Geometry of heat and mass transfer in dry snow: A review of theory and experiment

Porous materials are common on the Earth's surface and in the crust. Accordingly, their physical properties have received a lot of attention. A century ago, Maxwell and Rayleigh each modeled the physical properties of aggregate materials as discrete spheres embedded in continuous matrices. Although the particles of interest in snow are not spheres and do have interconnections, these basic models give first-order predictions of the thermal conductivity. In the last 3 decades, scientists have attempted to make the predictions more precise by determining the effect of geometry on heat and mass flow using basic physical models and data collected from images of planar sections of aggregates. Under favorable circumstances, physical parameters and quantitative microscopic parameters of an aggregate may be highly correlated, but physical understandings of the geometric effects are not likely to arise from such studies until physical models can be based on measurable fundamental parameters. In snow, as in other aggregates, that goal seems to be a long way from realization.

[1]  Salvatore Torquato,et al.  Rigorous bounds on the fluid permeability: Effect of polydispersivity in grain size , 1990 .

[2]  P. R. Kry The Relationship between the Visco-Elastic and Structural Properties of Fine-Grained Snow , 1975 .

[3]  S. C. Colbeck,et al.  Snow Metamorphism and Classification , 1987 .

[4]  S. Colbeck Thermodynamics of snow metamorphism due to variations in curvature , 1980 .

[5]  S. Colbeck The vapor diffusion coefficient for snow , 1993 .

[6]  J. Bear Dynamics of Fluids in Porous Media , 1975 .

[7]  D. Pitman,et al.  Effective Thermal Conductivity of Snow at −88°, −27°, and −5°C , 1967 .

[8]  K. Elder,et al.  Hydrologic characteristics and water balance of an Alpine Basin in the Sierra Nevada , 1991 .

[9]  S. Torquato,et al.  Bounds on the conductivity of a suspension of random impenetrable spheres , 1986 .

[10]  J. Koplik,et al.  Conductivity and permeability from microgeometry , 1984 .

[11]  V. Alonso,et al.  Glaciers in Picos de Europa, Cordillera Cantábrica, northwest Spain , 1994, Journal of Glaciology.

[12]  R. Barry,et al.  Large scale effects of seasonal snow cover , 1987 .

[13]  James G. Berryman,et al.  Use of digital image analysis to estimate fluid permeability of porous materials: Application of two-point correlation functions , 1986 .

[14]  Keith Attenborough,et al.  On the application of rigid-porous models to impedance data for snow , 1988 .

[15]  J. Koplik On the effective medium theory of random linear networks , 1981 .

[16]  R. Davis Links Between Snowpack Physics and Snowpack Chemistry , 1991 .

[17]  John Crank,et al.  The Mathematics Of Diffusion , 1956 .

[18]  O. Wiener,et al.  Die theorie des Mischkörpers für das Feld der stationären Strömung , 1912 .

[19]  R. Ehrlich,et al.  Petrography and reservoir physics; II, Relating thin section porosity to capillary pressure, the association between pore types and throat size , 1991 .

[20]  T. Allen Particle Size Measurement , 1965, Nature.

[21]  O. Johansen Thermal Conductivity of Soils , 1977 .

[22]  Arthur W. Rose,et al.  Porous media: Fluid transport and pore structure (2nd Ed.) , 1993 .

[23]  C. Bentley,et al.  Unified theory of electrical conduction in firn and ice: Site percolation and conduction in snow and firn , 1994 .

[24]  J. Dozier,et al.  Towards predicting temporal changes of the spectral signature of snow in visible and near-infrared wavelengths , 1993, Annals of Glaciology.

[25]  John C. Russ,et al.  The Image Processing Handbook , 2016, Microscopy and Microanalysis.

[26]  Morrel H. Cohen,et al.  Quantitative methods for microgeometric modeling , 1982 .

[27]  W. Woodside,et al.  CALCULATION OF THE THERMAL CONDUCTIVITY OF POROUS MEDIA , 1958 .

[28]  H. Gubler Model for dry snow metamorphism by interparticle vapor flux , 1985 .

[29]  J. Maxwell A Treatise on Electricity and Magnetism , 1873, Nature.

[30]  S. Colbeck,et al.  Theory of metamorphism of dry snow , 1983 .

[31]  K. Easterling,et al.  Phase Transformations in Metals and Alloys , 2021 .

[32]  E. Brun,et al.  A numerical model to simulate snow-cover stratigraphy for operational avalanche forecasting , 1992, Journal of Glaciology.

[33]  E. Weibel Stereological Methods. Practical methods for biological morphometry , 1979 .

[34]  F. C. Frank,et al.  On the Kinematic Theory of Crystal Growth and Dissolution Processes, II , 1972 .

[35]  O. Buser A rigid frame model of porous media for the acoustic impedance of snow , 1986 .

[36]  Hiromu Shimizu,et al.  Air Permeability of Deposited Snow , 1970 .

[37]  P. R. Kry Quantitative Stereological Analysis of Grain Bonds in Snow , 1975, Journal of Glaciology.

[38]  Engineering Properties of Snow , 1977 .

[39]  T. Okada On the thermal conductivity of snow , 1905 .

[40]  H. Ahlmann,et al.  Snow Structure and Ski Fields , 1937 .

[41]  Ice The international classification for seasonal snow on the ground , 1990 .

[42]  Peter V. Hobbs,et al.  The sintering and adhesion of Ice , 1964 .

[43]  P. Mayewski,et al.  An ice-core record of atmospheric response to anthropogenic sulphate and nitrate , 1990, Nature.

[44]  R. Alley Fabrics in Polar Ice Sheets: Development and Prediction , 1988, Science.

[45]  R. Sommerfeld,et al.  A Branch Grain Theory of Temperature Gradient Metamorphism , 1983 .

[46]  H. Gubler Determination of the Mean Number of Bonds per snow grain And of the Dependence of the Tensile Strength of Snow on Stereological Parameters , 1978, Journal of Glaciology.

[47]  C. Benson,et al.  Field Experiments on the Development of Depth Hoar , 1972 .

[48]  Salvatore Torquato,et al.  Random Heterogeneous Media: Microstructure and Improved Bounds on Effective Properties , 1991 .

[49]  J. Bezdek,et al.  FCM: The fuzzy c-means clustering algorithm , 1984 .

[50]  M. Q. Edens,et al.  Changes in microstructure of snow under large deformations , 1991, Journal of Glaciology.

[51]  Manfred A. Lance Measurements of Thermal Parameters in Antarctic Snow and Firn , 1985, Annals of Glaciology.

[52]  Masao Doi,et al.  A New Variational Approach to the Diffusion and the Flow Problem in Porous Media , 1976 .

[53]  Susan Marshall,et al.  Snow hydrology in a general circulation model , 1994 .

[54]  J. Dozier,et al.  Preparation of serial sections in dry snow specimens , 1986 .

[55]  R. Perla Snow in strong or weak temperature gradients. Part II: Section-plane analysis , 1985 .

[56]  James G. Berryman,et al.  Normalization constraint for variational bounds on fluid permeability , 1985 .

[57]  Fes A. de Scally,et al.  Relative importance of snow accumulation and monsoon rainfall data for estimating annual runoff, Jhelum basin, Pakistan , 1994 .

[58]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[59]  J. Bernasconi Conduction in anisotropic disordered systems: Effective-medium theory , 1974 .

[60]  K. Taylor,et al.  Analysis of snow feedbacks in 14 general circulation models , 1994 .

[61]  Scott Kirkpatrick,et al.  An introduction to percolation theory , 1971 .

[62]  Jeff Dozier,et al.  Opportunities to improve hydrologic data , 1992 .

[63]  Robert Ehrlich,et al.  Petrography and reservoir physics I: Objective classification of reservoir porosity , 1991 .

[64]  K. N. Eshleman,et al.  Episodic acidification of freshwater systems in Canada — Physical and geochemical processes , 1994 .

[65]  Richard B. Alley,et al.  Three-Dimensional Coordination Number from Two-Dimensional Measurements: A New Method , 1986, Journal of Glaciology.

[66]  Colleagues,et al.  Physical Studies on Deposited Snow. I. ; Thermal Properties. , 1955 .

[67]  S. Colbeck,et al.  Classification of seasonal snow cover crystals , 1986 .

[68]  G. T. Tsao,et al.  Thermal Conductivity of Two-Phase Materials , 1961 .

[69]  Matthew Sturm,et al.  Thermal conductivity measurements of depth hoar , 1992 .

[71]  Ukichiro Nakaya,et al.  Snow Crystals , 2014 .

[72]  I. F. Macdonald,et al.  Three‐dimensional reconstruction of porous media from serial section data , 1990 .

[73]  S. Prager,et al.  Viscous Flow through Porous Media , 1961 .

[74]  W. Good Laboratory techniques for the characterisation of snow structures , 1989 .

[75]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[76]  J. Devaux L’économie radio-thermique des champs de neige et des glaciers , 1933 .

[77]  J. Coetzee,et al.  The osmotic effect of glutaraldehyde‐based fixatives on plant storage tissue , 1986 .

[78]  R. Alley,et al.  Abrupt increase in Greenland snow accumulation at the end of the Younger Dryas event , 1993, Nature.

[79]  H. G. Jones Snow chemistry and biological activity: a particular perspective on nutrient cycling , 1991 .

[80]  R. A. Sommerfeld,et al.  The classification of snow metamorphism , 1970 .

[81]  Eizi Akitaya Studies on Depth Hoar , 1974 .

[82]  S. Colbeck Statistics of coarsening in water-saturated snow , 1986 .

[83]  W. Kingery Regelation, Surface Diffusion, and Ice Sintering , 1960 .

[84]  J. Jouzel,et al.  Climate instabilities: Greenland and Antarctic records , 1994 .

[85]  J. Fastook,et al.  A Finite-element Model of Antarctica: sensitivity test for meteorological mass-balance relationship , 1994, Journal of Glaciology.

[86]  S. Colbeck Temperature dependence of the equilibrium form of ice , 1985 .

[87]  M. Christon,et al.  A 2-D MICROSCOPIC SIMULATION OF HEAT AND MASS TRANSPORT IN DRY SNOW , 1990 .

[88]  Donald K. Perovich,et al.  A statistical description of the microstructure of young sea ice , 1991 .

[89]  George C. Lee,et al.  Cold Region Structural Engineering , 1986 .

[90]  R. Perla,et al.  Snow in strong or weak temperature gradients. Part I: Experiments and qualitative observations , 1985 .

[91]  R. L. Brown,et al.  Observations on the Growth Process and Strength Characteristics of Surface Hoar , 1984 .

[92]  O. W. Witzell,et al.  THERMAL CONDUCTIVITY OF GRAPHITE-SILICONE OIL AND GRAPHITE-WATER SUSPENSIONS , 1958 .

[93]  L. Rayleigh,et al.  LVI. On the influence of obstacles arranged in rectangular order upon the properties of a medium , 1892 .

[94]  A. J. Friedland,et al.  Chemical and isotopic tracers of snowmelt flowpaths in a subalpine watershed , 1995 .

[95]  H. Brinkman A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles , 1949 .

[96]  J. Bolzan,et al.  Accumulation-rate variations around Summit, Greenland , 1994, Journal of Glaciology.

[97]  J. B. Walsh,et al.  The effect of pressure on porosity and the transport properties of rock , 1984 .

[98]  H. Auracher HEAT TRANSFER IN FROST AND SNOW , 1978 .

[99]  E. Adams,et al.  Model for effective thermal conductivity of a dry snow cover composed of uniform ice spheres , 1993, Annals of Glaciology.

[100]  R. Jordan A One-dimensional temperature model for a snow cover : technical documentation for SNTHERM.89 , 1991 .

[101]  R. Irani,et al.  Particle Size: Measurement, Interpretation, and Application , 1963 .