We used a terrestrial radar interferometer (TRI) at Helheim Glacier, Greenland, in August 2013, to study the effects of tidal forcing on the terminal zone of this tidewater glacier. During our study period, the glacier velocity was up to 25 m d–1. Our measurements show that the glacier moves out of phase with the semi-diurnal tides and the densely packed melange in the fjord. Here detrended glacier displacement lags behind the forecasted tidal height by ∼8 hours. The transition in phase lag between the glacier and the melange happens within a narrow (∼500 m) zone in the fjord in front of the ice cliff. The TRI data also suggest that the impact of tidal forcing decreases rapidly up-glacier of the terminus. A flowline model suggests this pattern of velocity perturbation is consistent with weak ice flowing over a weakly nonlinear bed.

Simple theory supports field observations (Lawson and others, 1998 that subGlaciol water flow out of overdeepenings can cause accretion of layered, debris-bearing ice to the bases of glaciers. The large meltwater flux into a temperate glacier at the onset of summer melting can cause rapid water flow through expanded basal cavities or other flow paths. If that flow ascends a sufficiently steep slope out of an overdeepèning, the water will supercool as the pressure-melting point rises, and basal-ice accretion will occur. Diurnal, occasional or annual fluctuations in water discharge will cause variations in accretion rate, debris content of accreted ice or subsequent diagenesis, producing layers. Under appropriate conditions, net accretion of debris-bearing basal ice will allow debris fluxes that are significant in the glacier sediment budget.

We present a comprehensive approach (including field data, remote sensing and an anisotropic ice-flow model) to characterize Halvfarryggen ice dome in coastal Dronning Maud Land, Antarctica. This is a potential drill site for the International Partnerships in Ice Core Sciences, which has identified the need for ice cores covering atmospheric conditions during the last few millennia. We derive the surface topography, the ice stratigraphy from radar data, and accumulation rates which vary from 400 to 1670 kg m−2 a−1 due to preferred wind directions and changing surface slope. The stratigraphy shows anticlines and synclines beneath the divides. We transfer Dansgaard–Johnsen age–depth scales from the flanks along isochrones to the divide in the upper 20–50% of the ice thickness and show that they compare well with the results of a full-Stokes, anisotropic ice-flow model which predicts (1) 11 ka BP ice at 90% of the ice thickness, (2) a temporally stable divide for at least 2700–4500 years, (3) basal temperatures below the melting point (−12°C to −5°C) and (4) a highly developed crystal orientation fabric (COF). We suggest drilling into the apices of the deep anticlines, providing a good compromise between record length and temporal resolution and also facilitating studies of the interplay of anisotropic COF and ice flow.

Inverse problems are used to estimate model parameters from observations. Many inverse problems are ill-posed because they lack stability, meaning it is not possible to find solutions that are stable with respect to small changes in input data. Regularization techniques are necessary to stabilize the problem. For nonlinear inverse problems, iterative inverse methods can be used as a regularization method. These methods start with an initial estimate of the model parameters, update the parameters to match observation in an iterative process that adjusts large-scale spatial features first, and use a stopping criterion to prevent the overfitting of data. This criterion determines the smoothness of the solution and thus the degree of regularization. Here, iterative inverse methods are implemented for the specific problem of reconstructing basal stickiness of an ice sheet by using the shallow-shelf approximation as a forward model and synthetically derived surface velocities as input data. The incomplete Gauss-Newton (IGN) method is introduced and compared to the commonly used steepest descent and nonlinear conjugate gradient methods. Two different stopping criteria, the discrepancy principle and a recent- improvement threshold, are compared. The IGN method is favored because it is rapidly converging, and it incorporates the discrepancy principle, which leads to optimally resolved solutions.

Previous studies using Fourier transformation (FT) methods to analyze subglacial roughness have shown promise for distinguishing between different types of subglacial landscape from raw subglacial elevation data. We derive a two-parameter FT roughness index {ξ, η}, where • is based on the FT of elevation (as previously considered in isolation), and η is based on both the FT of elevation and the FT of bed-slope profile. In this way, we take account of both vertical and horizontal irregularities in subglacial surfaces. We demonstrate the statistical veracity of using {ξ, η} to consider roughness in terms of obstacle amplitudes and spacing, and consider the use of {ξ, η} in studies of ice dynamics and subglacial geomorphological interpretation. We show that {ξ, η} can be linked to basal sliding rates on the metre scale, and can be used to differentiate further than single-parameter roughness indices between different classes of subglacial landscape, in particular between erosional and depositional settings.

As a complement to earlier measurements on the friction of both granular fresh-water ice and S2 columnar salt-water ice, new experiments were performed on the friction of S2 columnar fresh-water ice sliding against itself at low velocities (5 × 10−7 to 5 × 10−1 m s−1) and at −10°C, using the same double-shear device as was used earlier. The results showed that under a given set of experimental conditions the kinetic coefficient of friction of S2 fresh-water ice compares favorably with that of the other two variants.The experiments also revealed friction-induced surface cracks and recrystallized grains.These deformation features are explained, respectively, in terms of fracture mechanics and an earlier model of dynamic recrystallization in ice.

A theoretical model is developed to describe the steady-state behavior of interconnected, water-filled cavities at the glacier bed. Physically plausible cavities should contain constrictions along the flow path, with flow in the wider sections being relatively sluggish. Mean flow rates in cavities may be at least one order of magnitude less than in channels incised into the basal ice (R channels). Melting due to viscous dissipation - the process that allows R channels to exist - probably plays a minor or negligible role, as compared to glacier sliding, in determining the size of cavities. Furthermore, a system of subglacial cavities should not show a tendency for localization of flow in a few main conduits, as does an R-channel system. If water pressure rises to within several bars of overburden pressure, the rate of cavity closure by creep falls below the rate of cavity opening by sliding and melting, with cavities then becoming unstable. Subsequent evolution of the drainage system should depend upon the total melt-water flux. Circumstances may arise in which cavities and channels act as conduits for melt water; such a configuration would probably show unusual transient behavior.

Moraine ridges have formed annually at Skálafellsjökull, south-east Iceland since about A.D. 1912. These ridges are asymmetrical with a steeper distal slope, and their surface morphology reflects their internal structure. Most ridges are formed at the glacier margin, and they form a series of concentric arcs about it. Their plan form reflects small details of the ice-front morphology. Some ridges are composed of boulders released from the ice by ablation and swept together by glacier re-advances, but most have a core of deformed till. Those which were ice-cored have a surface veneer of resedimented debris consisting of ice-slope colluvium and sediment-flow deposits. Lodgement tills at Skálafellsjökull have a two-layer structure, with a weak upper horizon apparently formed by dilation during subglacial shearing of the till. Ridges are composed of this sheared material and overlie undisturbed lodgement till at depth. Subglacial shearing results in a discharge of till towards the glacier margin and its accumulation there when glacier retreat ceases in winter. Till may also be extruded from beneath ice at the margin as a result of loading by the ice, and subsequently bulldozed into a ridge by a winter readvance of the glacier.

The contribution of glaciers to sea-level rise and their effects on landscape evolution depend on the poorly known relationship between sliding speed and drag at the ice/bed interface. Results from experiments with a new rotary laboratory device demonstrate empirically for the first time a double-valued drag relationship like that suggested by some sliding theories: steady drag on a rigid, sinusoidal bed increases, peaks and declines at progressively higher sliding speeds due to growth of cavities in the lee sides of bed undulations. Drag decreases with increased sliding speed if cavities extend beyond the inflection points of up-glacier facing surfaces, so that adverse bed slopes in contact with ice diminish with further cavity growth. These results indicate that shear tractions on glacier beds can potentially decrease due to increases in sliding speed driven by weather or climate variability, promoting even more rapid glacier motion by requiring greater strain rates to produce resistive stresses. Although a double-valued drag relationship has not yet been demonstrated for the complicated geometries of real glacier beds, both its potential major implications and the characteristically convex stoss surfaces of bumps on real glacier beds provide stimulus for exploring the effects of this relationship in ice-sheet models.

Within the framework of core-drilling through the permafrost of the active rock glacier Murtèl–Corvatsch in the Swiss Alps, subfossil stem remains of seven different bryophyte species were found at a depth of 6 m below surface and about 3 m below the permafrost table in samples from massive ice. The composition of the moss species points to the former growth of the recovered mosses in the nearest surroundings of the drill site. A total of 127 pollen and spores captured by the mosses and representing 23 taxa were determined. The local vegetation during deposition time must be characterized as a moss-rich alpine grassland meadow rich in Cyperaceae, Poaceae, Chenopodiaceae and Asteraceae, comparable to today’s flora present around the study site. For l4C analysis, accelerator mass spectrometry had to be used due to the small sample mass (about 0.5 mg Carbon content). The mean conventional 14C age of 2250 ± 100 years (1σ variability) corresponds to ranges in the calibrated calendar age of 470–170 BC and 800 BC to AD 0 at statistical probabilities of 68% and 95%, respectively. This result is compared with the present-day flow field as determined by high-precision photogrammetry and with information about the thickness, vertical structure and flow of the permafrost from borehole measurements. Total age of the rock glacier as a landform is on the order of 104 years; the development of the rock glacier most probably started around the onset of the Holocene, when the area it now occupies became definitely deglaciated. The bulk of the ice/rock mixture within the creeping permafrost must be several thousand years old. Characteristic average values are estimated for (1) surface velocities through time (cm a-1), (2) long-term ice and sediment accretion rates (mm a-1) on the debris cone from which the rock glacier develops, (3) retreat rates (1–2 mm a-1) of the cliff which supplies the debris to the debris cone and rock glacier, and (4) ice content of the creeping ice/rock mixture (50–90% by volume). The pronounced supersaturation of the permafrost explains the steady-state creep mode of the rock glacier.

An interferogram reflecting the motion of Black Rapids Glacier, Alaska, U.S.A., was obtained from two European Remote-sensing Satellite (ERS-1) syntheticaperture radar (SAR) images, acquired on 22 and 25 January 1992. We investigate whether the interferometric data are quantitatively consistent with terrestrial velocity measurements along three transverse profiles. These terrestrial data are from different years (1987, 1990, 1996) and cover different periods (6–28 April, 23 May–7 July and a whole year) than the SAR interferogram. Terrestrial ice velocity at the date of the SAR imagery is obtained via seasonal and annual corrections that are calculated from other terrestrial velocity measurements available at higher time resolution for selected sites on the glacier. Interferometric and terrestrial velocity are in excellent agreement if a (terrestrially measured) surface-normal velocity component (v⊥) is properly accounted for. This suggests that both the interferometric velocities and the conversions of terrestrial data to the winter period are reliable. The terrestrial velocity measurements show that ice flow in the upper ablation area (14–16 km sites) changes from longitudinal compression in mid-winter (v⊥ = + 0.82 cm d−1) to moderate longitudinal extension during summer (v⊥ ≈ –0.25 cm d−1). In the lower ablation area, the seasonal variations of the longitudinal strain rate are much smaller: +1.0 and about +0.85 cm d−1 for the respective mid-winter and summer values of v⊥ at the 20 km site.

Glacier roughness at sub-metre scales is an important control on the ice surface energy balance and has implications for scattering energy measured by remote-sensing instruments. Ice surface roughness is dynamic as a consequence of spatial and temporal variation in ablation. To date, studies relying on singular and/or spatially discrete two-dimensional profiles to describe ice surface roughness have failed to resolve common patterns or causes of variation in glacier surface morphology. Here we demonstrate the potential of close-range digital photogrammetry as a rapid and cost-effective method to retrieve three-dimensional data detailing plot-scale supraglacial topography. The photogrammetric approach here employed a calibrated, consumer-grade 5 Mpix digital camera repeatedly imaging a plot-scale (≤25 m2) ice surface area on Midtre Lovénbreen, Svalbard. From stereo-pair images, digital surface models (DSMs) with sub-centimetre horizontal resolution and 3 mm vertical precision were achieved at plot scales ≤4 m2. Extraction of roughness metrics including estimates of aerodynamic roughness length (z0) was readily achievable, and temporal variations in the glacier surface topography were captured. Close-range photogrammetry, with appropriate camera calibration and image acquisition geometry, is shown to be a robust method to record sub-centimetre variations in ablating ice topography. While the DSM plot area may be limited through use of stereo-pair images and issues of obliquity, emerging photogrammetric packages are likely to overcome such limitations.

Firn-density variations have been studied in the lower accumulation area of the Greenland ice sheet (1440-1620 m a.s.l.) near Pâkitsoq, West Greenland. The main control on density in the near-surface firn layer (of 5-10 m thickness) is the formation of ice layers by the refreezing of meltwater that reaches depths of 2-4 m below the surface. The density variations are described by the ratio of annual surface melt M to the annual accumulation C. The ratio M/C is about 0.6 at the run-off limit (at about 1400 m a.s.l. in the study area) where refreezing of meltwater transforms snow into impermeable ice. The mean density of near-surface firn decreases with elevation, reflecting a decrease in melt with elevation. There is a surprising decrease in firn density at depths of more than about 4 m below the 1991 summer surface, which reflects lower melt rates and/or higher accumulation in the early 1980s and late 1970s when this firn was passing through the surface layer. The formation of such low-density firn may have partially contributed to the 1978-85 thickening of the ice sheet observed by satellite-radar altimetry. Near-surface firn density is therefore very sensitive to climate change and might be an attractive target for climate monitoring.

In this paper we present a simulation approach to mapping avalanche risk with application to settlements in Iceland. Two simulation models are developed to calculate the probability of avalanches travelling a certain distance, and of the flow being a specific width. These two simulation models, in combination with knowledge of the average frequency of avalanche occurrence, the variability in avalanche direction and the degree of loss caused by an avalanche, permit risk values to be determined for the areas of concern.

An ice-thickness distribution model based on physical ice classes is formulated. Pack ice is subdivided into open water, two different types of undeformed ice, and rafted, rubble and ridged ice. Evolution equations for each ice class are formulated and a redistribution between the ice classes is calculated according to a functional form depending on the ice compactness, thickness and velocity divergence. The ice-thickness distribution model has been included in a coupled ice–ocean model, and numerical experiments have been carried out for a simulation of the Baltic Sea ice season. The extended ice classification allows separation of thermally and mechanically produced ice. Inherent thermodynamic growth/melting rates of the ice classes can be introduced into the model, giving a more detailed seasonal evolution of the pack ice. In addition, the model provides more information about the surface properties of pack ice.

Numerical experiments for the Baltic Sea show that both the sub-basin and inter-basin ice characteristics were realistically simulated by the model. Deformed-ice production was related to storm activity. Most of the deformation was produced in the coastal zone, which is also an important region for thermodynamically produced ice because of the ice growth in leads. The modelled mechanical growth rates of ice were 0.5–3 cm d−1 on a basin scale, close to the thermodynamic ice-production rates. The deformed-ice fraction was 0.2 in mid-winter and increased to 0.5–1.0 during spring.

Using airborne and spaceborne high-resolution digital elevation models and laser altimetry, we present estimates of interannual and multi-decadal surface elevation changes on the Bering Glacier system, Alaska, USA, and Yukon, Canada, from 1972 to 2006. We find: (1) the rate of lowering during 1972–95 was 0.9 ± 0.1 m a−1; (2) this rate accelerated to 3.0 ± 0.7 m a−1 during 1995–2000; and (3) during 2000–03 the lowering rate was 1.5 ± 0.4 m a−1. From 1972 to 2003, 70% of the area of the system experienced a volume loss of 191 ± 17 km3, which was an area-average surface elevation lowering of 1.7 ± 0.2 m a−1. From November 2004 to November 2006, surface elevations across Bering Glacier, from McIntosh Peak on the south to Waxell Ridge on the north, rose as much as 53 m. Up-glacier on Bagley Ice Valley about 10 km east of Juniper Island nunatak, surface elevations lowered as much as 28 m from October 2003 to October 2006. NASA Terra/MODIS observations from May to September 2006 indicated muddy outburst floods from the Bering terminus into Vitus Lake. This suggests basal–englacial hydrologic storage changes were a contributing factor in the surface elevation changes in the fall of 2006.

Mass, water, and energy balances were measured lit the Ivory Glacier, South Island, New Zealand from 1969 to 1975 as part of an I.H.D. programme of representative basin studies. Ivory Glacier is a small cirque glacier within the high-precipitation maritime environment of Westland and was chosen initially for convenience of study rather than representativeness. Mass-balance investigations included a detailed study of the sampling efficiency of a pole network. Annual mass balance was consistently negative during the study period. The run-off pattern was dominated by rain. The estimated annual mean precipitation is 9630 mm for 1971-75. Snow represents about 25% of annual precipitation. Melt contributed 21% of run-off including 9% contributed by melt of perennial snow and ice. The relative contributions of different fluxes to the energy balance during summer are: net radiation 52%, sensible heat 29%, and latent heat 17%. Heat content of precipitation contributes significantly to the energy balance during individual rain-storms and is probably significant during periods of high precipitation in spring and autumn. Climatic characteristics and behaviour of Ivory Glacier appear to follow regional trends in the Southern Alps and the glacier is considered to be reasonably representative.

Findelengletscher, Switzerland, advanced about 250 m between 1979 and 1985, and retreated thereafter. Subglacial water pressure, surface velocity and surface strain rate were determined at several sites. The measurements were made early in the melt seasons of 1980, 1982, 1985 and 1994 and in the autumn of 1983 and the winter of 1984. Changes of surface geometry were assessed from aerial photographs.

The estimated basal shear stress changed little between 1982 and 1994. Nevertheless, large changes in the relationship of subglacial water pressure and surface velocity were observed, which cannot be reconciled with the most commonly used sliding law unless it is modified substantially. Consideration of possible reasons indícales that a change in the subglacial drainage system occurred, probably involving a change in the degree of cavity interconnection. Isolated cavities damp the variations in sliding velocity that normally result from changes in water pressure, because the pressure in isolated cavities decreases as the sliding speed increases. In contrast, by transmitting water-pressure fluctuations to a larger area of the bed, interconnected cavities amplify the effect of water-pressure fluctuations on sliding speed. Thus, we suggest that an observed decrease in velocity (for a given water pressure) between 1982 and 1994 was a consequence of a decrease in the interconnectedness of the subglacial cavity system.

We develop a formal thin-plate treatment of the viscoelastic flexure of floating ice shelves as an initial step in treating various problems relevant to ice-shelf response to sudden changes of surface loads and applied bending moments (e.g. draining supraglacial lakes, iceberg calving, surface and basal crevassing). Our analysis is based on the assumption that total deformation is the sum of elastic and viscous (or power-law creep) deformations (i.e. akin to a Maxwell model of viscoelasticity, having a spring and dashpot in series). The treatment follows the assumptions of well-known thin-plate approximation, but is presented in a manner familiar to glaciologists and with Glen’s flow law. We present an analysis of the viscoelastic evolution of an ice shelf subject to a filling and draining supraglacial lake. This demonstration is motivated by the proposition that flexure in response to the filling/drainage of meltwater features on the Larsen B ice shelf, Antarctica, contributed to the fragmentation process that accompanied its collapse in 2002.