Measurements of the dependence of snow albedo on wavelength, zenith angle, grain size, impurity content, and cloud cover can be interpreted in terms of single-scattering and multiple-scattering radiative transfer theory. Ice is very weakly absorptive in the visible (minimum absorption at λ = 0.46 µm) but has strong absorption bands in the near infrared (near IR). Snow albedo is therefore much lower in the near IR. The near-IR solar irradiance thus plays an important role in snowmelt and in the energy balance at a snow surface. The near-IR albedo is very sensitive to snow grain size and moderately sensitive to solar zenith angle. The visible albedo (for pure snow) is not sensitive to these parameters but is instead affected by snowpack thickness and parts-per-million amounts (or less) of impurities. Grain size normally increases as the snow ages, causing a reduction in albedo. If the grain size increases as a function of depth, the albedo may suffer more reduction in the visible or in the near IR, depending on the rate of grain size increase. The presence of liquid water has little effect per se on snow optical properties in the solar spectrum, in contrast to its enormous effect on microwave emissivity. Snow albedo is increased at all wavelengths as the solar zenith angle increases but is most sensitive around λ =1 µm. Many apparently conflicting measurements of the zenith angle dependence of albedo are difficult to interpret because of modeling error, instrument error, and inadequate documentation of grain size, surface roughness, and incident radiation spectrum. Cloud cover affects snow albedo both by converting direct radiation into diffuse radiation and also by altering the spectral distribution of the radiation. Cloud cover normally causes an increase in spectrally integrated snow albedo. Some measurements of spectral flux extinction in snow are difficult to reconcile with the spectral albedo measurements. The bidirectional reflectance distribution function which apportions the reflected solar radiation among the various reflection angles must be known in order to interpret individual satellite measurements. It has been measured at the snow surface and at the top of the atmosphere, but its dependence on wavelength, snow grain size, and surface roughness is still unknown. Thermal infrared emissivity of snow is close to 100% but is a few percent lower at large viewing angles than for overhead viewing. It is very insensitive to grain size, impurities, snow depth, liquid water content, or density. Solar reflectance and microwave emissivity are both sensitive to various of these snowpack parameters. However, none of these parameters can be uniquely determined by satellite measurements at a single wavelength; a multichannel method is thus necessary if they are to be determined by remote sensing.

Optical Properties of Snow

A new GCM land surface scheme is introduced, incorporating three soil layers with physically based calculations of heat and moisture transfers at the surface and across the layer boundaries. Snow-covered and snow-free areas are treated separately. The energy balance equation is solved iteratively for the surface temperature; the surface infiltration rate is calculated using a simplified theoretical analysis allowing for surface ponding. Snow cover is modelled as a discrete ‘soil’ layer.

The results generated by CLASS are compared with those of an older model incorporating the force-restore method for the calculation of surface temperature and a bucket-type formulation for the ground moisture. Several month-long test runs are carried out in stand-alone mode. It is shown that the surface temperature in the old scheme responds more slowly to diurnal forcing and more quickly to longer term forcing than that modelled by CLASS, while its one-layer representation of soil moisture proves incapable of reproducing changes in the surface fluxes owing to surface variations of moisture content. Finally, the lumped treatment of snow and soil in the old scheme results in an extremely fast disappearance of the snow pack under certain conditions.

Class—A Canadian land surface scheme for GCMS. I. Soil model

Creep experiments on fine-grained ice reveal the existence of three creep regimes: (1) a dislocation creep regime; (2) a superplastic flow regime in which grain boundary sliding is an important deformation process; and (3) a basal slip creep regime in which the strain rate is limited by basal slip. Dislocation creep in ice is likely climb-limited, is characterized by a stress exponent of 4.0, and is independent of grain size. Superplastic flow is characterized by a stress exponent of 1.8 and depends inversely on grain size to the 1.4 power. Basal slip limited creep is characterized by a stress exponent of 2.4 and is independent of grain size. A fourth creep mechanism, diffusional flow, which usually occurs at very low stresses, is inaccessible at practical laboratory strain rates even for our finest grain sizes of approximately 3 micrometers. A constitutive equation based on these experimental results that includes flow laws for these four creep mechanisms is described. This equation is in excellent agreement with published laboratory creep data for coarse-grained samples at high temperatures. Superplastic flow of ice is the rate-limiting creep mechanism over a wide range of temperatures and grain sizes at stresses less than or equal to 0.1 MPa, conditions which overlap those occurring in glaciers, ice sheets, and icy planetary interiors.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000JB900336

Superplastic deformation of ice: Experimental observations

The Canadian Climate Centre second generation general circulation model (GCMII) is described. The description emphasizes aspects in which the new model differs from the 1984 model (GCMI) as described by Boer and collaborators. Important features of the new version include an interactive cloudiness parameterization, improved solar and terrestrial radiative beating calculations, a more sophisticated treatment of land surface processes, and a simple ocean mixed-layer model with a thermodynamic sea ice component. Results from a ten-year climate simulation made with the new model are presented and compared with observed climatology. The comparison is made for the December-February and June-August periods. The model reproduces the observed climatology in a generally successful manner.

The Canadian Climate Centre Second-Generation General Circulation Model and Its Equilibrium Climate

The point-load strength test

Measurement of tensile strength by diametral compression of discs and annuli

The general properties of snow are described with a view to engineering applications of data. Following an introduction and a short note on the origins of snow, data are given for fall velocities of snow particles, and for mass flux and particle concentrations in falling snow and blowing snow. Notes on the structural properties of deposited snow cover grain size, grain bonds, bulk density, overburden pressure, and permeability. A section on impurities deals with stable and radioactive isotopes, chemical impurities, insoluble particles, living organisms, acidity, and gases. Mechanical properties are treated only selectively, and the reader is referred to another paper for comprehensive coverage. The selective treatment deals with stress waves and strain waves, compressibility, effects of volumetric strain on deviatoric strain, and specific energy for comminution. The section on thermal properties covers heat capacity, latent heat, conductivity, diffusivity, heat transfer by vapor diffusion, heat transfer and vapor transport with forced convection, and thermal strain. The section on electrical properties opens with a brief discussion on dielectric properties of ice, and proceeds to a summary of the dielectric properties of snow, including dielectric dispersion, permittivity, dielectric loss, and d.c. conductivity. There are also notes on the thermoelectric effect and on electrical charges in falling and blowing snow. The section on optical properties deals with transmission and attenuation of visible radiation, with spectral reflectance, and with long-wave emissivity. The review concludes with some comments on engineering problems that involve snow, and the requirements for research and development.

/pdf/engineering-properties-of-snow-2zpjsthmfz.pdf

Engineering Properties of Snow

Techniques for making precise uniaxial tests for strength and deformability of ice are described. Results are given for tests made in uniaxial tension and uniaxial compression at constant displacement rate, using bubbly polycrystalline ice. These results include stress/strain curves, elastic moduli, rupture or yield strengths, and failure strains, all for a range of strain-rates. A few results for ice doped with hydrogen fluoride are also given. The fracture mechanism for ice is discussed, and the test results are compared with data reported by previous investigators.

Deformation and Fracture of Ice Under Uniaxial Stress

Deformation and failure of ice under constant stress or constant strain-rate

Creep tests on homogeneous, isotropic polycrystalline ice gave an apparent activation energy for creep of 16.4 kcal/mol (68.8 kJ/mol) over the temperature range −10° to −60° C. Above −10° C the Arrhenius relation for temperature dependence is invalid, and creep rate becomes progressively more temperature dependent as the melting point is approached. Between −20° and −50° C the apparent activation energy for creep of a single crystal of ice was found to be 16.5 kcal/mol (69.1 kJ/mol). A complete creep curve for a single crystal loaded in uniaxial compression parallel to the basal plane was qualitatively similar to the classical creep curve; creep rate at all stages was very much faster than for polycrystalline ice under the same conditions. Creep tests on polycrystalline ice at 0° C gave a stress/strain-rate relation for that temperature, but its precise meaning is unclear, since recrystallization complicated the results.

/pdf/effect-of-temperature-on-the-creep-of-ice-ma018ls5nh.pdf

Malcolm Mellor

Papers

Measurement of tensile strength by diametral compression of discs and annuli

Engineering Properties of Snow

Deformation and Fracture of Ice Under Uniaxial Stress

Deformation and failure of ice under constant stress or constant strain-rate

Effect of temperature on the creep of ice