We propose a general framework for iceberg-calving models that can be applied to any calving margin. The framework is based on mass continuity, the assumption that calving rate and terminus velocity are not independent and the simple idea that terminus thickness following a calving event is larger than terminus thickness at the event onset. The theoretical, near steady-state analysis used to support and analyze the framework indicates that calving rate is governed, to first order, by ice thickness, thickness gradient, strain rate, mass-balance rate and backwards melting of the terminus; the analysis furthermore provides a physical explanation for a previously derived empirical relationship for ice-shelf calving (Alley and others, 2008). In the calving framework the pre- and post-calving terminus thicknesses are given by two unknown but related functions. The functions can vary independently of changes in glacier flow and geometry, and can therefore account for variations in calving behavior due to external forcings and/or self-sustaining calving processes (positive feedbacks). Although the calving framework does not constitute a complete calving model, any thickness-based calving criterion can easily be incorporated into the framework. The framework should be viewed as a guide for future attempts to parameterize calving.

An analysis of motion in the terminus region of LeConte Glacier, Alaska, U.S.A., delineates mechanisms that are important to tidewater glacier stability. This glacier is undergoing rapid retreat. Since 1995 it has retreated 2 km and thinned >125 m at the present location of the terminus. Ice velocities in this region are quite high; at the terminus they exceed 27 m d−1. Our analysis reveals that fluctuations in speed and surface elevation are forced by ocean tides, surface melt and precipitation. The nearterminus ice speed is 180° out of phase with the tide, such that high tide corresponds to low speed. Smaller, melt-forced diurnal variations in speed are present throughout the lowermost 7 km. Speed-ups in excess of 10% of the mean often occur after rainstorms as a result of increased basal water pressure and storage, but the relation is not simple. The velocity does not vary over the spring and summer seasons.

We report on analysis of meteorological data for the period 27 May–20 August 2004, from two automatic weather stations on McCall Glacier, Alaska, USA, aimed at studying the relationship between climate and ablation. One station is located on a mountain ridge and the other in the ablation area where we also analyzed the energy balance. The weather station on the glacier measured an average temperature of 5.3°C (at 2 m height above surface) and wind speed of 3.1 m s−1 (at 3 m height). A sonic height ranger and ablation stakes indicate a specific mass balance of –1.94 ± 0.09 m w.e between 15 June and 20 August. The specific mass balance calculated from the surface energy balance, –2.06 ± 0.18 m w.e., is in close correspondence to this. The latter is the sum of 0.12 m w.e. of snowfall, 0.003 m w.e. of deposition and –2.18 m w.e. of melt. Net radiation contributes 74% of the melt energy. Compared to ablation measurements in the early 1970s, summer ablation was large. This increase is explained by a combination of a relatively higher net radiation, a lower albedo and larger turbulent heat fluxes that led to more energy being available for melting. No single meteorological variable can be isolated as being the principal reason for the high ablation, however. The lower ice albedo (0.19) is possibly due to ash deposits from forest fires.

Mountain glaciers integrate climate processes to provide an unmatched signal of regional climate forcing. However, extracting the climate signal via intercomparison of regional glacier mass-balance records can be problematic when methods for extrapolating and calibrating direct glaciological measurements are mixed or inconsistent. To address this problem, we reanalyzed and compared long-term mass-balance records from the US Geological Survey Benchmark Glaciers. These five glaciers span maritime and continental climate regimes of the western United States and Alaska. Each glacier exhibits cumulative mass loss since the mid-20th century, with average rates ranging from −0.58 to −0.30 m w.e. a−1. We produced a set of solutions using different extrapolation and calibration methods to inform uncertainty estimates, which range from 0.22 to 0.44 m w.e. a−1. Mass losses are primarily driven by increasing summer warming. Continentality exerts a stronger control on mass loss than latitude. Similar to elevation, topographic shading, snow redistribution and glacier surface features often exert important mass-balance controls. The reanalysis underscores the value of geodetic calibration to resolve mass-balance magnitude, as well as the irreplaceable value of direct measurements in contributing to the process-based understanding of glacier mass balance.

During 2000–07, five giant icebergs (B15A, B15J, B15K, C16 and C25) adrift in the southwestern Ross Sea, Antarctica, were instrumented with global positioning system (GPS) receivers and other instruments to monitor their behavior in the near-coastal environment. The measurements show that collision processes can strongly influence iceberg behavior and delay their progress in drifting to the open ocean. Collisions appear to have been a dominant control on the movement of B15A, the largest of the icebergs, during the 4-year period it gyrated within the limited confines of Ross Island, the fixed Ross Ice Shelf and grounded C16. Iceberg interactions in the near-coastal regime are largely driven by ocean tidal effects which determine the magnitude of forces generated during collision and break-up events. Estimates of forces derived from the observed drift trajectories during the iceberg-collisioninduced calving of iceberg C19 from the Ross Ice Shelf, during the iceberg-induced break-off of the tip of the Drygalski Ice Tongue and the break-up of B15A provide a crude estimate of the stress scale involved in iceberg calving. Considering the total area the vertical face of new rifts created in the calving or break-up process, and not accounting for local stress amplification near rift tips, this estimated stress scale is 104 Pa.

Annual equilibrium-line altitude (ELA) and surface mass balance of Glacier Blanc, Ecrins region, French Alps, were reconstructed from a 25 year time series of satellite images (1981–2005). The remote-sensing method used was based on identification of the snowline, which is easy to discern on optical satellite images taken at the end of the ablation season. In addition, surface mass balances at the ELA were reconstructed for the same period using meteorological data from three nearby weather stations. A comparison of the two types of series reveals a correlation of r > 0.67 at the 0.01 level of significance. Furthermore, the surface mass balances obtained from remote-sensing data are consistent with those obtained from field measurements on five other French glaciers (r = 0.76, p < 0.01). Also consistent for Glacier Blanc is the total mass loss (10.8 m w.e.) over the studied period. However, the surface mass balances obtained with the remote-sensing method show lower interannual variability. Given that the remote-sensing method is based on changes in the ELA, this difference probably results from the lower sensitivity of the surface mass balance to climate parameters at the ELA.

The inverse barometer effect (IBE) is the isostatic response of ocean surface height to changes in atmospheric pressure (P air) at a rate of about 1 cm hPa−1. The IBE is a significant contributor to variability of ice-shelf surface elevation (η ice), as we demonstrate with simultaneous global positioning system measurements of η ice and local measurements of P air from the Amery, Brunt and Ross Ice Shelves, Antarctica. We find that an IBE correction is justified for frequencies (ω) covering the “weather band”, 0.03 < ω < 0.5 cpd (cycles per day). The IBE correction reduces the standard deviation of the weather-band signal of η ice from ∼9 cm to ∼3 cm. With this correction, the largest remaining high-frequency error signal in η ice is the inaccuracy of the present generation of Antarctic tide models, estimated to be of order 10 cm for most of Antarctica.

The genesis of some types of patterned ground, including hummocks, frost boils and sorted stone circles, has been attributed to differential frost heave (DFH). However, a theoretical model that adequately describes DFH has yet to be developed and validated. In this paper, we present a mathematical model for the initiation of DFH, and discuss how variations in physical (i.e. soil/vegetation properties) and environmental (i.e. ground/air temperatures) properties affect its occurrence and length scale. Using the Fowler and Krantz multidimensional frost-heave equations, a linear stability analysis anda quasi-steady-state real-time analysis are performed. Results indicate that the following conditions positively affect the spontaneous initiation of DFH: silty soil, small Young’s modulus, small non-uniform surface heat transfer or cold uniform surface temperatures, and small freezing depths. The initiating mechanism for DFH is multidimensional heat transfer within the freezing soil. Numerical integration of the linear growth rates indicates that expression of surface patterns can become evident on the 10–100 year time-scale.

We use a finite-element model of coupled ice-stream/ice-shelf flow to study the sensitivity of Pine Island Glacier, West Antarctica, to changes in ice-shelf and basal conditions. By tuning a softening coefficient of the ice along the glacier margins, and a basal friction coefficient controlling the distribution of basal shear stress underneath the ice stream, we are able to match model velocity to that observed with interferometric synthetic aperture radar (InSAR). We use the model to investigate the effect of small perturbations on ice flow. We find that a 5.5–13% reduction in our initial ice-shelf area increases the glacier velocity by 3.5–10% at the grounding line. The removal of the entire ice shelf increases the grounding-line velocity by > 70%. The changes in velocity associated with ice-shelf reduction are felt several tens of km inland. Alternatively, a 5% reduction in basal shear stress increases the glacier velocity by 13% at the grounding line. By contrast, softening of the glacier side margins would have to be increased a lot more to produce a comparable change in ice velocity. Hence, both the ice-shelf buttressing and the basal shear stress contribute significant resistance to the flow of Pine Island Glacier.

Extensive albedo data from Storglaciären, Sweden, during nine summers are analyzed, focusing on the effect of surface slope on measurements and on the influence of clouds on albedo of both snow and ice surfaces. On clear-sky days, albedo continuously dropped throughout the day by > 0.3 when derived from measurements in a horizontal plane over the slightly sloping surface. When we correct for the tilt effect, over frozen surfaces the apparent decrease in albedo largely disappeared, while over melting surfaces it became significantly less pronounced. This emphasizes the need to correct horizontally measured data for slope when they are used, for example, as ground truth for satellite-derived albedo, or in high-resolution glacier melt runoff models. Albedo varied by > 0.1 due to cloud fluctuations. To quantify cloud effects, albedo changes between successive (half-)hourly and daily data were regressed against corresponding changes in cloudiness expressed by the ratio of global radiation to top-of-atmosphere solar radiation. The resulting relationship over snow explains 66% of oberved albedo changes using hourly, and 42% using daily, time-steps. Over ice, the corresponding values are 28% and 0%. Hence, cloudiness is a dominating factor in determining short-term variability of albedo over snow, whereas over ice the observed large day-to-day variability ( > 20%) is mainly attributed to changes in the physical characteristics of the weathering crust. Results suggest that cloud effects should be incorporated into models treating snow and ice surfaces separately.

Assessment of the sensitivity of surface mass balance and equilibrium-line altitude (ELA) to climate change is crucial for simulating the future evolution of glaciers. Such an assessment has been carried out using an extensive dataset comprising numerous measurements of snow accumulation and snow and ice ablation made on four French glaciers over the past 16 years. Winter mass balance shows a complicated pattern with respect to altitude, with no clear linear relationship. Although the ratios of winter mass balance to valley precipitation differ considerably from site to site, they are relatively constant over time. Relationships between snow/ice ablation and temperature are stable, with no link with altitude. The mean snow and ice positive degree-day (PDD) factors are 0.003 and 0.0061 m w.e. °C−1 d−1. This analysis shows that, at a given site, ablation depends mainly on the amount of snow precipitation and on cumulative PDDs. The sensitivity of annual ablation to temperature change increases almost linearly from 0.25 m w.e. °C−1 at 3500 m to 1.55 m w.e. °C−1 at 1650 m. ELA sensitivity to temperature change was found to range from 50 to 85 m °C−1.

The ionic and isotopic characteristics of bulk waters emanating from the cold-based Longyearbreen, central Svalbard, in 2004 are examined to determine lithological, hydrological and glaciological controls on water composition, solute provenance and chemical denudation. The geology consisted of reactive coal seams and associated sedimentary rocks. Acidity caused by microbial-mediated oxidation of sulfides and, to a lesser extent, nitrogen-bearing minerals was neutralized by congruent dissolution of dolomite and incongruent weathering of silicates in open-system subglacial drainage channels. The ablation season was divided into an early melt season, a peak-flow period and a late melt season. The runoff distribution during these periods was 1.7%, 89.7% and 8.6%, respectively, whereas the solute flux distribution was 1.9%, 82.1% and 16.0%, respectively. Comparisons between different annual solute flux estimation methods indicated that extrapolation of peak-flow period data significantly underestimated both the early- and late-melt-season solute fluxes. About 3.8% of the solutes derived from sea-salt spray, 0.7% from acid aerosol deposition and 95.5% from crustal/organic sources. The physical and chemical conditions resulted in diffusion of CO2 rather than atmospheric drawdown. The cation-equivalent weathering rate and the crustal solute yield were 322 ΣmEq+m−2 a−1 and 22 t km−2 a−1, respectively, which are within the regional range of Svalbard. However, the chemical weathering intensity was as high as 940 ΣmEq+ m−3 owing to the relatively low specific discharge of 0.34 m a−1.

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.

We consider an idealized problem of a sphere of ice growing symmetrically in a spherical cavity within a porous rock in order to identify and quantify different physical mechanisms that can result in fracturing the rock. We show that if the permeability of the rock is very small then high pressures can develop in the cavity as the water inside it expands on freezing. However, given typical permeabilities of most rocks, the pressure is relieved by flow out of the cavity through the rock pores. When ice fills the cavity, there remains a microscopic film of water separating the ice from the rock, owing to disjoining forces, and these forces can stress the rock and have the potential to fracture it. The elastic pressure in the rock depresses the freezing temperature, which can limit the potential for fracturing. This simple example reveals the important interactions between disjoining forces, elasticity and fluid flow in determining the pressure exerted during freezing of water-saturated cavities in rocks.

Seismometers deployed over a 3 year period on icebergs in the Ross Sea and on the Ross Ice Shelf, Antarctica, reveal that impulsive sources of ocean surface waves are frequent (e.g. ∼200 events per year in the Ross Sea) in the ice-shelf and iceberg-covered environment of coastal Antarctica. The 368 events recorded by our field deployment suggest that these impulsive events are generated by glaciological mechanisms, such as (1) small-scale calving and edge wasting of icebergs and ice-shelf fronts, (2) edge-on-edge closing and opening associated with iceberg collisions and (3) possibly the impulsive opening of void space associated with ice-shelf rifting and basal crevasse formation. The observations described here provide a background of glaciogenic ocean-wave phenomena relevant to the Ross Sea and suggest that these phenomena may be exploited in the future (using more purposefully designed observation schemes) to understand iceberg calving and ice-shelf disintegration processes.

In this study we present 19 new or re-analysed series of glacier-wide seasonal mass balance for the Swiss Alps based on direct measurements. The records partly start around 1920 and continue until today. Previously unpublished and unevaluated observations of point winter and annual balance are compiled from various sources and archives. These highly valuable datasets have not yet been consistently evaluated and were thus unavailable to the scientific community. Using distributed modelling for spatial interpolation and extrapolation and homogenization of the point measurements, we infer continuous series of area-averaged mass balance. The results are validated against independent decadal ice volume changes from photogrammetric surveys. Six of the new seasonal series cover 60 years and more and add a substantial amount of information on the variations of regional glacier mass change. This will strengthen the worldwide collection of glacier monitoring data, especially for the data-sparse period before the 1980s. We compare our results to existing long-term series and present an updated assessment of mass-balance variability and glacier sensitivity throughout the European Alps.

Mapping changes in glacier extent from repeat optical satellite data has revealed widespread glacier decline in nearly all regions of the world over the past few decades. While numerous studies have documented the changes of the outlet glaciers of the Northern and Southern Patagonia Icefields (NPI/SPI), information about glacier changes in the Patagonian Andes (to the north of the NPI) is much scarcer. Here we present an assessment of area changes for glaciers mainly located in the Palena district of Chile based on glacier inventories for 1985, 2000 and 2011 that were derived from two consecutive Landsat scenes and a digital elevation model. The analysis revealed a dramatic area decline for the largest glaciers and total area loss of 25% from 1985 to 2011. The lower parts of several larger glaciers (>10 km2) melted completely. Area loss below 1000 m elevation was 50–100% in both periods, and 374 glaciers out of 1664 disappeared. The number of proglacial lakes increased from 223 to 327 and their area expanded by 11.6 km2 (59%) between 1985 and 2011. Seasonal snow persisting at high elevations in the 2011 scene was a major obstacle to glacier delineation, so the obtained area change rate of ~1% a–1 over the entire period is a lower-bound estimate. The observed climate trends (e.g. cooling in Puerto Montt) are in contrast to the observed shrinkage.

Global positioning system (GPS) data are now routinely used for many glaciological applications. In some common cases, systematic errors are unmodelled at the data-processing stage, although they are often presumed insignificant. In this paper, I investigate these assumptions for three different scenarios: (1) measurements on a moving glacier; (2) measurements on a floating ice shelf; and (3) precise height determination over large elevation ranges, such as for aircraft positioning in lidar/laser altimeter missions. In each case, systematic errors are shown to be present in the coordinate solutions that have a far greater magnitude than the formal error estimates produced by the GPS processing software, under certain conditions. If these coordinate biases go undetected, short- and long-term measurements of horizontal ice velocity or rates of ice-thickness change may be erroneous and the coordinates could not be expected to match rigorously processed data or results from different processing techniques. More rigorous processing strategies are discussed that allow for bias-free parameter estimation.

Two tunnels were dug through a small cirque glacier to the rock wall behind (a) the névé, and (b) the lower glacier. The upper tunnel revealed shattering of the rock wall due to the freezing of melt water. The bedrock at the end of the lower tunnel was both smoothed and fractured. The problem is to account for the fracturing of the resistant gneiss where the temperature remains at 0° C. throughout the year. The solution offered is that the release of pressure beneath a thick glacier immediately downstream from a roche moutonnée, or from a small steep step, enables the stresses locked within the gneiss to crack the rock. These stresses result from the gradual removal of the overburden, since the gneiss consolidated under the pressure of thousands of metres of rock strata. The glacier can later remove the jointed and broken rock.

This investigation uses Landsat images from 12 days in 1999 and 2000 to study the spatial and temporal variation in surface albedo of a glacier with a rugged topography: Morteratschgletscher, Switzerland. Our retrieval method considers all processes that substantially influence the relationship between the satellite signal and the surface albedo. The correction for the anisotropy of the reflected radiation field of ice and snow ranges up to 0.10, depending on wavelength band, solar zenith angle and surface type. We analyzed the uncertainties in the retrieval method and mainly expect errors in satellite-derived albedos for areas with large variation in topography and high albedos. The latter is due to application of bidirectional reflectance distribution function (BRDF) parameterizations for the anisotropic correction to albedos outside the parameterizations’ validity. On average, satellite-derived albedos exceed the measured surface albedo by 0.03. The glacier tongue is characterized by bands of low and high albedo, relating to ice with higher and lower concentrations of debris. The ice albedo shows no dependence on altitude, except at 2000–2200 m a.s.l. It increases during summer, which is likely associated with rainfall, as concluded from a comparison between summer rainfall and measured albedos.