Abstract

Permanent snow and ice cover great portions of the Arctic and the Antarctic. It appears in winter months in northern parts of America, Asia, and Europe. Therefore snow is an important component of the hydrological cycle. Also, it is a main regulator of the seasonal variation of the planetary albedo. This seasonal change in albedo is determined largely by the snow cover. However, the presence of pollutants and the microstructure of snow (e.g., the size and shape of grains, which depend also on temperature and on the age of the snow) are also of importance in the variation of the snow’s spectral albedo. The snow’s spectral albedo and its bidirectional reflectance are studied theoretically. The albedo also determines the spectral absorptance of snow, which is of importance, e.g., in studies of the heating regime in snow. We investigate the influence of the nonspherical shape of grains and of close-packed effects on snow’s reflectance in the visible and the near-infrared regions of the electromagnetic spectrum. The rate of the spectral transition from highly reflective snow in the visible to almost totally absorbing black snow in the infrared is governed largely by the snow’s grain sizes and by the load of pollutants. Therefore both the characteristics of snow and its concentration of impurities can be monitored on a global scale by use of spectrometers and radiometers placed on orbiting satellites.

© 2004 Optical Society of America

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2003

A. A. Kokhanovsky, V. V. Rozanov, E. P. Zege, H. Bovensmann, J. P. Burrows, “A semi-analytical cloud retrieval algorithm using backscattering radiation in 04.–2.4 μm spectral range,” J. Geophys. Res. D 108, 10.1029/2001JD001543 (2003).

A. A. Kokhanovsky, “Optical properties of irregularly shaped particles,” J. Appl. Phys. D 36, 915–923 (2003).
[CrossRef]

T. H. Painter, J. Dozier, D. A. Roberts, R. E. Davis, R. O. Green, “Retrieval of subpixel snow-covered area and grain size from imaging spectrometer data,” Remote Sens. Environ. 85, 64–77 (2003).
[CrossRef]

2002

A. A. Kokhanovsky, “Reflection and polarization of light by semi-infinite turbid media: simple approximations,” J. Colloid Interface Sci. 251, 429–431 (2002).
[CrossRef]

A. A. Kokhanovsky, “The accuracy of selected approximations for the reflection function of a semi-infinite turbid medium,” J. Appl. Phys. D 35, 1057–1062 (2002).
[CrossRef]

B. Barkey, M. Bailey, K.-N. Liou, J. Hallett, “Light-scattering properties of plate and column ice crystals generated in a laboratory cold chamber,” Appl. Opt. 41, 5792–5796 (2002).
[CrossRef] [PubMed]

2001

W. Li, K. Stamnes, B. Chen, “Snow grain size retrieved from near-infrared radiances at multiple wavelengths,” Geophys. Res. Lett. 28, 1699–1702 (2001).
[CrossRef]

R. A. Massom, H. Eicken, C. Haas, M. O. Jeffris, M. R. Drinkwater, M. Sturm, A. P. Worby, X. Wu, V. I. Lytle, S. Ushio, K. Morris, P. A. Reid, S. G. Warren, I. Allison, “Snow on Antarctic ice,” Rev. Geophys. 39, 413–445 (2001).
[CrossRef]

T. H. Painter, B. Duval, W. H. Thomas, M. Mendez, S. Heintzelman, J. Dozier, “Detection and quantification of snow algae with an airborne spectrometer,” Appl. Environ. Microbiol. 67, 5267–5272 (2001).
[CrossRef] [PubMed]

G. Horneck, P. Rettberg, G. Reitz, J. Wehner, U. Eschweiler, K. Strauch, C. Panitz, V. Starke, C. Baumstark-Khan, “Protection of bacterial spores in space, a contribution to the discussion on panspermia,” Origins Life Evol. Biosphere 31, 527–547 (2001).
[CrossRef]

2000

G. Horneck, “The microbial world and the case for Mars,” Planet. Space Sci. 48, 1053–1063 (2000).
[CrossRef]

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

V. A. Loiko, G. I. Ruban, “Absorption and scattering of light by a photolayer with closely packed particles,” Opt. Spectrosc. 88, 834–839 (2000).
[CrossRef]

A. W. Nolin, S. Liang, “Progress in bi-directional reflectance modeling and applications for surface particulate media: snow and soils,” Remote Sens. Rev. 18, 307–342 (2000).
[CrossRef]

T. Aoki, T. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, F. Nishio, “Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface,” J. Geophys. Res. 105, 10,219–10,236 (2000).
[CrossRef]

1999

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovitskij, 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. Transfer 63, 409–432 (1999).
[CrossRef]

T. Nousiainen, K. Muinonen, “Light scattering by Gaussian, randomly oscillating raindrops,” J. Quant. Spectrosc. Radiat. Transfer 63, 643–666 (1999).
[CrossRef]

1998

P. Yang, 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, F. Guirado, “Hemispherical-directional reflectance measurements of natural snow in the 0.9–1.45 μm spectral range: comparison with adding-doubling modelling,” Ann. Glaciol. 26, 59–63 (1998).

1997

M. Fily, B. Bourdlles, J. P. Dedieu, 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]

D. Domingue, B. Hartmon, A. Verbiscer, “The scattering properties of natural terrestrial snow versus icy satellite surfaces,” Icarus 128, 28–48 (1997).
[CrossRef]

A. A. Kokhanovsky, A. Macke, “Integral light scattering and absorption characteristics of large nonspherical particles,” Appl. Opt. 36, 8785–8790 (1997).
[CrossRef]

1996

A. Macke, J. Mueller, E. Raschke, “Scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

K. Muinonen, T. Nusiainen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

1994

S. Marshall, R. Oglesby, “An improved snow hydrology for GCMs. 1. Snow cover fraction, albedo, grain size, and age,” Climate Dynam. 10, 21–37 (1994).

T. C. Grenfell, S. G. Warren, P. C. Mullen, “Reflection of solar radiation by the Antarctic snow surface at ultraviolet, visible, and near-infrared wavelengths,” J. Geophys. Res. 99, 18,669–18,684 (1994).
[CrossRef]

1988

T. Aoki, T. Aoki, M. Fukabori, Y. Tachibana, F. Nishio, T. Oishi, “Spectral albedo observation of the snow field at Barrow,” Polar Meteorol. Glaciol. 12, 1–9 (1988).

1987

A. P. Ivanov, S. A. Makarevich, A. Y. Khairullina, “On specific features of radiation propagation in tissues and bioliquids with closely packed particles,” J. Appl. Spectrosc. 47, 662–668 (1987).
[CrossRef]

1984

1983

C. F. Bohren, “Colors of snow, frozen waterfalls, and icebergs,” J. Opt. Soc. Am. 12, 1646–1651 (1983).
[CrossRef]

1982

S. G. Warren, “Optical properties of snow,” Rev. Geophys. Space Phys. 2, 67–89 (1982).
[CrossRef]

1981

W. J. Wiscombe, S. G. Warren, “A model for the spectral albedo of snow. I. Pure snow,” J. Geophys. Res. 37, 2712–2733 (1981).

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

1979

C. F. Bohren, R. L. Beschta, “Snowpack albedo and snow density,” Cold Regions Sci. Technol. 1, 47–50 (1979).
[CrossRef]

1974

C. F. Bohren, B. R. Barkstrom, “Theory of the optical properties of snow,” J. Geophys. Res. 79, 4527–4535 (1974).
[CrossRef]

1962

G. V. Rozenberg, “Optical characteristics of thick weakly absorbing scattering layers,” Dokl. Akad. Nauk SSSR 145, 775–777 (1962).

1955

R. C. Hubley, “Measurement of diurnal variations in snow albedo on Lemon Greek Glacier, Alaska,” J. Glaciol. 2, 560–563 (1955).
[CrossRef]

1952

Allison, I.

R. A. Massom, H. Eicken, C. Haas, M. O. Jeffris, M. R. Drinkwater, M. Sturm, A. P. Worby, X. Wu, V. I. Lytle, S. Ushio, K. Morris, P. A. Reid, S. G. Warren, I. Allison, “Snow on Antarctic ice,” Rev. Geophys. 39, 413–445 (2001).
[CrossRef]

Aoki, T.

T. Aoki, T. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, F. Nishio, “Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface,” J. Geophys. Res. 105, 10,219–10,236 (2000).
[CrossRef]

T. Aoki, T. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, F. Nishio, “Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface,” J. Geophys. Res. 105, 10,219–10,236 (2000).
[CrossRef]

T. Aoki, T. Aoki, M. Fukabori, Y. Tachibana, F. Nishio, T. Oishi, “Spectral albedo observation of the snow field at Barrow,” Polar Meteorol. Glaciol. 12, 1–9 (1988).

T. Aoki, T. Aoki, M. Fukabori, Y. Tachibana, F. Nishio, T. Oishi, “Spectral albedo observation of the snow field at Barrow,” Polar Meteorol. Glaciol. 12, 1–9 (1988).

Bailey, M.

Barkey, B.

Barkstrom, B. R.

C. F. Bohren, B. R. Barkstrom, “Theory of the optical properties of snow,” J. Geophys. Res. 79, 4527–4535 (1974).
[CrossRef]

Baumstark-Khan, C.

G. Horneck, P. Rettberg, G. Reitz, J. Wehner, U. Eschweiler, K. Strauch, C. Panitz, V. Starke, C. Baumstark-Khan, “Protection of bacterial spores in space, a contribution to the discussion on panspermia,” Origins Life Evol. Biosphere 31, 527–547 (2001).
[CrossRef]

Beschta, R. L.

C. F. Bohren, R. L. Beschta, “Snowpack albedo and snow density,” Cold Regions Sci. Technol. 1, 47–50 (1979).
[CrossRef]

Bohren, C. F.

C. F. Bohren, “Colors of snow, frozen waterfalls, and icebergs,” J. Opt. Soc. Am. 12, 1646–1651 (1983).
[CrossRef]

C. F. Bohren, R. L. Beschta, “Snowpack albedo and snow density,” Cold Regions Sci. Technol. 1, 47–50 (1979).
[CrossRef]

C. F. Bohren, B. R. Barkstrom, “Theory of the optical properties of snow,” J. Geophys. Res. 79, 4527–4535 (1974).
[CrossRef]

Bourdlles, B.

M. Fily, B. Bourdlles, J. P. Dedieu, 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]

Bovensmann, H.

A. A. Kokhanovsky, V. V. Rozanov, E. P. Zege, H. Bovensmann, J. P. Burrows, “A semi-analytical cloud retrieval algorithm using backscattering radiation in 04.–2.4 μm spectral range,” J. Geophys. Res. D 108, 10.1029/2001JD001543 (2003).

Burrows, J. P.

A. A. Kokhanovsky, V. V. Rozanov, E. P. Zege, H. Bovensmann, J. P. Burrows, “A semi-analytical cloud retrieval algorithm using backscattering radiation in 04.–2.4 μm spectral range,” J. Geophys. Res. D 108, 10.1029/2001JD001543 (2003).

Chen, B.

W. Li, K. Stamnes, B. Chen, “Snow grain size retrieved from near-infrared radiances at multiple wavelengths,” Geophys. Res. Lett. 28, 1699–1702 (2001).
[CrossRef]

Davis, R. E.

T. H. Painter, J. Dozier, D. A. Roberts, R. E. Davis, R. O. Green, “Retrieval of subpixel snow-covered area and grain size from imaging spectrometer data,” Remote Sens. Environ. 85, 64–77 (2003).
[CrossRef]

Dedieu, J. P.

M. Fily, B. Bourdlles, J. P. Dedieu, 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]

Dik, V. P.

A. P. Ivanov, V. A. Loiko, V. P. Dik, Light Propagation in Close-Packed Media (Nauka i Tekhnika, Minsk, Belarus, 1988).

Dlugach, J. M.

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovitskij, 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. Transfer 63, 409–432 (1999).
[CrossRef]

Domingue, D.

D. Domingue, B. Hartmon, A. Verbiscer, “The scattering properties of natural terrestrial snow versus icy satellite surfaces,” Icarus 128, 28–48 (1997).
[CrossRef]

Dozier, J.

T. H. Painter, J. Dozier, D. A. Roberts, R. E. Davis, R. O. Green, “Retrieval of subpixel snow-covered area and grain size from imaging spectrometer data,” Remote Sens. Environ. 85, 64–77 (2003).
[CrossRef]

T. H. Painter, B. Duval, W. H. Thomas, M. Mendez, S. Heintzelman, J. Dozier, “Detection and quantification of snow algae with an airborne spectrometer,” Appl. Environ. Microbiol. 67, 5267–5272 (2001).
[CrossRef] [PubMed]

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

Drinkwater, M. R.

R. A. Massom, H. Eicken, C. Haas, M. O. Jeffris, M. R. Drinkwater, M. Sturm, A. P. Worby, X. Wu, V. I. Lytle, S. Ushio, K. Morris, P. A. Reid, S. G. Warren, I. Allison, “Snow on Antarctic ice,” Rev. Geophys. 39, 413–445 (2001).
[CrossRef]

Duval, B.

T. H. Painter, B. Duval, W. H. Thomas, M. Mendez, S. Heintzelman, J. Dozier, “Detection and quantification of snow algae with an airborne spectrometer,” Appl. Environ. Microbiol. 67, 5267–5272 (2001).
[CrossRef] [PubMed]

Eicken, H.

R. A. Massom, H. Eicken, C. Haas, M. O. Jeffris, M. R. Drinkwater, M. Sturm, A. P. Worby, X. Wu, V. I. Lytle, S. Ushio, K. Morris, P. A. Reid, S. G. Warren, I. Allison, “Snow on Antarctic ice,” Rev. Geophys. 39, 413–445 (2001).
[CrossRef]

Eschweiler, U.

G. Horneck, P. Rettberg, G. Reitz, J. Wehner, U. Eschweiler, K. Strauch, C. Panitz, V. Starke, C. Baumstark-Khan, “Protection of bacterial spores in space, a contribution to the discussion on panspermia,” Origins Life Evol. Biosphere 31, 527–547 (2001).
[CrossRef]

Fast, P.

K. Muinonen, T. Nusiainen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

Fily, M.

M. Fily, B. Bourdlles, J. P. Dedieu, 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]

Fukabori, M.

T. Aoki, T. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, F. Nishio, “Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface,” J. Geophys. Res. 105, 10,219–10,236 (2000).
[CrossRef]

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T. H. Painter, B. Duval, W. H. Thomas, M. Mendez, S. Heintzelman, J. Dozier, “Detection and quantification of snow algae with an airborne spectrometer,” Appl. Environ. Microbiol. 67, 5267–5272 (2001).
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