The spatial characteristics for all glaciers in the North Cascades National Park Complex, USA, were estimated in 1958 and again in 1998. The total glacier area in 1958 was 117.3 ± 1.1 km2; by 1998 the glacier area had decreased to 109.1 ± 1.1 km2, a reduction of 8.2 ± 0.1 km2 (7%). Estimated volume loss during the 40 year period was 0.8 ± 0.1 km3 of ice. This volume loss contributes up to 6% of the August–September stream-flow and equals 16% of the August–September precipitation. No significant correlations were found between magnitude of glacier shrinkage and topographic characteristics of elevation, aspect or slope. However, the smaller glaciers lost proportionally more area than the larger glaciers and had a greater variability in fractional change than larger glaciers. Most of the well-studied alpine glaciers are much larger than the population median, so global estimates of glacier shrinkage, based on these well-studied glaciers, probably underestimate the true magnitude of regional glacier change.

Spatial and temporal variations in aerodynamic roughness length (z0) on Haut Glacier d’Arolla, Switzerland, during the 1993 and 1994 ablation seasons are described, based on measurements of surface microtopography. The validity of the microtopographic z0 measurements is established through comparison with independent vertical wind profile z0 measurements over melting snow, slush and ice. The z0 variations are explained through correlation and regression analyses, using independent measurements of meteorological and surface variables, and parameterizations are developed to calculate z0 variations for use in surface energy-balance melt models. Several independent variables successfully explain snow z0 variation through their correlation with increasing surface roughness, caused by ablation hollow formation, during snowmelt. Non-linear parameterizations based on either accumulated melt or accumulated daily maximum temperatures since the most recent snowfall explain over 80% of snow z0 variation. The z0 following a fresh snowfall on an ice surface is parameterized based on relationships with the underlying ice z0, snow depth and accumulated daily maximum temperatures. None of the independent variables were able to successfully explain ice z0 variation. Although further comparative studies are needed, the results lend strong support to the microtopographic technique of measuring z0 over melting glacier surfaces.

This paper presents observations and measurements of debris characteristics and ice-shelf dynamics in the ablation region of the McMurdo Ice Shelf in the Ross Sea sector of Antarctica. Ice-shelf surface processes and dynamics are inferred from a combination of sedimentological descriptions, ground-penetrating radar investigations and through ablation, velocity and ice-thickness measurements. Field data show that in the study area the ice shelf moves relatively slowly (1.5–18.3ma–1), has high ablation rates (43–441 mm during 2003/04 summer) and is thin (6–22 m). The majority of debris on the ice shelf was originally transported into the area by a large and dynamic ice-sheet/ice-shelf system at the Last Glacial Maximum. This debris is concentrated on the ice-shelf surface and is continually redistributed by surface ablation (creating an ice-cored landscape of large debris-rich mounds), ice-shelf flow (forming medial moraines) and meltwater streams (locally reworking material and redistributing it across the ice-shelf surface). A conceptual model for supraglacial debris transport by contemporary Antarctic ice shelves is presented, which emphasizes these links between debris supply, surface ablation and ice-shelf motion. Low-velocity ice shelves such as the McMurdo Ice Shelf can maintain and sequester a debris load for thousands of years, providing a mechanism by which ice shelves can accumulate sufficient debris to contribute to sediment deposition in the oceans.

A newly developed hammer was used to insert two autonomous probes 0.8 m and 2.1 m into clast-rich subglacial till under Black Rapids Glacier, Alaska, USA. Both probes were instrumented with a dual-axis tilt sensor and a pore-water pressure transducer. The data are compared to a 75 day record of surface velocities. Till deformation at depth was found to be highly seasonal: it is significant during an early-season speed-up event, but during long periods thereafter measured till deformation rates are negligible. Both tilt records show rotation around the probe axis, which indicates a change in tilt direction of about 30°. The tilt records are very similar, suggesting spatial homogeneity on the scale of the probe separation (4 m horizontal and 3.3 m vertical). There is evidence that during much of the year sliding of ice over till or deformation of a thin till layer (<20 cm) accounts for at least two-thirds of total basal motion. Basal motion accounts for 50–70% of the total surface motion. The inferred amount of ice–till sliding is larger than that found at the same location in a previous study, when surface velocities were about 10% lower. We suggest that variations in ice–till coupling account for the observed variations in mean annual speed.

The effect of spatial variations in ice thickness, accumulation rate and lateral flow divergence on radar-detected isochrone geometry in ice sheets is computed using an analytical method, under assumptions of a steady-state ice-sheet geometry, a steady-state accumulation pattern and a horizontally uniform velocity shape function. By using a new coordinate transform, we show that the slope of the isochrones (with a normalized vertical coordinate) depends on three terms: a principal term which determines the sign of the slope, and two scale factors which can modify only the amplitude of the slope. The principal term depends only on a local characteristic time (ice thickness divided by accumulation rate minus melting rate) between the initial and final positions of the ice particle. For plug flow, only the initial and final values have an influence. Further applications are a demonstration of how the vertical velocity profile can be deduced from sharp changes in isochrone slopes induced by abrupt steps in bedrock or mass balance along the ice flow. We also demonstrate ways the new coordinate system may be used to test the accuracy of numerical flow models.

Azimuth dependence of a normalized radar cross-section (σº) over the Greenland ice sheet is modeled with a simple surface scattering model. The model assumes that azimuth anisotropy in surface roughness at scales of 3–300 m is the primary mechanism driving the modulation. To evaluate the contribution of azimuth anisotropy in surface roughness to the radar backscatter, the model is compared to models based on isotropic surface roughness. The models are inverted to estimate snow surface properties using σº measurements from the C-band European Remote-sensing Satellite advanced microwave instrument in scatterometer mode. Results indicate that the largest mesoscale rms surface slopes are found in the lower portions of the dry snow zone. Estimates of the preferential direction in surface roughness are highly correlated with katabatic wind fields over Greenland, which is consistent with wind-formed sastrugi as the dominant mechanism causing azimuth modulation of σº. The maximum improvement of the azimuth modulation surface model compared to its isotropic counterparts occurs in the lower regions of the dry snow zone where the azimuth variability of σº is the largest. In regions with azimuth modulation over 1 dB, the mean root-mean-square error estimate of the azimuth-dependent surface scattering model is 0.46 dB compared with 0.70 dB for similar models using isotropic roughness.

We present a technique that modifies and extends down-hole target methods to provide absolute measures of uncertainty in radar-reflector depth of origin. We use ice-core profiles to model wave propagation and reflection, and then cross-correlate the model results with radio-echo sounding (RES) data to identify the depth of reflector events. Stacked traces recorded with RES near the EPICA drill site in Dronning Maud Land, Antarctica, provide reference radargrams, and dielectric properties along the deep ice core form the input data to a forward model of wave propagation that produces synthetic radargrams. Cross-correlations between synthetic and RES radargrams identify differences in propagation wave speed. They are attributed to uncertainties in pure-ice permittivity and are used for calibration. Removing conductivity peaks results in the disappearance of related synthetic reflections and enables the unambiguous relation of electric signatures to RES features. We find that (i) density measurements with g-attenuation or dielectric profiling are too noisy below the firn–ice transition to allow clear identification of reflections, (ii) single conductivity peaks less than 0.5 m wide cause the majority of prominent reflections beyond a travel time of about 10 µs (~900m depth) and (iii) some closely spaced conductivity peaks within a range of 1–2m cannot be resolved within the RES or synthetic data. Our results provide a depth accuracy to allow synchronization of age–depth profiles of ice cores by RES, modeling of isochronous internal structures, and determination of wave speed and of pure-ice properties. The technique successfully operates with dielectric profiling and electrical conductivity measurements, suggesting that it can be applied at other ice cores and drill sites.

Proportional straining experiments have been performed on columnar-grained S2 freshwater ice biaxially compressed across the columns at –10°C at a strain rate of (4.5 ± 1.5) × 10–3 s–1. The results are compared with those obtained earlier (Iliescu and Schulson, 2004) from the same kind of material deformed to terminal failure under the same conditions, but through proportional loading. The exercise shows that the biaxial strength is practically independent of the path taken, at least under low confinement where Coulombic shear faulting limits terminal failure. First-year sea ice is expected to exhibit the same behavior.

The roughness of the snow-free surface of the glacier midre Lovénbreen, Svalbard, has been investigated on scales between 1 mm and 300 m. It is shown that the roughness is reasonably well described by scale-free (fractal) models for scales longer than a few metres and shorter than about 100 mm. However, there is a break in the behaviour between these scales which can be characterized by a definite scale length of 70–500 mm and a root-mean-square height variation between around 6 and 70 mm. The aerodynamic roughness length contributed by these features is estimated to be 0.3–1.5 mm. Features on this scale are consistent with the observed microwave backscattering properties of the glacier.

Numerical model studies describing the dynamics of ice sheets are usually aimed at cold- ice regions of mainland Antarctica. Contrary to these ice bodies with temperatures well below the pressure-melting point at the ice surface, the ice caps on sub-Antarctic islands, such as King George Island, can be considered as polythermal or even temperate. This implies that they may contain nonnegligible amounts of water percolating through the ice matrix. We present three different modifications to a three-dimensional, thermomechanically coupled, higher-order model previously applied to cold-ice regions. We discuss the effect of these modifications on the ice dynamics obtained for diagnostic model runs. The modifications comprise changes to the enhancement factor in Glen’s flow law, the choice of negligible or non-negligible water content and the choice of a threshold altitude below which the ice surface is set to pressure-melting point conditions. All modifications lead to non-linear changes in the resulting horizontal flow velocities. The changes in velocity amplitudes obtained with these modifications compared to simulations without any modification range between 64% and ~400%. This implies that they should be considered in time-dependent simulations of temperate-ice dynamics.

Reorientation of individual crystal glide planes, as isotropic surface ice is deformed during its passage to depth in an ice sheet, creates a fabric and associated anisotropy. We adopt an evolving orthotropic viscous law which was developed to reflect the induced anisotropy arising from the mean rotation of crystal axes during deformation. This expresses the deviatoric stress in terms of the strain rate, strain and three structure tensors based on the principal stretch axes, and involves one fabric response function which determines the strength of the anisotropy. The initial isotropic response enters as a multiplying factor depending on a strain-rate invariant and incorporating a temperature-dependent rate factor. The fabric response function has been constructed by correlations with complete (idealized) uniaxial compression and shearing responses for both ‘cold’ and ‘warm’ ice. The possible effects of such fabric evolution are now illustrated by determining steady radially symmetric flow solutions for an ice sheet with a prescribed temperature distribution and subject to an elevation-dependent surface accumulation/ablation distribution, zero basal melting and a prescribed basal sliding law. Comparisons are made with solutions for the conventional isotropic viscous law, for a flat bed, for a bed with a single modest slope hump and for a bed with a single modest slope hollow, for both cold and warm ice.

A minimal model of a tidewater glacier based solely on mass conservation is compared with two one-dimensional numerical flowline models, one with the calving rate proportional to water depth, and the other with the flotation criterion as a boundary condition at the glacier terminus. The models were run with two simplified bed geometries and two mass-balance formulations. The models simulate the full cycle of length variations and the equilibrium states for a tidewater glacier. This study shows that the branching of the equilibrium states depends significantly on the bed geometry. The similarity between the results of the three models indicates that if there is a submarine undulation at the terminus of a tidewater glacier, any model in which the frontal ice loss is related to the water depth yields qualitatively the same non-linear behaviour. For large glaciers extending into deep water, the flotation model causes unrealistic behaviour.

Controls on glacier calving rates are receiving increased scientific interest. At fresh-watercalving glaciers, limnological factors might be more important than glaciological ones. Measurements of thermo-erosional notch development at the calving ice cliff of Tasman Glacier, New Zealand, suggest that the calving rates at this glacier are directly controlled by the rate of thermal undercutting. Notch formation rates typically vary between 10 and 30 cm d–1 (maximum rate 65cmd–1) in summer, corresponding to an average calving rate of 34 m a–1. Notch formation is slower than waterline melt and is controlled by water temperatures and circulation, cliff geometry, debris supply and water-level fluctuations. The latter shift the position of undercutting, resetting the level of the notch formation process and thereby slowing it. The geometry of the notch and the debris supply determine the extent of influence of the lake on notch water temperatures and circulation. Hence, water temperatures in the lake are not necessarily indicative of the rate of notch formation. The prediction of rate of notch formation from far-field variables is hampered by the complex interaction of the influencing factors. The significance of thermal undercutting as a calving rate-controlling process decreases with increasing ice velocities, calving rates and surface gradients.