Studies of the chemical stratigraphy in the snow near Vostok station, which is near the centre of the East Antarctic ice sheet, show that sodium exhibits annual concentration differences of up to a factor of ten. Similar work on the 952 m Vostok ice core enabled accumulation rates along selected parts of the core to be determined. This in turn enables the core to be dated. The accumulation rate in this central region of the East Antarctic ice sheet for the last 50000 years has been determined and is presented. An interesting result is that the accumulation rate during the last glacial period is only half that in post-glacial times. Results from the bottom of the core provide some evidence of a past surge in the East Antarctic ice sheet.

A 10 m deep core and a 2 m pit were achieved in December 1977 on the ice cap of James Ross Island (Antarctic Peninsula) 3 km westward of the main dome at an altitude of 1 500 m. The 10 m temperature was −14.2°C. The core was cut into 106 samples which have been used for density, total β radioactivity, electroconductivity, and deuterium-content measurements. The age at the bottom of the bore hole has been estimated to be 1 965±1 year and a mean annual snow accumulation rate 37.7±3.0 g cm−2 a−1 is calculated over the last 13 years. By comparing our results with those obtained in other areas of the Peninsula, the climate of the upper part of James Ross Island seems to follow the climatic regime of the western coast. A preliminary chemical analysis of the pit samples leads us to conclude that the snow impurities are mainly sea-salt derived. The conductivity measurements show a clearly defined peak at the end of 1967 which could be linked with the volcanic eruption of the Deception Island volcano in December 1967. The interest of the studied location is discussed in view of further more extended glaciological investigations and particularly a possible coring to the bottom.

Transverse profiles and velocities which have been measured on the ablation zone of Mer de Glace more or less continuously since 1891 contradict the Weertman–Nye theory of glacier kinematic waves. Faint broad waves, which undoubtedly result from fluctuations in the balance, travel down the glacier faster than this theory predicts. (This theory having first been completed by taking changes in width with time and with distance down the glacier into account.) On the other hand, velocity fluctuations are synchronous and more or less the same over the entire length studied (6 km).

These discrepancies result from bottom friction being of the solid type, i.e. independent of sliding velocity. Friction should also be almost insensitive to discharge in subglacial waterways, since in the steady state energy for keeping them open, not entirely flooded, and at atmospheric pressure, is superabundant. The sliding velocities at all cross-profiles are thus controlled by some areas where the body of the glacier suffers strong deformation because the valley shape is far from cylindrical. One such controlling zone exists on Mer de Glace owing to the existence of a subglacial transverse shoulder. A new perturbation equation and a new rough expression for wave velocity are given.

Intervals between Forbes’ bands were plotted on seven aerial surveys between 1939 and 1979. Progressive tilting of the slices of blue, dusty ice from the position from which these dark bands proceed and progressive lowering of their exposed edge must be taken into account. This analysis confirms the validity of our simple model for velocity fluctuations and allows us to estimate the entire series since the year 1888.

The paper tries to reconcile the facts that there are often useful correlations between ablation or run-off and air temperature while net radiation is usually the major source of ablation energy. Equations are derived from the energy balance to describe statistics for the ablation-temperature relation in terms of statistics for the relations between individual energy fluxes and air temperature. As examples, statistics are evaluated for four published series from Arctic Canada. Although the net radiation is the largest energy source in all four cases, the ablation rate is moderately well correlated with temperature and poorly correlated with net radiation. This is because the sensible heat flux is more variable than the radiation in three cases and is itself better correlated with temperature in all four cases. The major contributions to the increase of ablation rate with temperature (on average 6.3 kg m−2 d−1 deg−1) are due to sensible heat, followed by latent heat with a small contribution from net radiation. The resulting ablation-temperature model explains about half the variance of ablation rate. The main application of such a simple model is for the estimation of ablation totals in areas where glaciological and hydrological data are sparse.

In this article the distribution of stress and velocities in glaciers and ice sheets is reinvestigated. We first derive the general equations governing non-linear viscous flow under plane deformations and formulate the relevant boundary conditions, including, in particular, a proper treatment of the accumulation–ablation mechanism. It is then shown how the emerging set of non-linear equations for the established boundary-value problem can be separated into a system covering steady-state problems on the one hand, and transient, time-dependent processes on the other hand. This separation is performed under the assumption that steady-state stresses are larger than the corresponding transient counterparts, suggesting a linearization of the transient equations with regard to the stresses. The steady-state equations are then analysed for the special case of an infinitely long, nearly parallel-sided slab. With the assumption that bottom undulations are small as compared to the glacier thickness it is shown that the original non-linear boundary-value problem can be decomposed into an infinite hierarchy of boundary-value problems defined on the simpler domain of the exactly parallel-sided slab, all of which are linear except for the lowest order one. Since its solution is readily available, the determination of the velocities and stresses due to bedrock protuberances is basically a linear problem, even though the constitutive response may be non-linear.

Assuming harmonic bedrock undulations we show for a Navier–Stokes fluid that the transfer of the bedrock undulations to the surface strongly depends on the mean inclination of the slab, but, more importantly, does now show a maximum when plotted as a function of wavelength λ. This result is contradictory to the corresponding results of Budd (1970[a]) and implies serious drawbacks to his calculations of longitudinal stresses and strain-rates in his subsequent article (Budd, 1970[b]). Yet, it is not true that for maximal transfer of bottom protuberances to the surface a distinct wavelength would not exist. The calculations of Budd must rather be extended to include non-linear constitutive behaviour, variations of temperature with depth, and sliding at the bed. It then turns out that under certain circumstances maximal transfer of bottom undulations to the surface in a distinct wavelength domain (3 < λ < 5) may indeed exist. Sliding at the bed and vertical temperature variation thereby play a decisive role.

Equally important is the stress distribution at the base, in particular the influence of the longitudinal strain effects on the latter. Rheological non-linearities, vertical temperature variations, and the sliding law at the bed play an important role and are investigated in detail.

For non-linear constitutive behaviour and spatially dependent temperature-variation solutions must be sought numerically. The finite-difference scheme used suggests a generalization of Glen’s flow law so as to account for a nearly linear behaviour at low strain-rates.

We conclude with a perspective of possible extensions of the general theory to various other time-dependent and time-independent problems.

An extensive system of mirabilite (Na2SO4 · 10H2O) beds has been mapped on the Ross Ice Shelf near Black Island. The salt beds are normally underlain by a thin layer of mud and their surface is covered by a non-marine algal mat and boulder lag. These authors suggest the salt has been formed by the displacement of sub-ice-shelf brines to the ice-shelf surface. Evidence also suggests that other terrestrial mirabilite beds in the McMurdo Sound area were formed in the same manner and deposited by the Ross Ice Shelf during its Wisconsin retreat from McMurdo Sound. Mirabilite salt in the dry valleys, southern Victoria Land, may have also originated from melt waters which dissolved ice-shelf mirabilite beds.

During 1974–75 glaciologic and geologic studies were conducted on a small (0.17 km2) avalanche-nourished glacier in the North Cascade Range of Washington. The approximate equilibrium-line altitude (ELA) for this ice body, informally called “Vesper” glacier, lies at 1475 m, some 300 m below the regional ELA value. Estimated annual accumulation was 6 100±675 mm during the two years of study; 15 to 30% of this flux resulted from avalanche and wind–transported snow. Average annual ablation during the period was 5 350 mm, giving a total net balance of + 1 600 mm for the two-year study period. “Vesper” glacier persists well below the regional snow-line because of excessive local precipitation, substantial avalanche contributions, and a favourable north-facing aspect.

Neoglacial moraines indicate that maximum ELA lowering in this period was approximately 165 m and occurred prior to a.d. 1670. Minor re-advances occurred during the nineteenth century. These reconnaissance measurements are consistent with the sparse geologic data reported from other glaciers in the Cascade Range. While the relationship between regional lowering of snow-line and avalanche activity is uncertain at present, these data suggest that avalanche-nourished glaciers provide a useful record of climatic fluctuations.

The object of the research is to determine whether direct methods from the calculus of variations can provide convenient approximate solutions of complex problems in glacier mechanics. The Ritz technique is used to minimize an appropriate functional. Coordinate functions obtained from a finite-element model are combined with a coordinate function that is the solution of a related problem. The finite-element coordinate functions make localized adjustments to the related solution. Solutions of two sample problems are presented. An analysis of the closure of an intergranular vein in ice at the melting point is based upon a variational principle for velocities. An analysis of the flow of ice in a cylindrical channel is based upon a variational principle for stresses.

Frequently the reservoir region of a cold surge-type glacier has a temperate base, while in a region surrounding the reservoir the base is cold. We analyse the slump process in such a reservoir region— that is, the process whereby material flows toward the lower end of the region and forms a critical wave profile there. The model agrees qualitatively with observations of Trapridge Glacier, Yukon Territory, Canada, which is currently experiencing a critical pre-surge condition. Calculations based on the model give good agreement with the surge cycle time of Rusty Glacier, Yukon Territory. Laboratory experiments show that a large-amplitude slump-induced wave profile forms prior to a surge. Experimental surges were produced with velocity increases of order one hundred.

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.

In order to interpret observed short-term variations of the sliding velocity of a glacier the effect of a variable subglacial water pressure on the sliding velocity has been studied using an idealized numerical model. In particular the transient stages of growing or shrinking water-filled cavities at the ice-bedrock interface were analysed. It was found that the sliding velocity was larger when cavities were growing than when they had reached the steady-state size for a given water pressure. The smallest sliding velocities occurred while cavities were shrinking. When cavitation is substantial a small drop of water pressure below the steady-state value (e.g. by 0.5 bar) can temporarily cause backward sliding. A limiting water pressure at which sliding becomes unstable is derived. The consequences of more realistic assumptions than those of the model are discussed.

In a field and laboratory study we discuss the formation, growth, and wave-absorption properties of grease ice. Our field observations show that grease-ice formation occurs under cold windy conditions in both leads and polynyas. In leads grease ice forms in the open water, then is herded to the down-wind edge of the lead; in polynyas a Langmuir circulation herds the grease ice into long plumes parallel to the wind. In the laboratory we grow grease ice in a wave tank and measure its wave absorption properties for single-frequency, two-dimensional waves. On a large scale we find that the thickness of the grease ice, which increases away from the paddle, is determined by a balance between the wave-momentum flux and the free-surface tilt. On a small scale our photographs show that the crystals which make up the grease ice consist of discs measuring about 1 mm in diameter and 1–10 µm thick, which at low rates of shear sinter together into larger clumps yielding a viscosity increase. To measure this non-linear viscosity, we study the decay of wave amplitude between two critical distances measured inwards from the leading edge. The first occurs when the depth of grease ice exceeds k−1 where k is the wave number; the second further distance is a line of transition from liquid to solid behavior which we call the dead zone. Between these two distances the wave amplitude decays with a linear slope α, which increases as (a0k)2 where a0 is the wave amplitude in open water. Concurrent measurements of ice concentration show that it increases from values of 18–22% at the leading edge to a local maximum of 32–44% at the dead zone, while the values at the dead zone increase non-linearly with a0k. Finally, comparison of the observed α to that calculated from a yield-stress viscosity model shows if the yield-stress coefficient is proportional to the incident wave-momentum flux, the model predicts the observed α.

Thickness changes of ice sheets are, except perhaps at the snout region, small as compared to unity. This suggests using a coordinate stretching so as to make the surface changes in the new coordinates of order one. The explicit occurrence of the smallness parameter in the governing equations then allows us to search for perturbation solutions in various problems. Here, it is shown that the classical formula for the basal shear stress follows easily from such a perturbation procedure. Furthermore it can be improved to account for longitudinal strain effects. As compared to previous work in this area, these formulae are explicit and allow us to take vertical variations of material properties into account in a straightforward manner.

During the June-July 1979 expedition a large variety of micro-forms was observed at the surface of the Quelccaya ice cap, their altitudinal distribution being primarily controlled by the heat budget. At 5200–5300 m penitentes are best developed, with azimuth orientation and inclination of features conforming to the insolation geometry around local noon. At a westward-facing slope in 5360–5380 m a set of penitentes striking parallel to the contours is superimposed on the pattern dominating at the lower elevations. The ablation forms of penitentes give way to various deposition features above a transition zone around 5400 m in broad agreement with the larger net all-wave radiation and greater importance of melting at lower elevations. The succession of forms with an upward change from surface-parallel plates to elaborate dendritic forms appears to be controlled by the temperature conditions. The conspicuous development of forms encountered during the 1979 expedition appears characteristic of prolonged absence of fresh snow-fall subsequent to a season with abundant precipitation.

This paper describes the growth of sea ice and the salinity profiles observed in Eclipse Sound near Pond Inlet, Baffin Island, Canada, during the winter of 1977–78. A numerical method of calculation has been developed to incorporate the variations in snow conditions and physical properties of ice and snow during the growth season. It is shown that the growth rate can be predicted reasonably well. It is also shown that the vertical salinity profile in the ice towards the end of the season, provides a record of previous climatological conditions. A dependence has been shown between the predicted growth rate and the measured salinity.

Laboratory experiments were performed to determine the optical properties of young salt ice and to examine correlations between the optical properties and the state of the ice. Ice was grown at different temperatures (–10, –20, –30, and –37°C) from water of different salinities (0, 16, and 31‰). The experiments were conducted in a cylindrical tank 1 m in diameter designed to approximate natural ice growth and to permit in situ optical measurements. Observed incident, reflected, and transmitted irradiances were used in conjunction with a modified Dunkle and Bevans photometric model to determine spectral albedos and extinction coefficients. Cold ice only 0.25 m thick had albedos which were comparable to the values for 2 to 3 m multi-year ice examined by previous researchers during the summer melt season; extinction coefficients were 1.5 to 15 times greater. As the ice temperature and hence brine volume decreased, both albedo and extinction coefficient increased; when the ice temperature dropped below the eutectic point, they increased sharply. In addition, ice grown at lower air temperatures had greater albedos and extinction coefficients even when ice temperatures were the same. Variations in the optical properties of the ice are determined by changes in the amount of brine and its distribution; thus the optical properties of salt ice depend not only on ice temperature but on initial growth rate. Variations in ice salinity over the range 4‰ to 14‰ produced no detectable changes in the optical properties.

Significant new information on radiation transmittance through ice in the photosynthetically active range (400–700 nm) has been collected at an inland lake near Ann Arbor, Michigan, U.S.A., and at one site on the Great Lakes (lat. 46° 46´ N., long. 84° 57´ W.). Radiation transmittance through clear, refrozen slush, and brash ice varied according to snow cover, ice type, atmospheric conditions, and solar altitude.

Snow cover caused the greatest diminution of radiation. During periods of snow melt, radiation transmittance through snow-covered ice surfaces increased slightly. Moderate diurnal variations of radiation transmittance (about 5%) are attributed to solar altitude changes and associated changes in the direct- diffuse balance of solar radiation combined with the type of ice surface studied. Variations in radiation transmittance of nearly 20% over short periods of time are attributed to abrupt changes from a clear to a cloudy atmosphere.

A two-layer reflectance–transmittance model illustrates the interaction of layers in an ice cover such as snow or frost overlying clear ice. Upper layers of high reflectance have considerable control on the overall transmittance and reflectance of an ice cover.

Bottom melting rates have been calculated for a large number of sites on George VI Ice Shelf from measurements of its kinematic behaviour. No simple explanation for the melt-rate pattern was found in terms of ice-shelf parameters, assuming steady-state conditions. Values of apparent melt rates varied from 1 to 8 m a−1 of ice. Along different flow lines the melt rate would sometimes increase with distance from the grounding line and sometimes the melt rate would decrease with distance. Large melt rates were found both where ice flowed off Palmer Land and where the ice shelf butted against Alexander Island. Although oceanographic conditions probably control bottom melting rates the complex pattern with large spatial variation seems to indicate that some areas of ice shelf are changing in thickness.

Application of the gravity flow theory to the percolation of melt water through the firn in the accumulation area of a temperate glacier explains the occurrence of shock fronts in the melt-water flux. The time of propagation of a shock front moving from the surface through the entire firn was calculated under various assumptions. Various time input functions of melt-water flux at the surface with constant total input volumes yield only slight differences in the time of propagation of the shock front at greater depths. The dependence of the time of propagation of a shock front on the input volume, on snow parameters, and on the total thickness of the firn was calculated. An approximately linear relation was found to exist between the time of propagation of a shock front moving through the firn and the total thickness of the firn. The drainage of melt water from the firn after the summer ablation period is also quantitatively explained by the gravity flow theory. All results are in good agreement with experimental data.

Snow and firn samples from 2 and 5 m deep pits were analyzed for seven sites on the Ross Ice Shelf, Antarctica. Na, Mg, Ca, and K concentrations change with depth, the range of concentrations being approximately 10 : 1 for all four elements. The changes in concentrations for the four elements at any one site are highly correlated, suggesting that the impurities are introduced into the snow-pack simultaneously by the same mechanisms.

Pronounced periodic structure of the vertical chemical profiles leads to strong correlations (γ> 0.9) of the chemical features from site to site separated by distances up to 440 km.

Assuming that the observed chemical features are periodic as a function of depth due to temporal variations caused by large-scale phenomena, then the wavelength (in depth) of these features should be proportional to the accumulation. Under the assumptions, the linear regression ratio of one site to another will give the relative accumulations at these sites. The ratios of snow accumulation estimated by these chemical methods agree, within a few per cent, with the ratios for the same sites estimated by total β-activity or stratigraphic methods.

It is suggested that the chemical variations with depth are caused by meteorological events which may have seasonal changes in frequency and intensity. It is also suggested that the most-favored season for the production of chemical-concentration maxima is autumn because of the documented higher frequency of precipitating storms on the Ross Ice Shelf and the minimum in sea-ice extent at that time of year.