The two-dimensional, time-dependent flow of an arbitrarily shaped ice mass can be successfully modeled with the finite-element technique on a small computer. Methods developed for automatically generating the mesh data greatly simplify the data preparation and optimize the numerical simulations. Using quadratic basis functions permits the flow to be approximated quite adequately by only two element rows (five nodes vertically). Mixed-order basis functions, however, must be used so that numerical oscillations do not set in, and the ends of the ice mass, where the thickness tends to zero, must be treated carefully. Time simulations to a steady-state condition are necessary to test such numerical models adequately.

South Cascade Glacier, Washington, is currently close to equilibrium. A bedrock sill dominates the bed topography in the lower half of the glacier, rising to a height of about 20% of the ice thickness. This sill produces a maximum increase in the overall thickness of about 6–7% compared to what the thickness would have been if the sill were not present. Finally, this glacier does not appear to be sliding much, if at all, despite its maritime alpine environment. This could help explain the difficulties encountered when trying to measure sliding and basal water pressures on the same glacier (Hodge, 1979), or it could imply that drag exerted by the valley walls has a significantly greater effect than conventional shape-factor concepts imply.

The custatic changes of the ocean in prehistoric and historical times are linked with the fate of the ocean-based salt industry, and are recognized as erratic. An hypothesis is proposed to explain these erratic changes with albedo changes of the polar ice sheets, caused in turn by erratic volcanic dust fall-out. Ash layers in Antarctic ice cores are connected with historical dislocations of maritime civilizations.

Albedo changes associated with the dusting of ice sheets are considered to be the cause of the decline of periods of glacierization generally. Such albedo changes are connected with volcanic activity on the one hand, and loess formation on the other, caused in turn by the growth of the ice sheets.

Steady plane flow under gravity of an axisymmetric ice sheet resting on a horizontal rigid bed, subject to surface accumulation and ablation, basal drainage, and basal sliding is treated according to a power law between shear traction and velocity. The surface accumulation is taken to depend on height, and the drainage and sliding coefficient also depend on the height of overlying ice. The ice is described as a general non-linearly viscous incompressible fluid, and temperature variation through the ice sheet is neglected. Illustrations are presented for Glen’s power law (including the special case of a Newtonian fluid), and the polynomial law of Colbeck and Evans. The analysis follows that of Morland and Johnson (1980) where the analogous problem for an ice sheet deforming under plane flow was considered. Comparisons are made between the two models and it is found that the effect of the third dimension is to reduce (or leave unchanged) the aspect ratio for the cases considered, although no general formula can be obtained. This reduction is seen to depend on both the surface accumulation and the sliding law.

The typical U-shaped cross-section of glaciated valleys is well known but little understood. If a climatic change results in a glacier occupying a deep river valley, and some erosion is assumed to occur wherever the ice makes contact with the bedrock, then a partial change from the “V” to “U” section is to be expected. A more potent agency in such a change is probably the sapping of the valley sides by the alternate freezing and thawing of melt-water flowing down to, and under, the glacier. This has been briefly suggested by de Martonne and worked out somewhat more fully in the case of cirques1

Measurements have been made using two different methods of the rate at which the glacier Austerdalsbreen is slipping past its side wall at four sites. The rate of slipping varies from site to site in a way which seems to be connected with the details of glacier flow in the neighbourhood, and in all cases is less than the slip previously measured further up-glacier at the foot of one of the ice falls, and is also a smaller fraction (about one sixth) of the flow rate in the centre of the glacier. One of the methods measured the velocity of the last metre of ice, and this method gave movements which were more erratic than the other method, which measured velocity a few metres from the edge. This suggests that protuberances of rock and boulders lodged between the ice and the rock wall cause local variations in flow which are smoothed out in a few metres. The results are discussed in connection with the process of glacial erosion.

Numerical glacier and ice-sheet models compute evolving ice geometry and velocity fields using various stress-balance approximations and boundary conditions. At high spatial resolution, with horizontal mesh/grid resolutions of a few kilometers or smaller, these models usually require time steps shorter than climate-coupling time scales because they update ice thickness after each velocity solution. High-resolution performance is degraded by the stability restrictions of such explicit time-stepping. This short note, which considers the shallow ice approximation and Stokes models as stress-balance end members, clarifies the scaling of numerical model performance by quantifying simulation cost per model year in terms of mesh resolution and the number of degrees of freedom. The performance of current-generation explicit time-stepping models is assessed, and then compared to the prospective performance of implicit schemes. The main results highlight the key roles played by the algorithmic scaling of stress-balance solvers and coupled, implicit-step solvers.

An in-depth analysis of seven samples from the Siple Dome (Antarctica) ice core, using optical microscopy and electron backscatter diffraction, illustrates rotational recrystallization or polygonization in the fine-grained region of the core between 700 and 800 m. Between 640 and 700 m, the microstructure is characterized by a bimodal grain-size distribution and a broken girdle fabric with evidence of polygonization. From 727 to 770 m, mean grain size decreases and a single-maximum fabric is found, and, by 790 m, mean grain size has again increased and a multiple-maxima fabric manifests itself. We compare grain-size distribution, c- and a-axis orientation, and misorientation between adjacent grains. We found that misorientations between adjacent grains in the 727–770 m region were predominantly low-angle and typically around a common a-axis, suggesting polygonization. This conclusion is supported by radar evidence of a physical disturbance at 757 m, which may be correlated with higher than usual strain in the 700–800 m range. Below 770 m, larger less regular misorientations and textural evidence show that migration recrystallization is the primary recrystallization mechanism.

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.

A method of continuously recording the r.f. power returned from a sub-glacial ice/rock or ice/water interface is described. Illustrations of the records produced are given and their relevance to the reconstruction of the small scale roughness of a reflecting surface is discussed.

Ogives form beneath active ice falls whose heads are situated near or below the firn line. They consist of curved bands of alternating white, bubbly, less dense ice and darker, denser ice with fewer bubbles, extending throughout the thickness of the glacier. The difference in character is held to be due to the different conditions in the upper ice fall, through which the ice passes in one year at high speed. In summer the thin and shattered ice is exposed to high temperatures and melt water, while in winter the conditions are of Arctic-type throughout the thickness of the attenuated ice. A lane of ice on the Gornergletscher, originating as cold, dry snow with no melt water present, illustrates the character and origin of the white bubbly ice. The greater elevation of this cold-snow ice and the waves formed beneath the ice falls are considered to be the result of the lesser thermal conductivity and greater albedo of the white bubbly ice.

Dual frequency (X-band and L-band) synthetic-aperture radar imagery of sea ice is examined to show the differences between the bands and their complementary nature for resolving ambiguities in interpretation. High backscatter at X-band from visibly smooth thin ice is not observed at L-band. One hypothesis is that the high X-band backscatter may be caused by a reflective layer at the snow/ice interface. A second hypothesis is that the high X-band backscatter may be caused by moisture in the snow. A third hypothesis states that the phenomenon may be due to snow flowers. High backscatter at L-band is observed for slush on open water. The return is very weak at X-band, thus allowing distinction of slush by comparing L-band and X-band images. High intensity, but only partial returns from icebergs at L-band have been observed. The hypothesis is that internal iceberg/sea-water reflections are occurring. Some signals are directed away from the antenna, other reinforced signals are returned, producing very bright images. Occasionally, time-delayed signals are returned causing a false image at far range from the iceberg. The conclusion is that L-band is a poor choice for studies of iceberg distribution and size, but a good choice for iceberg detection because of the high reinforced returns from many icebergs and the low return from the adjacent sea ice. The penetration and subsequent signal loss of L-band in glacial ice, when compared to high X-band returns, may be useful to map glacierized land masses.

The sliding law is defined as a basal boundary condition for the large-scale bulk ice flow, relating the tangential traction τb, overburden pressure pb, and tangential velocity ub on a smoothed-out mean bed contour. This effective bed is a lower boundary viewed on the scale of the bulk ice flow and is not the physical ice/rock or sediment interface. The sliding relation reflects on the same scale the complex motion taking place in the neighbourhood of the physical interface. The isothermal steady-state ice-sheet analysis of Morland and Johnson (1980, 1982) is applied to known surface profiles from the Greenland ice sheet and Devon Island ice cap, with their corresponding mass-balance distributions, to determine τb, pb, and ub for each case. These basal estimates are used in turn to construct, using least-squares correlation, polynomial representations for an overburden dependence λ(pb) in the adopted form of sliding law τb ═ λ(pb)ub1/m with m ≥ 1.

The two different data sets determine functions λ(pb) of very different magnitudes, reflecting very different basal conditions. A universal sliding law must therefore contain more general dependence on basal conditions, but the two relations determined appear to describe the two extremes. Hence use of both relations in turn to determine profiles compatible with given mass-balance distributions can be expected to yield extremes of the possible profiles, and further to show the sensitivity of profile form to variation of the sliding relation. The theory is designed as a basis for reconstruction of former ice sheets and their dynamics which are related to the two fundamental determinants of surface mass balance and basal boundary condition.

Two-dimensional finite-element calculations of velocity and temperature fields have been applied to the energy balance of a cross-section of Barnes Ice Cap, Baffin Island, Canada. The flow plane currently is cooling near the ice divide and warming near the margin. Long-term simulations show a net warming trend followed by a cooling trend with a steady-state average temperature similar to the present. Sensitivity studies on an idealized version of the flow plane show that the overall temperature responds less than surface-temperature forcing, because a negative feedback in temperature advection is substantially larger than a positive feed-back in strain heating. The response times of the flow plane by itself are somewhat faster but of the same magnitude as response times that would be estimated from one-dimensional modeling. When bedrock-temperature calculations are included, response times increase an order of magnitude, but these do not substantially affect the short-term response.

Previously the author had suggested that frazil nucleation occurs by a mechanism analogous to spinodal decomposition, aided by turbulence. After further study the following points are made: (1) No critical point exists between solid and liquid; this rules out true spinodal decomposition. (2) Pure water can be supercooled to -40°C; at -40°C the theoretical energy barrier to nucleation is about 10 -19 J. Frazil forms after supercooling less than 0.1 deg; at this temperature the theoretical energy barrier is about 10-14 J. (3) Theory shows that turbulence increases the energy barrier. (4) Turbulence may aid dissipation of heat of solidification, but not sufficiently to account for observed frazil formation at small supercoolings. (5) The author's evidence that frazil can begin to form at supercoolings as small as 0.02 deg suggests that no nucleus except ice itself can account for "heterogeneous" nucleation of frazil.

The objective of this research is to model snow's response to dynamic, impact loading. Two constitutive relationships are considered: elastic and Maxwell-viscoelastic. These material models are applied to laboratory experiments consisting of 1000 individual impacts across 22 snow column configurations. The columns are 60 cm tall with a 30 cm by 30 cm cross-section. The snow ranges in density from 135 to 428 kg m−3 and is loaded with both short-duration (~1 ms) and long-duration (~10 ms) impacts. The Maxwell-viscoelastic model more accurately describes snow's response because it contains a mechanism for energy dissipation, which the elastic model does not. Furthermore, the ascertained model parameters show a clear dependence on impact duration; shorter duration impacts resulted in higher wave speeds and greater damping coefficients. The stress wave's magnitude is amplified when it hits a stiffer material because of the positive interference between incident and reflected waves. This phenomenon is observed in the laboratory and modeled with the governing equations.