The longitudinal component of the velocity of a particle at or near a glacier surface is considered, its position as a function of time being termed its trajectory. Functional relationships are derived for obtaining the trajectory from the spatial distribution of velocity and for obtaining the velocity distribution from the trajectory. It is established that the trajectory end-points impose only an integral condition on the velocity distribution, and that no individual point on the velocity distribution can be determined if only the end-points are known. An example is given of a deduced velocity distribution that is consistent with (although not uniquely determined by) the end-points of several trajectories on the lower reach of Columbia Glacier, Alaska. It is shown that constructing a velocity distribution by assigning the average trajectory velocity to the trajectory mid-point can be subject to errors of several per cent for velocity distribution features that are typical of actual glaciers. The error in this method is determined, and closed-form expressions for the trajectory are obtained, for linear velocity distributions and for two classes of second-degree distributions. The class of functions is identified to which the velocity distribution must belong for this error to be zero.

The effect of pressurized subglacial water on the sliding process is examined by a parameter called the “bed separation index”. This index indicates the relative extent of cavity formation by combining the effects of variation of bed-normal stress across undulations (Kamb, 1970) and steady-state water pressure in a Röthlisberger conduit at the glacier bed. Data from three glaciers of widely varying size are used to test the correlation of the bed separation index with inferred sliding rates. For Columbia Glacier and Ice Stream B in West Antarctica it is shown that high water pressure enhances sliding. More complete data from the third test case. Variegated Glacier, are used to compare a number of possible formulations of a “sliding law”. A Weertman-type power law (exponent c. 3), modified for the effect of subglacial water pressure, appears to be most preferable. Other formulations, including the “lubrication factor” hypothesis used by Budd (1975) are tentatively rejected. Consideration of the temporal variations of the “bed separation index” indicate that, on short time scales of days and weeks, variations of water pressure can dominate the sliding process. A rapid order-of-magnitude increase in water discharge causes a hundredfold transient increase in the water pressure. A bi-modal hydraulic regime is revealed for water flow transverse to the direction of main ice flow. This behavior is in accord with the observation of a sudden acceleration of the ice due to increased sliding in early summer or following heavy rainstorms.

It is argued that in temperate mountain glaciers, waterways are subglacial. It is shown that the theory of Spring and Hutter (1981) for intraglacial flooded conduits leads to an equation for the grade line which differs from Röthlisberger’s (1972) only by negligible terms, and a slight modification of the exponent of the discharge. For a subglacial flooded waterway two important processes should instead be introduced: the enhancement of plastic deformation on the up-stream side of bumps, and the heat afforded by ground water (which in winter accounts for most of the discharge). The theory modified in this way explains why Röthlisberger had to adopt an unrealistic value for the rheological parameter of ice. It leads to the conclusion that in areas which are not overdeepened, most of the year subglacial waterways should remain not flooded and at atmospheric pressure. The case of overdeepening is examined. Finally the implications of this new model for glacier sliding theory are demonstrated.

Numerical calculations by finite elements show that the variation of horizontal velocity with depth in the vicinity of a symmetric, isothermal, non-slipping ice ridge deforming on a flat bed is approximately consistent with prediction from laminar flow theory except in a zone within about four ice thicknesses of the divide. Within this near-divide zone horizontal shear strain-rate is less concentrated near the bottom and downward velocity is less rapid in comparison to the flanks. The profiles over depth of horizontal and vertical velocity approach being linear and parabolic respectively. Calculations for various surface elevation profiles show these velocity profile shapes are insensitive to the ice-sheet geometry.

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.

To clear up the changes which had happened at the subglacial catchment of glacier d’Argentière, an extensive study, with 31 borings and a coring down to the bottom (240 m) was performed in 1979/80, just upstream from the catchment, in an overdeepened area. The behaviour of the water level during boring with a hot water jet, and just after, was different from one bore hole to another, mainly because transient leaks appeared in the walls of bore holes. Next, the water level fluctuated slowly, in the same way in most of the deep bore holes, showing that glacier ice below about 100 m deep is slightly pervious. What is so measured is the pore pressure of water in deep ice. The piezometric gradient between bore holes, and the time lag between fluctuations of water level, which increases with distance from the right bank, shows that there is no waterway at the bottom of the overdeepened area, save at its up-stream end. Most of the melt water must flow between ice and rock along the right bank, its free surface rising by about 150 m during the increased discharge in June. No clear-cut correlation between the bottom pore pressure and the air temperature or the discharge at the subglacial catchment down-stream was found.

Results of systematic movement studies carried out by means of an automatic camera on Unteraargletscher since 1969 are discussed together with supplementary theodolite measurements made at shorter intervals and over a longer section of the glacier. In addition to the typical spring/early summer maximum of velocity known from other glaciers, an upward movement of up to 0.6 m has been recorded at the beginning of the melt season. It was followed, after a few fluctuations of the vertical velocity, by an equal but slower downward movement which continued at an almost constant rate for about three months. Possible explanations of the uplift are discussed, the most satisfactory explanation being water storage at the bed. The observations then suggest that this storage system is efficiently connected with the main subglacial drainage channels only during times of very high water pressure in the channels. Detailed measurements showed that the times of maximum horizontal velocity coincided with the times of maximum upward velocity rather than with the times when the elevation of the surveyed poles had reached a maximum. On the basis of the hypothesis of water storage at the bed this finding means that the sliding velocity is influenced mainly by the subglacial water pressure and the actual, transient stage of cavity development, while the amount of stored water is of lesser influence.

Walder recently analyzed the initial instability of water flow in a sheet under a glacier that is produced by greater heat production in the flowing water and thus the larger rate of ice melting where a perturbation has increased the water sheet thickness. We have looked at the problem from the other presumed final state. We assume that instabilities have finally caused all the water to flow in channels (R-channels) at the bed. We investigated whether these channels can collect enough of the water that is produced by the geothermal heat and the heat sliding to remain in existence. When a basal shear stress is present, the distance out to which a channel can collect water is not that much greater than the channel radius itself. It is concluded that it is not likely for the channel to be able to collect appreciable amounts of water that is produced at the bed. Hence despite the indication that an instability initially might grow in a water sheet, this instability either cannot develop to the point when the water flow is primarily in channels or else the water flow alternates cyclically between a state primarily of sheet flow and a state of channel flow. It would appear that the channels that do exist under a glacier have their primary origin in the melt water from the upper surface that pours down moulins and thus is already channelized by the time it reaches the bed.

Mean multi-year values of the components of external mass and energy exchange in the ice sheet, moisture, radiation, and heat balances in the system Antarctic ice sheet/atmosphere have been estimated by various methods.

The major features of the above-mentioned balances have been determined as absolute and relative values. For the moisture balance, income of advective moisture is equal to 100%; loss due to accumulation of moisture in the ice sheet is 83%, due to sink into the atmosphere is 15%, and sink from the ice sheet surface is 2%. As for the radiation balance it has been found that income due to radiation at the top of the atmosphere and absorbed by the atmosphere long-wave radiation are 57% and 43%, respectively; loss due to reflected short-wave radiation is 35%, atmospheric long-wave radiation is 78%, and net outgoing radiation from the surface is 9%. Heat budget components have been found as follows: income due to absorbed short-wave radiation is 49%, advection of heat is 40%, and latent heat from phase transition of advective moisture is 11%; loss due to outgoing long-wave radiation is 98%, heat from phase transition of atmospheric moisture is 2%.

The Antarctic ice sheet is a vast area of heat sink. Constant negative surface radiation balance and low temperature of the ice sheet suggest that the latter will exist at any small amount of precipitation and, therefore, current glaciation of Antarctica is rather stable.

The first extensive and far-reaching investigations of the Sino-German Joint Expedition to the Ch’ing-hai–Hsi-tsang (Qinghai–Xizang) Plateau in the glacierized region of the Amne Machin (Anyemaqen) started work in the area and compiled the glacial inventory in that region. In the past 15 years scientists have found that the majority of glaciers in the Amne Machin (Anyemaqen) have been advancing whereas most glaciers in Ch’i-lien Shan (Qilian Shan), adjacent to Amne Machin (Anyemaqen), have been retreating during the same period. This is a problem worthy of study by glaciologists. Through investigation and analysis, it is also found that Ha-lung (Halong) glacier has the character of a surging glacier. The author tentatively forecasts the next surge of Ha-lung (Halong) glacier and the tendency of variations of glaciers in Ch’i-lien Shan (Qilian Shan) in the near future.

The ice velocity slowdown occurring at Lewis Glacier, Mount Kenya, during the twentieth century has continued beyond 1978. In an earlier paper, a surface velocity decrease approaching 50% was predicted between 1978 and 1985. Measurements to January 1982, halfway through the period, reveal trends generally in line with this forecast: a velocity reduction of order 20% has taken place. The mass flux decreased by at least 25%. Intra-annual variability in velocity pattern and magnitude is apparent; comparatively rapid values occur during the January–February dry season.

Observations obtained in a long-term monitoring program on Lewis Glacier, Mount Kenya, include measurements of net balance and velocity at a stake network over the period 1978–82, and airborne mapping of the glacier surface topography at the beginning and end of this interval. Horizontal and vertical flow components and mass continuity are evaluated along the longitudinal axis of the glacier.

The largest horizontal velocity at the surface is about 5 m a−1, while the submergent vertical velocity at the surface in the upper, and the emergent component in the lower glacier are of the order of 1–2 m a−1. Horizontal and vertical flow components in the interior of the glacier are calculated from the surface observations under plausible assumptions. Isotachs and streamlines plotted in a longitudinal–vertical cross-section permit the estimation of representative residence times of ice within Lewis Glacier. The largest values for the longest trajectories with submergence at the surface in the uppermost area of the glacier and emergence near the snout are of the order of a few centuries. However, such estimates are compromised, in particular, by the continuing non-equilibrium conditions of Lewis Glacier.

Mass continuity is directly related to the vertical motion field. In the upper area of the glacier the submergence velocity exceeds the rise of glacier surface observed with respect to the stake network, while in the lower glacier the emergent flow component falls short of the local negative net balance. This differing behavior of altitudinal zones is consistent with the fact that actual lowering of the glacier surface topography documented by the repeated airborne mappings is larger than expected from the stake network in the upper but less in the lower glacier. This differing behavior of altitude zones appears mitigated by the tendency for confluence in the upper and diffluence in the lower glacier.

The relationship between supraglacial lateral moraines and lateral dump moraines at Arolla. Switzerland, is discussed. A detailed study of the lateral moraines of glacier de Tsidjiore Nouve reveals their complex form (as superimposed and nested ridges) and the current mode of development (possibly related to the passage of a kinematic wave). Sedimentological analysis indicates that much of the constituent debris is of supraglacial origin; it is transported either directly from the base of slopes flanking the Pigne d’Arolla ice-fall or via englacial septa comprising marginal sediment incorporated in the accumulation zone. A calculation of the volume of debris in the lateral moraines suggests that glacier de Tsidjiore Nouve has recently been more active in transporting and depositing supraglacial debris than in glacial erosion sensu stricto.

Field study of the bergschrund of a small avalanche-cone glacier at the base of Mt Chephren, in Banff National Park, has been carried out as part of a general exploratory study of glacier-head crevasses in the Canadian Rockies. The bergschrund consists of a wide, shallow, partly bedrock-floored gap, underneath which extends a nearly vertical Randkluft, and a small, offset, subsidiary crevasse (or crevasses). The following observations regarding the behavior of the bergschrund and ice adjacent to it are of particular interest: (1) topography of the subglacial bedrock is a control on the location of the main bergschrund and subsidiary crevasses, (2) the main bergschrund and subsidiary crevasse(s) are connected by subglacial gaps between bedrock and ice; the gaps are part of the “bergschrund system”, (3) snow/ice immediately down-glacier of the bergschrund system moves nearly vertically downward in response to rotational flow of the glacier, allowing the bergschrund components to keep the same location and size from year to year, (4) an independent accumulation, flow, and ablation system exists in the snow/ice up-glacier of the bergschrund system. (5) most of the void space in the bergschrund system is maintained through the winter, although the wide, shallow part of the main bergschrund fills up with snow, (6) some mass transfer of snow/ice occurs across the bergschrund system, (7) displacement across the bergschrund due to flow of the main glacier body results in significantly more snow being deposited each winter down-glacier of the bergschrund than up-glacier of it.

In a snow pit, incorporating about 2.5 a of accumulation, on the 4 450 m high Colle Gnifetti, Monte Rosa, various snow characteristics, isotopes (δ18O, 3H), electrical conductivity, dust, trace elements, and pollen were investigated. The aim of this study was to develop a key for the stratigraphic interpretation of cores from cold, high-alpine firn areas. It appears that the strong influence of wind results in mixing and re-sedimentation processes in the surface layers. Nevertheless, by interpreting several parameters in a combined way, it is possible to classify a large number of the layers according to their season and sometimes to their place of origin. Apart from the melt layers, which only appear in early summer to summer layers, other prominent features are the (Saharan) dust falls, characterized by dust and conductivity peaks.

Isotropic points are structurally stable features of any complicated field of stress or strain-rate, and therefore will almost always be present on the surface of a glacier. A given isotropic point for strain-rate will belong to one of six different classes, depending on the pattern (lemon, star, or monstar) of principal directions and the contours (ellipses or hyperbolas) of constant principal strain-rate values in its neighbourhood. The central isotropic point on a glacier should theoretically have a monstar pattern, but the contours around it may sometimes be elliptic and sometimes hyperbolic. Nearby, but not coincident with it there will be an isotropic point for stress. This will also have a monstar pattern but, in contrast to the strain-rate point, the contours around it must be hyperbolic. Published examples are consistent with these conclusions. In addition to isotropic points for strain-rate a glacier surface will contain isolated points of pure shear; these also can be classified into six different types. Stable features of this kind give information about the essential structure of a tensor field and form useful points of comparison between observation and numerical simulation.

A comprehensive series of dye tracer tests was undertaken over two summers at Pasterzengletscher, Austria, and from these a number of important conclusions can be drawn. A lateral division of drainage on the lower tongue was proved, but this was not determined by the direction of oblique crevasses. Water from many moulins passed into two or more drainage courses, as shown by repeated patterns of multiple peaks on the time/concentration curves. The spatial pattern of travel times from different moulins on the tongue was complex, although it remained stable over time. Repeated tracer tests showed that throughflow velocities varied by up to an order of magnitude during a single day. Maximum velocities occurred at the time of peak discharge, and probably the large diurnal velocity variations are caused by changes in the proportion of the length which has channel-full pressure flow. However, seasonal velocity variations were much smaller, although changes in outflow discharge were larger than in the diurnal case. This gives strong support to the concept that channels adjust in size to the average water discharge passing through, and that these changes occur over a matter of days or a few weeks.

Eight submarine ice cliffs have been observed on the west side of McMurdo Sound. Three of these cliffs (Miers Valley, Cape Chocolate, and Strand Moraines) are associated with known ice-cored moraines and are justifiably regarded as underwater exposures of ice cores in the adjacent coast. The ice cliffs at Explorers Cove and near Herbertson Glacier may also be underwater exposures of ice cores which may be present in adjacent moraines. Some of these ice cliffs may represent unusual submarine accretionary sea-ice structures.

18O and deuterium content was measured in snow and ice samples collected from two crevasses on temperate glaciers high in the Andes and in the Himalaya. The results show that, due to intense exposure to sun, a significant part of the annual accumulation of snow is removed by melting and sublimation, the latter being predominant. There is strong empirical evidence that in natural conditions which are characteristic of both the glaciers studied sublimation of the snow cover can be approximated by the thermodynamic equilibrium process. The short-term fluctuations, though slightly moderated, and longer-term variations can still be observed in the deeper parts of the glaciers in spite of firnification of the snow.