There are no direct methods to measure the boundary condition at the base of a glacier. Here, we propose a method that works by iteratively changing boundary conditions until a satisfactory fit to surface observations is obtained. The method is an accelerated version of one known as Kozlov–Maz’ya iteration. We apply it to the problem of ice flow through a transverse cross-section, and show it to be effective by solving the inverse problem for a sequence of synthetic data. We also apply the method to two real glaciers, Athabasca and Perito Moreno, one of which has a known basal velocity distribution.

Rapid thinning and velocity increase on major Greenland outlet glaciers during the last two decades may indicate that these glaciers became unstable as a consequence of the Jakobshavn effect (Hughes, 1986), with terminus retreat leading to increased discharge from the interior and consequent further thinning and retreat. To assess whether recent trends deviate from longer-term behavior, we measured glacier surface elevations and terminus positions for Jakobshavn Isbræ, West Greenland, using historical photographs acquired in 1944, 1953, 1959, 1964 and 1985. These results were combined with data from historical records, aerial photographs, ground surveys, airborne laser altimetry and field mapping of lateral moraines and trimlines, to reconstruct the history of changes since the Little Ice Age (LIA). We identified three periods of rapid thinning since the LIA: 1902–13, 1930–59 and 1999–present. During the first half of the 20th century, the calving front appears to have been grounded and it started to float during the late 1940s. The south and north tributaries exhibit different behavior. For example, the north tributary was thinning between 1959 and 1985 during a period when the calving front was stationary and the south tributary was in balance. The record of intermittent thinning, combined with changes in ice-marginal extent and position of the calving front, together with changes in velocity, imply that the behavior of the lower parts of this glacier represents a complex ice-dynamical response to local climate forcings and interactions with drainage from the interior.

We present spatial patterns of glacier fluctuations from the Cordillera Blanca, Peru, (glacier area, terminus elevations, median elevations and hypsography) at decadal timescales derived from 1970 aerial photography, 2003 SPOT5 satellite data, Geographic Information Systems (GIS) and statistical analyses. We derived new glacier outlines from the 2003 SPOT images, and ingested them in the Global Land and Ice Measurements from Space (GLIMS) glacier database. We examined changes in glacier area on the eastern and western side of the Cordillera in relation to topographic and climate variables (temperature and precipitation). Results include (1) an estimated glacierized area of 569.6 ± 21 km2 in 2003, (2) an overall loss in glacierized area of 22.4% from 1970 to 2003, (3) an average rise in glacier terminus elevations by 113 m and an average rise in the median elevation of glaciers by 66 m, showing a shift of ice to higher elevations, especially on the eastern side of the Cordillera, and (4) an increase in the number of glaciers, which indicates disintegration of ice bodies. Annual air temperature showed a significant upward trend in the last 30 years, with larger temperature increases at lower elevations. There was a slight but not significant decrease in precipitation. Our results are consistent with glacier retreat and warming trends noted in the last three decades in the tropics.

Experiments have been conducted on the French full-scale experimental site at Lautaret pass to improve our understanding of the action of snow avalanches on obstacles. The ultimate objective is to provide realistic pressure distribution models suitable for use in civil engineering design and to eliminate the restrictive assumptions currently used in this field. We focus on the feasibility of using the inverse method to quantify the action of the avalanche from its effects on realistic structures rather than from sensors placed directly in the flow. This approach takes into account the interactions between the flow and the obstacle and ensures that the result is effectively the action experienced by the obstacle. The inverse analysis procedure is developed and validated using both numerical and laboratory tests. In situ tests carried out at the Lautaret site to determine the avalanche action at different scales confirm the reliability of this original approach. Its intrinsic characteristics make it especially suitable for application to different structures to provide new knowledge in this complex field.

Alpine permafrost distribution is controlled by a great number of climatic, topographic and soil-specific factors, including snow cover, which plays a major role. In this study, a one-dimensional finite-element numerical model was developed to analyze the influence of individual snow-specific and climatic factors on the ground thermal regime. The results indicate that the most important factor is snow depth. Snow depths below the threshold value of 0.6 m lack sufficient insulation to prevent low atmospheric temperatures from cooling the soil. The date of first winter snow insulation and variations in mean annual air temperature (MAAT) are also shown to be important. Delays in early-winter snow insulation and in summer snow disappearance are shown to be of approximately equal significance to the ground thermal conditions. Numerical modelling also indicates that the duration of effective thermal resistance of snow cover governs the slope of the linear dependency between MAAT and mean annual ground surface temperatures (MAGST). Consequently, the most direct effect of a long-term rise in air temperatures on ground temperatures is predicted under a thin snow cover with early snowmelt in spring and/or where a large change in the date of total snowmelt occurs, in response to atmospheric warming.

Our main goal is to exemplify the study of ice-stream dynamics via Bayesian statistical analysis incorporating physical, though imperfectly known, models using data that are both incomplete and noisy. The physical–statistical models we propose account for these uncertainties in a coherent, hierarchical manner. The initial modeling assumption estimates basal shear stress as equal to driving stress, but subsequently includes a random corrector process to account for model error. The resulting stochastic equation is incorporated into a simple model for surface velocities. Use of Bayes’ theorem allows us to make inferences on all unknowns given basal elevation, surface elevation and surface velocity. The result is a posterior distribution of possible values that can be summarized in a number of ways. For example, the posterior mean of the stress field indicates average behavior at any location in the field, and the posterior standard deviations describe associated uncertainties. We analyze data from the ‘Northeast Greenland Ice Stream’ and illustrate how scientific conclusions may be drawn from our Bayesian analysis.

Using dense networks of three-component seismometers installed in direct contact with the ice, the seismic activity of Gornergletscher, Switzerland, was investigated during the summers of 2004 and 2006, as subglacial water pressures varied drastically. These pressure variations are due to the diurnal cycle of meltwater input as well as the subglacial drainage of Gornersee, a nearby marginal ice-dammed lake. Up to several thousand seismic signals per day were recorded. Whereas most icequakes are due to surface crevasse openings, about 200 events have been reliably located close to the glacier bed. These basal events tend to occur in clusters and have signals with impulsive first arrivals. At the same time, basal water pressures and ice-surface velocities were measured to capture the impact of the lake drainage on the subglacial hydrological system and the ice-flow dynamics. Contrary to our expectations, we did not observe an increase of basal icequake activity as the lake emptied, thereby raising the subglacial water pressures close to the flotation level for several days. In fact, the basal icequakes were usually recorded during the morning hours, when the basal water pressure was either low or decreasing. During the high-pressure period caused by the drainage of the lake, no basal icequakes were observed. Furthermore, GPS measurements showed that the glacier surface was lowering during the basal seismic activity. These observations lead us to conclude that such icequakes are connected to the diurnal variation in glacier sliding across the glacier bed.

We conducted a seismic and radar survey of the central part of midtre Lovénbreen, a small, polythermal valley glacier in Svalbard. We determined the physical properties of the material beneath the glacier by measuring the reflection coefficient of the bed by comparing the energy of the primary and multiple reflections, and deriving the acoustic impedance. By making reasonable assumptions about the properties of the basal ice, we determined the acoustic impedance of the bed material as (6.78 ± 1.53) × 106 kg m−2 s−1. We interpret the material beneath the glacier to be permafrost with up to 50% ice, and we speculate that the material may be frozen talus similar to a deposit observed directly by others beneath another Svalbard glacier. The implication for midtre Lovénbreen is that the basal material beneath the present glacier is not able to support fast flow. We conclude that midtre Lovénbreen has most likely had limited capability for faster flow in the past, with motion dominated by internal deformation. Midtre Lovénbreen is used as a ‘study glacier’ for the scientific community in Svalbard, and a large number of studies have been based there. Our results show that it cannot be used as an analogue for larger glaciers in Svalbard, having distinct basal boundary conditions.

We investigate snowpack properties at a site in west-central Greenland with ground-penetrating radar (GPR), supplemented by stratigraphic records from snow pits and shallow firn cores. GPR data were collected at a validation test site for CryoSat (T05 on the Expéditions Glaciologiques Internationales au Groenland (EGIG) line) over a 100 m × 100 m grid and along 1 km sections at frequencies of 500 and 800 MHz. Several internal reflection horizons (IRHs) down to a depth of 10 m were tracked. IRHs are usually related to ice-layer clusters in vertically bounded sequences that obtain their initial characteristics near the surface during the melt season. Warm conditions in the following melt season can change these characteristics by percolating meltwater. In cold conditions, smaller melt volumes at the surface can lead to faint IRHs. The absence of simple mechanisms for internal layer origin emphasizes the need for independent dating to reliably interpret remotely sensed radar data. Our GPR-derived depth of the 2003 summer surface of 1.48 m (measured in 2004) is confirmed by snow-pit observations. The distribution of IRH depths on a 1 km scale reveals a gradient of increasing accumulation to the northeast of about 5 cm w.e. km−1. We find that point measurements of accumulation in this area are representative only over several hundred metres, with uncertainties of about 15% of the spatial mean.

Ice-sheet models (ISMs) developed to simulate the behaviour of continental-scale ice sheets under past, present or future climate scenarios are subject to a number of uncertainties from various sources. These sources include the conceptualization of the ISM and the degree of abstraction and parameterizations of processes such as ice dynamics and mass balance. The assumption of spatially or temporally constant parameters (such as degree-day factor, atmospheric lapse rate or geothermal heat flux) is one example. Additionally, uncertainties in ISM input data such as topography or precipitation propagate to the model results. In order to assess and compare the impact of uncertainties from model parameters and climate on the GLIMMER ice-sheet model, a parametric uncertainty analysis (PUA) was conducted. Parameter variation was deduced from a suite of sensitivity tests, and accuracy information was deduced from input data and the literature. Recorded variation of modelled ice extent across the PUA runs was 65% for equilibrium ice sheets. Additionally, the susceptibility of ISM results to modelled uncertainty in input topography was assessed. Resulting variations in modelled ice extent in the range of 0.8–6.6% are comparable to that of ISM parameters such as flow enhancement, basal traction and geothermal heat flux.

A passive seismic study was carried out underneath Glacier d’Argentière, Mont Blanc, France, where an array of seismometers was installed in a subglacial access tunnel. The data show a very high emissivity from the glacier. Fracturing can be discriminated from serac falls using the signal characteristics. We apply seismic array methods to locate the sources of these signals, using a two-step grid search in the parameter space. Four clusters of activity are found close to the network, showing that this fracturing does not take place uniformly over the glacier, but rather in isolated small zones. We compute a local magnitude using regional earthquakes for calibration. The magnitudes follow a classical Gutenberg–Richter law in the range ML = −3 to 0.15, showing that no characteristic size events dominate the process. We suggest that those spatial clusters of icequakes could reveal the heterogeneous nature of the friction at the base of the glacier, with patches of high frictional stresses locally generating intense fracturing within the ice mass.

Annual-layer thickness data, spanning AD 1534–2001, from an ice core from East Rongbuk Col on Qomolangma (Mount Everest, Himalaya) yield an age–depth profile that deviates systematically from a constant accumulation-rate analytical model. The profile clearly shows that the mean accumulation rate has changed every 50–100 years. A numerical model was developed to determine the magnitude of these multi-decadal-scale rates. The model was used to obtain a time series of annual accumulation. The mean annual accumulation rate decreased from ∼0.8 m ice equivalent in the 1500s to ∼0.3 m in the mid-1800s. From ∼1880 to ∼1970 the rate increased. However, it has decreased since ∼1970. Comparison with six other records from the Himalaya and the Tibetan Plateau shows that the changes in accumulation in East Rongbuk Col are broadly consistent with a regional pattern over much of the Plateau. This suggests that there may be an overarching mechanism controlling precipitation and mass balance over this area. However, a record from Dasuopu, only 125 km northwest of Qomolangma and 700 m higher than East Rongbuk Col, shows a maximum in accumulation during the 1800s, a time during which the East Rongbuk Col and Tibetan Plateau ice-core and tree-ring records show a minimum. This asynchroneity may be due to altitudinal or seasonal differences in monsoon versus westerly moisture sources or complex mountain meteorology.

The mass balance of Glacier de Sarennes, French Alps, has been measured since 1949, using the glaciological method based on core and ablation stake data, and area extrapolations, to find the overall glacier balance. The cumulative balance obtained in this way is very dependent on systematic errors that can increase linearly with the number, N, of measurement years, whereas random errors rise with . The volumetric-balance method based on aerial photogrammetry provides results whose errors do not depend on the number of years. This method was used to test field measurements for the period 1952–2003 and gives a mass balance of −32.30 ± 1.04 m w.e. compared to −34.89 ± 1.15 m w.e. based on field data. The discrepancy between the two methods is discussed on the basis of a careful error analysis. Moreover, the possibility of using the volumetric method to detect biases in field measurements is evaluated in terms of two types of errors. The number and locations of measurement sites required to account for all the spatial and temporal variabilities of the mass balance is discussed by variance analysis. Methodological implications and recommendations are presented to provide mass-balance measurements of the best possible accuracy.

High-resolution surface velocity measurements and passive seismic observations from Rutford Ice Stream, West Antarctica, 40 km upstream from the grounding line are presented. These measurements indicate a complex relationship between the ocean tides and currents, basal conditions and ice-stream flow. Both the mean basal seismicity and the velocity of the ice stream are modulated by the tides. Seismic activity increases twice during each semi-diurnal tidal cycle. The tidal analysis shows the largest velocity variation is at the fortnightly period, with smaller variations superimposed at diurnal and semi-diurnal frequencies. The general pattern of the observed velocity is two velocity peaks during each semi-diurnal tidal cycle, but sometimes three peaks are observed. This pattern of two or three peaks is more regular during spring tides, when the largest-amplitude velocity variations are observed, than during neap tides. This is the first time that velocity and level of seismicity are shown to correlate and respond to tidal forcing as far as 40 km upstream from the grounding line of a large ice stream.

Volcán Villarrica (39°25′12″ S, 71°56′27″ W; 2847 m a.s.l.) is an active ice-capped volcano located in the Chilean lake district. The surface energy balance and glacier frontal variations have been monitored for several years, using automatic weather stations and satellite imagery. In recent field campaigns, surface topography was measured using Javad GPS receivers. Daily changes in snow-, ice-and tephra-covered areas were recorded using an automatic digital camera installed on a rock outcrop. In spite of frequently damaging weather conditions, two series of consecutive images were obtained, in 2006 and 2007. These photographs were georeferenced to a resampled 90 m pixel size SRTM digital elevation model and the reflectance values normalized according to several geometric and atmospheric parameters. The resulting daily maps of surface albedo are used as input to a distributed glacier-melt model during a 12 day mid-summer period. The spatial pattern of cumulative melt is complex and controlled by the distribution of airfall and wind-blown tephra, with extremely high melt rates occurring downwind of the crater and exposed ash banks. The camera images are also used to visualize the pattern of glacier crevassing. The results demonstrate the value of terrestrial photography in understanding the energy and mass balance of the glacier, including the generation of meltwater, and the potential value of the technique for monitoring volcanic activity and potential hazards associated with ice–volcano interactions during eruptive activity.

The microstructures of particle-free granular freshwater ice and ice containing 1 wt.% of 50 ± 10 mm uniformly distributed particles were investigated before and after compressive creep to ∼10% strain with stresses of 1.45 MPa at −10°C and 0.4 MPa at −5°C. Creep rates of particle-containing ice were always higher than those of particle-free ice. For an initial stress of 1.45 MPa at −10°C, dynamic recrystallization occurred with new grains nucleating and growing along grain boundaries for both sets of specimens, and the ice with particles showed a higher nucleation rate. Under creep with an initial stress of 0.4 MPa at −5°C, dynamic recrystallization also occurred by the nucleation and growth of new grains along the grain boundaries for ice containing particles, but recrystallization in the particle-free ice occurred through grain boundary migration.

In 1973, surface velocities were measured for the first time on an unstable hanging glacier to predict its collapse. The observed velocities have been shown to increase as a power-law function of time up to infinity at the theoretical time of failure (known as ‘finite time singularity’). This is the characteristic signature of critical phenomena and has been observed in the case of various other naturally occurring ruptures such as earthquakes, landslides and snow avalanches. Recent velocity measurements performed on Weisshorn and Mönch hanging glaciers, Switzerland, confirmed this behaviour, while log-periodic oscillations superimposed on this general acceleration were also detected. Despite different rupture mechanisms in both cases, the log frequency of the oscillations is shown to be the same. The seismic activity was recorded near the unstable Weisshorn hanging glacier, simultaneously with the velocity measurements. Results show dramatically increasing icequake activity 3 days before the final collapse. Combined motion–seismic monitoring seems to be a promising way to accurately predict the breaking-off of hanging glaciers. Such a combined analysis is also useful for capturing the physical mechanisms of rupture in natural heterogeneous materials.

If basal-water discharge and pressure are sufficiently high, a soft-bedded glacier will slip over its bed by ploughing, the process in which particles that span the ice–bed interface are dragged across the bed surface. Results of laboratory experiments indicate that resistance to ploughing can decrease with increasing ploughing velocity (velocity weakening). During ploughing at various velocities (15–400 m a−1), till was compacted in front of idealized particles, causing pore pressures there that were orders of magnitude higher than the ambient value. This excess pore pressure locally weakened the till in shear, thereby decreasing ploughing resistance by a factor of 3.0–6.6 with a six-fold increase in ploughing velocity. Characteristic timescales of pore-pressure diffusion and compaction down-glacier from ploughing particles depend on till diffusivity, ploughing velocity and sizes of ploughing particles. These timescales accurately predict the ranges of these variables over which excess pore pressure and velocity weakening occurred. Existing ploughing models do not account for velocity weakening. A new ploughing model with no adjustable parameters predicts ploughing resistance to no worse than 38% but requires that excess pore pressures be measured. Velocity weakening by this mechanism may affect fast glacier flow, sediment transport by bed deformation and basal seismicity.

Despite the large amount of subglacial lakes present underneath the East Antarctic ice sheet and the melt processes involved, the hydrology beneath the ice sheet is poorly understood. Changes in subglacial potential gradients may lead to subglacial lake outbursts, discharging excess water through a subglacial drainage system underneath the ice sheet. Such processes can eventually lead to an increase in ice flow. In this paper, a full Stokes numerical ice-sheet model was employed which takes into account the ice flow over subglacial water bodies in hydrostatic equilibrium with the overlying ice. Sensitivity experiments were carried out for small perturbations in ice flow and basal melt rate as a function of ice thickness, general surface slope, ice viscosity and lake size, in order to investigate their influence on the subglacial potential gradient and the impact on subglacial lake drainage. Experiments clearly demonstrate that small changes in surface slope are sufficient to start and sustain episodic subglacial drainage events. Lake drainage can therefore be regarded as a common feature of the subglacial hydrological system and may influence, to a large extent, the present and future behavior of large ice sheets.