Abstract
The albedo of snow for different cloudiness conditions is an important parameter in the Earth's radiation budget analysis and in the study of snowpack's thermal conditions. In this study an efficient approximate method is derived to calculate the incident spectral solar flux and snow-cover albedo in terms of different atmospheric, cloud, and snow parameters. The global flux under partially cloudy skies is expressed in terms of the clear sky flux and a coefficient which models the effect of scattering and absorption by cloud patches and multiple reflections between the cloud base and snowcover. The direct and the diffuse components of the clear sky flux are obtained using the spectral flux outside the atmosphere and the spectral transmission coefficients for absorption and scattering by molecules and aerosols.
The spectral snow reflectance model considers both specular surface reflection and volumetric multiple scattering. The surface reflection is calculated by using a crystal-shape-dependent bidirectional reflectance distribution function; the volumetric multiple scattering is calculated by using a crystal-size-dependent approximate solution in the radiative transfer equation. The input parameters to the model are atmospheric precipitable water, ozone content, turbidity, cloud optical thickness, the size and shape of ice crystals of snow and surface pressure. The model yields spectral and integrated solar flux and snow reflectance as a function of solar elevation and fractional cloudcover.
The model is illustrated using representative parameters for the Antarctic coastal regions. The albedo for a clear sky depends inversely on the solar elevation. At high elevations the albedo depends primarily upon the grain size; at low elevation the albedo depends on grain size and shape. The gradient of the albedo-elevation curve increases as the grains become larger and faceted. The albedo for a densely overcast sky is a few percent higher than the clear-sky albedo at high elevations. A simple relationship between grain size and the overcast albedo is obtained. For a set of grain size and shape, the albedo as a function of solar elevation and fractional cloud cover is tabulated.
Similar content being viewed by others
References
Asano, S., Sato, M. and Hansen, J.: 1979, ‘Scattering By Randomly Oriented Ellipsoids: Application to Aerosol and Cloud Problems’, in E. R. Kreins (ed.), Fourth National Aeronautics and Space Administration Weather and Climate Program Science Review, NASA-CP-2076.
Barkstrom, B. R.: 1972, ‘Some Effects of Multiple Scattering On the Distribution of Solar Radiation in Snow and Ice’, J. Glaciol. 11, 357–368.
Barkstrom, B. R. and Querfeld, C. W.: 1975, ‘Concerning the Effect of Anisotropic Scattering and Finite Depth On the Distribution of Solar Radiation in Snow’, J. Glaciol. 14, 107–124.
Bergen, J. D.: 1975, ‘A Possible Relation of Albedo to the Density and Grain Size of Natural Snow Cover’, Water Resources Res. 11, 745–746.
Bohren, C. F. and Barkstrom, B. R.: 1974, ‘Theory of the Optical Properties of Snow’, J. Geophys. Res. 79, 4527–4535.
Bryazgin, N. N. and Koptev, A. P.: 1969, ‘Spectral Albedo of Snow-Ice Cover’, Problemy Arktiki i Antarktiki, 33, 79–83.
Catchpole, A. J. W. and Moodie, D. M.: 1971, ‘Multiple Reflection In Arctic Regions’, Weather 26, 157–163.
Choudhury, B. J.: 1979a, Snow Albedo Variation With Solar Altitude and Fractional Cloud Cover Computer Sciences Corporation, CSC/TR-79/6004.
Choudhury, B. J.: 1979b, On Bidirectional and Directional Solar Reflectance of Snow Computer Sciences Corporation, CSC/TR-79/6017.
Choudhury, B. J.: 1979c, ‘Radiative Properties of Snow for Clear Sky Solar Radiation’, Computer Sciences Corporation, CSC/TR-79/6025 (also Cold Regions Science and Technology, to be published).
Choudhury, B. J. and Chang, A. T. C.: 1979, ‘Two-Stream Theory of Reflectance of Snow’, IEEE Transactions on Geoscience Electronics, GE-17, 63-68.
Choudhury, B. J. and Chang, A. T. C.: 1980, ‘On the Angular Variation of the Solar Reflectance of Snow’, J. Geophys. Research (to be published).
Curran, R. J., Wexler, R. and Nack, M. L.: 1978, Albedo Climatology Analysis and the Determination of Fractional Cloud Cover, Goddard Space Flight Center, NASA-TM-79576.
Cuzzi, J. N. and Pollack, J. B.: 1978, ‘Saturn's Rings: Particle Composition and Size Distribution as Constrained by Microwave Observations’, Icarus 33, 233–262.
Dave, J. V. and Braslau, N.: 1975, ‘Effect of Cloudiness on the Transfer of Solar Energy Through Realistic Model Atmosphere’, J. Appl. Meteorol. 14, 388–395.
Dirmhirn, I. and Eaton, F. D.: 1975, ‘Some Characteristics of the Albedo of Snow’, J. Appl. Meteorol. 14, 375–379.
Dunkle, R. V. and Bevans, J. T.: 1956, ‘An Approximate Analysis of the Solar Reflectance and Transmittance of a Snow Cover’, J. Meteorol. 13, 212–216.
Feigelson, E. M.: 1978, ‘Preliminary Radiation Model of a Cloudy Atmosphere, Part I — Structure of Cloud and Solar Radiation’, Beitrage zur Physik der Atmosphäre 51, 203–229.
Hanson, K. J.: 1960, ‘Radiation Measurement of the Antarctic Snowfields, a Preliminary Report’, J. Geophys. Res. 65, 935–946.
Hahn, D. C. and Shukla, J.: 1976, ‘An Apparent Relationship Between Eurasian Snow Cover and Indian Monsoon Rainfall’, J. Atm. Sci. 33, 2461–2462.
Herman, G. F.: 1977, ‘Solar Radiation in Summertime Arctic Stratus Clouds’, J. Atm. Sci. 34, 1423–1433.
Hobbs, P. V.: 1974, Ice Physics, Oxford, Clarendon Press.
Irvine, W. M. and Pollack, J. B.: 1968, ‘Infrared Optical Properties of Water and Ice Spheres’, Icarus 8, 324–360.
Joseph, J. H., Wiscombe, W. J. and Weinman, J. A.: 1976, ‘The Delta-Eddington Approximation for Radiative Flux Transfer’, J. Atm. Sci. 33, 2452–2459.
Kellogg, W. W.: 1975, ‘Climatic Feedback Mechanisms Involving the Polar Regions’, in G. Weller and S. A. Bowling (eds.) Climate of the Arctic, University of Alaska Press.
Korff, H. C. and Vonder Haar, T. H.: 1972, ‘The Albedo of Snow In Relation to the Sun Position’, Conference On Atmospheric Radiation, Fort Collins, Colorado, American Meteorological Society.
Kukla, G. J. and Kukla, H. J.: 1974, ‘Increased Surface Albedo in the Northern Hemisphere’, Science 183, 709–714.
Lacis, A. A. and Hansen, J. E.: 1974, ‘A Parameterization for the Absorption of Solar Radiation in the Earth's Atmosphere’, J. Atm. Sci. 31, 118–133.
Leckner, B.: 1978, ‘The Spectral Distribution of Solar Radiation at the Earth's Surface-Element of a Model’, Solar Energy, 20, 143–150.
Liljequist, G. H.: 1956, ‘Energy Exchange of an Antarctic Snow-Field; Short-Wave Radiation, in Norwegian-British-Swedish Antarctic Expedition 1949–52’, Scientific Results Vol. 2 part 1A, Norsk Polarinstitute, Oslo, Norway.
McKee, T. B. and Cox, S. K.: 1974, ‘Scattering of Visible Radiation by Finite Clouds’, J. Atm. Sci. 31, 1885–1892.
Mellor, M.: 1977, ‘Engineering Properties of Snow’, J. Glaciol. 19, 15–66.
Middleton, W. E. K. and Mungall, A. G.: 1952, ‘The Luminous Directional Reflectance of Snow’, J. Opt. Soc. America 42, 572–579.
Nieman, R. A.: 1977, A Comparison of Radiosonde Temperature and Humidity Profile Data Bases, Computer Sciences Corporation, CSC/TM-77/6133.
Rango, A.: 1975, Operational Applications of Satellite Snowcover Observations, National Aeronautics and Space Administration, NASA-SP-391.
Robinson, N.: 1966, Solar Radiation pp. 117–120, Elsevier, New York.
Rusin, N. P.: 1964, Meteorological and Radiational Regime of Antarctica, Israel Program for Scientific Translations, Jerusalem, Israel.
Schmetz, J. and Raschke, E.: 1979, ‘An Application of a Two-Stream Approximation to Calculations of the Transfer of Solar Radiation in an Atmosphere with Fractional Cloud Cover’, Contributions to Atmospheric Physics, 52, 151–160.
Schneider, S. H. and Dickinson, R. H.: 1976, ‘Parameterization of Fractional Cloud Amounts in Climate Models: The Importance of Modeling Multiple Reflection’, J. Appl. Meteorol. 15, 1050–1056.
Sivkov, S. I.: 1971, Computation of Solar Radiation Characteristics, Israel Program for Scientific Translation, Jerusalem, Israel.
Sovolev, V. V.: 1975, Light Scattering in Planetary Atmospheres, Chapter 8. Pergamon Press, New York.
Trowbridge, T. S. and Reitz, K. P.: 1975, ‘Average Irregularity Representation of a Rough Surface for Ray Reflection’, J. Opt. Soc. America 65, 531–536.
Vowinckel, E. and Orvig, S.: 1962, ‘Relation Between Solar Radiation Icome and Cloud Type in the Arctic’, J. Appl. Meteorol. 1, 552–559.
Williams, J.: 1975, ‘The Influence of Snowcover on the Atmospheric Circulation and Its Role in Climatic Change’, J. Appl. Meteorol. 14, 137–152.
Wiscombe, W. J.: 1975, ‘Solar Radiation Calculation for Arctic Summer Stratus Conditions’, in G. Weller and S. A. Bowling (eds.) Climate of the Arctic, University of Alaska Press.
Wiscombe, W. J. and Warren, S. G.: 1979, ‘A New Model for the Spectral Albedo of Snow. I: Pure Snow’, National Center for Atmospheric Research, NCAR/0304/79-09.
Wolff, M.: 1975, ‘Polarization of Light Reflected from a Rough Planetary Surface’, Applied Optics 14, 1395–1405.
Zudnkowski, W. G. and Strand, R.: 1969, ‘Light Scattering Constants for a Water Cloud’, Pure Appl. Geophys. 19, 45–66.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Choudhury, B.J., Chang, A.T.C. The albedo of snow for partially cloudy skies. Boundary-Layer Meteorol 20, 371–389 (1981). https://doi.org/10.1007/BF00121380
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00121380