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.

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.

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.

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.

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.

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.

Neoglacial to historic and recent fluctuations of the firn field and one glacier on Popocatépetl, Mexico, include advance prior to 1519 to possible mid-Neoglaciation stadial position on gentle, north flanks at 4 150 m, then retreat up-valley to 4 335 m by 1906, and to 4 435 m by 1920 at 7 m/year. After volcanic eruptions and melting to about 4 800 m in 1921, growth of firn field and advance of a thin ice lobe before 1949 to 4 573 m by 1950, then retreat in next eight years at about 34 m/year, re-advance of the firn edge as an ice bulge to about 4 700 m by 1968, and as a thick double-lobed glacier to about 4 600 m by 1978 and 1979. A 37 year crevasse study shows continuous active firn-field movement on the north-west side of the cone.