In 1972 and 1995, shallow ice temperatures were measured at identical locations and depths on polythermal McCall Glacier, Brooks Range, Alaska, U.S.A. Mean annual ice temperatures at 10 m depth have systematically increased by > 1 K for the ablation area (1400–1900 m), while closer to the firn area, where meltwater percolation and refreezing play a role, they remained approximately unchanged. Interpreting these findings in terms of climate change requires careful consideration of the observed thinning of the glacier, which causes lowering of the surface through an existing vertical temperature gradient. Such temperature gradients can be particularly large in the ablation areas of polythermal glaciers; on McCall Glacier they are on the order of 0.2 K m−1. We also study the evolution of a 75 m deep temperature profile measured at one location in 1972 using a one-dimensional heat-diffusion model. We find that this profile was in approximate equilibrium with the mean surface temperature extrapolated from the 1972 data. Using the observed rate of surface lowering and measured rates of vertical advection, we find that both the measured temperature change and the vertical temperature gradient at 10 m depth can be reproduced only if the mean annual surface temperature on McCall Glacier has increased by 1.1 ± 0.3 K between 1972 and 1995. This result is consistent with the observed trend toward more negative mass balances on the glacier in the 1990s.

We use simple numerical and analytical models of ice flow and heat flow to characterize the shape of isochrones and isotherms beneath moving ice divides. Both nonlinear ice flow and reduced accumulation (wind scouring) at a divide can cause reduced downward flow in a region about one ice thickness wide under a divide. Greater downward velocities on the flanks cause isochrones and isotherms to become arched at depth. The magnitudes and shapes of these arches depend on the history of divide position. Arch amplitudes decrease by approximately e−1 for each increase in migration rate of 3–5 times the accumulation rate, the arches become asymmetric, with steeper leading edges and more gentle trailing edges, and the arch apex lags behind the divide. Isochrone and isotherm shapes can be used to infer past divide motions. In advection-dominated ice sheets, isochrone shapes record a longer history of divide position than do isotherm shapes. The opposite is true for diffusion-dominated ice sheets, in which a spatial array of ice-temperature measurements might extend the recorded history of divide position.

Rapid flow of the Des Moines lobe of the Laurentide ice sheet may have been related to its unlithified substrate. New reconstructions of the lobe, based on moraine elevations, sediment subsidence during moraine deposition, and flow-direction indicators, indicate that the lobe may have been ∼3 times thicker than in previous reconstructions. Nevertheless, implied basal shear stresses are <15 kPa, so internal ice deformation was not significant. Instead, the lobe likely moved by a combination of sliding, plowing of particles through the bed surface, and bed shear. Consolidation tests on basal till yield preconsolidation stresses of 125–300 kPa, so effective normal stresses on the bed were small. A model of sliding and plowing indicates that at such stresses most particles gripped by the ice may have plowed easily through the till bed, resulting in too small a shear traction on the bed to shear it at depth. Consistent with this prediction, measurements of orientations of clasts in basal till yield a weak fabric, implying pervasive bed shear strain less than ∼2, although some stronger fabrics have been reported by others. We infer, tentatively, that movement was principally at the bed surface by plowing.

In the past it has often been difficult to compare results of different types of snow-structural information. Grain-size and correlation length are such parameters of granular media, and there exist different definitions and different measurement methods for both of them. The relation between these parameters is analyzed from theoretical and from experimental points of view, considering optical and microwave properties. For spherical ice grains the connecting formulas are simple, but for other shapes the two parameters are not directly related. Care must be taken in the measurement procedure. Especially if grain-size is regarded as the maximum extent of connected ice particles, the results are likely to lead to extreme overestimates. Therefore it is concluded that grain-size should be complemented by an additional size parameter, namely, the surface-to-volume ratio of equivalent spheres, i.e. a measure of the correlation length. Methods to determine this quantity in the laboratory have been known for a long time. Methods to obtain such measurements in the field are described here.

There are several cases in which large overthrusts and sub-horizontal faults appear to have occurred in temperate or cold glaciers. As a contribution to solving the problem of their origin, the stress field when there is an abrupt change in the bottom boundary conditions is determined, assuming ice to be isotropic, third-power-law viscous. Deviatoric stresses vary with the distance r to the singularity as r−1/4, and strain rates as r−3/4. They are computed numerically to a multiplicative factor, which is determined by the conditions at a large distance, but not computed here. Although the apparent viscosity varies as r1/2 times a function of the polar angle, the stress field around the singularity is not essentially different from that obtained assuming a constant viscosity. Some considerations on the apparition of faults follow, but at the scale of the microrelief the adopted model becomes oversimplified.

Structural glaciological, sedimentological and geophysical techniques are used to provide new insight concerning the formation of band ogives and associated structures at Bas Glacier d’Arolla, Switzerland. Sedimentary stratification, crevasse traces and transverse foliation are identified as planar structures in the lower icefall and glacier tongue. Stratification and crevasse traces are progressively deformed into, and enhance, the transverse foliation found in the glacier tongue. Three-dimensional geometry has been defined using ground-penetrating radar, which portrays four main characteristics: (i) deep reflectors interpreted as the ice/bed interface, (ii) alternating reflection-rich and reflection-poor zones interpreted as ogives, (iii) up-glacier-dipping reflectors, interpreted as planar structures, and (iv) down-glacier-dipping reflectors of uncertain origin. At the glacier surface, each band ogive consists of a light and dark band. The dark bands contain more intense foliation which, on differential weathering, traps fine debris. Clasts and clear ice of basal character within dark ogive bands suggest that basal ice has been raised to the glacier surface. The most applicable model for the formation of band ogives at Bas Glacier d’Arolla is a refinement of Posamentier’s (1978) “reverse faulting” hypothesis. In this context, multiple shear zones are formed, through which basal ice is uplifted to the glacier surface to produce the dark, foliated ogive bands. This model fits observations reported from other glaciers with band ogives.

A noticeable trait of iceberg ice is the presence of several sets of planar features cross-cutting each other at various angles. Close-up views of these features show that they consist of an array of individual air inclusions that differ in size, shape and spatial distribution. In none of the cases resolvable at the scale of our observations were these inclusions physically linked to form a continuous fracture plane, although they may have originated as such. All postdate the formation of ice veins.

In this paper, a higher-order numerical flowline model is presented which is numerically stable and fast and can cope with very small horizontal grid sizes (<10 m). The model is compared with the results from Blatter and others (1998) on Haut Glacier d’Arolla, Switzerland, and with the European Ice-Sheet Modelling Initiative benchmarks (Huybrechts and others, 1996). Results demonstrate that the significant difference between calculated basal-drag and driving-stress profiles in a fixed geometry disappears when the glacier profile is allowed to react to the surface mass-balance conditions and reaches a steady state. Dynamic experiments show that the mass transfer in higher-order models occurs at a different speed in the accumulation and ablation areas and that the front position is more sensitive to migration compared to the shallow-ice approximation.

Glacier de Saint-Sorlin, French Alps, left terminal moraines at 1.3, 2.9 and 3.7 km ahead of the present terminus. According to proxy data and to historical maps, these were formed in the 19th, 18th and 17th centuries, respectively. A plateau at 2700–2625 m was then surrounded by ice but never became an accumulation area. This fact shows that the equilibrium-line altitude (ELA) on the glacier never dropped below 2300 m. The following simple models apply sufficiently to yield reliable estimations of past ELA: (1) a uniform and constant vertical gradient of the mass balance, down to the terminus; and (2) a plane bed, with a slope of 8.5° and a uniform width. Then in a steady situation the accumulation–area ratio is 1/2. Compared to the mean for 1956–72, at the onset of the Little Ice Age the balances were higher by 3.75 m ice a−1, and the ELA was 400 m lower. Correlations between 1956–72 balances and meteorological data suggest that during the melting season the 0°C isotherm was about 800 m lower, while the winter precipitation at low altitudes did not change. These correlations may have been different in the past, but an equal lowering of the ELA and of the 0°C isotherm, as assumed by several authors, seems excluded.

The numerical integration of the heat-conduction equation is one of the main components in a thermodynamic sea-ice model. The spatial resolution in the ice normally varies from a minimum of three layers up to a few tens of layers. The temporal resolution varies from a few minutes up to hours. In this paper the impact of numerical resolution on the prediction of a one-dimensional thermodynamic ice model is studied. Analytical solutions for idealized cases were derived and compared with the numerical results. For the full ice model, groups of simulations were made, applying average climatic weather-forcing data corresponding to the ice-freezing, ice-thermal equilibrium and ice warm-up seasons. Special attention was paid to the effect of model spatial resolution. Early in the freezing season, the influence of resolution on model predictions is not significant. When the shortwave radiation becomes large, its absorption within the ice or snow cover was found to modulate the effect of numerical resolution on predictions of ice temperature and surface heat fluxes (e.g. the model run with a coarse spatial resolution yielded large daily variations in surface temperature). Resolution also affects the in-ice temperature profile. For process studies, a two-layer scheme for the solar radiation penetrating into the ice is suitable for a fine-spatial-resolution ice model.

Based on observations and model calculations, the retreat over the last two decades of Hansbreen, a tidewater glacier in southern Spitsbergen, Svalbard, is investigated. The observations of the calving-front position between 1982 and 1998 show an abrupt retreat in 1990, which is suggested to be related to a depression in the glacier bed. The observed seasonal variations of the front position are mainly due to variations of the calving rate. The observations of Hansbreen further indicate that during periods of slow front-position changes, melting at the water-line may play an important role in triggering the process of calving. The evolution of Hansbreen between 1982 and 1998 is simulated with a numerical model for the dynamics of tidewater glaciers. Using a flotation criterion for calving in which for each time-step the part of the glacier terminus which is below a critical height above buoyancy is removed, we are able to reproduce the observed rapid retreat of Hansbreen through the depression in the glacier bed. From the observations and model calculations, we conclude that the rapid retreat is mainly an effect of basal topography in the terminus region and not a direct response to a change in mass balance.

In the past, two-dimensional images of internal snow structure have been obtained through plane surface sections or thin sections. These techniques are time-consuming and necessarily destroy the snow specimen. Computed tomography (CT) allows similar images to be obtained, but in a more efficient and non-destructive manner. To demonstrate the methodology, a CT scanner was used to obtain cross-sectional images over time of a snow sample undergoing kinetic-growth metamorphism. Densities calculated from the CT images correlated well to density measured using a traditional method. A procedure was developed that allows the CT image to be converted to binary in an objective manner. Employing innovative stereological software, the microstructural properties (grain diameter, bond diameter, neck length and intercept length) of the snow were then measured from the two-dimensional CT images. The presented methodology provides significant improvements over previous techniques, requiring less time and labor to obtain high-quality microstructural data.

Using a series of combined compression–simple-shear experiments, it has been possible to investigate strain distributions and crystal-orientation fabrics related to varying layer orientation in ice. A variety of flattening strains accompanied by layer buckling, simple shear and the development of a lenticular layering are produced in anisotropic ice masses. In samples where the creep curve has only just reached a minimum strain rate, the c-axis preferred orientation is similar to that in the starting material, with specific c-axis concentrations affected by the extent of preserved host grains. At shear strains where γ ≤ 1, it was found that the c-axis preferred orientations were highly variable depending on the magnitude of strain, strain distribution and upon the modification and degree of rotation of initial c-axis preferred orientation. However, once recrystallization dominates in high-strain zones (γ ≥ 1), there is a rapid development of an asymmetric two-maxima fabric with little evidence of any contributions from inherited fabric elements. The final c-axis pattern is asymmetric with respect to the direction of shortening, with a strong maximum at ∼80° to the shear zone, with a sense of asymmetry in the direction of the shear, and a secondary maximum lying at ∼50° to the plane of shearing.

Stake surveys on Glacier de Saint-Sorlin, French Alps, during the period 1957–76 show that annual surface velocities fit a linear vectorial model, with a term depending on the site, another on the year, and an important random component. Strain rates, viscosities and stresses at shallow depth are computed using strain triangles of hectometric (102 m) size. Between 1961/62 and 1972/73 the isotropic point, where streamlines cease to converge, moved downstream about 200 m. This trend may explain increasing velocities. Crevasses appear where annual strain is > 1.2%. Faults limit the effective shear stress at the surface to about 0.38 bar. Ten modes of flow are distinguished, instead of only two for the two-dimensional model (compressive and extensive). The gradients of shallow stresses, which ensure extra driving forces, are computed with another mosaic of triangles of similar size (stress triangles). There are also important extra driving forces at the bottom, which force the flow to deviate from the direction of the steepest surface slope. Two criteria allow elimination of stress triangles where these unknown basal extra driving forces are important. Even so, no sliding law in terms of mean annual values can be obtained. This study shows that the classical perturbation theory, which explains advances and retreats by the arrival of kinematic waves, is unsuitable for glaciers of kilometric size.

The proxy for temperature (δ signal) in ice cores is stored in the snow/ice during precipitation events and hence reflects the temperature at which precipitation is formed (here approximated by the inversion temperature Ti) weighted with the accumulation. Results from a 14 year integration (1980–93) with a regional atmospheric model (RACMO, ΔX = 55 km) show that the annual mean accumulation-weighted inversion temperature (Ti,w) and the annual mean Ti are not covariant in time at four out of the five deep-drilling sites considered, mainly due to year-to-year variations in the seasonality of precipitation. As a consequence, the surface temperature (Ts,core) derived from RACMO output, using a method analogous to the retrieval of the surface temperature from ice-core δ signals, deviates from the directly modelled surface temperature Ts on interannual time-scales. Results from a 5 year sensitivity integration, forced with a 2 K temperature increase, show an 18% overestimation of the increase in Ts,core relative to the increase in Ts due to a change in the relationship between the inversion strength and the surface temperature in a different climate regime. Similar errors may occur in deriving the temperature difference between Last Glacial Maximum and present-day climate from δ signals in ice cores.

Helicopter-borne 135 MHz short-pulse radar profiles of the Bagley Ice Field, southern Alaska, U.S.A., have been analyzed to determine the nature of radio-wave propagation through crevassed, stratified, wet and draining firn. Diffractions characterize the firn horizons along the trunk, and reflections characterize those of overlying snow-fields. Dynamic stacking was used to form and determine firn depths, and unstacked diffraction analysis to determine firn-layer properties. Refractive indices range from 4.1 to 4.5 for the near-surface, from 1.7 to 2.1 at about 13–17 m depth along the main trunk, and to 2.6 to 58 m depth within a snowfield. Average trunk values correspond with volumetric water contents of about 0.09, which agree with values measured for other glaciers. The analysis of the airborne-recorded diffractions is confirmed by deriving the approximate refractive index of water from a supraglacial lake-bottom diffraction. The lack of snowfield diffractions suggests that crevassing and not firn structure caused the trunk diffractions. The reasonable values of the indices imply that the diffractions originated from single points or edges orthogonal to the profile transect, and they predict low interlayer transmission losses. The snowfield penetration suggests that several hundred meters might be penetrated in uncrevassed accumulation zones with improved system design.

The 50 year time series of mass balance on Glacier de Sarennes is one of the longest in the French Alps, and so is often used as a reference for glacier variations in the French Alps. Meteorological data can be used to extend the series backwards in time. Martin (1978) proposed such a reconstruction for the 1882–1977 period. With 50 years of observations, we show that the classical method used by Martin is too dependent on the calibration period. We therefore try to improve the accuracy of this reconstruction using the Vincent and Vallon (1997) method which takes into account the albedo change of the surface during the ablation period (this is called the daily method). This new method appears to be stable in time. Once calibrated, the daily method is applied to reconstruct the 1881–1949 period. The new reconstruction is compared to a volumetric balance between two maps from 1906 and 1981. It appears that both reconstructions (classical and daily) fail to render the trend correctly over a long period of time. The cumulative centred mass balance correlates well (r2 = 0.62) with the hydrological mass-balance series of Aletschgletscher, Switzerland.