Linear models of the relationships between meteorological observations and the flow of river Tungnaá at the western margin of glacier Vatnajökull were investigated by means of spectral analysis and estimation of the impulse response. Most of the variation of Tungnaá is confined to the lowest frequencies and the diurnal variations. The temperature has most effect on the rapid variations around 1 cycle/day whereas the largest coherences with the precipitation are in the lowest frequencies. The wind explains over 20% of the variations in the frequency range from 0–1 cycle/day, but this is partly due to its coherence with the precipitation. The time lag between changes in the temperature and the river is about 2 h, but the time lag between precipitation and the river is longer. Analysis of longer records of daily observations from Ϸjórsá shows that the coherence of the run-off and temperature increases at frequencies too low to be estimated from these data. At frequencies over 1 cycle/day most of the observed variations of the river cannot be explained by means of a linear relationship with the meteorological series.

The proposed method is to use a radio-echo sounder located on the surface of the ice sheet and to record the shape of the pulses returned from the rock bed. If the instrument is moved horizontally, the shape of the returning pulse will change, large differences occurring in horizontal distances of the order of the wavelength of the radiation, say 5 m. The spatial pattern of this variation, being largely determined by the details of the reflecting rock bed, is expected to remain fixed in position while the ice moves. It thus forms a fixed reference against which ice movement can be measured at places far removed from fixed landmarks. Analogue experiments in the laboratory, using ultrasonic waves in air in place of radio waves in ice, suggest that it should be easy to detect a movement of λ/10, 0.5 m, and, with further refinement, much smaller movements. A field test is in preparation.

Cylindrical samples of ice with 0.0 to 0.35 volume fraction fine sand were tested in unconfined uniaxial compression at stresses between 5.3 and 6.4 bar and at temperatures between −7.4 and −9.4° C. Secondary creep rates were obtained from the slope of the total strain vs. time curve and were normalized to 5.6 bar and −9.1° C. Creep rates in ice with low sand concentrations were in some cases higher and in other cases lower than in clean ice. However at higher sand concentrations the creep rate decreases exponentially with increasing volume fraction sand. The latter results are in general agreement with theories developed to explain dispersion hardening of metals, and suggest that each sand grain is surrounded by a tangled network of secondary dislocations which impede passage of primary glide dislocations.

In his now classic book L’dy Arktiki [Arctic ice], Zubov discussed the melting of sea ice during the Arctic summer by thermal interaction with the surrounding water and derived an expression which indicates that the proportion of open water increases exponentially with time until total ice-free conditions result. His equation predicts that the time required for complete decay of the ice cover after initial break-up is greater than one month and more likely as long as two months for representative values of incident shortwave radiation and initial ice thickness upon break-up. It is unlikely that above-freezing temperatures persist for this length of time.

To explain the observed complete disintegration of the annual ice cover in many sheltered areas of the Arctic, a modified model of the thermal decay process has been introduced. This model takes into account the influence of radiation absorbed by the ice which was not included in the Zubov formulation. Considerable reduction in the time required for complete decay, generally by about a factor of 2 if an albedo of 0.4 is assumed for the ice surface, is obtained.

Under-ice sonar profiles and surface laser profiles of the Arctic pack ice have been analyzed using power-spectrum techniques to extract significant spectral peaks corresponding to spatial periodicies in the ice. The analysis suggests that, for a section of ice sampled by two intersecting under-ice profiles, the ridges are not randomly oriented. Moreover, the lineation or directionality of the ridges may be approximately determined from the two intersecting profiles. Also the spectra from surface profiles of multi-year ice and from surface profiles of first-year ice are of a much different nature, thus suggesting a technique for determining ice types from laser profiles.

Multiple scattering of the solar flux in snow and “bubbly” ice can account for the variable albedo, the non-specular reflection, the non-exponential flux decrease near the surface, and the large upward flux within the medium. The scattering problem has been formulated and solved exactly, assuming isotropic scattering in a plane-parallel, semi-infinite, grey medium. The solution shows a non-exponential flux decrease near the surface and an exponential decrease deep in the medium. For such a medium, the albedo will increase with decreasing solar altitude in a manner which agrees to within one per cent of observed snow albedos in the Antarctic.

A theory is developed to describe the vertical percolation of water in isothermal snow. The general theory of Darcian flow is reviewed to establish a reasonable physical basis for the construction of a model. It is shown that in simple gravity drainage, capillarity is negligible compared with gravity since values of water saturation are generally in the “mid-range”. It is postulated that the permeability to the water phase increases as a certain function of the water saturation, and porosity is assumed to decrease linearly with depth. Ice layers and other inhomogeneities are treated in the theory by considering the permeability of the snow with the inhomogeneities included. A method by which this value of permeability can be calculated is presented using the method of characteristics.

The theory is applied to the Seward Glacier firn where Sharp measured water fluxes at various depths. A periodic surface flux is assumed and the particular solution for water flux at any depth is given. From this solution the wave forms passing each depth are constructed and compared with the measured ones. Although the experimental data are affected by the presence of ice layers, the comparison between theory and experiment is favorable and the theory is thought to be essentially correct.

Partial differential equations are derived to describe isotope fractionation between ice and water phases in temperate snow caps and glaciers. Numerical solutions are obtained and shown to be consistent with laboratory experiments and measurements of deuterium concentrations in temperate glaciers. The process of isotope fractionation as described is manifested by application of the model to tritium fractionation in temperate snow caps.

A two-dimensional finite element computer program has been used to compute the elastic stress distribution in realistic multi-layered snow packs. Computations have been done on three-layered and five-layered snow packs intended to simulate conditions on the Lift Gully at Berthoud Pass, Colorado. Calculations have been performed to determine the effect of a layer of new snow and the effect of a weak sub-layer. Stress levels were obtained which are reasonable compared with available snow strength data.

Investigations were made of the ice structures, air-bubble size distributions, and heat exchanges of water drops frozen freely-floating in the purified air of a vertical wind tunnel. Drop diameters varied from 1 to 8 mm, air temperature from −1 to −18.5°C; the ice phase was initiated artificially. It was found that the mass of ice in a freezing drop increases linearly with time. Both mean air bubble and crystal sizes decrease in a regular fashion as the air temperature decreases, whereas the bubble concentration increases. Histograms show a preferred tangential orientation of the projections into the plane of observation of the crystallographic hexagonal axis (c′-axes), a preference which weakens as the temperature decreases.

Quantitative investigations have been made of ice-cored dirt cones on Bersaerkerbræ in north-east Greenland. Experiments were also undertaken to evaluate field observations. Measurements included: maximum cone dimensions, sediment thickness and particle size, cone growth rates, slope angles and the temperature distribution within the debris layer and ice core. Particle size, which has not been stressed in previous studies, and related liquid consistency limits, appear as the dominant controls in cone formation, independent of debris thickness within the observed range of 10 mm to 125 mm. A threshold grain-size for dirt-cone inception was found, between 0.2 mm and 0.6 mm. The growth of cones was usually not more than 50% of the ablation over “clean” ice. Temperature measurements within dirt cones has enabled heat-flow studies to be made, evaluating the thermal conductivity of a sediment layer and the heat transfer involved in melting the ice core. A simple model of dirt-cone dynamics is proposed, characterized by negative feedbacks and describing a steady-state system.

Using geometrical arguments, Haefeli developed a stress analysis for slabs of compressible viscous materials. His analysis was based on a key parameter called the creep angle. A generalization of the creep angle, called the deformation-rate coefficient, is derived by replacing geometrical arguments with continuum mechanics. Once the deformation-rate coefficient is found from in situ measurements, the stress field of the slab can be determined from a set of hyperboic partial differential equations.

This paper elaborates on the note by Andrews and others (1971). It demonstrates that one may obtain any arbitrary value of r between two series of observations by adjusting the mean values of the two series before cumulating them. A computer simulation is used to illustrate the behavior of random Normal series cumulated under varying conditions.