Solute acquisition by Alpine glacial meltwaters is the result of the coupling of different pairs of reactions, one of which usually involves dissolved gases. Hence, the availability of atmospheric gases to solution is an important control on the composition of glacial meltwaters. The chemical compositions of the two main components of the bulk meltwater, quick flow and delayed flow, are dominated by different geochemical processes. Delayed flow waters are solute-rich and exhibit high p(CO2) characteristics. The slow transit of these waters through a distributed drainage system and the predominance of relatively rapid reactions, such as sulphide oxidation and carbonate dissolution, in this environment maximize solute acquisition. Quick-flow waters are dilute, both because of their rapid transit through ice-walled conduits and open channels, and because the weathering reactions are fuelled by relatively slow gaseous diffusion of (CO2) into solution, despite solute acquisition being dominated by rapid surface exchange reactions. As a consequence, quick flow usually bears a low or open-system p(CO2) signature. Bulk meltwaters are more likely to exhibit low p(CO2) values when suspended-sediment concentrations are high, which promotes post-mixing reactions. This conceptual model suggests that the composition of both quick flow and delayed flow is likely to be temporally variable, since kinetic, rather than equilibrium, factors determine the composition.

A 50 MHz ground-penetrating radar was used to detect horizontal layers in the snowpack along a longitudinal profile on Nordenskjöldbreen, a Svalbard glacier. The profile passed two shallow and one deep ice-core sites. Two internal radar reflection layers were dated using parameters measured in the deep core. Radar travel times were converted to water equivalent, yielding snow-accumulation rates along the profile for three time periods: 1986–99, 1963–99 and 1963–86. The results show 40–60% spatial variability in snow accumulation over short distances along the profile. The average annual accumulation rate for 1986–99 was found to be about 12% higher than for the period 1963–86, which indicates increased accumulation in the late 1980s and 1990s.

We describe exact solutions to the thermomechanically coupled shallow-ice approximation in three spatial dimensions. Although artificially constructed, these solutions are very useful for testing numerical methods. In fact, they allow us to verify a finite-difference scheme, that is, to show that the results of our numerical scheme converge to the correct continuum values as the grid is refined in three dimensions. Comparison of numerical results with exact solutions has helped us to precisely quantify and understand some of the numerical errors we are making. Our verified numerical scheme shows the basal temperature spokes which arose in the EISMINT (European Ice Sheet Modelling INiTiative) II intercomparison (Payne and others, 2000). A careful analysis describes these warm spokes as numerical errors which occur when the derivative of the strain-heating term with respect to the temperature is large. On the other hand, the appearance of basal temperature spokes in a verified numerical scheme strongly suggests that they are a feature of the EISMINT II experiment F continuum problem. In fact, they are clear evidence of an unstable equilibrium point of the continuum problem. This paper is a sequel to Bueler and others (2005) which addresses exact solutions and verification in the isothermal case.

A flow model is described for the Camp Century area in Greenland. The horizontal velocity profile along the core is assumed to be uniform from the surface down to y = 400 m above the bottom. Below this level, the horizontal velocity vx, is assumed to decrease proportionally to y. Furthermore, at a given y, vx is assumed to be proportional to the distance x from the ice divide. The resulting vertical strain-rate under steady-state conditions gives the age of the ice as a function of y. The flow model has explained the measured temperature profile, and the time scale has been verified by comparison between observed stable isotope variations and past climatic changes (at least 70 000 years back in time) estimated by other methods.

Measurements of light transmission and reflection were carried out on first-year sea ice near Point Barrow, Alaska, and on multi-year ice near Fletcher’s Ice Island in the Beaufort Sea (lat. 84° N., long. 77°W.). Spectral albedos (400-1 000 nm) and extinction coefficients (400-800 nm) were determined for melt ponds, snow, and various types of bare ice. Albedos were largest in the 400-600 nm range, decreasing toward longer wavelengths at a rate which appeared to be related to the liquid-water content of the near-surface layers. Extinction coefficients remained nearly constant between 400 and 550 nm, but increased rapidly above 600 nm. At 500 nm, albedos ranged from 0.25 over mature melt ponds to 0.93 over dense dry snow, while the corresponding extinction coefficients ranged from 0.6 to 16 m-1. Intensity profiles taken in the upper 50 cm of the ice indicated that the extinction coefficient at a particular wavelength was nearly constant with depth below 15 cm, although the bulk extinction coefficient decreased with depth because of the strong attenuation in the red. Near the surface it was found that multi-year ice absorbed slightly more energy than did first-year blue ice, but at depths below 10 cm the flux divergence in the first-year ice was three to four times larger than that in the multi-year ice. A simple procedure is described for estimating light transmission and absorption within the ice under clear or cloudy skies from total flux measurements at the surface. Methods by which satellite data could be used to estimate regional albedos, melt-pond fraction, and lead area are also presented.

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.

Glacier surface mass balance evaluated over the actual glacier geometry depends not only on climatic variations, but also on the dynamic adjustment of glacier geometry. Therefore, it has been proposed that reference-surface balances calculated over a constant glacier hypsometry are better suited for climatic interpretation. Here we present a comparison of 82 year modelled time series (1926-2008) of conventional and reference-surface balance for 36 Swiss glaciers. Over this time period the investigated glaciers have lost 22% of their area, and ice surface elevation close to the current glacier terminus has decreased by 78 m on average. Conventional balance in the last decade, at −0.91 mw.e.a-1, is 0.14 m w.e. a-1 less negative than the reference-surface balance. About half of the negative (stabilizing) feedback on mass balance due to glacier terminus retreat is compensated by more negative mass balances due to surface lowering. Short-term climatic variability is clearly reflected in the conventional mass-balance series; however, the magnitude of the long-term negative trend is underestimated compared to that found in the reference-surface balance series. Both conventional and reference-surface specific balances show large spatial variability among the 36 glaciers.

Both lake-calving Yakutat Glacier (337 km2), Alaska, USA, and its parent icefield (810 km2) are experiencing strong thinning, and under current climate conditions will eventually disappear. Comparison of digital elevation models shows that Yakutat Glacier thinned at area-averaged rates of 4.76 ± 0.06 m w.e.a−1 (2000–07) and 3.66 ± 0.03 m w.e.a−1 (2007–10). Simultaneously, adjacent Yakutat Icefield land-terminating glaciers thinned at lower but still substantial rates (3.79 and 2.94 m w.e.a−1 respectively for the same time periods), indicating lake-calving dynamics helps drive increased mass loss. Yakutat Glacier terminates into Harlequin Lake and for over a decade sustained a ∼3 km long floating tongue, which started to disintegrate into large tabular icebergs in 2010. Such floating tongues are rarely seen on temperate tidewater glaciers. We hypothesize that this difference is likely due to the lack of submarine melting in the case of lake-calving glaciers. Floating-tongue ice losses were evaluated in terms of overall mass balance and contribution to sea-level rise. The post-Little Ice Age collapse of Yakutat Icefield was driven in part by tidewater calving retreats of adjacent glaciers, the lake-calving retreat of Yakutat Glacier, a warming climate and by the positive feedback mechanisms through surface lowering.

To avoid some of the limitations of studying soft-bed processes through boreholes, a prism of simulated till (1.8 m × 1.6 m × 0.45 m) with extensive instrumentation was constructed in a trough blasted in the rock bed of Engabreen, a temperate glacier in Norway. Tunnels there provide access to the bed beneath 213 m of ice. Pore-water pressure was regulated in the prism by pumping water to it. During experiments lasting 7–12 days, the glacier regelated downward into the prism to depths of 50–80 mm, accreting ice-infiltrated till at rates predicted by theory. During periods of sustained high pore-water pressure (70–100% of overburden), ice commonly slipped over the prism, due to a water layer at the prism surface. Deformation of the prism was activated when this layer thinned to a sub-millimeter thickness. Shear strain in the till was pervasive and decreased with depth. A model of slip by ploughing of ice-infiltrated till across the prism surface accounts for the slip that occurred when effective pressure was sufficiently low or high. Slip at low effective pressures resulted from water-layer thickening that increased non-linearly with decreasing effective pressure. If sufficiently widespread, such slip over soft glacier beds, which involves no viscous deformation resistance, may instigate abrupt increases in glacier velocity.

Glacier surface mass-balance measurements on Greenland started more than a century ago, but no compilation exists of the observations from the ablation area of the ice sheet and local glaciers. Such data could be used in the evaluation of modelled surface mass balance, or to document changes in glacier melt independently from model output. Here, we present a comprehensive database of Greenland glacier surface mass-balance observations from the ablation area of the ice sheet and local glaciers. The database spans the 123 a from 1892 to 2015, contains a total of ~3000 measurements from 46 sites, and is openly accessible through the PROMICE web portal (http://www.promice.dk). For each measurement we provide X, Y and Z coordinates, starting and ending dates as well as quality flags. We give sources for each entry and for all metadata. Two thirds of the data were collected from grey literature and unpublished archive documents. Roughly 60% of the measurements were performed by the Geological Survey of Denmark and Greenland (GEUS, previously GGU). The data cover all regions of Greenland except for the southernmost part of the east coast, but also emphasize the importance of long-term time series of which there are only two exceeding 20 a. We use the data to analyse uncertainties in point measurements of surface mass balance, as well as to estimate surface mass-balance profiles for most regions of Greenland.

A 1995 surge of Variegated Glacier, Alaska, USA, is discussed in the context of its six 20th-century predecessors, especially the previous surge in 1982/83 which was studied in detail. The average time between surge initiations is 15 years. The 1995 surge was considerably weaker than its predecessors, having a single phase or at most a very weak second phase. The 1995 surge confirms that there is a seasonal cycle, with surge initiation in winter and termination in the first part of the melt season, and a correlation between weather and both surge termination date and surge extent. Two days of record high temperature correlated with the termination of the 1995 surge. The most obvious issue is the absence of a strong second surge phase (as there was in the 1982/83 surge) culminating in a surge extent more in line with that of the predecessors. This is considered in the light of a simple criterion for surge initiation and re-initiation which depends upon the evolving basal shear stress.

Volume–area scaling is a common tool for deriving future volume evolutions of valley glaciers and their contribution to sea-level rise. We analyze the performance of scaling relationships for deriving volume projections in comparison to projections from a one-dimensional ice-flow model. The model is calibrated for six glaciers (Nigardsbreen, Rhonegletscher, South Cascade Glacier, Sofiyskiy glacier, midre Lovénbreen and Abramov glacier). Volume evolutions forced by different hypothetical mass-balance perturbations are compared with those obtained from volume–area (V-A), volume–length (V-L) and volume–area–length (V-A-L) scaling. Results show that the scaling methods mostly underestimate the volume losses predicted by the ice-flow model, up to 47% for V-A scaling and up to 18% for V-L scaling by the end of the 100 year simulation period. In general, V-L scaling produces closer simulations of volume evolutions derived from the ice-flow model, suggesting that V-L scaling may be a better approach for deriving volume projections than V-A scaling. Sensitivity experiments show that the initial volumes and volume evolutions are highly sensitive to the choice of the scaling constants, yielding both over- and underestimates. However, when normalized by initial volume, volume evolutions are relatively insensitive to the choice of scaling constants, especially in the V-L scaling. The 100 year volume projections differ within 10% of initial volume when the V-A scaling exponent commonly assumed, γ = 1.375, is varied by −30% to +45% (γ = [0.95, 2.00]) and the V-L scaling exponent, q = 2.2, is varied by −30% to +45% (q = [1.52, 3.20]). This is encouraging for the use of scaling methods in glacier volume projections, particularly since scaling exponents may vary between glaciers and the scaling constants are generally unknown.

The drift trajectory of giant iceberg C-7 traversing the Weddell Sea, Antarctica, for > 2 years was successfully simulated. Application of the “classical” driving forces like wind and ocean currents resulted in a significant discrepancy between modeled and observed iceberg velocities in the western Weddell Sea. The most realistic drift pattern in space and time was achieved by adding a sea-ice force which represents the ability of a dense sea-ice cover (≥90%) to lock in icebergs and collect the momentum of the wind over an area much larger than the area of the iceberg proper. This process was parameterized using a sea-ice strength P which depends on sea-ice concentration and thickness, both having highest values in winter and in the western Weddell Sea which is covered with multi-year sea ice. As a consequence of the sensitivity to sea ice, the timing of the iceberg drift becomes important, revealing the region off Brunt Ice Shelf (eastern Weddell Sea) as a location where bergs either continue westward with the coastal current or follow a southern branch onto the shallow continental shelf.

Near ice shelves around Antarctica the ocean becomes supercooled and has been observed to carry small suspended ice crystals. Our measurements demonstrate that these small crystals are persistently present in the water column beneath the winter fast ice, and when incorporated in sea ice they reduce the mean grain size of the sea-ice cover. By midwinter, larger ice crystals below the ice/water interface are observed to form a porous sub-ice platelet layer with an ice volume fraction of 0.25 ± 0.06. The magnitude and direction of the oceanic heat flux varied between (5 ± 6) Wm-2 (upwards) and (-15 ± 10) Wm-2 (downwards) in May, but by September it settled between (-6 ± 2) and (-11 ± 2) W m-2. The negative values imply that the ocean acts as a heat sink which is responsible for the growth of 12% of the ice thickness between June and September. This oceanic contribution should not be ignored in models of Antarctic sea-ice thickness close to an ice shelf.

High-resolution radar images of Glaciar Moreno, Argentina, acquired by the Shuttle Imaging Radar C (SIR-C) on 9 and 10 October 1994 at 24 cm wavelength (L-band), are utilized to map the glacier velocity both interferometrically and using the phase correlation method. The precision of the interferometric ice velocities is 1.8 cm d-1 (6 m a-1) (1σ). The phase correlation method measures ice velocity with a precision of 14 cm d-1 (50 m a-1) with image data at a 6 m sample spacing acquired 1 day apart. Averaged strain rates are measured with a precision of 10-4 d-1 at a 240 m sample spacing with the phase correlation method, and 10-5 d-l with radar interferometry. The phase correlation method is less precise than radar interferometry, but it performs better in areas of rapid flow, is more robust to temporal changes in glacier scattering and measures the glacier velocity in two dimensions with only one image pair. Using this technique, we find that Glaciar Moreno flows at 400 m a-1 in the terminal valley and 800 m a-1 at the calving front, in agreement with velocities recorded a decade ago. Assuming steady-state flow conditions, the vertical strain rates measured by SIR-C are combined with prior data on mass ablation to estimate the glacier thickness and ice discharge. The calculated discharge is 0.6 ± 0.2 km3 ice a-1 at 300 m elevation, and 1.1 ± 0.2 km3 ice a-1 at the equilibrium-line elevation (1150 m), which yields a balance accumulation of 6 ± 1 m ice a-1.

Observation of the terminus behavior of 38 North Cascade glaciers, Washington, U.S.A., since 1890 shows three different types of glacier response: (1) Continuous retreat from the Little Ice Age (LIA) advanced positions from 1890 to approximately 1950, followed by a period of advance from 1950 to 1976, and then retreat since 1976. (2) Rapid retreat from 1890 to approximately 1950, slow retreat or equilibrium from 1950 to 1976, and moderate to rapid retreat since 1976. (3) Continuous retreat from 1890 to the present.

Type 1 glaciers are notable for steeper slopes, extensive crevassing and higher terminusregion velocities. Type 2 glaciers have intermediate velocities, moderate crevassing and intermediate slopes. Type 3 glaciers have low slopes, modest crevassing and low terminusregion velocities. This indicates that the observed differences in the response time and terminus behavior of North Cascade glaciers in reaction to climate change are related to variations in specific characteristics of the glaciers. The response time is approximately 20–30 years on type 1 glaciers, 40–60 years on type 2 glaciers and a minimum of 60–100 years on type 3 glaciers. The high correlation in annual balance between North Cascade glaciers indicates that microclimates are not the key to differences in behavior. Instead it is the physical characteristics — slope, terminus velocity, thickness and accumulation rate — of the glacier that determine recent terminus behavior and response time. The delay between the onset of a mass-balance change and initiation of a noticeable change in terminus behavior has been observed on 21 glaciers to be 4–16 years. This initial response time applies to both positive and negative changes in mass balance.

Analysis of air extracted from bubbles of polar ice showed the anthropogenic increase of atmospheric CO2 concentration during the past few hundred years (preindustrial concentration 280 ppmv) and, unexpectedly, that the concentration also increased due to natural causes from 200 to 280 ppmv during the transition from the last glacial epoch to the Holocene. However, more detailed reconstructions based on ice-core analyses suggested that some of the additional observed variations were actually due to the modification of CO2 concentration in the bubbles by chemical reactions between impurities in the ice. Detailed analyses of acidity, the carbonate concentration, the concentration of oxidation agents like hydrogen peroxide (H2O2), and organic compounds (e.g. formaldehyde (HCHO)) along short intervals of ice cores, representing only a few annual layers, allowed us to investigate these chemical reactions. The records are not conclusive but they indicate that the oxidation of organic compounds is at least as important as acid–carbonate reactions. Ice containing a low mean carbonate and a low H2O2 concentration, as well as a small scattering of CO2 results obtained on several adjacent samples representing a few annual layers at most, is at present the best guarantee for reliable results of the atmospheric CO2 concentration.

Determining a calving law valid for all glaciological and environmental regimes has proven to be a difficult problem in glaciology. For this reason, most models of the calving process are semi-empirical, with little connection to the underlying fracture processes. In this study, I introduce methods rooted in statistical physics to show how calving laws, valid for any glaciological domain, can emerge naturally as a large-spatial-scale/long-temporal-scale limit of an underlying continuous or discrete fracture process. An important element of the method developed here is that iceberg calving is treated as a stochastic process and that the probability an iceberg will detach in a given interval of time can be described by a probability distribution function. Using limiting assumptions about the underlying probability distribution, the theory is shown to be able to simulate a range of calving styles, including the sporadic detachment of large, tabular icebergs from ice tongues and ice shelves and the more steady detachment of smaller-sized bergs from tidewater/outlet glaciers. The method developed has the potential to provide a physical basis to include iceberg calving into numerical ice-sheet models that can be used to produce more realistic estimates of the glaciological contribution to sea-level rise.

Modelling the response of Himalayan glaciers to rapid climate change is an important problem. The poorly understood effects of debris cover and the variable response of the glaciers have made it difficult to understand their dynamics. We propose a simple model for debris-covered glaciers and validate it against data from Dokriani Glacier, India. Numerical investigations of the model show that the response of debris-covered glaciers to a warming climate has two timescales. There is a period when the glacier loses ice by thinning but the front is almost stationary and it develops a long, slow-flowing tongue. This stationary period, which can be >100 years for glaciers with a large extent of debris cover, is negligible for bare glaciers. The quasi-stagnant tongue does not develop in response to cooling. An analysis of remote-sensing data in the light of these results indicates that the variable response of the glaciers in the Himalaya is consistent with a climate that is warming on average, but has considerable spatial variability in the warming rates. We estimate the average warming rate to be about the same as the global average.

A pixel-based methodology has been established for automatic identification of icebergs in satellite synthetic aperture radar (SAR) images acquired during different seasons and for different sea- ice conditions. This includes, in particular, smaller icebergs (longitudinal axis 100 m to 18.5 km). Investigations were carried out for two test regions located in the Weddell Sea, Antarctica, using images of the Envisat Advanced SAR (ASAR) at HH polarization and of the European Remote-sensing Satellite-2 (ERS-2) SAR (VV-polarized). From the former, a sequence of Image Mode and Wide Swath Mode data are available for the whole of 2006. The ERS data were acquired around the tip of the Antarctic Peninsula in spring and summer months of the years 2000-03. The minimum size of icebergs that could be identified in the IM images was <0.02 km2. Radar backscattering coefficients of icebergs, sea ice and open water were determined separately. We demonstrate that the error in separating icebergs from their surroundings (sea ice or open water) depends on meteorological, oceanographic and sea-ice conditions. Also the pre-processing of the SAR images (e.g. speckle reduction) influences iceberg recognition. Differences in detection accuracy as a function of season could not be substantiated for our test sites, but have in general to be taken into account, as results of other investigations indicate.