Abstract

The optical properties of snowpacks composed of spherical and nonspherical particles artificially prepared in a cold laboratory are investigated by measuring spectral albedos. The measured spectral albedo in the spectral region λ=0.352.5μm is compared with the theoretically calculated albedo, for which a Monte Carlo radiative transfer model is employed for multiple scattering combined with the Mie theory and the ray-tracing technique for single scattering by snow particles. Since the spherical particles are a little aggregate, the effects of a cluster of the spheres on snow albedo are examined using a generalized multiparticle Mie-solution model [Appl. Opt. 34, 4573 (1995); J. Quant. Spectrosc. Radiat. Transf. 79–80, 1121 (2003)]. The snow albedo of a cluster of the spheres can be represented with that of the singe sphere slightly larger than its component of the cluster in case of small grains. The observed albedos for the spherical snow particles agree with the theoretically calculated ones for the snow grain size measured in the snow pit work. The snow albedos for the nonspherical particles, which were dendrites, are influenced by the branch width and the branch length, based on a comparison of the theoretically calculated albedo by using circular cylindrical snow particles and the observed albedo. The snow albedo in the near-infrared region depends on the branch width only when the branch length is sufficiently greater than the branch width. The comparison between the spherical and nonspherical snow particles indicates that the spectral albedo of the nonspherical particles can be represented by using an equal volume–area ratio sphere.

© 2006 Optical Society of America

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    [CrossRef]

2005

H. Motoyoshi, Te. Aoki, M. Hori, O. Abe, and S. Mochizuki, "Possible effect of anthropogenic aerosol deposition on snow albedo reduction at Shinjo, Japan," J. Meteorol. Soc. Jpn. 83, 137-148 (2005).
[CrossRef]

2004

J. Hansen and L. Nazarenko, "Soot climate forcing via snow and ice albedos," Proc. Natl. Acad. Sci. USA 101, 423-428 (2004).
[CrossRef]

A. A. Kokhanovsky and E. P. Zege, "Scattering optics of snow," Appl. Opt. 43, 1589-1602 (2004).
[CrossRef] [PubMed]

2003

Te. Aoki, A. Hachikubo, and M. Hori, "Effects of snow physical parameters on shortwave broadband albedos," J. Geophys. Res. 108, 101029 (2003).
[CrossRef]

Y.-I. Xu and N. Khlebtsov, "Orientation-averaged radiative properties of an arbitrary configuration of scatterers," J. Quant. Spectrosc. Radiat. Transf. 79-80, 1121-1137 (2003).
[CrossRef]

2002

T. Tanikawa, Te. Aoki, and F. Nishio, "Remote sensing of snow grain size and snow impurities from Airborne Multispectral Scanner data using a snow bidirectional reflectance distribution function model," Ann. Glaciol. 34, 74-80 (2002).
[CrossRef]

2001

M. Hori, Te. Aoki, K. Stamnes, B. Chen, and W. Li, "Preliminary validation of the GLI cryosphere algorithms with MODIS daytime data," Polar Meteorol. Glaciol. 15, 1-20 (2001).

T. Nakamura, O. Abe, T. Hasegawa, R. Tamura, and T. Ohta, "Spectral reflectance of snow with a known grain-size distribution in successive metamorphism," Cold Regions Sci. Technol. 32, 13-26 (2001).
[CrossRef]

2000

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, "Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface," J. Geophys. Res. 105, 10219-10236 (2000).
[CrossRef]

A. W. Nolin and J. Dozier, "A hyperspectral method for remotely sensing the grain size of snow," Remote Sens. Environ. 74, 207-216 (2000).
[CrossRef]

1999

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovotskij, and N. T. Zakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Radiat. Transf. 63, 409-432 (1999).
[CrossRef]

T. C. Grenfell and S. G. Warren, "Relationship of a nonspherical ice particle by a collection of independent sphere for scattering and absorption of radiation," J. Geophys. Res. 104, 31,697-31,709 (1999).
[CrossRef]

1998

T. H. Painter, D. A. Roberts, R. O. Green, and J. Dozier, "The effect of grain size on spectral mixture analysis of snow-covered area from AVIRIS data," Remote Sens. Environ. 65, 320-332 (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).

C. Sergent, C. Leroux, E. Pougatch, and F. Guirado, "Hemispherical-directional reflectance measurements of natural snow in the 0.9-1.45 μm spectral range: comparison with adding-doubling modeling," Ann. Glaciol. 26, 59-63 (1998).

C. Leroux, J. Deuzé, P. Goloub, C. Sergent, and M. Fily, "Ground measurements of the polarized bidirectional reflectance of snow in the near-infrared spectrum domain: Comparisons with model results," J. Geophys. Res. 103, 19,721-19,731 (1998).
[CrossRef]

Te. Aoki, Ta. Aoki, M. Fukabori, Y. Tachibana, Y. Zaizen, F. Nishio and T. Oishi, "Spectral albedo observation on the snow field at Barrow, Alaska," Polar Meteorol. Glaciol. 12, 1-9 (1998).

1997

M. Fily, B. Bourdelles, J. P. Dedieu, and C. Sergent, "Comparison of in situ and Landsat Thematic Mapper derived snow grain characteristics in the Alps," Remote Sens. Environ. 59, 452-460 (1997).
[CrossRef]

M. I. Mishchenko and A. Macke, "Asymmetry parameters of the phase function for isolated and densely packed spherical particles with multiple internal inclusions in the geometric optics limit," J. Quant. Spectrosc. Radiat. Transf. 57, 767-794 (1997).
[CrossRef]

1996

1995

1994

M. I. Mishchenko, "Asymmetry parameters of the phase function for densely packed scattering grains," J. Quant. Spectrosc. Radiat. Transf. 52, 95-110 (1994).
[CrossRef]

T. C. Grenfell, S. G. Warren, and P. C. Mullen, "Reflection of solar radiation by the Antarctic snow surface at ultraviolet, visible, and near-infrared wavelengths," J. Geophys. Res. 99, 18669-18684 (1994).
[CrossRef]

P. Ya. Groisman, T. R. Karl, and R. W. Knight, "Observed impact of snow cover on the heat balance and the rise of continental spring temperatures," Science 263, 198-200 (1994).
[CrossRef] [PubMed]

1993

B. Bourdelles and M. Fily, "Snow grain-size determination from Landsat imagery over Terre Adélie, Antarctica," Ann. Glaciol. 17, 86-92 (1993).

L. Kou, D. Labrie, and P. Chýlek, "Refractive indices of water and ice in the 0.65 to 2.5 μm spectral range," Appl. Opt. 32, 3531-3540 (1993).
[CrossRef] [PubMed]

1989

T. P. Barnett, L. Dümenil, U. Schlese, E. Roeckner, and M. Latif, "The effect of Eurasian snow cover on regional and global climate variations," J. Atmos. Sci. 46, 661-685 (1989).
[CrossRef]

1984

1983

P. Chýlek, V. Ramaswamy, and V. Srivastava, "Albedo of soot-contaminated snow," J. Geophys. Res. 88, 10837-10843 (1983).
[CrossRef]

1982

S. G. Warren, "Optical properties of snow," Rev. Geophys. Space Phys. 20, 67-89 (1982).
[CrossRef]

1981

T. C. Grenfell, "A visible and near-infrared scanning photometer for field measurements of spectral albedo and irradiance under polar conditions," J. Glaciol. 27, 476-481 (1981).

T. C. Grenfell, D. K. Perovich, and J. A. Ogren, "Spectral albedos of an alpine snowpack," Cold Regions Sci. Technol. 4, 121-127 (1981).
[CrossRef]

1980

W. J. Wiscombe and S. G. Warren, "A model for the spectral albedo of snow. I. Pure snow," J. Atmos. Sci. 37, 2712-2733 (1980).
[CrossRef]

S. G. Warren and W. J. Wiscombe, "A model for the spectral albedo of snow. II. Snow containing atmospheric aerosols," J. Atmos. Sci. 37, 2734-2745 (1980).
[CrossRef]

1979

1978

M. Kuhn and L. Siogas, "Spectroscopic studies at McMurdo, South Pole, and Siple Stations during the austral summer 1977-1978," Antarct. J. U. S. 13, 178-179 (1978).

1977

T. C. Grenfell and G. A. Maykut, "The optical properties of ice and snow in the Arctic basin," J. Glaciol. 18, 445-463 (1977).

Abe, O.

H. Motoyoshi, Te. Aoki, M. Hori, O. Abe, and S. Mochizuki, "Possible effect of anthropogenic aerosol deposition on snow albedo reduction at Shinjo, Japan," J. Meteorol. Soc. Jpn. 83, 137-148 (2005).
[CrossRef]

T. Nakamura, O. Abe, T. Hasegawa, R. Tamura, and T. Ohta, "Spectral reflectance of snow with a known grain-size distribution in successive metamorphism," Cold Regions Sci. Technol. 32, 13-26 (2001).
[CrossRef]

Aoki, Ta.

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, "Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface," J. Geophys. Res. 105, 10219-10236 (2000).
[CrossRef]

Te. Aoki, Ta. Aoki, M. Fukabori, Y. Tachibana, Y. Zaizen, F. Nishio and T. Oishi, "Spectral albedo observation on the snow field at Barrow, Alaska," Polar Meteorol. Glaciol. 12, 1-9 (1998).

Aoki, Te.

H. Motoyoshi, Te. Aoki, M. Hori, O. Abe, and S. Mochizuki, "Possible effect of anthropogenic aerosol deposition on snow albedo reduction at Shinjo, Japan," J. Meteorol. Soc. Jpn. 83, 137-148 (2005).
[CrossRef]

Te. Aoki, A. Hachikubo, and M. Hori, "Effects of snow physical parameters on shortwave broadband albedos," J. Geophys. Res. 108, 101029 (2003).
[CrossRef]

T. Tanikawa, Te. Aoki, and F. Nishio, "Remote sensing of snow grain size and snow impurities from Airborne Multispectral Scanner data using a snow bidirectional reflectance distribution function model," Ann. Glaciol. 34, 74-80 (2002).
[CrossRef]

M. Hori, Te. Aoki, K. Stamnes, B. Chen, and W. Li, "Preliminary validation of the GLI cryosphere algorithms with MODIS daytime data," Polar Meteorol. Glaciol. 15, 1-20 (2001).

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, "Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface," J. Geophys. Res. 105, 10219-10236 (2000).
[CrossRef]

Te. Aoki, Ta. Aoki, M. Fukabori, Y. Tachibana, Y. Zaizen, F. Nishio and T. Oishi, "Spectral albedo observation on the snow field at Barrow, Alaska," Polar Meteorol. Glaciol. 12, 1-9 (1998).

Barnett, T. P.

T. P. Barnett, L. Dümenil, U. Schlese, E. Roeckner, and M. Latif, "The effect of Eurasian snow cover on regional and global climate variations," J. Atmos. Sci. 46, 661-685 (1989).
[CrossRef]

Bourdelles, B.

M. Fily, B. Bourdelles, J. P. Dedieu, and C. Sergent, "Comparison of in situ and Landsat Thematic Mapper derived snow grain characteristics in the Alps," Remote Sens. Environ. 59, 452-460 (1997).
[CrossRef]

B. Bourdelles and M. Fily, "Snow grain-size determination from Landsat imagery over Terre Adélie, Antarctica," Ann. Glaciol. 17, 86-92 (1993).

Chen, B.

M. Hori, Te. Aoki, K. Stamnes, B. Chen, and W. Li, "Preliminary validation of the GLI cryosphere algorithms with MODIS daytime data," Polar Meteorol. Glaciol. 15, 1-20 (2001).

Chýlek, P.

L. Kou, D. Labrie, and P. Chýlek, "Refractive indices of water and ice in the 0.65 to 2.5 μm spectral range," Appl. Opt. 32, 3531-3540 (1993).
[CrossRef] [PubMed]

P. Chýlek, V. Ramaswamy, and V. Srivastava, "Albedo of soot-contaminated snow," J. Geophys. Res. 88, 10837-10843 (1983).
[CrossRef]

Darbinjan, R. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, and B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics (Springer, 1980).

Dedieu, J. P.

M. Fily, B. Bourdelles, J. P. Dedieu, and C. Sergent, "Comparison of in situ and Landsat Thematic Mapper derived snow grain characteristics in the Alps," Remote Sens. Environ. 59, 452-460 (1997).
[CrossRef]

Deuzé, J.

C. Leroux, J. Deuzé, P. Goloub, C. Sergent, and M. Fily, "Ground measurements of the polarized bidirectional reflectance of snow in the near-infrared spectrum domain: Comparisons with model results," J. Geophys. Res. 103, 19,721-19,731 (1998).
[CrossRef]

Dlugach, J. M.

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovotskij, and N. T. Zakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Radiat. Transf. 63, 409-432 (1999).
[CrossRef]

Dozier, J.

A. W. Nolin and J. Dozier, "A hyperspectral method for remotely sensing the grain size of snow," Remote Sens. Environ. 74, 207-216 (2000).
[CrossRef]

T. H. Painter, D. A. Roberts, R. O. Green, and J. Dozier, "The effect of grain size on spectral mixture analysis of snow-covered area from AVIRIS data," Remote Sens. Environ. 65, 320-332 (1998).
[CrossRef]

Dümenil, L.

T. P. Barnett, L. Dümenil, U. Schlese, E. Roeckner, and M. Latif, "The effect of Eurasian snow cover on regional and global climate variations," J. Atmos. Sci. 46, 661-685 (1989).
[CrossRef]

Elepov, B. S.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, and B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics (Springer, 1980).

Fily, M.

C. Leroux, J. Deuzé, P. Goloub, C. Sergent, and M. Fily, "Ground measurements of the polarized bidirectional reflectance of snow in the near-infrared spectrum domain: Comparisons with model results," J. Geophys. Res. 103, 19,721-19,731 (1998).
[CrossRef]

M. Fily, B. Bourdelles, J. P. Dedieu, and C. Sergent, "Comparison of in situ and Landsat Thematic Mapper derived snow grain characteristics in the Alps," Remote Sens. Environ. 59, 452-460 (1997).
[CrossRef]

B. Bourdelles and M. Fily, "Snow grain-size determination from Landsat imagery over Terre Adélie, Antarctica," Ann. Glaciol. 17, 86-92 (1993).

Fukabori, M.

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, "Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface," J. Geophys. Res. 105, 10219-10236 (2000).
[CrossRef]

Te. Aoki, Ta. Aoki, M. Fukabori, Y. Tachibana, Y. Zaizen, F. Nishio and T. Oishi, "Spectral albedo observation on the snow field at Barrow, Alaska," Polar Meteorol. Glaciol. 12, 1-9 (1998).

Goloub, P.

C. Leroux, J. Deuzé, P. Goloub, C. Sergent, and M. Fily, "Ground measurements of the polarized bidirectional reflectance of snow in the near-infrared spectrum domain: Comparisons with model results," J. Geophys. Res. 103, 19,721-19,731 (1998).
[CrossRef]

Green, R. O.

T. H. Painter, D. A. Roberts, R. O. Green, and J. Dozier, "The effect of grain size on spectral mixture analysis of snow-covered area from AVIRIS data," Remote Sens. Environ. 65, 320-332 (1998).
[CrossRef]

Grenfell, T. C.

T. C. Grenfell and S. G. Warren, "Relationship of a nonspherical ice particle by a collection of independent sphere for scattering and absorption of radiation," J. Geophys. Res. 104, 31,697-31,709 (1999).
[CrossRef]

T. C. Grenfell, S. G. Warren, and P. C. Mullen, "Reflection of solar radiation by the Antarctic snow surface at ultraviolet, visible, and near-infrared wavelengths," J. Geophys. Res. 99, 18669-18684 (1994).
[CrossRef]

T. C. Grenfell, "A visible and near-infrared scanning photometer for field measurements of spectral albedo and irradiance under polar conditions," J. Glaciol. 27, 476-481 (1981).

T. C. Grenfell, D. K. Perovich, and J. A. Ogren, "Spectral albedos of an alpine snowpack," Cold Regions Sci. Technol. 4, 121-127 (1981).
[CrossRef]

T. C. Grenfell and G. A. Maykut, "The optical properties of ice and snow in the Arctic basin," J. Glaciol. 18, 445-463 (1977).

Groisman, P. Ya.

P. Ya. Groisman, T. R. Karl, and R. W. Knight, "Observed impact of snow cover on the heat balance and the rise of continental spring temperatures," Science 263, 198-200 (1994).
[CrossRef] [PubMed]

Guirado, F.

C. Sergent, C. Leroux, E. Pougatch, and F. Guirado, "Hemispherical-directional reflectance measurements of natural snow in the 0.9-1.45 μm spectral range: comparison with adding-doubling modeling," Ann. Glaciol. 26, 59-63 (1998).

Hachikubo, A.

Te. Aoki, A. Hachikubo, and M. Hori, "Effects of snow physical parameters on shortwave broadband albedos," J. Geophys. Res. 108, 101029 (2003).
[CrossRef]

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, "Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface," J. Geophys. Res. 105, 10219-10236 (2000).
[CrossRef]

Hansen, J.

J. Hansen and L. Nazarenko, "Soot climate forcing via snow and ice albedos," Proc. Natl. Acad. Sci. USA 101, 423-428 (2004).
[CrossRef]

Hasegawa, T.

T. Nakamura, O. Abe, T. Hasegawa, R. Tamura, and T. Ohta, "Spectral reflectance of snow with a known grain-size distribution in successive metamorphism," Cold Regions Sci. Technol. 32, 13-26 (2001).
[CrossRef]

Hori, M.

H. Motoyoshi, Te. Aoki, M. Hori, O. Abe, and S. Mochizuki, "Possible effect of anthropogenic aerosol deposition on snow albedo reduction at Shinjo, Japan," J. Meteorol. Soc. Jpn. 83, 137-148 (2005).
[CrossRef]

Te. Aoki, A. Hachikubo, and M. Hori, "Effects of snow physical parameters on shortwave broadband albedos," J. Geophys. Res. 108, 101029 (2003).
[CrossRef]

M. Hori, Te. Aoki, K. Stamnes, B. Chen, and W. Li, "Preliminary validation of the GLI cryosphere algorithms with MODIS daytime data," Polar Meteorol. Glaciol. 15, 1-20 (2001).

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

Kargin, B. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, and B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics (Springer, 1980).

Karl, T. R.

P. Ya. Groisman, T. R. Karl, and R. W. Knight, "Observed impact of snow cover on the heat balance and the rise of continental spring temperatures," Science 263, 198-200 (1994).
[CrossRef] [PubMed]

Khlebtsov, N.

Y.-I. Xu and N. Khlebtsov, "Orientation-averaged radiative properties of an arbitrary configuration of scatterers," J. Quant. Spectrosc. Radiat. Transf. 79-80, 1121-1137 (2003).
[CrossRef]

Knight, R. W.

P. Ya. Groisman, T. R. Karl, and R. W. Knight, "Observed impact of snow cover on the heat balance and the rise of continental spring temperatures," Science 263, 198-200 (1994).
[CrossRef] [PubMed]

Kokhanovsky, A. A.

A. A. Kokhanovsky and E. P. Zege, "Scattering optics of snow," Appl. Opt. 43, 1589-1602 (2004).
[CrossRef] [PubMed]

A. A. Kokhanovsky, Optics of Light Scattering Media: Problems and Solutions (Wiley, 1998).

Kou, L.

Kuhn, M.

M. Kuhn and L. Siogas, "Spectroscopic studies at McMurdo, South Pole, and Siple Stations during the austral summer 1977-1978," Antarct. J. U. S. 13, 178-179 (1978).

Labrie, D.

Latif, M.

T. P. Barnett, L. Dümenil, U. Schlese, E. Roeckner, and M. Latif, "The effect of Eurasian snow cover on regional and global climate variations," J. Atmos. Sci. 46, 661-685 (1989).
[CrossRef]

Leroux, C.

C. Sergent, C. Leroux, E. Pougatch, and F. Guirado, "Hemispherical-directional reflectance measurements of natural snow in the 0.9-1.45 μm spectral range: comparison with adding-doubling modeling," Ann. Glaciol. 26, 59-63 (1998).

C. Leroux, J. Deuzé, P. Goloub, C. Sergent, and M. Fily, "Ground measurements of the polarized bidirectional reflectance of snow in the near-infrared spectrum domain: Comparisons with model results," J. Geophys. Res. 103, 19,721-19,731 (1998).
[CrossRef]

Li, W.

M. Hori, Te. Aoki, K. Stamnes, B. Chen, and W. Li, "Preliminary validation of the GLI cryosphere algorithms with MODIS daytime data," Polar Meteorol. Glaciol. 15, 1-20 (2001).

Liljequist, G. H.

G. H. Liljequist, "Energy exchange of an Antarctic snow field: Short-wave radiation (Maudheim 71°03′S, 10°56′W)," in Norwegian-British-Swedish Antarctic Expedition, 1949-1952, Scientific Results (Norsk Polarinstitutt, 1956), Vol. 2, part 1A.

Liou, K. N.

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

Macke, A.

M. I. Mishchenko and A. Macke, "Asymmetry parameters of the phase function for isolated and densely packed spherical particles with multiple internal inclusions in the geometric optics limit," J. Quant. Spectrosc. Radiat. Transf. 57, 767-794 (1997).
[CrossRef]

A. Macke and M. I. Mishchenko, "Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles," Appl. Opt. 35, 4291-4296 (1996).
[CrossRef] [PubMed]

Mackowski, D. W.

Marchuk, G. I.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, and B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics (Springer, 1980).

Maykut, G. A.

T. C. Grenfell and G. A. Maykut, "The optical properties of ice and snow in the Arctic basin," J. Glaciol. 18, 445-463 (1977).

Mikhailov, G. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, and B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics (Springer, 1980).

Mishchenko, M. I.

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovotskij, and N. T. Zakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Radiat. Transf. 63, 409-432 (1999).
[CrossRef]

M. I. Mishchenko and A. Macke, "Asymmetry parameters of the phase function for isolated and densely packed spherical particles with multiple internal inclusions in the geometric optics limit," J. Quant. Spectrosc. Radiat. Transf. 57, 767-794 (1997).
[CrossRef]

A. Macke and M. I. Mishchenko, "Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles," Appl. Opt. 35, 4291-4296 (1996).
[CrossRef] [PubMed]

M. I. Mishchenko, D. W. Mackowski, and L. D. Travis, "Scattering of light by bispheres with touching and separated components," Appl. Opt. 34, 4589-4599 (1995).
[CrossRef] [PubMed]

M. I. Mishchenko, "Asymmetry parameters of the phase function for densely packed scattering grains," J. Quant. Spectrosc. Radiat. Transf. 52, 95-110 (1994).
[CrossRef]

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

Mochizuki, S.

H. Motoyoshi, Te. Aoki, M. Hori, O. Abe, and S. Mochizuki, "Possible effect of anthropogenic aerosol deposition on snow albedo reduction at Shinjo, Japan," J. Meteorol. Soc. Jpn. 83, 137-148 (2005).
[CrossRef]

Motoyoshi, H.

H. Motoyoshi, Te. Aoki, M. Hori, O. Abe, and S. Mochizuki, "Possible effect of anthropogenic aerosol deposition on snow albedo reduction at Shinjo, Japan," J. Meteorol. Soc. Jpn. 83, 137-148 (2005).
[CrossRef]

Mullen, P. C.

T. C. Grenfell, S. G. Warren, and P. C. Mullen, "Reflection of solar radiation by the Antarctic snow surface at ultraviolet, visible, and near-infrared wavelengths," J. Geophys. Res. 99, 18669-18684 (1994).
[CrossRef]

Nakamura, T.

T. Nakamura, O. Abe, T. Hasegawa, R. Tamura, and T. Ohta, "Spectral reflectance of snow with a known grain-size distribution in successive metamorphism," Cold Regions Sci. Technol. 32, 13-26 (2001).
[CrossRef]

Nazaraliev, M. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, and B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics (Springer, 1980).

Nazarenko, L.

J. Hansen and L. Nazarenko, "Soot climate forcing via snow and ice albedos," Proc. Natl. Acad. Sci. USA 101, 423-428 (2004).
[CrossRef]

Nishio, F.

T. Tanikawa, Te. Aoki, and F. Nishio, "Remote sensing of snow grain size and snow impurities from Airborne Multispectral Scanner data using a snow bidirectional reflectance distribution function model," Ann. Glaciol. 34, 74-80 (2002).
[CrossRef]

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, "Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface," J. Geophys. Res. 105, 10219-10236 (2000).
[CrossRef]

Te. Aoki, Ta. Aoki, M. Fukabori, Y. Tachibana, Y. Zaizen, F. Nishio and T. Oishi, "Spectral albedo observation on the snow field at Barrow, Alaska," Polar Meteorol. Glaciol. 12, 1-9 (1998).

Nolin, A. W.

A. W. Nolin and J. Dozier, "A hyperspectral method for remotely sensing the grain size of snow," Remote Sens. Environ. 74, 207-216 (2000).
[CrossRef]

Ogren, J. A.

T. C. Grenfell, D. K. Perovich, and J. A. Ogren, "Spectral albedos of an alpine snowpack," Cold Regions Sci. Technol. 4, 121-127 (1981).
[CrossRef]

Ohta, T.

T. Nakamura, O. Abe, T. Hasegawa, R. Tamura, and T. Ohta, "Spectral reflectance of snow with a known grain-size distribution in successive metamorphism," Cold Regions Sci. Technol. 32, 13-26 (2001).
[CrossRef]

Oishi, T.

Te. Aoki, Ta. Aoki, M. Fukabori, Y. Tachibana, Y. Zaizen, F. Nishio and T. Oishi, "Spectral albedo observation on the snow field at Barrow, Alaska," Polar Meteorol. Glaciol. 12, 1-9 (1998).

Painter, T. H.

T. H. Painter, D. A. Roberts, R. O. Green, and J. Dozier, "The effect of grain size on spectral mixture analysis of snow-covered area from AVIRIS data," Remote Sens. Environ. 65, 320-332 (1998).
[CrossRef]

Perovich, D. K.

T. C. Grenfell, D. K. Perovich, and J. A. Ogren, "Spectral albedos of an alpine snowpack," Cold Regions Sci. Technol. 4, 121-127 (1981).
[CrossRef]

Pougatch, E.

C. Sergent, C. Leroux, E. Pougatch, and F. Guirado, "Hemispherical-directional reflectance measurements of natural snow in the 0.9-1.45 μm spectral range: comparison with adding-doubling modeling," Ann. Glaciol. 26, 59-63 (1998).

Ramaswamy, V.

P. Chýlek, V. Ramaswamy, and V. Srivastava, "Albedo of soot-contaminated snow," J. Geophys. Res. 88, 10837-10843 (1983).
[CrossRef]

Roberts, D. A.

T. H. Painter, D. A. Roberts, R. O. Green, and J. Dozier, "The effect of grain size on spectral mixture analysis of snow-covered area from AVIRIS data," Remote Sens. Environ. 65, 320-332 (1998).
[CrossRef]

Roeckner, E.

T. P. Barnett, L. Dümenil, U. Schlese, E. Roeckner, and M. Latif, "The effect of Eurasian snow cover on regional and global climate variations," J. Atmos. Sci. 46, 661-685 (1989).
[CrossRef]

Schlese, U.

T. P. Barnett, L. Dümenil, U. Schlese, E. Roeckner, and M. Latif, "The effect of Eurasian snow cover on regional and global climate variations," J. Atmos. Sci. 46, 661-685 (1989).
[CrossRef]

Sergent, C.

C. Sergent, C. Leroux, E. Pougatch, and F. Guirado, "Hemispherical-directional reflectance measurements of natural snow in the 0.9-1.45 μm spectral range: comparison with adding-doubling modeling," Ann. Glaciol. 26, 59-63 (1998).

C. Leroux, J. Deuzé, P. Goloub, C. Sergent, and M. Fily, "Ground measurements of the polarized bidirectional reflectance of snow in the near-infrared spectrum domain: Comparisons with model results," J. Geophys. Res. 103, 19,721-19,731 (1998).
[CrossRef]

M. Fily, B. Bourdelles, J. P. Dedieu, and C. Sergent, "Comparison of in situ and Landsat Thematic Mapper derived snow grain characteristics in the Alps," Remote Sens. Environ. 59, 452-460 (1997).
[CrossRef]

Shuter, V.

Siogas, L.

M. Kuhn and L. Siogas, "Spectroscopic studies at McMurdo, South Pole, and Siple Stations during the austral summer 1977-1978," Antarct. J. U. S. 13, 178-179 (1978).

Sorensen, J. A.

Srivastava, V.

P. Chýlek, V. Ramaswamy, and V. Srivastava, "Albedo of soot-contaminated snow," J. Geophys. Res. 88, 10837-10843 (1983).
[CrossRef]

Stamnes, K.

M. Hori, Te. Aoki, K. Stamnes, B. Chen, and W. Li, "Preliminary validation of the GLI cryosphere algorithms with MODIS daytime data," Polar Meteorol. Glaciol. 15, 1-20 (2001).

Sydor, M.

Tachibana, Y.

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, "Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface," J. Geophys. Res. 105, 10219-10236 (2000).
[CrossRef]

Te. Aoki, Ta. Aoki, M. Fukabori, Y. Tachibana, Y. Zaizen, F. Nishio and T. Oishi, "Spectral albedo observation on the snow field at Barrow, Alaska," Polar Meteorol. Glaciol. 12, 1-9 (1998).

Tamura, R.

T. Nakamura, O. Abe, T. Hasegawa, R. Tamura, and T. Ohta, "Spectral reflectance of snow with a known grain-size distribution in successive metamorphism," Cold Regions Sci. Technol. 32, 13-26 (2001).
[CrossRef]

Tanikawa, T.

T. Tanikawa, Te. Aoki, and F. Nishio, "Remote sensing of snow grain size and snow impurities from Airborne Multispectral Scanner data using a snow bidirectional reflectance distribution function model," Ann. Glaciol. 34, 74-80 (2002).
[CrossRef]

Travis, L. D.

Warren, S. G.

T. C. Grenfell and S. G. Warren, "Relationship of a nonspherical ice particle by a collection of independent sphere for scattering and absorption of radiation," J. Geophys. Res. 104, 31,697-31,709 (1999).
[CrossRef]

T. C. Grenfell, S. G. Warren, and P. C. Mullen, "Reflection of solar radiation by the Antarctic snow surface at ultraviolet, visible, and near-infrared wavelengths," J. Geophys. Res. 99, 18669-18684 (1994).
[CrossRef]

S. G. Warren, "Optical constants of ice from the ultraviolet to microwave," Appl. Opt. 23, 1206-1225 (1984).
[CrossRef] [PubMed]

S. G. Warren, "Optical properties of snow," Rev. Geophys. Space Phys. 20, 67-89 (1982).
[CrossRef]

W. J. Wiscombe and S. G. Warren, "A model for the spectral albedo of snow. I. Pure snow," J. Atmos. Sci. 37, 2712-2733 (1980).
[CrossRef]

S. G. Warren and W. J. Wiscombe, "A model for the spectral albedo of snow. II. Snow containing atmospheric aerosols," J. Atmos. Sci. 37, 2734-2745 (1980).
[CrossRef]

Wiscombe, W. J.

S. G. Warren and W. J. Wiscombe, "A model for the spectral albedo of snow. II. Snow containing atmospheric aerosols," J. Atmos. Sci. 37, 2734-2745 (1980).
[CrossRef]

W. J. Wiscombe and S. G. Warren, "A model for the spectral albedo of snow. I. Pure snow," J. Atmos. Sci. 37, 2712-2733 (1980).
[CrossRef]

Xu, Y.-I.

Y.-I. Xu and N. Khlebtsov, "Orientation-averaged radiative properties of an arbitrary configuration of scatterers," J. Quant. Spectrosc. Radiat. Transf. 79-80, 1121-1137 (2003).
[CrossRef]

Y.-I. Xu, "Electromagnetic scattering by an aggregate of spheres," Appl. Opt. 34, 4573-4588 (1995).
[CrossRef] [PubMed]

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).

Yanovotskij, E. G.

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovotskij, and N. T. Zakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Radiat. Transf. 63, 409-432 (1999).
[CrossRef]

Zaizen, Y.

Te. Aoki, Ta. Aoki, M. Fukabori, Y. Tachibana, Y. Zaizen, F. Nishio and T. Oishi, "Spectral albedo observation on the snow field at Barrow, Alaska," Polar Meteorol. Glaciol. 12, 1-9 (1998).

Zakharova, N. T.

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovotskij, and N. T. Zakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Radiat. Transf. 63, 409-432 (1999).
[CrossRef]

Zege, E. P.

Ann. Glaciol.

B. Bourdelles and M. Fily, "Snow grain-size determination from Landsat imagery over Terre Adélie, Antarctica," Ann. Glaciol. 17, 86-92 (1993).

T. Tanikawa, Te. Aoki, and F. Nishio, "Remote sensing of snow grain size and snow impurities from Airborne Multispectral Scanner data using a snow bidirectional reflectance distribution function model," Ann. Glaciol. 34, 74-80 (2002).
[CrossRef]

C. Sergent, C. Leroux, E. Pougatch, and F. Guirado, "Hemispherical-directional reflectance measurements of natural snow in the 0.9-1.45 μm spectral range: comparison with adding-doubling modeling," Ann. Glaciol. 26, 59-63 (1998).

Antarct. J. U. S.

M. Kuhn and L. Siogas, "Spectroscopic studies at McMurdo, South Pole, and Siple Stations during the austral summer 1977-1978," Antarct. J. U. S. 13, 178-179 (1978).

Appl. Opt.

Cold Regions Sci. Technol.

T. C. Grenfell, D. K. Perovich, and J. A. Ogren, "Spectral albedos of an alpine snowpack," Cold Regions Sci. Technol. 4, 121-127 (1981).
[CrossRef]

T. Nakamura, O. Abe, T. Hasegawa, R. Tamura, and T. Ohta, "Spectral reflectance of snow with a known grain-size distribution in successive metamorphism," Cold Regions Sci. Technol. 32, 13-26 (2001).
[CrossRef]

Contrib. Atmos. Phys.

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

J. Atmos. Sci.

W. J. Wiscombe and S. G. Warren, "A model for the spectral albedo of snow. I. Pure snow," J. Atmos. Sci. 37, 2712-2733 (1980).
[CrossRef]

S. G. Warren and W. J. Wiscombe, "A model for the spectral albedo of snow. II. Snow containing atmospheric aerosols," J. Atmos. Sci. 37, 2734-2745 (1980).
[CrossRef]

T. P. Barnett, L. Dümenil, U. Schlese, E. Roeckner, and M. Latif, "The effect of Eurasian snow cover on regional and global climate variations," J. Atmos. Sci. 46, 661-685 (1989).
[CrossRef]

J. Geophys. Res.

Te. Aoki, A. Hachikubo, and M. Hori, "Effects of snow physical parameters on shortwave broadband albedos," J. Geophys. Res. 108, 101029 (2003).
[CrossRef]

P. Chýlek, V. Ramaswamy, and V. Srivastava, "Albedo of soot-contaminated snow," J. Geophys. Res. 88, 10837-10843 (1983).
[CrossRef]

T. C. Grenfell, S. G. Warren, and P. C. Mullen, "Reflection of solar radiation by the Antarctic snow surface at ultraviolet, visible, and near-infrared wavelengths," J. Geophys. Res. 99, 18669-18684 (1994).
[CrossRef]

T. C. Grenfell and S. G. Warren, "Relationship of a nonspherical ice particle by a collection of independent sphere for scattering and absorption of radiation," J. Geophys. Res. 104, 31,697-31,709 (1999).
[CrossRef]

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, "Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface," J. Geophys. Res. 105, 10219-10236 (2000).
[CrossRef]

C. Leroux, J. Deuzé, P. Goloub, C. Sergent, and M. Fily, "Ground measurements of the polarized bidirectional reflectance of snow in the near-infrared spectrum domain: Comparisons with model results," J. Geophys. Res. 103, 19,721-19,731 (1998).
[CrossRef]

J. Glaciol.

T. C. Grenfell and G. A. Maykut, "The optical properties of ice and snow in the Arctic basin," J. Glaciol. 18, 445-463 (1977).

T. C. Grenfell, "A visible and near-infrared scanning photometer for field measurements of spectral albedo and irradiance under polar conditions," J. Glaciol. 27, 476-481 (1981).

J. Meteorol. Soc. Jpn.

H. Motoyoshi, Te. Aoki, M. Hori, O. Abe, and S. Mochizuki, "Possible effect of anthropogenic aerosol deposition on snow albedo reduction at Shinjo, Japan," J. Meteorol. Soc. Jpn. 83, 137-148 (2005).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transf.

Y.-I. Xu and N. Khlebtsov, "Orientation-averaged radiative properties of an arbitrary configuration of scatterers," J. Quant. Spectrosc. Radiat. Transf. 79-80, 1121-1137 (2003).
[CrossRef]

M. I. Mishchenko, "Asymmetry parameters of the phase function for densely packed scattering grains," J. Quant. Spectrosc. Radiat. Transf. 52, 95-110 (1994).
[CrossRef]

M. I. Mishchenko and A. Macke, "Asymmetry parameters of the phase function for isolated and densely packed spherical particles with multiple internal inclusions in the geometric optics limit," J. Quant. Spectrosc. Radiat. Transf. 57, 767-794 (1997).
[CrossRef]

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovotskij, and N. T. Zakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Radiat. Transf. 63, 409-432 (1999).
[CrossRef]

Polar Meteorol. Glaciol.

M. Hori, Te. Aoki, K. Stamnes, B. Chen, and W. Li, "Preliminary validation of the GLI cryosphere algorithms with MODIS daytime data," Polar Meteorol. Glaciol. 15, 1-20 (2001).

Te. Aoki, Ta. Aoki, M. Fukabori, Y. Tachibana, Y. Zaizen, F. Nishio and T. Oishi, "Spectral albedo observation on the snow field at Barrow, Alaska," Polar Meteorol. Glaciol. 12, 1-9 (1998).

Proc. Natl. Acad. Sci. USA

J. Hansen and L. Nazarenko, "Soot climate forcing via snow and ice albedos," Proc. Natl. Acad. Sci. USA 101, 423-428 (2004).
[CrossRef]

Remote Sens. Environ.

A. W. Nolin and J. Dozier, "A hyperspectral method for remotely sensing the grain size of snow," Remote Sens. Environ. 74, 207-216 (2000).
[CrossRef]

M. Fily, B. Bourdelles, J. P. Dedieu, and C. Sergent, "Comparison of in situ and Landsat Thematic Mapper derived snow grain characteristics in the Alps," Remote Sens. Environ. 59, 452-460 (1997).
[CrossRef]

T. H. Painter, D. A. Roberts, R. O. Green, and J. Dozier, "The effect of grain size on spectral mixture analysis of snow-covered area from AVIRIS data," Remote Sens. Environ. 65, 320-332 (1998).
[CrossRef]

Rev. Geophys. Space Phys.

S. G. Warren, "Optical properties of snow," Rev. Geophys. Space Phys. 20, 67-89 (1982).
[CrossRef]

Science

P. Ya. Groisman, T. R. Karl, and R. W. Knight, "Observed impact of snow cover on the heat balance and the rise of continental spring temperatures," Science 263, 198-200 (1994).
[CrossRef] [PubMed]

Other

Intergovernmental Panel for Climate Change (IPCC),Climate Change 2001: The Scientific Basis: Contribution of Working Group I to the Third Assessment Report of the International Panel on Climate Change (Cambridge U. Press, 2001).

G. H. Liljequist, "Energy exchange of an Antarctic snow field: Short-wave radiation (Maudheim 71°03′S, 10°56′W)," in Norwegian-British-Swedish Antarctic Expedition, 1949-1952, Scientific Results (Norsk Polarinstitutt, 1956), Vol. 2, part 1A.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

A. A. Kokhanovsky, Optics of Light Scattering Media: Problems and Solutions (Wiley, 1998).

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, and B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics (Springer, 1980).

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Figures (9)

Fig. 1
Fig. 1

(Color online) (a) Photographs of the cold laboratory, albedo observation system, and WRS. (b) Schematic illustration of the instrument setup for the snow container and light source in the cold laboratory. The snow was produced by an artificial snowfall system, which was set beneath the ceiling of the cold laboratory. The snow lies on a 3 m × 5 m snow container with a metal wall 0.2 m high. The light source moves above the snow container when the optical measurement is made. Parameters are snow depth d and height h of WRS above the snow surface. The WRS (6 × 6 cm) is placed at h = 10 cm above the snow surface and positioned 1 m from the side of the snow container.

Fig. 2
Fig. 2

(Color online) Directivity of the light intensity emitted from a lamp as a function of the emitted zenith angle Θ L , which is normalized by the intensity at the nadir (Θ L = 0°). There is almost no spectral dependence of directivity.

Fig. 3
Fig. 3

(Color online) Micrographs of artificial snow crystals: (a) spherical particles (case S) and (b) dendrites (case D).

Fig. 4
Fig. 4

Vertical profiles of snow parameters observed during snow pit work for (a) spherical particles (case S) and (b) dendrites (case D). S and D in snow type mean spherical particles and dendrites, respectively. The snow grain size was measured at a 10 μm resolution using a handheld lens. There were two grain size dimensions: one half the length of the major axis of the dendrites or a cluster of aggregated spherical grains (r 1), and one half the branch width of the dendrites or each spherical particle (r 2). The lower part, designated by a black bar of snow layers from the bottom to 20 cm, was enclosed by a metal wall, while the upper part was exposed.

Fig. 5
Fig. 5

Observed spectral albedos for spherical particles (case S) and dendrites (case D), difference of spectral albedos for cases S and D, and theoretically calculated albedos by using DA-RTM for case S (r eff = 10, 20, and 50 μm). The observed spectral albedos were obtained by averaging five spectral albedos calculated from five pairs of measurements for downward and upward fluxes.

Fig. 6
Fig. 6

Comparison between the observed spectral albedos for spherical particles (case S) and theoretically calculated albedos using MC-RTM for spherical particles with r eff = 10, 20, and 50 μm. The latter were calculated with a two-snow-layer model (first layer surface to 5 cm; second layer 5–31 cm), under the same conditions as those in Fig. 1.

Fig. 7
Fig. 7

Comparison between measured spectral albedos for dendrites (case D) and theoretically calculated albedos using MC-RTM for the five kinds of cylindrical ice particles (unit: μm) listed in Table 2. The latter were calculated with a two-snow-layer model (first layer surface to 31.5 cm; second layer 31.5–57 cm), under the same conditions as those in Fig. 1.

Fig. 8
Fig. 8

Comparison of theoretically calculated albedos by using DA-RTM and MC-RTM for r eff = 20 μm (case S). The observed albedos are also provided for reference. The circle indicates the calculated albedo under the assumption that the snow wall is completely covered by a metal wall (MC-RTM1), and the cross indicates the assumption of real instrument conditions, under which the snow wall is not completely covered by the snow container (MC-RTM2), as described in Fig. 1.

Fig. 9
Fig. 9

Theoretically calculated albedos using MC-RTM as a function of the WRS's height h for the snow with spherical particles of r eff = 20 μm.

Tables (2)

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Table 1 Results of Micrograph Measurements of the Dendrites

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Table 2 Radius of the Equal V A Sphere r VA Determined by Assuming the Snow Grains to be Circular Cylinders

Equations (124)

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λ = 0.35 2.5 μm
10%
15   ° C
3   m × 5   m
0 .2   m
3 .2   m × 5 .7   m
300   W   m 2
3.3   m
20 ° C
57   cm
31 .5   cm
10   μm
( r 1 )
( r 2 )
r 1
r 2
5   cm
10 30   μm
5   cm
20 40   μm
( 0 31 .5   cm )
r 1 < 500   μm
r 2 = 10 30   μm
( 31 .5 57   cm )
16 ° C
λ = 0.35 2.5 μm ,
3   nm
λ =0 .35 1 .0   μm
10   nm
λ =1 .0 2 .5   μm
( 6   cm × 6   cm )
10   cm
1   m
r = 10   μm
λ = 0.55   μm
r = 15   μm
λ = 2.2   μm
λ = 0.55   μm
λ = 2.2   μm
r V = 14.4 , 25.6
32.3   μm
λ = 0.55   μm
λ = 2.2   μm
ω ˜ S = 0.977
ω ˜ C 3 = 0.974
ω ˜ C 5 = 0.972
ω ˜ C 10 = 0.961
α C
α S
50 °
( α S α C ) / α S × 100
0.03 %
λ = 0.55   μm
1.43 %
2.70 %
14.36 %
λ = 2.2   μm
0 .35 λ 1 .4   μm
λ   1 .45   μm
( λ = 0.35
2.2   μm)
λ = 1.5
2.0   μm
α > 0 .95
λ = 0.55   μm
r eff = 10
50   μm
31   cm
0 .155   g / cm 3
r eff = 20   μm
λ 1.4   μm
λ < 1.4   μm
r eff
( r eff = 10
50   μm
d s = 5   cm
ρ s = 0.155 g / cm 3
d s = 26   cm
ρ ¯ s = 0.276 g / cm 3
ρ ¯ s
r eff = 20   μm
r 2
( 10 30   μm )
r 2
189.3   μm
d s = 31.5   cm
ρ ¯ s = 0.033 g / cm 3
ρ ¯ s
d s = 25.5   cm
ρ s = 0.272 g / cm 3
d s
ρ s
λ = 1.5 2.2   μm
R = 14   μm
380   μm
R = 14   μm
( 14 .2   μm )
( 189.3   μm )
( L R )
R = 14   μm
r 2 ( 10 30   μm )
( V / A )
V / A
V / A
r V A
r V A = 3 R L 2 ( R + L ) .
r V A 20   μm
( 14   μm )
r 2 ( 10 30   μm )
r eff
20   μm
r V A 20   μm
V / A
r 2
λ = 0.35 2.5   μm
20   μm
V / A
18 20   μm
r 2
h = 12 15   cm
h M
h < h M
h > h M
h > h M

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