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.

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.

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.

Some generally accepted views on joints in rocks, particularly exfoliation joints, are summarized. Lewis’ pressure release hypothesis is assessed in relation thereto. An additional hypothesis is suggested whereby the existing stress system in rocks due to the removal of overburden which would favour exfoliation, would be augmented by freezing of the saturated rock when the ice retreats, so triggering this type of extension joint.

Two neighboring Patagonian glaciers are described. They are fed from the same ice field but one is advancing and the other retreating. Various possible causes of this phenomenon are described.

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.

Shallow firn cores, in addition to a near-basal ice core, were recovered in 2018 from the Quelccaya ice cap (5470 m a.s.l) in the Cordillera Vilcanota, Peru, and in 2017 from the Nevado Illimani glacier (6350 m a.s.l) in the Cordillera Real, Bolivia. The two sites are ~450 km apart. Despite meltwater percolation resulting from warming, particle-based trace element records (e.g. Fe, Mg, K) in the Quelccaya and Illimani shallow cores retain well-preserved signals. The firn core chronologies, established independently by annual layer counting, show a convincing overlap indicating the two records contain comparable signals and therefore capture similar regional scale climatology. Trace element records at a ~1–4 cm resolution provide past records of anthropogenic emissions, dust sources, volcanic emissions, evaporite salts and marine-sourced air masses. Using novel ultra-high-resolution (120 μm) laser technology, we identify annual layer thicknesses ranging from 0.3 to 0.8 cm in a section of 2000-year-old radiocarbon-dated near-basal ice which compared to the previous annual layer estimates suggests that Quelccaya ice cores drilled to bedrock may be older than previously suggested by depth-age models. With the information collected from this study in combination with past studies, we emphasize the importance of collecting new surface-to-bedrock ice cores from at least the Quelccaya ice cap, in particular, due to its projected disappearance as soon as the 2050s.

Instead of starting with an initially dry, below sea-level basin undergoing glacierization, as was done in an earlier. model, the present computations are based on the existence of an open channel connecting the Ross and Bellingshausen Seas. The period of glacierization begins as the sea in the channel freezes permanently and acquires accumulation, both from local precipitation and transport from the adjacent mountains. Times of growth of the ice shelf, by combined freezing from below and accumulation of 10 and 20 cm. yr.−1, respectively, are determined for the case of a linear temperature profile in the ice. After the ice shelf becomes grounded further growth is by accumulation only. Steady-state temperature profiles for ice sheets 2,300 and 4,300 m. thick are computed under assumption of constant geothermal heat flux of 10−6 cal. cm.−1 sec.−1 and compared with observed temperatures in the 300 m. drill hole at Byrd Station. Basal melting of the 4,300 m. thick ice is found to exist only for the smaller accumulation rate.

The effect of down-slope motion and sinking of ice strata on the vertical temperature profile of the surface layer is studied with aid of the Benfield-Radok formula. Assuming no climatic temperature change and an initial temperature gradient at the ice crest of 1° C. increase per 100 m. increase in depth, the curve of best fit of all those tried is for a sinking rate of 20 cm. yr.−1 and a down-slope speed of 85 m. yr.−1 (2,130 yr. of motion from the crest).

A 3-year record of weekly snow water equivalent (SWE) accumulation at Summit Camp, central Greenland ice sheet, obtained by direct sampling, is presented. While the overall SWE accumulation of 24.2 cm w.e. a−1 matches long-term ice core estimates, variability increases at shorter timescales. Half of the annual SWE accumulation occurs during a few large events, with the average accumulation rate decreasing 35% between the first and second halves of the record coinciding with exceptional anticyclonic conditions in the spring and summer of 2019. No seasonality in accumulation is detected. Rather, local accumulation rates appear to be significantly impacted by wind redistribution that obscures temporal patterns in snowfall. Surface snow density is consistent, on average, with previously measured values but does not correlate with near surface temperature or wind speed. Two surface mass balance reanalysis models significantly underestimate accumulation rates at Summit Camp. This is concerning because such models are often used to estimate ice-sheet mass loss.

Avalanche data were obtained by direct observation of the Vaughan Lewis Icefall. Magnitude, time and location of each ice fall were recorded and the resulting data were analyzed statistically. An inverse relationship was found between the relative frequency and the magnitude of the avalanches. A significant diurnal variation in avalanche rate was also detected. During the early morning hours the avalanche rate reached a maximum. No secondary increase in the avalanche frequency was observed during the evening cooling period. The data indicated that a given ice fall results in an increased probability of an ice fall occurring shortly thereafter. After approximately 4 min the effect of a given avalanche no longer correlates with succeeding avalanches.

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

The basal deformation of a gravity-driven linear creeping flow sliding frictionless over slowly varying bed undulations in two dimensions is analysed analytically, using results from second-order perturbation theory. One of the key results is that, close to sinusoidal bedrock undulations, up to two different spatial regions of local extrusion flow may arise. The offset and onset of extrusion flow is controlled primarily by the amplitude-to-wavelength ratio. Above the crest of a sinusoidal bed line, a local maximum of the surface-parallel velocity develops for ε : = ak < 0.138, where a is the amplitude and k is the wave number. As ε increases from zerо to this critical value, the vertical position of the velocity maximum moves from kz = 1 to kz ≈ 1.98, where z is the vertical distance above the mean bed line. Within and above the trough of a sinusoid, a region of local minimum of the surface-parallel velocity component develops, which shifts from kz = 1 towards the bed line as ε increases front zero to 1/2. Below this velocity minimum, and for some distance above the velocity maximum, the surface-parallel velocity increases with depth. This type of extrusion flow will cause a reversal of borehole-inclination profiles close to the bedrock.