Dynamic surficial changes and changes in the position of the firn line and the areal extent of Hofsjökull ice cap, Iceland, were studied through analysis of a time series (1973–98) of synthetic-aperture radar (SAR) and Landsat data. A digital elevation model of Hofsjökull, which was constructed using SAR interferometry, was used to plot the SAR backscatter coefficient (σ°) vs elevation and air temperature along transects across the ice cap. Seasonal and daily σ° patterns are caused by freezing or thawing of the ice-cap surface, and abrupt changes in σ° are noted when the air temperature ranges from ∼−5° to 0°C. Late-summer 1997 σ° (SAR) and reflectance (Landsat) boundaries agree and appear to be coincident with the firn line and a SAR σ° boundary that can be seen in the January 1998 SAR image. In January 1994 through 1998, the elevation of this σ° boundary on the ice cap was quite stable, ranging from 1000 to 1300 m, while the equilibrium-line altitude, as measured on the ground, varied considerably. Thus the equilibrium line may be obscured by firn from previous years. Techniques are established to measure long-term changes in the elevation of the firn line and changes in the position of the ice margin.

An ice-thickness distribution model based on physical ice classes is formulated. Pack ice is subdivided into open water, two different types of undeformed ice, and rafted, rubble and ridged ice. Evolution equations for each ice class are formulated and a redistribution between the ice classes is calculated according to a functional form depending on the ice compactness, thickness and velocity divergence. The ice-thickness distribution model has been included in a coupled ice–ocean model, and numerical experiments have been carried out for a simulation of the Baltic Sea ice season. The extended ice classification allows separation of thermally and mechanically produced ice. Inherent thermodynamic growth/melting rates of the ice classes can be introduced into the model, giving a more detailed seasonal evolution of the pack ice. In addition, the model provides more information about the surface properties of pack ice.

Numerical experiments for the Baltic Sea show that both the sub-basin and inter-basin ice characteristics were realistically simulated by the model. Deformed-ice production was related to storm activity. Most of the deformation was produced in the coastal zone, which is also an important region for thermodynamically produced ice because of the ice growth in leads. The modelled mechanical growth rates of ice were 0.5–3 cm d−1 on a basin scale, close to the thermodynamic ice-production rates. The deformed-ice fraction was 0.2 in mid-winter and increased to 0.5–1.0 during spring.

A mechanical model with circular symmetry is examined to test the hypothesis that the Martian ice caps are composed of flowing water ice, together with some rock debris. In contrast with most or all previous models, no assumption of a steady state is made. Instead the accumulation and ablation is assumed to be insignificant, and it is suggested that after a sufficient time the profile would have settled down to a particular collapsing form calculated by Halfar (1983). Higher modes of flow would have decayed relatively quickly. To calculate the time constant, it is necessary to consider carefully the distribution of temperature with depth. The time constant is sensitive to the grain-size, which is assumed to be 1–10 mm and is a significant unknown, as is also the effect of preferred crystal orientation. Apart from this, the main uncertainty is the value of the upward heat flux. With a heat flux of 30 mW m−2, the water-ice hypothesis is consistent with an age of about 107 years for both the north and the south polar caps, the north cap being the younger by a factor of about 7.

The depth of reflecting layers in Arctic ice sheets has been determined by electromagnetic echo sounding, using a varying distance between transmitter and receiver to determine the radar wave velocity. The depth of the radar reflecting layers is compared with a profile of electrical conductivity measurements (ECMs) from the Greenland Ice Core Project (GRIP) ice core, in order to determine the velocity of the radar waves in the ice cap. By using several reflecting layers, it is possible to isolate the firn correction of the wave velocity and to estimate the accuracy of the calculated electromagnetic wave velocity. The measured firn correction is compared with the correction calculated from the density profile, and a comparison between the depth profiles of ECM and radar based on the corrected electromagnetic wave velocity is presented. This profile shows that acid layers, which originate from major volcanic eruptions, show up as reflecting radar horizons.

It is of practical importance to have a description on time-scales of 1–100 years of the relationship between the mass imbalance of an ice sheet and its rate of change of thickness. In this paper, a linearized treatment of the relationship is described. Closed-form expressions are derived that relate the time-variant density in an isothermal firn layer to the fluctuations in accumulation rate and density that occur at the surface. These expressions are used to provide a spectral description of the contribution of surface accumulation and surface density fluctuations to the rate of change of thickness of an ice sheet. Using these, the contribution of firn densification to the variability of ice-sheet thickness is examined as a function of the time interval over which the ice sheet is observed. This contribution is illustrated for sites in Antarctica and Greenland. It is concluded that it is important to give greater attention than hitherto to the spatial scale of accumulation fluctuations if satellite observations of ice-sheet elevation change are to be used to estimate ice-sheet imbalance over short time intervals.

An old portable 60 MHz radar has been upgraded with a new digital data-processing and -acquisition system and a new antenna construction enabling a fast and low-cost installation on a Twin Otter aircraft. Augmented by a laser altimeter and kinematic global positioning system (GPS), the system has the capability of acquiring accurate data on location and ice-surface elevation, and adequate-quality data on ice thickness. The system has been applied successfully in mapping the Nioghalvfjerdsfjorden glacier, northeast Greenland, in spite of the difficult conditions with melting water on the glacier surface. The measurements from the floating part of the glacier have been evaluated by comparison of radar data with laser-altimeter and in situ measurements.

A one-dimensional second-order closure model and in situ observations on a melting glacier surface are used to investigate the suitability of bulk and profile methods for determining turbulent fluxes in the presence of the katabatic wind-speed maximum associated with glacier winds. The results show that profile methods severely underestimate turbulent fluxes when a wind-speed maximum is present. The bulk method, on the other hand, only slightly overestimates the turbulent heat flux in the entire region below the wind-speed maximum and is thus much more appropriate for use on sloping glacier surfaces where katabatic winds dominate and wind-speed maxima are just a few meters above the surface.

Mass-balance and dynamic measurements carried out on glacier de Saint Sorlin since 1957 provide a good opportunity to study the dynamics of this glacier. Ice-flow analysis shows that dynamic changes have been important over the last 40 years and that these changes are not consistent with the concepts usually used in glacier modelling. Present velocities are larger than the 1960 velocities, although the thickness decreased everywhere (10–30 m in the ablation zone). A simple numerical ice-flow model which does not include longitudinal stress gradients has been used to investigate these phenomena. This model allows us to infer the sliding velocity from observed surface and calculated deformation velocities. We conclude that: (1) the sliding velocity cannot be described by Weertman analysis or empirical relations which link the sliding to the thickness and surface slope; (2) the inferred sliding velocity is uniform over at least half of the glacier; and (3) there is no clear link between the sliding process and the quantity of water coming from surface ablation. Furthermore, it may not be reasonable to calibrate model flow parameters from geometry changes because the surface geometry is relatively insensitive to velocity changes over some decades.

We have tested the ability of a 1.12–1.76 GHz bandwidth airborne Frequency Modulation–Continuous Wave (FM-CW) radar with an effective pulse duration of 3 ns to penetrate temperate ice of the ablation zone of Black Rapids Glacier, central Alaska, U.S.A. We used high-gain horn antennas to suppress clutter, and tested over cold and nearly ideal surface conditions. Englacial horizons dipping to at least 60 m depth were found along three sections of one axial profile. More narrow-band (1.21–1.29 GHz), low-resolution (24 ns pulse duration) profiles from a fourth section detected events at about 100–150 m depth. Comparative profiles recorded with a 100 MHz short-pulse-type radar reproduce the horizons of two of the sections, and verify the penetration in all cases. All horizons are composed of diffractions. We interpret voids from the phase of the 100 MHz diffractions within one of the horizons. The diffraction nature of the horizons, the void interpretation and the proximity to a nearby and up-glacier pothole field lead us to conclude that the horizons within two of the sections are meandering drainage channels. A more complex, branching structure with near-surface horizons profiled within the third section much farther down-glacier may also be a complex drainage system fed by near-surface melting. The FM-CW signal-to-clutter-noise ratios of some of the targets predict that they could be detected at 200 m depth in the 1–2 GHz range. Significant performance improvements at maximum vertical resolution could be achieved with higher-gain antennas.

An indirect methodology for determining the distribution of mass balance at high spatial resolution using remote sensing and ice-flow modelling is presented. The method, based on the mass-continuity equation, requires two datasets collected over the desired monitoring interval: (i) the spatial pattern of glacier surface-elevation change, and (ii) the mass-flux divergence field. At Haut Glacier d’Arolla, Valais, Switzerland, the mass-balance distribution between September 1992 and September 1993 is calculated at 20 m resolution from the difference between the pattern of surface-elevation change derived from analytical photogrammetry and the mass-flux divergence field determined from three-dimensional, numerical flow modelling constrained by surface-velocity measurements. The resultant pattern of mass balance is almost totally negative, showing a strong dependence on elevation, but with large localized departures. The computed distribution of mass balance compares well (R2 = 0.91) with mass-balance measurements made at stakes installed along the glacier centre line over the same period. Despite the highly optimized nature of the flow-modelling effort employed in this study, the good agreement indicates the potential this method has as a strategy for deriving high spatial and temporal-resolution estimates of mass balance.

Medial moraines form striking dark stripes that widen non-linearly, steepen laterally and increase in relief down-glacier from the equilibrium line. Coalescence of these low-ablation-rate features can feed back strongly on the mass balance of a glacier snout. Ablation-dominated medial moraines originate from debris delivered to glacier margins, producing a debris-rich septum between tributary streams of ice below their confluence. Emergence of this ice below the equilibrium line delivers debris to the glacier surface, which then moves down local slopes of evolving morainal topography. A quantitative description of moraine evolution requires specification of the debris concentration field within the glacier, treatment of the melt-rate dependence on debris thickness, and characterization of processes that transport debris once it emerges onto the ice surface. Debris concentration at glacier tributary junctions scales with the erosion rates and the lengths of the tributary-valley walls, and inversely with the tributary ice speeds. Melt rate is damped exponentially by debris, with a ∼10 cm decay scale. Debris flux across the glacier surface scales with the product of debris thickness and local slope. Analytical and numerical results show that medial moraines should develop cross-glacier profiles with parabolic crests and linear slopes, and should widen with age and hence distance down-glacier. Debris should be both thin and uniform over the moraine. Observed faster-than-linear growth of moraine widths with distance reflects the increasing ablation rate down-glacier. Increase in medial moraine cover reduces the local average ablation rate, allowing the glacier to extend further down-valley than meteorology alone would suggest. This feedback is especially effective when moraines merge.

One crucial condition for the interpretation of ice-core records is the establishment of an accurate time-scale. This task is especially difficult for glacier sites in a complex topography such as the Alps, due to the often irregular deposition of fresh precipitation. In this work, dating techniques were applied to an Alpine ice core from upper Grenzgletscher, Monte Rosa massif (4200 m a.s.l.), representing about two-thirds of the total glacier thickness. They are based on (i) the radioactive decay of the isotope 210Pb, (ii) seasonally varying signals such as the concentrations of NH4+ and the isotopic ratio δ18O, and (iii) stratigraphic markers from Saharan dust falls, atmospheric nuclear weapon tests and the reactor accident in Chernobyl. From the combined application of these dating methods, a time period of 1937–94 covered by the ice core was derived. Dating uncertainty is <1 year for the period 1970–94 and ± 2 years for the period 1937–69. The observed thinning of the annual layers as a function of depth could be well described by a simple kinematic glacier flow model.

The mean, steady-state particle velocity in gravity-driven glacial flow over sinusoidal, sloping ground is computed using a Lagrangian description of motion. A Newtonian viscous fluid approximation is used for the ice. The glacier surface is free to move and is not subject to any stresses. At the bottom, the ice is frozen to the ground. The non-linear interaction between the basic downslope Poiseuille flow and the bottom corrugations yields a mean Lagrangian perturbation velocity that is always directed in the upslope direction near the ground. The requirement of mass balance imposes a mean negative surface slope in the corrugated region and an associated downslope perturbation flow in the upper part of the glacier. The no-slip condition at the wavy bottom induces a strong velocity shear in the ice, and particularly at the base. Analysis shows that the shear heating associated with shortwave perturbations could, in the case of a marginally frozen ground, lead to melting and subsequent sliding at wave crests along the bottom, while the ice stays frozen at the troughs. It is suggested that for glaciers the resulting high strain rates could lead to crevassing.

We analyzed the possible controls on the distribution of surge-type glaciers in Svalbard using multivariate logit models including 504 glaciers and a large number of glacial and geological attributes. Specifically we examined the potential effect of geological boundaries, mass-balance conditions and thermal regime on surging. It was found that long glaciers with relatively steep slopes overlying young fine-grained sedimentary lithologies with orientations in a broad arc clockwise from northwest to southeast are most likely to be of surge type. No relation between lithological boundaries and surge potential could be established. Possible explanations for length being conducive to surging are transport-distance-related substrate properties, distance-related attenuation of longitudinal stresses and the possible relation between thermal regime and glacier size. Analysis of glaciers with recorded radioecho sounding reveals that a polythermal regime, accumulation-area ratios close to balance and a large elevation span increase the surge potential. The logit models also enabled us to detect 19 new surge-type glaciers, to reclassify six glaciers as normal and to identify unusual surge-type glaciers. Our model results suggest that a polythermal regime and fine-grained potentially deformable beds are conducive to the surge potential of Svalbard glaciers.

We have obtained common offset, common midpoint (CMP) and borehole vertical (VRP) ground-penetrating radar profiles close to the margin of Falljökull, a small, steep temperate valley glacier situated in southeast Iceland. Velocity analysis of CMP and VRP surveys provided a four-layered velocity model. This model was verified by comparison between the depths of englacial reflectors and water channels seen in borehole video, and from the depths of boreholes drilled to the bed. In the absence of sediment within the glacier ice, radar velocity is inversely proportional to water content. Using mixture models developed by Paren and Looyenga, the variation of water content with depth was determined from the radar velocity profile. At the glacier surface the calculated water content is 0.23–0.34% (velocity 0.166 m ns−1), which rises sharply to 3.0–4.1% (velocity 0.149 m ns−1) at 28 m depth, interpreted to be the level of the piezometric surface. Below the piezometric surface the water content drops slowly to 2.4–3.3% (velocity 0.152 m ns−1) until ∼102 m depth where it falls to 0.09–0.14% (velocity 0.167 m ns−1). The water content of the ice then remains low to the glacier bed at about 112 m. These results suggest storage of a substantial volume of water within the glacier ice, which has significant implications for glacier hydrology, ice rheology and interpretations of both radar and seismic surveys.

A review of in situ and remote-sensing data covering the ice shelves of the Antarctic Peninsula provides a series of characteristics closely associated with rapid shelf retreat: deeply embayed ice fronts; calving of myriad small elongate bergs in punctuated events; increasing flow speed; and the presence of melt ponds on the ice-shelf surface in the vicinity of the break-ups. As climate has warmed in the Antarctic Peninsula region, melt-season duration and the extent of ponding have increased. Most break-up events have occurred during longer melt seasons, suggesting that meltwater itself, not just warming, is responsible. Regions that show melting without pond formation are relatively unchanged. Melt ponds thus appear to be a robust harbinger of ice-shelf retreat. We use these observations to guide a model of ice-shelf flow and the effects of meltwater. Crevasses present in a region of surface ponding will likely fill to the brim with water. We hypothesize (building on Weertman (1973), Hughes (1983) and Van der Veen (1998)) that crevasse propagation by meltwater is the main mechanism by which ice shelves weaken and retreat. A thermodynamic finite-element model is used to evaluate ice flow and the strain field, and simple extensions of this model are used to investigate crack propagation by meltwater. The model results support the hypothesis.

Towards accounting for the dynamic response of glaciers and ice caps in the estimation of their contribution to sea-level rise due to global warming, a mass-balance degree-day model is coupled to a geometric glacier model. The ice dynamics are treated implicitly in the geometric model by using scaling parameters that have been extensively investigated in the literature. The model is tested by presenting a case-study of the glacier Hintereisferner, Austrian Alps. The results are compatible with geomorphological data and other modelling studies. An estimate is made of the volume decrease due to initial disequilibrium. An extensive sensitivity study using generalized glacier shapes and sizes allows a comparison of results with dynamic theory. According to the geometric model, glaciers with a narrowing channel change more with a change in mass balance than glaciers with a widening channel, due to their shape and the way in which that shape changes with a changing climate. Also their response time is longer. As time progresses after a mass-balance perturbation, the longer response time for continental glaciers compared to glaciers with larger mass turnover offsets the effect of their smaller static sensitivity. Thus, although for the next century we may expect greater changes in volume from alpine glaciers, the equilibrium or committed change is greater for the continental glaciers.

A detailed study of a proglacial bedrock site and a subglacial cavity of an outlet of Øksfjordjøkelen, Norway, is presented together with observations from the foreland of Konowbreen, Spitsbergen. Striation directions and subglacial observations indicate that local ice-flow paths were highly variable, deviating at angles of approximately 90° from the main ice-flow direction. Stepped bedrock topography appears conducive to the production of highly variable ice-flow paths, because the high bed roughness creates a locally variable stress regime within the ice, including low-pressure, lee-side areas into which ice can flow. If ice flow is sustained along a specific path and the ice contains debris, then abrasion should produce an erosional bedform. Models are proposed whereby locally variable ice-flow patterns could produce erosional bedforms, which would be described as p-forms, purely through mechanical abrasion.

The ice-sheet margin at Russell Glacier, West Greenland, advanced ∼7 m a−1 between 1968 and 1999. As the ice advanced over moraine ridges, small changes in position caused major changes in the routing of proglacial water and sediment. These included changes in the distribution of ice-marginal lakes, in the periodic drainage of ice-dammed lakes, in the routing and sediment content of meltwater draining into the proglacial zone, and in the release of sediment from the moraines by erosion and mass movements. Proglacial hydrology and sediment flux appear to be controlled not simply by glacier mass balance, but by evolving ice-marginal geomorphology, which must be accounted for in palaeoenvironmental interpretation of proglacial sediments.