Model calculations are made of the magnitude of the shift of the portion of an ice divide on a two dimensional ice sheet and of the “center” (the position of highest elevation) of a circular ice sheet when the rate of accumulation is different on different sides or in different sectors of an ice sheet. It is concluded that gross changes in the accumulation pattern are required to cause an appreciable shift of the position of ice divides or ice centers if the positions of the edge of the ice sheet are fixed.

A partly phenomenological theory and model are constructed of cyclically surging glaciers. During the after-surge portion of a surge cycle the lower portion of a glacier becomes increasingly stagnant. The upper part of the glacier gradually becomes more active as both its thickness and the magnitude of its basal shear stress increase. In the region between these two parts, called by us the trigger zone, the value of the derivative of the basal shear stress in the longitudinal direction of the glacier gradually increases with time. The pressure gradient in the water at the base of a glacier is related to the derivative of the basal shear stress. The pressure gradient decreases as the basal shear-stress gradient increases. The pressure gradient actually can take on negative values, a condition which produces “up-hill” water flow at the base of a glacier. A surge is started in the trigger zone when water is dammed there by a zero water-pressure gradient. The zone of fast-sliding velocities propagates up the glacier from the trigger zone with a velocity of the order of a surge velocity. The fast-sliding velocity zone also propagates down the glacier because of increased melt-water production.

Methods are developed for determining the distributions of stress and effective viscosity in a glacier, under the assumptions: the ice is quasi-viscous, the flow is time independent, and acceleration forces are negligible. Measurements of the three-dimensional distribution of velocity are needed for their application. The differential equations of mechanical equilibrium, expressed in terms of viscosity, strain-rate components, mean stress, and their gradients, are viewed as equations to be solved for viscosity and mean stress subject to boundary conditions at the free upper surface. For certain rectilinear flow patterns, unique distributions of stress and effective viscosity can always be derived. For more complicated flow this is not necessarily so. However, it is still possible to choose the best values of rheological parameters in any trial flow law based on the requirement that the residuals to the equations of equilibrium be minimized in a mean-square sense. The techniques are applied to measurements of internal deformation made in nine bore holes on the Athabasca Glacier. At the center line the magnitude of the surface-parallel shear stress increases with depth more slowly than would be expected from a standard shape factor correction or the theoretical distribution of Nye. Correspondingly the lateral distribution of lateral shear stress shows the opposite relationships. In the lower one- to two-thirds of the depth corresponding to a range in effective stress from about 0.5 to 1.2 bars, the gross rheology of the ice is not distinguishably different from the experimentally determined flow law of Glen (n = 4.2, T = 0.02° C) as generalized by Nye. The results do not support the conclusion that the effective viscosity is higher than would be expected from Glen’s experiments as indicated by the more limited measurements of Paterson and Savage. Power-law parameters derived for the different bore holes considered separately show a spread, which suggests some rheological inhomogeneity. However, no definite conclusions can be drawn, because of direct measurement errors at the bore holes and less definable uncertainty in the interpolated distribution of velocity between the holes. The upper one- to two-thirds of the glacier constitutes an anomalous zone in which there is either a strong effect from a complex distribution of stress arising from longitudinal stress gradients or more complicated rheology than in a homogeneous power-law material.

A numerical model for three-dimensional, time-dependent glacier flow (Campbell and Rasmussen, 1970) treated the ice as a Newtonian viscous fluid and related its dynamics to two large-scale bulk parameters: the viscosity v determining the ice-to-ice friction, and a basal friction parameter A determining the ice-to-rock friction. The equations were solved using the relatively simple flow law of Bodvarsson (1955) in which the basal shear stress is proportional to volume transport. Recent research suggests that a more realistic basal flow law is one in which the basal shear stress to some lower power (1–3) is either proportional to the vertically averaged velocity (Glen, 1958; Nye, 1960, 1963[a], [b], [c], 1965[a], [b], [c]) or to the ratio of the vertically averaged velocity to glacier thickness (Budd and Jenssen, in press).

In the present study a generalized flow law incorporating all of the above bulk basal flow laws is applied to the Campbell–Rasmussen momentum equation to form a generalized two-dimensional transport equation, which, when combined with the continuity equation, yields a numerically tractable set of equations for three-dimensional, time-dependent glacier flow. Solutions of the model are shown for steady-state flow and surge advance and recovery for a typical valley glacier bed for powers 1, 2, and 3 for each of the basal flow laws for a steady-state climate input and a given ice-to-ice viscosity parameter.

From data taken on the British Trans-Arctic Expedition it is calculated that 9% of the Arctic Ocean surface between the North Pole and Spitsbergen was hummocked or ridged ice, 17% was unridged ice less than a year old, 73% was unridged old ice and 0.6% was ice-free. The mode of 250 thickness measurements taken through level areas of old floes along the entire traverse lies between 2.25 and 2.75 m. The mean end-of-winter thickness of the ice is calculated to be 4.6 m in the Pacific Gyral and 3.9 m in the Trans-Polar Drift Stream. From measurements of the percentage coverage and thickness of the various ice forms, it is calculated that the total annual ice accumulation in the Arctic Ocean is equivalent to a continuous layer of ice 1.1 m thick. 47% of this accumulation occurs in ice-free areas and under ice less than 1 year old. 20% of the total ice production is either directly or indirectly related to ridging or hummocking. An ice-ablation rate of 500 kg m−2 measured on a level area of a multi-year floe is compared with the rate on deformed and ponded ice. Greatest melting occurs on new hummocks and least on old smooth hummocks. The annual balance of ice older than 1 year but younger than multi-year ice is calculated from a knowledge of ice-drift patterns and the percentage coverage of first-year ice. The same calculations give a mean-maximum drift period of 5 years for ice in the Trans-Polar Drift Stream and 16 years in the Pacific Gyral. It is calculated that for the period February 1968 to May 1969 the annual ice export was 5 580 km3.

Budd’s expressions for strain-rate gradient along the centre line of a bounded ice shelf are shown to be applicable only to ice shelves with almost constant thickness and very small longitudinal strain-rates. A general expression is derived for creep in an ice shelf where the sole restriction is that of zero shear stresses in vertical planes. This is applied to the two special cases:

• (1) movement of an ice shelf restricted in at least one direction by sea-water pressure only;

• (2) movement of an ice shelf flowing between roughly parallel sides.

The determination of glacial ice thickness by vertical resistivity depth soundings relies upon the use of theoretical curves which neglect the effect of valley walls. To improve the utility of glacial resistivity measurements an analytical expression is derived for the apparent resistivity determined by a Wenner array oriented parallel to the strike of a layered trough embedded in a perfectly conducting half space. Numerical evaluation of this expression allows the effects of glacial cross-section to be determined. It is shown that the presence of valley walls and layering within the glacier can strongly effect the determination of total ice thickness, and a criterion for the reliable use of plane-layered master curves in the interpretation of field data is established. An apparent resistivity curve calculated for a layered trough is shown to give an excellent fit to field data published by Röthlisberger and Vögtli (1967).

The deformation of a strain triangle (≈6 km × 8 km × 11 km) located on first-year ice in the Beaufort Sea was observed over a two-week period in March 1971. Significant strain events (≈ 1.5%) were observed to occur during short (≈6 h) time periods. The long-term (one day or more) divergence rate varied between 0.04 and 0.08 × 10−3 h−1. Short-term divergence rates showed values as high as 0.29 × 10−3 h−1. The observed shearing motion indicated that the floes to the east were moving to the south relative to the floes to the west. This agrees with the shear pattern that might be expected considering the location of the station in the Pacific Gyre. Studies of fracture (lead and crack) orientations in the vicinity of the strain triangle indicate reasonable correlations with the orientation of the strain-rate ellipse. A qualitative relation is suggested between the fracture density and the long-term divergence rate. Correlations were also observed between the divergence of the wind field as computed from the surface pressure field and the ice divergence.

Available measurements of creep rates and dimensions of ice shelves are used, in conjunction with equations derived in a companion paper (Thomas, 1973), to evaluate the flow law parameters B and n for stresses down to 104 N m−2. The results show good agreement with laboratory work at higher stresses. Adoption of these values of B and n enables us to examine the restraining effects on an ice shelf of obstructions such as areas of grounding.

A history of the idea of transporting large icebergs to arid regions to provide a fresh-water source is presented and the problem is considered in four main parts: (1) Location of a supply of icebergs. Only in the Antarctic are supplies of large tabular icebergs available. Data on the size distribution of these icebergs are reviewed and it is concluded that icebergs of almost any desired size can readily be located. (2) Towing. Steady-state towing velocities of different sized icebergs are calculated based on estimates of the drag of the icebergs and the bollard pull of tugs. Because drag increases with velocity squared, large icebergs can only be towed at very slow velocities (<c. 0.5 m/s). However, tugs that can be built within the capabilities of current technology are capable of towing extremely large icebergs. (3) Melting in transit. Calculations of melting indicate that, although melting losses are significant and may be excessive for small icebergs, when large icebergs are towed, large amounts of ice are left when the iceberg arrives at its destination. Towing trajectories, travel times, and ice delivery rates are calculated for optimum routes between the Amery Ice Shelf and Western Australia (A–A) and the Ross Ice Shelf and the Atacama Desert (R–A). Forces included in these calculations are towing, air, water, gradient current and Coriolis. Transit times exceed 107 d (A–A) and 145 d (R–A) with over 50% of the initial ice delivered. (4) Economic feasibility. After total towing charges are paid, it is possible to deliver ice to Western Australia for 1.3 mills/m3 of water and to the Atacama Desert region for 1.9 mills/m3. These costs are appreciably less than the expected price of water delivered at these locations (8 mills/m3). The water delivered by the operation of one super-tug alone would irrigate 16 000 km2. Problems related to both iceberg transport and processing are reviewed and although substantial problems do exist, they appear to be within the capabilities of current technology.

It is suggested that the overall idea is indeed feasible and should be explored further by specific groups of experts.

Radio echo-sounding surveys of Antarctica and Greenland have revealed extensive layering within the ice. Formulae for the effective reflection coefficient, when viewed by a pulsed radar, are derived for isolated or multiple randomly spaced layers. In the latter case the variation in dielectric constant with depth is described by a vertical autocorrelation function and a standard deviation. Some measurements of the reflection coefficient of layers, and the dielectric absorption of ice are given. The significance of the fading of layer echoes and the possible causes of variations in the dielectric constant are considered and some further investigations are suggested.

It is concluded that the echo strengths found in the Antarctic may be explained by multiple layering, and that the necessary fractional change in the dielectric constant may be as small as 10−4. It is suggested that this change in dielectric constant may be due to differences in orientation of anisotropic ice crystals.

The morphology of the Barnes Ice Cap margin at the proglacial Generator Lake is described. Types of calving that take place into the lake are discussed, particularly an observed calving in July 1970 when an ice-ramp of about 0.4 × 106 m3 volume broke off due to a rise in lake level. Bending analyses which throw some light on the calving mechanism are presented.

Uniaxial compressive creep tests were performed on polycrystalline samples of glacier ice at stresses ranging from 0.06 bar to 1.0 bar under conditions similar to those actually occurring in a temperate glacier. Tests were conducted in an ice tunnel on the Blue Glacier, Mt Olympus, Washington, U.S.A., thus ensuring that the temperature remained at the pressure melting point.

The flow law proposed as an appropriate one-dimensional flow law for temperate glacier ice is a polynomial expression containing linear, cubic and fifth-order terms. This law provides a good fit to the data and is also consistent with the quasi-viscous creep data of Glen (1955).

In the summer of 1972, the amount of ice melt obtained by stake measurements on the McCall Glacier, Brooks Range, was compared with the discharge of a small controlled run-off site, and with heat balance calculations. For daily values the agreement was not always good; however, for the 11 d period for which the study was carried out, the agreement can be considered as excellent. The amount of ice melt calculated from run-off and heat balance gave 3.5 and 1.2% higher values, respectively, than the direct measurements. This is encouraging, insofar as it suggests that it may be possible to calculate the combined ice, water, and heat balance for the glacier as a whole.

Friction on the bed is assumed to obey Coulomb’s law of solid friction in the presence of interstitial pressure (Lliboutry, 1968). According to this, the friction is a maximum at certain places in the bottom of the valley. Assuming Glen’s non-linear creep law, the steady-state flow of ice along a regular cylindrical channel of parabolic section has been calculated. The results reproduce to high accuracy the distribution of velocity measured on the Athabasca Glacier (Raymond, 1971).

Although radio echo sounding equipment has been used with success for measuring the thickness of ice sheets in the Arctic and Antarctic, a valley glacier poses the additional problems of echoes from the valley walls, which may obscure the bottom echoes, and a high attenuation of radio waves in the ice. During July and August 1970, a study was carried out on Roslin Gletscher in Stauning Alper, East Greenland, to investigate the problems of radio echo sounding on a valley glacier. Results show that reflections from the valley walls are minimized by using sufficiently directional antennae, but attenuation of the signal in the ice is higher than that in polar ice at the same temperature. Water in and on the ice probably accounts for much of the attenuation, and the use of a lower frequency or measurements before the melt commences should give improved performance.

32Si dating of glacier ice has hitherto been complicated by the poor knowledge of the half life. Furthermore, fall-out of bomb-produced 32Si impedes the determination of the specific activity of cosmic-ray produced 32Si in recent precipitation. Measurements on well-dated pre-bomb samples from the Greenland ice sheet establish a calibration for 32Si dating of up to 1 000 year old polar ice samples of the magnitude of 1 metric ton. If the technique is used on temperate glaciers, samples of pre-bomb deposits (or from after 1970) must be collected for comparison with samples of old ice, using an apparent half life of 295±25 years. Due to secular cosmic-ray flux variations, the true half life of 32Si is estimated at the slightly higher value of 330±40 years.

Unusual seismic signals with weak P phases and well-developed monochromatic shear-wave trains have been recorded and their sources located near College Fiord, Alaska. Epicentral determinations show that they originate on or near glaciers. Some of the events have equivalent earthquake magnitudes of 2.0 to 2.5. These energy sources seem to be compatible with spasmodic glacier movement. Smaller events occur often—as many as 60 per day.

A reconnaissance was made of one of two small ice caps near the Robeson Channel coast of northern Ellesmere Island. It is shown that, after a period of net wastage, this ice cap is now thickening slightly and extending its margins. The present regime of the ice cap is a direct result of generally cooler summers in the last decade.