In temperate glacier ice, in situ, besides water veins, there are water lenses, on grain boundaries more or less perpendicular to the direction of maximum pressure p1 (at the grain scale). Geometry of veins is developed. Grains are modelled as equal tetrakaidecahedra. The stress and temperature fields around a vein at a smaller, microscopic scale are estimated and the water discharge by a Vein is calculated. The time-derivative of the cross-sectional area S of a vein is governed neither by energy dissipation in the water nor by plasticity, but by capillarity effects and salinity. A “vasodilator threshold” pd for water pressure pw in the veins is defined. Normally, Pw < Pd, then S has a stable value, the same for any orientation of the vein, and the microscopic temperature is uniform. The coefficient of permeability is proportional to (Pd-pw)−4, and thus a true Darcy law does not hold. As an application, the percolation of internal meltwater is studied; in an upper boundary layer about 2 m thick this meltwater flows upwards, because in the bulk of the glacier pw is very close to P1, whereas it is zero at the surface. When, exceptionally, pw > pd, S increases irreversibly. Whether it leads to the formation of “worm-holes” is discussed.

A field investigation of iceberg drift pattern and drift speed was conducted in September 2011 in Baffin Bay, northwest Greenland. Ten icebergs were equipped with GPS transponders during a field campaign. Above-waterline dimensions (length, width and height) of the icebergs were measured using a GPS/pressure altimeter and geometrically rectified digital photographs taken during the field campaign. Iceberg lengths, masses and drafts ranged from 95 to 450 m, 330 000 to 17 000 000 t and 70 to 260 m, respectively. The drift patterns and speeds were determined on the basis of GPS positions logged continuously at 1 hour intervals. The drift patterns differed significantly from iceberg to iceberg. The GPS signal was lost on six of the icebergs within the first 23 days of logging. Three transponders were transferring data for more than 5 months until the battery ran out of power. One transponder was sending data until summer 2012. The measured maximum drift speed was 68 cm s−1 (2.4 km h−1), and the mean drift speed for all ten icebergs was 10 cm s−1 (0.4 km h−1). Relations between iceberg size and drift speed were investigated, showing that icebergs with large surface areas moved at the highest speeds, which occurred particularly during strong wind conditions.

Mass-balance quantities at specific points on a glacier as defined in [IHD] (1970) relate either to annual maxima or minima in ice mass at that point (the stratigraphic system), or to values at the beginning and end of a hydrologic year (the annual or fixed-date system). Most quantities measured in the field relate to summer surfaces, which correspond to the annual minima at the measurement points. When stratigraphic system point values are integrated over a whole glacier, the result may be meaningless because annual maxima and minima and summer surfaces may form at different times at different places.

The combined system utilizes several kinds of data to derive meaningful area-average results that can be directly related to other hydrologic and meteorologic information. Measurements to summer surfaces at certain specific times, including the beginning and end of a hydrologic year, are added together with proper recognition of the types of material involved: old firn and ice, snow and superimposed ice of the year under study, new firn formed during that year, and late snow deposited toward the end of the year. Other “balance increment” terms relate values at the beginning and end of a hydrologic year to corresponding area-average balance minima. As a result, two types of “net balance” and many other terms are given precise meaning for a glacier as a whole. The scheme is sufficiently versatile to be used on any glacier, although the terms relating to summer surfaces are not defined on a glacier in which ablation or accumulation is continuous throughout a year.

Mountain glaciers and ice sheets often host marginal and subglacial lakes that are hydraulically connected through subglacial drainage systems. These lakes exhibit complex dynamics that have been the subject of models for decades. Here we introduce and analyze a model for the evolution of glacial lakes connected by subglacial channels. Subglacial channel equations are supplied with effective pressure boundary conditions that are determined by a simple lake model. While the model can describe an arbitrary number of lakes, we solve it numerically with a finite element method for the case of two connected lakes. We examine the effect of relative lake size and spacing on the oscillations. Complex oscillations in the downstream lake are driven by discharge out of the upstream lake. These include multi-peaked and anti-phase filling–draining events. Similar filling–draining cycles have been observed on the Kennicott Glacier in Alaska and at the confluence of the Whillans and Mercer ice streams in West Antarctica. We further construct a simplified ordinary differential equation model that displays the same qualitative behavior as the full, spatially-dependent model. We analyze this model using dynamical systems theory to explain the appearance of filling–draining cycles as the meltwater supply varies.

The way free water is distributed around contact points of ice grains is recorded by measuring the dielectric constant of the porous system which constitutes snow. Within the saturation range of 11% to 15% of the pore volume, a transitional range from the “pendular” to the “funicular” mode of distribution of free water occurs. By measuring the drainage-flow of free water through snow, additional information as to the upper limit of the pendular distribution is obtained. This upper limit is reached at a saturation of approximately 14% of the pore volume.

Measurements of change in length of a borehole, or displacements of poles and of subglacial Water pressure were combined with drainage tests and electrode tests in boreholes, in experiments near the northern margin of Gornergletscher, Valais, Switzerland, at the upstream side of an overdeepening. The measurements suggest that the subglacial drainage system consisted of discrete conduits at that location, presumably linked cavities on “clean” bedrock. Changes in subglacial water pressure were followed by variations in subglacial water storage, together with similar variations in elevation of a pole. The variations in subglacial water storage caused changes in cross-sections of subglacial passageways and thereby changed the frequencies of slug-test oscillations. Similar experiments conducted near the center line of the glacier revealed different subglacial conditions: impeded drainage through a sediment layer, and different depths of water levels in different boreholes. These results are discussed in relation to previous studies.

We consider a theory for shallow ice shelves that includes an isotropic damage variable. A zeroth-order shallow-shelf approximation allows a simple yet consistent treatment of both ice dynamics and damage evolution. We find that the damage variable (like temperature) has, in general, to vary with depth; a purely two-dimensional membrane theory can only be considered a rough approximation for isothermal ice shelves.

We use seismic refraction data to investigate the firn structure across a suture zone on the Amery Ice Shelf, East Antarctica, and the possible role of glacier dynamics in firn evolution. In the downstream direction, the data reveal decreasing compressional-wave velocities and increasing penetration depth of the propagating wave in the firn layer, consistent with $\sim$1 m firn thickening every 6 km. The boundary between the Lambert Glacier unit to the west and a major suture zone and the Mawson Escarpment Ice Stream unit to the east, is marked by differences in firn thicknesses, compressional-wave velocities and seismic anisotropy in the across-flow direction. The latter does not contradict the presence of a single-maximum crystal orientation fabric oriented 45–$90^{\circ }$ away from the flow direction. This is consistent with the presence of transverse simple shear governing the region's underlying ice flow regime, in association with elevated strain along the suture zone. The confirmation and quantification of the implied dynamic coupling between firn and the underlying ice requires integration of future seismic refraction, coring and modelling studies. Because firn is estimated to cover $\sim$98% of the Antarctic continent any such coupling may have widespread relevance to ice-sheet evolution and flow.

Isoglacihypses depicting the configuration of the glaciation threshold (= “glaciation limit”) in Washington broadly parallel the crest of the Cascade Range and curve around the west and south flanks of the Olympic Mountains. In both uplands the glaciation threshold rises inland (eastward) with a mean gradient of 10-12 m/km. However, the gradient in the Cascades is more variable (7-25 m/km) due to five east-trending troughs in the glaciation threshold surface that coincide with topographic depressions along the range crest and that apparently result from greater eastward penetration of moist maritime air.

Mean accumulation-season precipitation correlates strongly (r2 = 0.86) with altitude of the glaciation threshold in the North Cascade Range, but the correlation of glaciation threshold with altitude of the July freezing isotherm, determined from the calculated July lapse rate within the mountains, is much weaker (r2 = 0.40). Multiple regression analysis relating independent climatic variables that affect the height of the glaciation threshold indicates that 90.4% of variance is explained by accumulation-season precipitation and estimated mean annual temperature at the glaciation threshold.

The glaciation threshold during the greatest ice advance of the last (Fraser) glaciation in the southern North Cascade Range (c. 18 000-22 000 years B.P.) was 900 ± 100 m below that of the present. Depression of the glaciation threshold by this amount most likely resulted from a change in accumulation-season precipitation of no more than 30% from present values and a decrease in mean ablation-season temperature of 5-5 ± 1.5 deg.

We present a study of the mechanical (in)stability of the ephemeral waterfall ice structures that form from the freezing of liquid water seeping on steep rock. Three vertical structures were studied, two near Glacier d’Argentière, France, and one in the Valsavarenche valley, northern Italy. The generation of internal stresses in the ice structure in relation to air- and ice-temperature conditions is analyzed from pressure sensor records. Their role in the mechanical instability of the structures is discussed from a photographic survey of these structures. The main result is that dramatic air cooling (several °Ch−1 over several hours) and low temperatures (<−10°C), generating tensile stresses and brittleness, can trigger a spontaneous or climber-induced mechanical collapse, leading to unfavorable climbing conditions. Ice internal pressure fluctuations are also associated with episodes of marked diurnal air-temperature cycle, with mild days (few above 0) and cool nights (few below 0), through the occurrence of water ↔ ice phase transitions within the structure. These ice internal stress fluctuations seem, however, to have a local influence, are associated with warm (near 0), wet and therefore particularly soft ice and do not trigger a collapse of the structure.

We measured vertical strain in the firn at Siple Dome, Antarctica, using two systems, both of which measure relative displacements over time of metal markers placed in an air-filled borehole. One system uses a metal-detecting tuned coil, and the other uses a video camera to locate the markers. We compare the merits of the two systems. We combine steady-state calculations and a measured density profile to estimate the true vertical-velocity profile. This allows us to calculate a depth-age scale for the firn at Siple Dome. Our steady-state depth-age scale has ages ≈10-15% younger at any given depth when compared to depth-age scales derived by layer counting in a core 40 m away. The age of a visible ash layer at 97 m in the core is 665 ± 30 years, in agreement with a similar analysis conducted at Taylor Dome, Antarctica, where the same ash is also seen, providing an additional dated tie point between the two cores.

A newly designed eight-arm caliper–inclinometer probe for borehole logging is presented. The caliper sounding gives eight points of cross-sections of the borehole at 1 cm intervals along its axis. Regression circles and ellipses are calculated and used as obvious hypotheses to be tested in order to obtain information on strain rates in the horizontal planes and isotropic or anisotropic borehole closure. The scratching of identifiable marks into the wall of the borehole enables material displacement to be tracked, in particular in the vertical direction, thus providing information for determining vertical strain rates along the borehole. Measurements in two boreholes drilled on high-altitude glaciers in the Swiss Alps are used to demonstrate both the potential and the limitations of the probe and of the mathematical methods presented.

Glaciological investigations were carried out in 1994 on the glaciers in Hidden Valley, Mukut Himal, Nepal Himalayas, in order to make a comparison with observations made in 1974. Most of the glaciers were found to have retreated by 30–60 m in terminus elevation over the 20 years between the two studies. Rikha Samba Glacier, the longest glacier in the valley, has retreated by about 200m. The areal average of the amount of surface lowering and the volume loss of the glacier was estimated to be 12.6 m ice equivalent and 13% of the total mass, respectively. The annual mass balance of −0.35 m a−1 water equivalent was obtained as an average for 20 years, which is one of the largest negative values amongst small glaciers of the world.

Commercial cone penetration testing (CPT) equipment was adapted to allow penetrative testing in hard polar firn to depths of 10 m. The apparatus is hydraulically driven, rate-controllable and able to penetrate firn with a resistance of 10 MPa. It can be mounted on many types of typical polar vehicles, requiring connection to only hydraulics and 12 V electricity. Data recorded include both cone tip resistance and sleeve friction, a parameter not previously examined through such testing. This paper describes the development and calibration of the equipment and examines factors including snow density, penetration rate and cone size and shape that are shown to affect CPT interpretation. CPT can be used efficiently in polar environments to potentially provide estimates of physical parameters in hard firn to substantial depth.

An instrument which continuously records the run-off from a small, well-defined snow cover is described. The lysimeter is reasonably priced and effective, requiring only modest service attention; details of the records which it takes are given also. The relevance of the instrument to snow hydrology and to the energetics of a snow-cover is discussed.

The transfer of basal velocity anomalies to the surface of a glacier is investigated using a model of a planar parallel-sided slab (thickness H) of linear viscous rheology. Surface velocity parallel (us) and normal (vs) to the surface is calculated for various spatial distributions of basal velocity anomalies with components parallel (ub) and normal (vb) to the surface. Four scales of differing behavior can be identified depending on the spatial length L of the basal anomalies. At very short scales (L ≤ 1H) there is essentially no response at the surface. At short scales (1H ≤ L ≤ 5H), a basal anomaly ub induces a response in both us and vs. The spatial pattern of us is such that velocity peaks in us can be shifted from peaks in ub, and may differ in number. The amplitude of us is up to about 0.3|ub|. The amplitude of the cross-component effect vs may be greater than the amplitude of us. A basal anomaly vb induces a response in both vs and us. The pattern of vs is the same as the pattern of vb, and the amplitude of vs is up to about 0.7 |vb|. The amplitude of the cross-component effect us is less than the amplitude of vs. At intermediate scales (5H ≤ L ≤ 10H), results differ from the short scale in two respects; velocity peaks in us correspond with peaks in ub; and surface amplitudes are increased, except for cross-component effects for which surface amplitudes are of the same order as at the short scale. These cross-component effects at the short and intermediate scales show in particular that substantial anomalous surface-normal motions can be induced by deformation, even though the basal velocity anomaly is parallel to the surface. At long scales (10H ≤ L), the velocity anomaly at the surface is essentially the same as the anomaly at the bed. For all scales, the longitudinal strain-rate averaged over depth is larger in magnitude than the longitudinal strain-rate at the surface and, at the short scale, it may differ in sign, so that vs cannot be easily estimated from surface strain-rate. Although the simplifications of the model do not allow its rigorous quantitative application to field measurements, the results indicate the need for caution in interpreting surface-velocity variations in terms of basal velocity anomalies. It is important to establish the spatial pattern of surface motions for any chance of a confident interpretation in terms of basal motions.

Wind-packed snow in the form of slabs or crusts is an important part of alpine and polar snow covers. Yet, the formation process of such layers is poorly understood. For example, it remains unclear whether drifting snow is necessary for wind-packing or not. A better understanding of wind-packing could improve snow-cover models and avalanche danger forecasts and contribute to the assessment of mass balances in polar regions. We designed a closed-circuit, obround wind tunnel to study the process of wind crust formation. A SnowMicroPen was used to measure how the hardness of the snow evolved. The results show that no crust forms without saltation. Drifting snow is a necessary but not sufficient condition for wind-packing. The dynamics of erosion and deposition appear to be equally important.

The initial conditions needed for formation of moulins are crevasses and a supply of melt water. Water pouring into a crevasse may fill it until it overflows at the lowest point, which is normally near the margin. However, as the crevasse deepens, it intersects englacial channels through which the water can drain. These channels may be finger-tip tributaries in a dendritic system such as that described by Shreve (1972) and observed by Raymond and Harrison (1975). When the crevasse closes, heat in the melt water keeps the connection open and a moulin is formed. The englacial channel enlarges rapidly by melting, utilizing mechanical energy released by the descending water.

Descents into moulins, and mapping of structures exposed at the surface after many years of melting, demonstrate that the drainage channels leading down from the bottoms of the moulins have inclinations of 0–45° from the vertical. These channels trend in the direction of the original crevasse but appear to be deeper than the expected depth of the crevasse. They have not, even at depths of 50–60 m, become normal to the equipotential planes described by Shreve.

Quantitative effects of crystallographic orientation fabrics are incorporated into the flow law for isotropic polycrystalline ice by the introduction of an enhancement factor applied to the isotropic fluidity. An aggregate is viewed to a first approximation as a collection of grains deforming independently by basal glide. The influence of preferred orientations on the mean intragranular rate of strain is treated in terms of a redistribution of the magnitude and orientation of resolved basal shear stress. A quantitative measure of this effect on the fluidity of the aggregate is provided through the development of a geometric tensor and a stress configuration parameter. Intergranular interference is then considered as a dissipative process modifying the fluidity of the aggregate.

Empirical justification for the model at low octahedral shear stresses is provided by several laboratory creep tests on naturally anisotropic bore-hole specimens under both in situ and anomalous stress situations. Predicted enhancement factors ranged from approximately 0.2 to 2.8 and agree well with measured values. The tests were carried out in uniaxial compression and simple shear.

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.