atmos. Phys. 71, 223-248 (1998).

K. N. Liou, Y. Takano, and P. Yang, "Light scattering-and radiative transfer in ice crystal clouds: Applications to climate research," in Light Scattering by Nonspherical Particles, M.I.Mishchenko, J.W.Hovenier, and L.D.Travis, eds. (Academic, 2000), pp. 417-449.
[CrossRef]

Zander, R.

R. Zander, "Additional details on the near-infrared reflectivity of laboratory ice clouds," J. Geophys. Res. 73, 6581-6584 (1968).
[CrossRef]

R. Zander, "Spectral properties of ice clouds and hoarfrost," J. Geophys. Res. 71, 375-378 (1966).

Zardecki, A.

Appl. Opt. (8)

Atmos. Res. (1)

S. Kinne and K. N. Liou, "The effects of the nonsphericity and size distribution of ice crystals on the radiative properties of cirrus clouds," Atmos. Res. 24, 273-284 (1989).
[CrossRef]

Contrib. Atmos. Phys. (1)

P. Yang and K. N. Liou, "Single scattering properties of complex ice crystals in terrestrial atmosphere," Contrib. Atmos. Phys. 71, 223-248 (1998).

Geophys. Res. Lett. (1)

K. N. Liou and Y. Takano, "Interpretation of cirrus cloud polarization measurements from radiative transfer theory," Geophys. Res. Lett. 29, doi: (2002).
[CrossRef]

J. Atmos. Sci. (6)

Y. Takano and K. N. Liou, "Solar radiative transfer in cirrus clouds. Part II: Theory and computation of multiple scattering in an isotropic medium," J. Atmos. Sci. 46, 20-36 (1989).
[CrossRef]

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

S. C. Ou, K. N. Liou, Y. Takano, N. X. Rao, Q. Fu, A. J. Heymsfield, L. M. Miloshevich, B. Baum, and S. A. Kinne, "Remote sounding of cirrus cloud optical depths and ice crystal sizes from AVHRR data: verification using FIRE II IFO measurements," J. Atmos. Sci. 52, 4143-4158 (1995).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

(a) Water drops from the ultrasonic humidifier injected at the top of the chamber are nucleated near the middle of the chamber. The optical reflection of the ice cloud is studied at the open optical port and a laser beam traverses the cloud at an angle to monitor its optical depth. This drawing is not to scale as the growth column is much taller than the lower chamber. (b) Particles pulled through the sample tube by a suction impact on the upper surface of the 2.5 mm diameter sapphire window. A video microscope views the particles from below. This diagram is not to scale as the sapphire widow is enlarged for clarity.

Fig. 2
Fig. 2

Optical depth along the laser beam path as a function of laser beam extinction (I∕I 0) determined via a Monte Carlo ray-tracing method based on the experimental configuration and for particles measured during the thinning cloud case. Also shown are the corrections for the shorter experimental extinction path, corrections for a cloud of square hexagonal particles that have a length to width ratio of 1, and the extinction predicted by Beer's law.

Fig. 3
Fig. 3

(Color online) (a) Optical depth measured while the cloud reflection was monitored at 16.7° from nadir. The black squares indicate the approximate time that each reflection measurement from a wavelength of 550–850 nm occurs. The spike at approximately 550 s is from the laser beam occlusion due to the cleaning of the chamber as described in the text. The particles in the cloud are mostly very small plates, as shown in (b).

Fig. 4
Fig. 4

Single-scattering phase functions based on the particle habits described in Table 1 for the thinning cloud case (thin curve) and the plate and the dendritic plate cloud (thick curve). The vertical scale is truncated to indicate the extent of the forward intensities.

Fig. 5
Fig. 5

Measured average reflection of the cloud from 550 to 650 nm is shown by the black diamonds plotted as a function of the optical depth averaged over the period of the reflectance measurement. The error bars (2%) are based on uncertainties in the reflection measurement caused by cloud turbulence. The theoretical results are determined using a plane-parallel model with the observed cloud microphysics.

Fig. 6
Fig. 6

(Color online) (a) Normal optical depth measured when the reflection of the ice cloud is measured at the angles and times indicated by the horizontal bars. The large peaks are due to clearing the chamber bottom to prevent the buildup of ice crystals. Dendritic plates and plates make up the majority of particles as seen in the lower cloudscope image (b).

Fig. 7
Fig. 7

Reflection as a function of the sensing angle (triangles) observed during the cloud event of Fig. 6 and plane-parallel expectations for an optical depth of 0.33 using the theoretical single-scattering properties based on measured microphysics. Error bars (5%) reflect uncertainty due to the turbulence in the cloud.

Tables (1)

Tables Icon

Table 1 Observed Particle Microphysics and Parameters Used to Determine the Single-scattering Properties for Plane-parallel Model Calculations and Forward-scattering Correction Factor

Equations (6)

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U pf ( θ i ) = 0 θ i P ( θ ) sin ( θ ) d θ 0 π P ( θ ) sin ( θ ) d θ .
P ( θ ) = i = 1 N D = 0 D max P i ( θ ) C s , i ( D ) n i ( D ) d D ,
1 4 π Ω P ( θ ) d Ω = 1 ,
100 × D = 0 D max C s , i ( D ) n ( D ) d D i = 1 n D = 0 D max C s , i ( D ) n ( D ) d D ,
h = 0 .01263 D 0 .449 ,
P A = 3 a 2 2 3 + 4 ( L / 2 a ) 2 = S 4 ,

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