An existing thermodynamic ice-growth model (Semtner, 1976) has been tested for its ability to predict the growth of fast ice in McMurdo Sound, Antarctica. Significant discrepancies between observed and predicted ice thicknesses were found to occur, primarily due to the presence of sub-ice platelets and the formation of a snow-ice layer. Although these ice-growth processes are not well enough understood to permit rigorous physical modelling, it is shown that fairly simple modifications to the model greatly improve the accuracy of the thickness predictions, and serve to highlight the importance of these processes in the Antarctic fast-ice environment. Surface flooding and snow-ice formation are assumed to occur immediately upon the establishment of a positive hydrostatic water level, and a surface temperature in excess of a critical value, above which interconnecting channels in the ice matrix permit the flow of water to the surface. The presence of the sub-ice platelet layer is assumed to increase columnar ice growth at a rate proportional to the volume fraction of ice in the platelet layer, a simple technique but one that permits estimates of platelet-enhanced growth without detailed knowledge of oceanographic conditions. The resulting model predictions are in close agreement with measurements of fast-ice growth and decay in McMurdo Sound; however, data suitable for testing the model over a complete range of conditions and over multi-year cycles are not available at the present time.

Ice salinity and 18O/16O ratios were measured on 12 ice cores drilled from thick, multi-year land-fast sea ice (MLSI) off the north coast of Ellesmere Island, Canada. Fresh, brackish, and sea ice were identified in the ice cores using the 18O/16O ratios. Two cases are considered: case 1, which assumes that no isotopic fractionation occurs on freezing; and, case 2, which assumes that a maximum isotopic fractionation factor (a) of 1.003 applies. The amount of each ice type is variable among the cores, but overall the 12 cores comprise 29.6% brackish ice, 70.0% sea ice, and 0.4% fresh ice in case 1, and 42.3% brackish ice, 57.3% sea ice, and 0.4% fresh ice in case 2. The data suggest that time-dependent brackish sea-water stratification below the ice is quite common and is often associated with the inverted bottom topography. However, the stratification is not always confined to small, areally limited under-ice melt pools in inverted depressions, and neither is it a summer-only phenomenon. Brackish ice growth apparently occurs in a brackish water layer that in some instances underlies the ice sheet year-round. For both case 1 and case 2 the salinity distribution in brackish ice is positively skewed, with 50% of salinity values occurring in the range 0–0.49‰. Sea-ice salinity values are more evenly distributed. In case 1, brackish ice has mean salinity and mean δ18O values of 0.66 and –19.9‰, respectively, compared to mean values of 1.88 and –6.5‰ for the sea ice. In case 2, brackish ice has mean salinity and mean S18O values of 0.75 and –18.1% compared to mean values of 2.03 and –5.2‰ for the sea ice. The salinity of brackish ice and sea ice, ice-growth mechanisms, and the inclusion of brine in the sub-structure are discussed briefly.

Water in polycrystalline ice at its melting point forms a system of veins at the three-grain junctions. The veins join together at nodes, which are the four-grain junctions. The shape of a node, a tetrahedron with non-spherical faces and open corners, is determined completely by the dihedral angle for water in contact with a grain boundary. Using the observed value for this angle, namely 33.6°, the paper computes the tetrahedral shape. This is a surface-tension problem with initially unknown boundaries. The result shows that the ratio of vein volume to node volume is R = 0.072 l/d, where l is the average length of a vein between two nodes, and d is the vein diameter measured between edges. For example, in a specimen of ice grown from the melt in the laboratory R was 18.

The temperature field is derived for a sinusoidally varying surface temperature with varying solar radiation penetration. The growth rates of snow crystals are calculated to explain the rapidly growing layers of faceted crystals (i.e. depth hoar) that form just below the surface at high altitudes and in polar snow. The solutions also show that a layer of wet snow can exist just below the surface even on days when the surface temperature remains sub-freezing.

A substantial data set of digitally recorded radio echo-sounding data was collected over 44 ice masses in Spitsbergen and the ice caps on Nordaustlandet, Svalbard. These data have allowed quantitative analysis of bed and internal power-reflection coefficients. Substantial regional differences were observed and have been correlated with the presence of water and/or moraine at the bed and with the bulk thermal regime of the ice mass. Values of bed power-reflection coefficient varied between −40 ± 5 and −8 ± 6 dB. It is suggested that the ice caps in north-east Spitsbergen (possessing among the lowest reflection coefficients observed) are frozen to their beds as is much of Austfonna (in Nordaustlandet), and that such values imply the likelihood of a layer of debris-rich ice above the bedrock. It is proposed that significant quantities of water are present at the ice/bed interface of many of the glaciers in north-west Spitsbergen. Further, it is believed that two geological divides were detected. A number of extraordinary internal reflecting horizons are also discussed.

A numerical simulation of the Ross Ice Shelf, Antarctica, in which discharge from Ice Streams A-E is changed suddenly between extreme states, is used to investigate ice-shelf thickness and flow anomalies generated by ice-stream transience. At one extreme, ice-stream discharge rates specified as model boundary conditions are balanced individually with snow accumulation in the ice-stream catchment areas. At the other, discharge rates are fixed at current observed values which widely depart from mass balance. The simulated ice-shelf evolution between initial and final steady states suggests that ice-thickness and velocity fields adjust to new ice-stream conditions over a relatively short time span (approximately 500 years). In contrast, transitory geometrics of medial moraines and relict-crevasse bands persist over a longer time span (up to 2000 years). Contortions of medial moraines and relict-crevasse bands thus may provide a useful long-term history of past ice-stream activity. The past stoppage of Ice Stream C, for example, should be evident today in some medial moraine trajectories even if the stoppage occurred over 1000 years ago. Ice-shelf thickness fluctuations induced by ice-stream activity are generally restricted to the neighborhood of the grounding line. These fluctuations may constitute a trigger for ice-rise formation near ice-stream outlets.

A polarization-sensitive aperture-synthesis experiment has been carried out using radio-echo data from Storglaciären, Sweden. Echoes were recorded in each of three antenna configurations over an array of sites on the glacier surface. The echo information was transferred to a mainframe computer and manipulated in order to reveal any major individual targets present. Within a 100 m cube, six major targets were identified, each with its own echoing characteristics. Echo strengths indicate that the targets are probably cavities containing water. It cannot be determined whether they are isolated or parts of a continuous system.

Preliminary results are presented on a solution of the two-dimensional time-dependent continuity equation for mass conservation governing ice-sheet dynamics. The equation is solved using a column-averaged velocity to define the horizontal flux in a finite-element formulation. This yields a map-plane model where flow directions, velocities, and surface elevations are defined by bedrock topography, the accumulation/ablation pattern, and in the time-dependent case by the initial surface configuration. This alleviates the flow-band model limitation that the direction of flow be defined and fixed over the course of the modeling experiment. The ability of the finite-element method to accept elements of different dimensions allows detail to be finely modeled in regions of steep gradients, such as ice streams, while relatively uniform areas, such as areas of sheet flow, can be economically accommodated with much larger elements. Other advantages of the finite-element method include the ability to modify the sliding and/or flow-law relationships without materially affecting the method of solution.

Modeling experiments described include a steady-state reconstruction showing flow around a three-dimensional obstacle, as well as a time-dependent simulation demonstrating the response of an ice sheet to a localized decoupling of the bed. The latter experiment simulates the initiation and development of an ice stream in a region originally dominated by sheet flow. Finally, a simulation of the effects of a changing mass-balance pattern, such as might be anticipated from the expected carbon dioxide warming, is described. Potential applications for such a model are also discussed.

SYMBOLS USED

a(x,y) Accumulation/ablation rate.

A Flow-law parameter.

B Sliding-law parameter.

CijC Global capacitance matrix.

f Fraction of the bed melted.

Fij,F Global load vector.

g Acceleration of gravity.

hj,h Ice-surface elevation.

H Ice thickness.

k(x,y) Constitutive equation constant of proportionality.

kij Global stiffness matrix.

m Sliding-law exponent.

n Flow-law exponent.

ρ Density of ice.

σ(x,y) Ice flux.

t Time.

U Column-average ice velocity.

UF Column-average deformation (flow) velocity.

US Sliding velocity.

v Variational trial function.

x,y Map-plane coordinates.

A practical method is developed for calculating stresses and velocities at depth using field measurements of the geometry and surface velocity of glaciers. To do this, it is convenient to partition full stresses into lithostatic and resistive components. The horizontal gradient in vertically integrated lithostatic stress is the driving stress and it describes the horizontal action of gravity. The horizontal resistive stress gradients describe the reactions. Resistive stresses are simply related to deviatoric stresses and hence to strain-rates through a constitutive relation.

A numerical scheme can be used to calculate stresses and velocities from surface velocities and slope, and from ice thickness. There is no mathematical requirement that the variations in these quantities be small.

Resistive stresses and velocities at depth are calculated along the Byrd Station Strain Network, Antarctica, using field data. There are found to be large longitudinal variations in basal drag and this result is little affected by errors in the input data or by uncertainties in the constitutive relation for ice. Basal drag varies by a factor of about 2 along the strain network, and is usually equal to the driving stress to within 10–20%. Sites of high drag are not always correlated with basal topographic highs, indicating that some process such as basal water drainage is involved in controlling the friction at the bed. Basal sliding velocities are very sensitive to errors in measured surface velocities and the rate factor in Glen’s flow law. As a result, calculated sliding velocities are much less reliable than deep stresses, and need to be interpreted with caution.

Stresses at the surface and at depth are calculated for a stretch of Byrd Glacier, Antarctica. The calculations are based on photogrammetrically determined velocities and elevations, and on radio-echo-determined ice thicknesses. The results are maps of drags from each valley wall, of normal forces laterally and longitudinally, and of basal drag. Special challenges in the calculation are the numerical gridding of velocity, ensuring that unreasonable short-wavelength features do not develop in the calculation, and inference of ice thickness where there are no data.

The results show important variations in basal drag. For the floating part, basal drag is near zero, as expected. Within the grounded part, longitudinal components of basal drag are very variable, reaching 300 kPa with a dominant wavelength of 13 km. Generally, these drag maxima correlate with maxima in driving stress. Usually the across-glacier component of basal drag is small. An important exception occurs in the center of the grounded part of the glacier where the flow shows major deviations from the axis of the valley.

Other results are that side drag is roughly constant at 250 kPa along both margins of the glacier, tension from the ice shelf is about 100 kPa, and tension in the grounded part cycles between 250 and 150 kPa. Calculated deep velocities are too large and this is attributed to deficiencies in the conventional isotropic flow law used.

Two distinct medial moraines are located on the tongue of Ghiacciaio dei Forni (Rhaetian Alps, Italy); they are formed by the confluence of three ice streams. The two ice-cored medial moraines originate from rock outcrops situated below the snow line. The moraines, which on the surface comprise angular clasts, extend for approximately 2 km and reach a maximum height of 10 m. Nourishment of the moraines seems to be due primarily to the supraglacial debris derived from the rock walls. Measurements made in the late summer of 1985 provided evidence of the role played by differential ablation in the development of these moraines. Sedimentological analysis further confirmed the mainly supraglacial origin of the debris comprising the moraines.

The flow of ice over a bump under steady-state conditions has been studied both experimentally and numerically. The experiments were performed with the ice viscometer installed at the Laboratoire de Glaciologie et Géophysique de l'Environnement du C.N.R.S. (LGGE) in Grenoble, France. The flow was observed by means of a marker network photographed at fixed time intervals. The separation of the ice down-stream of the bump and the non-linearity of the generally accepted Glen’s flow law led to the modelling of this flow using a finite-element method. The results describe the velocity and stress fields in ice moving over a bump and obeying Glen’s flow law (until now only relatively rough approximations of these fields have been given in the literature). The comparison of the observed and calculated network deformations shows that, although ice flowing over a bump does not undergo steady creep, the use of Glen’s flow law with an exponent n = 3 remains justified when simulating the flow of a glacier over its bed under steady-state conditions.

Satellite-altimeter data over ice sheets provide the best tool for mapping their topography and its possible climatic variations. However, these data are affected by measurement errors, orbit errors, and slope errors. We develop here a three-step inversion technique which accommodates the a priori information on the expected topography and correctly handles and propagates the data errors: it estimates first a large-scale reference surface, then maps the residuals related to undulations, and finally iteratively corrects the slope error. The method is tested on overlapping small fragments of the Antarctic ice sheet, using a sub-set of Seasat data. Finally, a topographic map of Terre Adélie is produced. Over areas of small slopes, the a posteriori error should be of the order of 0.4 m. Using ERS-I data, it is therefore expected that climatic variations in the ice-sheet topography since the introduction of Seasat will be observable.

Analysis of the likely behavior of a water system developed between ice and an unconsolidated glacier bed suggests that, in the absence of channelized sources of melt water, the system will approximate a film of varying thickness. The effective pressure in such a film will be proportional to the basal shear stress but inversely proportional to the fraction of the bed occupied by the film. These hypotheses allow calculation of the sliding and bed-deformation velocities of a glacier from the water supply and basal shear stress, as discussed in the second and third papers in this series.

Basal motion of a glacier resting on an unconsolidated bed can arise from sliding between ice and bed, ploughing of clasts through the upper layer of the bed, pervasive deformation of the bed, or shearing across discrete planes in the bed. Theoretical analyses and limited observations of soft-bedded glaciers not dominated by supply of channelized melt water from the surface suggest that sliding will be slow if the bed contains abundant clasts in the 1–10 mm size range, and that high velocities by ploughing are unlikely though possible. Pervasive deformation usually will account for 60–100% of the basal velocity, and the strain-rate will be proportional to the basal shear stress and inversely proportional to the square or cube of the effective pressure. These hypotheses are based on results of part I in this series, and allow modeling of Ice Stream B, West Antarctica, in part III of this series.

Geophysical studies and glaciological analyses suggest strongly that Ice Stream B, West Antarctica, moves primarily by pervasive deformation of a meters thick subglacial till. Analysis of the longitudinal profile of the ice stream up-stream of the ice plain suggests that basal sliding is slow everywhere, that effective pressure decreases slowly down-stream, and that the strain-rate of pervasive shear is proportional to the basal shear stress and inversely proportional to the square or cube of the effective pressure. Discrete shearing may occur beneath the pervasively deforming zone. These and other hypotheses, which build on the analyses of the first two papers in this series, can be tested in the field.

We present here a shear-creep apparatus. This has been designed to study grain-boundary behaviour in ice bi-crystals. The design and dimensions of this apparatus were determined by taking into account the results of earlier tests, performed on the same types of sample. Improvement with the new device is obtained; it allows a displacement with two degrees of freedom in the grain-boundary plane, and direct observations of micro-structural changes during the test.

We have constructed a back-portable, impulse radar instrument that weighs roughly 12 kg, can be powered by dry cells, and records and stores data digitally. The radar is controlled by an on-board, purpose-built microcomputer that ensures simple field operation, facilitates modifications, and allows unattended operation when investigating time-varying targets. The transmitting unit is triggered from the receiver via an optical link and generates an electromagnetic wavelet by discharging two high-voltage capacitors through back-to-back silicon-controlled rectifiers into a resistively loaded dipole antenna. Successful field operations carried out during the summers of 1986 and 1987 include depth profiling, as well as studies of englacial and subglacial targets, on several temperate and sub-polar glaciers.