This paper presents a simple model to estimate ice ablation under a thick supraglacial debris cover. The key method employed in the model is to establish a link between the debris heat flux and the debris temperature at a certain depth when the heat transfer in the debris is described by a diffusion process. Given surface temperature, debris thermal properties and relevant boundary conditions, the proposed model can estimate mean debris temperature at interfaces of different debris layers using an iterative procedure, and then the heat flux for ice ablation. The advantage of the proposed model is that it only requires a few parameters to conduct the modeling, which is simpler and more applicable than others. The case study on Koxkar glacier, west Tien Shan, China, shows, in general, that the proposed model gives good results for the prediction of debris temperatures, except for an apparent phase shift between modeled and observed values. We suggest that this error is mainly due to complex phase relations between debris temperature and debris heat flux. The modeled ablation rates at three experimental sites also show good results, using a direct comparison with observed data and an indirect comparison with a commonly used energy-balance model.

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.

Surface-based ice-penetrating radar profiles were made across the active north margin (the Snake) of the upper part of Whillans Ice Stream (formerly Ice Stream B, branch B2), West Antarctica, at three locations. Low frequency (about 2 MHz) and the ground deployment of the radar allowed penetration through the near-surface zone of fracturing to detect internal layering and bed reflection characteristics on continuous profiles spanning from the slow-moving ice of Engelhardt Ridge well into the chaotic zone of the shear margin. Internal layers were tracked beneath the chaotic zone, where they are warped but remain continuous. The energy returned from internal layers showed no systematic changes associated with the transition from the undisturbed surface of the slow-moving ice into the fractured surface of the shear margin, thus indicating little effect from the surface crevasses on the penetration of the radar signal. Based on this calibration of the near-surface effects and corrections for path length, spreading and attenuation, we examine the spatial variation of bed reflectivity. Low bed reflectivity found under Engelhardt Ridge extends under the chaotic zone of the margin into fast-moving ice. We argue that the fast motion in a band along the margin is mediated by processes other than deformation of thick dilated till that is the source of lubrication allowing fast motion in the interior of the ice stream.

A survey of July 1st glacier, Qilian Shan, China, was carried out in 2002. Previously, the glacier’s boundary had been recorded in 1956, and further research had been carried out in the mid- 1970s and 1980s. Our survey reveals that area shrinkage and surface lowering have accelerated in the past 15 years. Surface elevation changes can result from changes in accumulation, surface melting and emergence velocity. The contributions of these elements to surface lowering are evaluated at the lower part of the glacier from observations of surface velocity, ice thickness and precipitation, and from temperature data near the glacier. Apart from the effect of glacier ice redistribution, our analysis reveals quantitatively that the recent accelerated glacier shrinkage has been caused by increasing temperature. Furthermore, it is established that meltwater discharge from the glacier in the past 17 years has increased due to glacier shrinkage, by about 50% over that from 1975 to 1985.

This paper introduces a new way to investigate in situ processes, the wireless multi-sensor probe, as part of an environmental sensor network. Instruments are housed within a ‘probe’ which can move freely and so behave like a clast. These were deployed in the ice and till at Briksdalsbreen, Norway. The sensors measure temperature, resistivity, case stress, tilt angle and water pressure and send their data to a base station on the glacier surface via radio links. These data are then forwarded by radio to a reference station with mains power 2.5 km away, from where they are sent to a web server in the UK. The system deployed during 2004/05 was very successful and a total of 859 probe days worth of data from the ice and till were collected, along with GPS, weather and diagnostic data about the system.

A series of satellite images of Mýrdalsjökull, Iceland, was analyzed in view of their value for mass-balance investigations. A combination of optical satellite images from the ASTER sensor and synthetic aperture radar data from ERS-2 and Envisat ASAR proved very useful. The glacier margin of Mýrdalsjökull was delineated on ASTER images from summer and winter 2004. With a time series of summer ASAR images it was possible to monitor the temporal and spatial development of the transient snowline (TSL) throughout the year 2004, as well as the firn line (FL) at the end of the balance year. An ‘inverse’ function was applied to visually enhance detail in the radar imagery. Winter radar images were not useful for mass-balance observations because of frequent surface melting, which prevented the transparency of the snow cover for C-band microwaves. Interannual mass-balance fluctuations were observed by comparing three radar images acquired in late summer 1998, 1999 and 2004 respectively. These fluctuations follow the same trend as the annual mean air temperature which shows a strong increasing trend between 1999 and 2004. An accumulation-area ratio of <0.43 was determined for 2004, indicating clear negative mass-balance conditions. Monitoring the TSL-FL with radar summer images for mass-balance studies, rather than the equilibrium line (EL), is suggested for large ice caps in maritime climates.

Extensive observations on Nivlisen, an ice shelf on Antarctica’s Atlantic coast, are analyzed and combined to obtain a new description of its complex glaciological regime. We generate models of ice thickness (primarily from ground-penetrating radar), ellipsoidal ice surface height (primarily from ERS-1 satellite altimetry), freeboard height (by utilizing precise sea surface information) and ice-flow velocity (from ERS-1/-2 SAR interferometry and GPS measurements). Accuracy assessments are included. Exploiting the hydrostatic equilibrium relation, we infer the ‘apparent air layer thickness’ as a useful measure for a glacier’s density deviation from a pure ice body. This parameter exhibits a distinct spatial variation (ranging from ≈2 to ≈16m) which we attribute to the transition from an ablation area to an accumulation area. We compute mass-flux and mass-balance parameters on a local and areally integrated scale. The combined effect of bottom mass balance and temporal change averaged over an essential part of Nivlisen is –654 ± 170 kg m–2 a–1, which suggests bottom melting processes dominate. We discuss our results in view of temporal ice-mass changes (including remarks on historical observations), basal processes, near-surface processes and ice-flow dynamical features. The question of temporal changes remains open from the data at hand, and we recommend further observations and analyses for its solution.

Past accumulation rate can be estimated from the measured number-density of bubbles in an ice core and the reconstructed paleotemperature, using a new technique. Density increase and grain growth in polar firn are both controlled by temperature and accumulation rate, and the integrated effects are recorded in the number-density of bubbles as the firn changes to ice. An empirical model of these processes, optimized to fit published data on recently formed bubbles, reconstructs accumulation rates using recent temperatures with an uncertainty of 41% (P < 0.05). For modern sites considered here, no statistically significant trend exists between mean annual temperature and the ratio of bubble number-density to grain number-density at the time of pore close-off; optimum modeled accumulation-rate estimates require an eventual ~2.02 ± 0.08 (P < 0.05) bubbles per close-off grain. Bubble number-density in the GRIP (Greenland) ice core is qualitatively consistent with independent estimates for a combined temperature decrease and accumulation-rate increase there during the last 5 kyr.

We present a model study investigating the summer evolution of supraglacial lakes on the Greenland ice margin. Using a one-dimensional (1-D) model we calculate the surface ablation for a bare ice surface and beneath supraglacial lakes for 30 days in the summers of 1999 and 2001. The surface ablation beneath the lake was enhanced by 110% in 1999 and 170% in 2001 compared with the ablation for bare ice. We then use the results from the 1-D model to further model the vertical and horizontal evolution of the supraglacial lakes, the results of which are compared with satellite images. Within the region of the ice sheet where supraglacial lakes presently occur, the area covered by supraglacial lakes is found to be more or less independent of the summer melt rate but controlled by topography. We therefore predict that, inside this region, the area covered by supraglacial lakes will remain constant even in a warmer climate. However, in a warmer climate, surface melting will occur higher on the ice sheet where small surface slopes favour formation of large supraglacial lakes. Enhanced surface melting beneath such lakes is a hitherto overlooked feedback mechanism related to climate warming.

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 work presents a method of mapping deformation-related sublimation patterns, formed on the surface of ice specimens, at microscopic resolution (3–4 μm pixel−1). The method is based on the systematic sublimation of a microtomed piece of ice, prepared either as a thick or a thin section. The mapping system consists of an optical microscope, a CCD video camera and a computer-controlled xy-stage. About 1500 images are needed to build a high-resolution mosaic map of a 4.5 × 9 cm section. Mosaics and single images are used to derive a variety of statistical data about air inclusions (air bubbles and air clathrate hydrates), texture (grain size, shape and orientation) and deformation-related features (subgrain boundaries, slip bands, subgrain islands and loops, pinned and bulged grain boundaries). The most common sublimation patterns are described, and their relevance for the deformation of polar ice is briefly discussed.

The instability of hanging glaciers and more generally of avalanching glaciers is discussed on the basis of observations performed on several glaciers located in the European Alps. A classification of avalanching glaciers is proposed, which allows a primary appreciation of the danger inherent in these glaciers. On the basis of field observations and results of numerical simulations of crevassing, the fracture processes which lead to major icefalls, as well as their recurrence, are analyzed. A method for predicting the time of failure is then discussed. The disaggregation of the unstable ice masses usually observed prior to large icefalls is investigated and its implications for the forecasting of icefalls analyzed.

We recorded electrical resistivity data at the base of four boreholes drilled through Haut Glacier d’Arolla, Switzerland. The data were acquired repetitively every hour over two diurnal hydrological cycles in the late melt season, separated by 10 days. Constrained three-dimensional (3-D) data inversion allowed reconstruction of hourly variations in bulk resistivity in the subglacial sediment layer. Inverted resistivity models reflect the establishment of channelized subglacial drainage in the study area between the two hydrological cycles, in agreement with previous work. Daily variations in bulk and water resistivity are in phase, and bulk resistivity amplitudes decrease away from the subglacial channel. Using selected electrical–hydraulic relationships, we estimate metre-scale changes in the hydraulic conductivity and porosity of the subglacial sediment layer, accounting for increasing clay content and decreasing median grain radius with distance from the channel. Hydraulic conductivity and porosity were respectively calculated to decrease from (6.4 ± 2.1) × 10–2ms–1 and 0.34 ± 0.01 at the channel to (3.3 ± 2.2) × 10–2ms–1 and 0.26 ± 0.01 at a distance of 5m from it. The hydraulic conductivity estimates are in agreement with previously inferred values, and the porosity estimates fall within the expected range for unlithified subglacial sediments. We conclude that collection and inversion of repeat 3-D subglacial resistivity data is feasible and has the capacity to generate multidimensional images of subglacial hydraulic processes and properties.

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.

Terminus fluctuation and area change in mountain glaciers in the middle Chinese Tien Shan over the past four decades are examined, based on Landsat multispectral scanner (MSS), Enhanced Thematic Mapper Plus (ETM+), Système Probatoire pour l’Observation de la Terre (SPOT) highresolution visible (HRV) imagery, topographical maps and China Glacier Inventory data using Geographical Information System (GIS) and remote-sensing techniques. This study shows that the glaciers in the study area have undergone continuous recession between 1963 and 2000. Over the past 37 years the total glacier area decreased from 55 × 106 m2 to 48 × 106 m2 (a 13% decrease). The glaciers at low elevations decreased more rapidly than those at high elevations. Seven of the ten large valley glaciers in the study area retreated by at least 150 ± 49 m during this period. The average rate of recession for these glaciers was 4–8 m a−1. The recession rate between 1986 and 2000 was larger than between 1963 and 1986. The glacier changes in the study area were similar to those in the Ürümqi river basin in the northern Chinese Tien Shan. It is apparent that temperature rise over the past four decades has had a profound impact on these glaciers.

Using Geographical Information System (GIS) and remote-sensing technologies, we describe quantitative measurements of glacier variations in the Geladandong mountain region of central Tibet. Data from Landsat images at three different times, 1973–76, 1992 and 2002, are compared with glacier areas digitized from a topographic map based on aerial photographs taken in 1969. We find that while some glaciers have advanced during the past 30 years, others have retreated. The area of retreat is much larger than that of advance. The total glacier area has decreased from 889km2 in 1969 to 847km2 in 2002, a reduction of almost 43 km2 (i.e. 4.8% decrease, or an average of 1.29km2 a–1). The variation of glacier area in the Geladandong mountain region is not as large as in other regions within the Tibetan Plateau. Glacier areas decreased 4.7km2 (i.e. an average of 0.68km2 a–1) during 1969–76, 15.4km2 (0.96km2 a–1) during 1976–92, and 22.4km2 (2.24km2 a–1) during 1992–2002, suggesting accelerated glacier retreat in recent years. The recession rates of glacier termini also increased. It is likely that the increase in summer air temperature is the major reason for glacier shrinkage in the Geladandong mountain region.