A three‐dimensional microstructure‐based photon‐tracking model of radiative transfer in snow

[1] Solar radiation is a key component of the energy budget of snow-covered landscapes. Even a thin snow cover reflects most of the incident sunlight and transmits little. An understanding of the interaction of solar radiation with snow is essential to the study of the snow thermodynamics, chemistry, hydrology, ecology, and remote sensing. To investigate this interaction, a microstructure-based photon-tracking algorithm is presented. The three-dimensional snow microstructure is provided either by a discrete element model defined by shape, size, and spatial arrangement of individual ice grains or by an X-ray microtomography image of a snowpack. The model uses refraction, Fresnel reflection, and absorption laws, and the only optical input parameters are the complex index of refraction and absorption coefficient. The model follows individual photons through the microstructure, a porous network of ice and air, applying the fundamental optics laws at the ice-air interfaces and within the ice. By firing tens of thousands of photons a detailed examination of the spectral radiance and irradiance above, below, and within the snowpack is possible. The model was compared to results from a discrete ordinates model, and its sensitivity to the microstructural representation was studied. It was applied to investigate changes in reflected, absorbed, and transmitted light as a function of wavelength, snow depth, grain size, and snow density, used to predict the amount and direction of scattering within the snowpack, and used to explore the interaction of a collimated beam with snow.

[1]  S. Warren,et al.  A Model for the Spectral Albedo of Snow. II: Snow Containing Atmospheric Aerosols , 1980 .

[2]  J. B. Ørbæk,et al.  Attenuation of solar radiation in Arctic snow: field observations and modelling , 2000, Annals of Glaciology.

[3]  M. Kuhn.  Bidirectional Reflectance of Polar and Alpine Snow Surfaces , 1985 .

[4]  Sergey A. Sokratov,et al.  A microstructural approach to model heat transfer in snow , 2005 .

[5]  K. Baker,et al.  Ozone depletion: ultraviolet radiation and phytoplankton biology in antarctic waters. , 1992, Science.

[6]  Thomas C. Grenfell,et al.  Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation: 2. Hexagonal columns and plates , 2003 .

[7]  K. Stamnes,et al.  Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media. , 1988, Applied optics.

[8]  Thomas C. Grenfell,et al.  A radiative transfer model for sea ice with vertical structure variations , 1991 .

[9]  Mark A. Hopkins,et al.  Identifying microstructural deformation mechanisms in snow using discrete-element modeling , 2005, Journal of Glaciology.

[10]  S. Warren,et al.  Solar-heating rates and temperature profiles in Antarctic snow and ice , 1993, Journal of Glaciology.

[11]  S. Warren,et al.  Optical constants of ice from the ultraviolet to the microwave. , 1984, Applied optics.

[12]  Rune Solberg,et al.  Subpixel mapping of snow cover in forests by optical remote sensing , 2003 .

[13]  A. Jones,et al.  Modelling photochemical NOX production and nitrate loss in the upper snowpack of Antarctica , 2002 .

[14]  Cécile Coléou,et al.  Three-dimensional snow images by X-ray microtomography , 2001, Annals of Glaciology.

[15]  Teruo Aoki,et al.  Effects of snow physical parameters on spectral albedo and bidirectional reflectance of snow surface , 2000 .

[16]  N. DiGirolamo,et al.  MODIS snow-cover products , 2002 .

[17]  Roger G. Barry,et al.  The parameterization of surface albedo for sea ice and its snow cover , 1996 .

[18]  A. Macke,et al.  Single Scattering Properties of Atmospheric Ice Crystals , 1996 .

[19]  G. Groot Gregory,et al.  Edge diffraction in Monte Carlo ray tracing , 1999, Optics + Photonics.

[20]  A. Ohmura,et al.  A field study of the hemispherical directional reflectance factor and spectral albedo of dry snow , 2006 .

[21]  M. Pinar Mengüç,et al.  A Monte Carlo ray tracing study of polarized light propagation in liquid foams , 2007 .

[22]  R. Huiskes,et al.  A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. , 1995, Journal of biomechanics.

[23]  R. V. Dunkle,et al.  AN APPROXIMATE ANALYSIS OF THE SOLAR REFLECTANCE AND TRANSMITTANCE OF A SNOW COVER , 1956 .

[24]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[25]  T. Painter,et al.  Measurements of the hemispherical-directional reflectance of snow at fine spectral and angular resolution , 2004 .

[26]  Robert G. Greenler,et al.  Rainbows, halos, and glories , 1980 .

[27]  P. Kaye,et al.  A 3D implementation of ray tracing combined with diffraction on facets: Verification and a potential application , 2006 .

[28]  B. Duval,et al.  Sierra Nevada, California, U.S.A., Snow Algae: Snow albedo changes, algal-bacterial interrelationships and ultraviolet radiation effects , 1995 .

[29]  S. Warren,et al.  Reflection of solar radiation by the Antarctic snow surface at ultraviolet, visible, and near‐infrared wavelengths , 1994 .

[30]  S. Warren,et al.  Spectral Bidirectional Reflectance of Antarctic Snow: Measurements and Parameterization , 2006 .

[31]  S. Warren,et al.  Visible and near-ultraviolet absorption spectrum of ice from transmission of solar radiation into snow. , 2006, Applied optics.

[32]  J. W. Govoni,et al.  Absorption coefficients of ice from 250 to 400 nm , 1991 .

[33]  Bruce R. Barkstrom,et al.  Theory of the optical properties of snow , 1974 .

[34]  John J. Kelley,et al.  On the Albedo of Snow in Antarctica: A Contribution to I.A.G.O. , 1988, Journal of Glaciology.

[35]  Z. Kam,et al.  Absorption and Scattering of Light by Small Particles , 1998 .

[36]  S. Madronich,et al.  Effects of snow cover on UV irradiance and surface albedo: A case study , 1998 .

[37]  Yoshihide Takano,et al.  Radiative Transfer in Cirrus Clouds. Part III: Light Scattering by Irregular Ice Crystals , 1995 .

[38]  T. Painter,et al.  Reflectance quantities in optical remote sensing - definitions and case studies , 2006 .

[39]  Donald K. Perovich,et al.  Radiation absorption coefficients of polycrystalline ice from 400–1400 nm , 1981 .

[40]  F. E. Nicodemus,et al.  Geometrical considerations and nomenclature for reflectance , 1977 .

[41]  D. Baillis,et al.  Radiative characteristics of beds made of large spheres containing an absorbing and scattering medium , 2005 .

[42]  Stephen G. Warren,et al.  Optical Properties of Snow , 1982 .

[43]  Thomas H. Painter,et al.  Measuring the expressed abundance of the three phases of water with an imaging spectrometer over melting snow , 2006 .

[44]  Thomas C. Grenfell,et al.  Representation of a nonspherical ice particle by a collection of independent spheres for scattering , 1999 .

[45]  Z. Ulanowski,et al.  Scattering from long prisms computed using ray tracing combined with diffraction on facets , 2003 .

[46]  Michael I. Mishchenko,et al.  Bidirectional Reflectance of Flat, Optically Thick Particulate Layers: An Efficient Radiative Transfer Solution and Applications to Snow and Soil Surfaces , 1999 .

[47]  Cécile Coléou,et al.  Full three-dimensional modelling of curvature-dependent snow metamorphism: first results and comparison with experimental tomographic data , 2003 .

[48]  A. G. Mungall,et al.  The Luminous Directional Reflectance of Snow , 1952 .

[49]  A. Nolin,et al.  The changing albedo of the Greenland ice sheet: implications for climate modeling , 1997, Annals of Glaciology.

[50]  Hjalmar Granberg,et al.  Forward scattering of fiber-containing surfaces studied by 3-D reflectance distribution simulations and measurements , 2003 .

[51]  R. Beschta,et al.  Snowpack albedo and snow density , 1979 .

[52]  Jean Luc Deuze,et al.  Ground measurements of the polarized bidirectional reflectance of snow in the near‐infrared spectral domain: Comparisons with model results , 1998 .

[53]  Stephen G. Warren,et al.  Effect of surface roughness on bidirectional reflectance of Antarctic snow , 1998 .

[54]  D. Beaglehole,et al.  The UV to IR transmittance of Antarctic snow , 1998 .

[55]  J. Dozier,et al.  A Hyperspectral Method for Remotely Sensing the Grain Size of Snow , 2000 .

[56]  T. Painter,et al.  Retrieval of subpixel snow-covered area and grain size from imaging spectrometer data , 2003 .

[57]  S. Warren,et al.  A Model for the Spectral Albedo of Snow. I: Pure Snow , 1980 .

[58]  J. J. Simpson,et al.  Anisotropic Reflectance of Snow Observed from Space over the Arctic and Its Effect on Solar Energy Balance , 2001 .