Uniqueness of the transition zone solution is discussed. It is argued that when it is assumed that the stresses are continuous at the grounding line, the ice-shelf solution at the grounding line should possess a zero slope. In order to avoid issues caused by the mathematical singularity of the solution, the same technique as that used to study the transition zone is applied to a similar problem of lifting an elastic sheet from a rigid substrate, which allows a better physical understanding. This exemplifies the effect of the bottom boundary condition of no vertical motion imposed up to a fixed grounding line position, while the forcing parameters, such as the flow rate, vary. Its effect is to produce multiple solutions due to suppression of the separation mechanism.

A model of a non-linearly viscous ice sheet is used to investigate the influence of net mass-balance pattern, basal boundary condition, and subglacial topography on the size and shape of ice sheets. The aim is to enable geological evidence of the extent of former ice sheets to be used as indicators of palaeoclimate. A series of curves are presented showing the relationships between ice-sheet span, net mass balance, and equilibrium-line altitude (ELA) for zero and complete isostatic compensation. These are applicable to a very wide range of basal boundary conditions. The way in which they can be used to reconstruct net mass-balance gradients for former ice sheets is demonstrated. Changes in the basal boundary condition only have a strong influence on glacier span when they occur in the terminal zone. Ice-sheet expansion and contraction is not merely accompanied by changes in snow-line elevation, but also by changes in the net mass-balance gradient. The combinations of these required to cause ice-sheet expansion and contraction are analysed. A non-linearly viscous model for ice suggests that ice-sheet volume changes may not be a simple function of their change in areal extent.

On 29 April 2015, four beacons were deployed onto an ice island in the Strait of Belle Isle to record positional data. The ice island later broke up into many fragments, four of which were tracked by the beacons. The relative influences of wind drag, current drag, Coriolis force, sea surface height gradient and sea-ice force on the drift of the tracked ice island fragments were analyzed. Using atmospheric and oceanic model outputs, the sea-ice force was calculated as the residual of the fragments' net forces and the sum of all other forces. This was compared against the force obtained through ice concentration-dependent relationships when sea ice was present. The sea-ice forces calculated from the residual approach and concentration-dependent relationships were significant only when sea ice was present at medium-high concentrations in the vicinity of the ice island fragments. The forces from ocean currents and sea surface tilt contributed the most to the drift of the ice island fragments. Wind, however, played a minimal role in the total force governing the drift of the four ice island fragments, and Coriolis force was significant when the fragments were drifting at higher speeds.

Experimental data from creep tests on polycrystalline ice samples highlight not only the non-Newtonian behavior of ice but also suggest a critical dependence of the various rheological parameters upon the applied hydrostatic pressure. We propose a new modeling framework, based on implicit theories of continuum mechanics, that generalizes two well-known constitutive models by taking into account the effect of the pressure in the description of ice in creep. To ascertain the validity of the proposed models, we fit the physical parameters with experimental data for the elongational flow of ice samples. The results show good agreement with the experimental creep curves. In particular, the proposed generalized models reproduce the increase of the creep rate due to the presence of hydrostatic pressure.

In work presented in 1883 and published in full in 1894, W.J. McGee made one of the first clear attempts to outline the main morphologic differences between glaciated valleys and valleys developed by processes dominant in more temperate areas. Moreover, with an unprecedented analysis of glacial erosion, he attempted for the first time to explain the evolution of glacial land forms in terms of theoretical predictions of patterns of erosion under valley glaciers. In the latter half of the nineteenth century, there was fierce debate over whether glaciers were even capable of significant erosion, so it is perhaps not surprising that McGee’s analysis of glacial erosion processes and land-form development received little attention in his own time. Despite this, McGee’s work provided some of the first really convincing glacial explanations for the development of land forms such as hanging valleys and U-shaped valleys, and these were developed more fully in later work by Davis (1900) and Gilbert (1903). In modern research, the use of theoretical erosion laws and a knowledge of ice dynamics to develop models of land-form development is emerging as a major theme in glacial geomorphology, marking a return to the methodology pioneered by W.J. McGee.

An approximate, analytic solution is found for the profile of a water-free crevasse in a field of closely spaced crevasses. The depth of penetration of the crevasses into the glacier is found. If the fracture strength of ice is taken to be zero, the penetration depth is equal to the value found by Nye and is independent of the crevasse spacing. This conclusion is in disagreement with results reported recently by R.A. Smith. If the fracture strength of ice is taken to be finite, the penetration depth is reduced if the spacing between crevasses is reduced.

The results of the analysis can be applied to other crack problems. In particular, it can be applied to thermal, secondary cracking that it is hoped occurs when cooling fluid flows through the cracks created by hydraulic fracture for the purpose of extracting geothermal heat from hot, dry rock masses.

Widespread wet-snow avalanches were observed on the southern boundary of Glacier National Park, Montana, in February 1979. Severe tilting, scarring, and breakage of trees were observed along a transverse trim-line of one path, 70 m from a wet-snow deposit. Tree-ring data were used to establish the date of occurrence, and the nature of damage was used to characterize the avalanche event. The event probably included a previously unrecognized dry-snow avalanche and associated wind blast. Such events present different problems for natural-hazard planning. The nature of vegetative damage along the margins of avalanche paths is shown to be a useful indicator of the characteristics of past unobserved avalanche events.

By introducing a coordinate stretching, the governing field equations of the creep flow of a non-Newtonian viscous medium down a uniform slope are solved to determine the differential equation describing the propagation of long surface waves caused by initial disturbances and/or time-dependent accumulation-rate The differential equation for the surface wave depends on the flow law of the non-Newtonian fluid, the boundary condition at the ice-bedrock interface, the bedrock topography and the thickness–wavelength ratio. For moderately long waves and small elevation above the mean thickness the results agree in their essentials with those of the kinematic wave theory and the forward wave equation with a diffusion term is derived, but when improving this by allowing higher elevations the Burger's equation and even more complex equations are obtained. To derive these results Glen’s flow law must be generalized to avoid infinitely fast changes in stress deviators close to zero Strain-rates, The range of applicability of the various equations is discussed.

Untersteincr and Nye (1968) calculated the possible future movement of Berendon Glacier, B.C. These calculations are repeated using much improved data and a slightly different method for computing the datum state. The predictions that result are very similar to those found in the earlier work. It is concluded, however, from mass-balance data, that the chance of the glacier rising sufficiently in the next 25 years to be a danger to the mining installations situated near the snout of the glacier is much greater than was previously considered. The sensitivity of the theory to changes in input data is discussed.

Structural analyses of ice collected from the bare ice surface in the region of the Sør-Rondane Mountains were carried out. Crystal-orientation fabrics and the disposition of surface cracks were investigated to determine the stress/strain configuration in the ice sheet near the mountains. Single-maximum fabric patterns with the axis of the maximum roughly perpendicular to the flow line on the horizontal plane were observed. It was deduced from the observations that the ice exhibits a fabric pattern indicating that the ice sheet is subjected to vertical shear strain between the ice flow and the nunataks.

Borehole optical stratigraphy (BOS) is a borehole video system and processing routine for investigating polar firn. BOS records brightness variations in the firn and is effective at identifying stratigraphic markers. BOS brightness logs have been used to count annual layers and measure vertical strain, even though a specific cause of the brightness variations has not been determined. Here we combine two models of light transport to examine potential errors with BOS and identify improvements which will allow the system to estimate optical grain size. We use a Monte Carlo radiative transfer model to estimate the influence of firn microstructure variations on borehole reflectance. We then use a ray-tracing algorithm to model the multiple reflections within the borehole that cause measured brightness variations. Multiple reflections cause the brightness measured at a point on the borehole wall to not necessarily be equal to the local wall reflectance. The ray tracing further shows that wall imperfections or variations in the camera position can produce brightness variations that are unrelated to changes in firn properties. Smooth walls and good stabilization of the camera help ensure that brightness variations result from variations in firn properties, and thus are a measure of firn stratigraphy, rather than artifacts.

A regression model calibrated on 23 cirques from the Sangre de Cristo Mountains, south-central Colorado, suggests that local-scale climatic controls interact with geologic materials to explain intramountain variation to cirque development. Topoclimatic effects maximize cirque development on ridges that project well above the Pleistocene glaciation limit, and in positions that minimize total radiation receipt. If an optimum topoclimate coincides with densely jointed (erosible) bedrock materials, cirque development will be at a maximum. However, cirque development can be deceptively poor in situations where a favorable topoclimate coincides with massive (sparsely jointed) bedrock materials. The interaction between local-scale climatic–geologic controls subsumes their independent effects. Significant correlation between cirque development and an individual process control may not emerge due to complications produced by one or more other controls.

A comparison of mesoscale strain measurements with the atmospheric pressure field and the wind velocity field indicate that the ice divergence rate and vorticity follow the local pressure and wind divergence with significant correlation. For low atmospheric pressures and converging winds the divergence rate was found to be negative with the vorticity being counter-clockwise. The inverse behavior was observed for high pressures and diverging winds. This behavior was shown to agree with predictions based upon the infinite boundary solution of a linearized drift theory in the absence of gradient current effects and using the constitutive law proposed by Glen (1970) for pack ice. The best least-squares values of the constitutive law parameters η and ζ were found to be ≈ 1012 kg/s. Using typical divergence rates these values yield compressive stresses of the magnitude of 105 N/m which are similar to values suggested by the Parmerter and Coon (1972) ridge model. In general, the infinite boundary solution of the linear drift equation indicates that in a low-pressure region that is reasonably localized in space, the ice would be expected to converge for high compactness (winter) and diverge for low compactness (summer).

Calculations were also carried out using a more general linear visco-elastic constitutive law that includes memory effects and which includes a generalized Hooke’s law as well as the Glen law as special cases. A best fit of this more general calculation with strain measurements indicates overall a better agreement with viscous behavior than with elastic behavior, with the frequency behavior of the estimated “viscosities” similar to the Glen law behavior at temporal frequencies less than ≈ 0.01 h−1.

The surface energy budget was investigated during a cruise through the pack ice in the Southern Ocean. The time of observation was close to mid-summer. Some of the more important findings were:

As an extension of an intensive study of Gulkana Glacier a 42 station gravimeter survey was made to gain some insight into its third dimension. This survey showed that the glacier’s main tongue occupies a complex valley composed essentially of two parallel channels separated by a medial ridge which extends southward from rock bastions in the accumulation zone. At mid-glacier the ice thickness in the larger eastern channel is 225 m., in contrast to 130 m. in the western channel. The medial ridge degenerates down-glacier probably disappearing within 2 km. of the glacier terminus. The basic surface flow pattern of the glacier described by Moores can be adequately explained by this basal topography. Seasonal velocity variations are possibly caused by melt-water basal lubrication with one channel being favored over the other at different times of the year, in agreement with observations by Elliston on the Gorner-Gletscher, Switzerland, and with the glacier sliding theory of Weertman.

A spectacular surge occurred on Peters Glacier, Alaska, in 1986 and 1987. Several observations on the glacier were made during the course of its surge. These observations are compared with those on other surging glaciers and then interpreted in terms of the ideas on surge mechanisms and dynamics as originally postulated by Post (unpublished) and further developed during the surge of Variegated Glacier by Kamb and others (1985) and Raymond and Harrison (1986, in press). It is shown that the concepts of rapid basal motion due to high water pressure at the glacier bed and the initiation of a surge during the winter due to a pressurization of the limited supply of basal water are well supported by these observations on the surge of Peters Glacier. An extremely high suspended sediment load rich in very fine material was observed, which also supports ideas on basal processes expected during this type of surge.

One interesting (and puzzling) feature of this surge cycle is that the termination of the surge occurred in late winter 1987, when surface melt water was at a minimum. This is in direct contrast to the termination of the surge on Variegated Glacier, which occurred during the period of peak ablation.

Since snow avalanches are believed to release from zones of localized weakness, knowledge of snow-strength patterns is important for determining slope stability and for applying effective avalanche-control measures. In this study, the spatial variability of snow resistance (an index of snow strength) and depth were measured and compared with terrain features on two inclined slopes. A refined instrument allowed the strength of an entire snow slab to be characterized in a short time. The spatial pattern of trees appeared to affect the pattern of snow depth at one site, where a significant linear relationship was found between snow depth and average snow resistance. These results suggest that localized snow-depth variations may be important in snow-strength genesis. Although a linear relationship existed at that site, additional factors may be critically relevant. A second site with more complex terrain features and less localized wind drifting did not show a linear relationship between depth and average resistance. Instead, complex patterns of resistance demonstrated that many factors contribute to snow resistance. In particular, die snow overlying rocks was found to have significantly weaker resistance than that in adjacent areas not over rocks.

The theory of Nye and of Weertman of traveling waves on glaciers is extended to cover the situation where the presence of abundant basal water or increased basal water pressure produces increased sliding of a glacier over its bed. It is found that the ratio of traveling-wave velocity to surface velocity is independent of the amount of water or the basal water pressure. The theoretical value of this ratio, about 4 to 5, agrees with that found in field measurements (the most recent data are from Mer de Glace). It is concluded that field observations of traveling-wave velocities lend strong support to any glacier sliding theory in which the sliding velocity is proportional to the basal shear stress raised to about a second to fifth power and in which the sliding velocity is a function of either or both the amount of water at the bed of a glacier and the pressure within this water.

The importance of glacier sliding has motivated a rich literature describing the thermomechanical interactions between ice, liquid water and bed materials. Early recognition of the gradient in melting temperature across small bed obstacles led to focused studies of regelation. An appreciation for the limits on ice deformation rates downstream of larger obstacles highlighted a role for cavitation, which has subsequently gained prominence in descriptions of subglacial drainage. Here, we show that the changes in melting temperature that accompany changes in normal stress along a sliding ice interface near cavities and other macroscopic drainage elements cause appreciable supercooling and basal mass exchange. This provides the basis of a novel formation mechanism for widely observed laminated debris-rich basal ice layers.

This paper contains a critical survey of the literature on the bearing capacity of floating ice plates. It consists of a discussion of general questions, a critical survey of analytical attempts to determine the bearing capacity of floating ice plates and a survey of field and laboratory tests on floating ice plates and their relation to the analytical results. It concludes with a systematic summary of the results, a discussion of observed shortcomings, and suggestions for needed investigations.