Reflectance Modeling for Real Snow Structures Using a Beam Tracing Model

It is important to understand reflective properties of snow, for example for remote sensing applications and for modeling of energy balances in snow packs. We present a method with which we can compare reflectance measurements and calculations for the same snow sample structures. Therefore, we first tomograph snow samples to acquire snow structure images (6 × 2 mm). Second, we calculated the sample reflectance by modeling the radiative transfer, using a beam tracing model. This model calculates the biconical reflectance (BR) derived from an arbitrary number of incident beams. The incident beams represent a diffuse light source. We applied our method to four different snow samples: Fresh snow, metamorphosed snow, depth hoar, and wet snow. The results show that (i) the calculated and measured reflectances agree well and (ii) the model produces different biconical reflectances for different snow types. The ratio of the structure to the wavelength is large. We estimated that the size parameter is larger than 50 in all cases we analyzed. Specific surface area of the snow samples explains most of the difference in radiance, but not the different biconical reflectance distributions. The presented method overcomes the limitations of common radiative transfer models which use idealized grain shapes such as spheres, plates, needles and hexagonal particles. With this method we could improve our understanding for changes in biconical reflectance distribution associated with changes in specific surface area.

[1]  Jon Holmgren,et al.  Snow-Shrub Interactions in Arctic Tundra: A Hypothesis with Climatic Implications , 2001 .

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

[3]  Reinhard Klette,et al.  Handbuch der Operatoren für die Bildbearbeitung , 1992 .

[4]  Brian Cairns,et al.  Multiple scattering by random particulate media: exact 3D results. , 2007, Optics express.

[5]  A simple snowpack/cloud reflectance and transmittance model from microwave to ultraviolet: the ice-lamella pack , 2000, Journal of Glaciology.

[6]  Martin Wild,et al.  Comparison of spectral surface albedos and their impact on the general circulation model simulated surface climate , 2002 .

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

[8]  Sergey A. Sokratov,et al.  Tomography of temperature gradient metamorphism of snow and associated changes in heat conductivity , 2004 .

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

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

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

[12]  J. Giddings,et al.  Diffusion theory applied to radiant energy distribution and albedo of snow , 1961 .

[13]  David L. Mitchell,et al.  Effective Diameter in Radiation Transfer: General Definition, Applications, and Limitations , 2002 .

[14]  Martin Schneebeli,et al.  Measuring specific surface area of snow by near-infrared photography , 2006 .

[15]  Martin Schneebeli,et al.  Stratigraphy and changes in hardness of snow measured by hand, ramsonde and snow micro penetrometer: a comparison with planar sections , 2003 .

[16]  Jeff Dozier,et al.  Stereological characterization of dry Alpine snow for microwave remote sensing , 1989 .

[17]  P. Rüegsegger,et al.  Direct Three‐Dimensional Morphometric Analysis of Human Cancellous Bone: Microstructural Data from Spine, Femur, Iliac Crest, and Calcaneus , 1999, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[18]  S. Sandmeier,et al.  Sensitivity analysis and quality assessment of laboratory BRDF data , 1998 .

[19]  Spectropolarised ray-tracing simulations in densely packed particulate medium , 2007 .

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

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

[22]  Jacqueline Lenoble,et al.  A MODEL FOR THE BIDIRECTIONAL POLARIZED REFLECTANCE OF SNOW , 1999 .

[23]  J. Dozier,et al.  The spectral bidirectional reflectance of snow , 1988 .

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

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

[26]  W. Steen.  Absorption and Scattering of Light by Small Particles , 1999 .

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

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

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

[30]  H. Lai,et al.  Extinction paradox and actual power scattered in light beam scattering: a two-dimensional study. , 2004, Journal of the Optical Society of America. A, Optics, image science, and vision.

[31]  J. Dozier,et al.  Climate and energy exchange at the snow surface in the Alpine Region of the Sierra Nevada: 1. Meteorological measurements and monitoring , 1992 .

[32]  M. Schneebeli.  Three-Dimensional Snow: How Snow Really Looks Like , 2000 .

[33]  Peter Lehmann,et al.  Modelling the effect of particle size, shape and orientation of light transfer through porous media , 2006 .

[34]  Bo-Cai Gao,et al.  Effect of ice crystal shape and effective size on snow bidirectional reflectance , 2006 .

[35]  C. Bohren,et al.  Asymptotic scattering efficiency of a large sphere , 1979 .

[36]  Ingo Meirold-Mautner,et al.  Measurements and model calculations of the solar shortwave fluxes in snow on Summit, Greenland , 2004, Annals of Glaciology.

[37]  R. Dobbins,et al.  Optical Scattering Cross Sections for Polydispersions of Dielectric Spheres , 1966 .

[38]  C. Gautier,et al.  A Three-Dimensional Radiative Transfer Model to Investigate the Solar Radiation within a Cloudy Atmosphere. Part II: Spectral Effects , 1998 .