A vertical temperature profile through the West Antarctic ice sheet (WAIS) at the summit of Siple Dome reveals an elevated geothermal flux. This could be the root cause for the existence of a dynamic ice-stream system in the WAIS. Siple Dome is still frozen on its bed, but adjacent ice streams have bed temperatures at the pressure-melting point of ice. Although present-day temperature increases due to climatic change do not have an immediate effect on the basal conditions that control the velocity of the ice, indirect effects like a rapid disintegration of the floating ice shelves or additional melt-water input at the surface could give rise to speed-up of the ice streams with an ensuing rise in sea level. Ongoing melt at the base of the ice and changes at the margins will allow continued rapid flow of the ice streams with a possibility of disintegration, within a relatively short period of time, of at least part of the WAIS.

Comparison of numerically computed solutions to exact (analytical) time-dependent solutions, when possible, is superior to intercomparison as a technique for verification of numerical models. At least two sources of such exact solutions exist for the isothermal shallow ice-sheet equation: similarity solutions and solutions with ‘compensatory accumulation’. In this paper, we derive new similarity solutions with non-zero accumulation. We also derive exact solutions with (i) sinusoidal-in-time accumulation and (ii) basal sliding. A specific test suite based on these solutions is proposed and used to verify a standard explicit finite-difference method. This numerical scheme is shown to reliably track the position of a moving margin while being characterized by relatively large thickness errors near the margin. The difficulty of approximating the margin essentially explains the rate of global convergence of the numerical method. A transformed version of the ice-sheet equation eliminates the singularity of the margin shape and greatly accelerates the convergence. We also use an exact solution to verify an often-used numerical approximation for basal sliding and we discuss improvements of existing benchmarks.

Determining the position and stability of the grounding line of a marine ice sheet is a major challenge for ice-sheet models. Here, we investigate the role of lateral shear and ice-shelf buttressing in grounding line dynamics by extending an existing boundary layer theory to laterally confined marine ice sheets. We derive an analytic expression for the ice flux at the grounding line of confined marine ice sheets that depends on both local bed properties and non-local ice-shelf properties. Application of these results to a laterally confined version of the MISMIP 1a experiment shows that the boundary condition at the ice-shelf front (i.e. the calving law) is a major control on the location and stability of the grounding line in the presence of buttressing, allowing for both stable and unstable grounding line positions on downwards sloping beds. These results corroborate the findings of existing numerical studies that the stability of confined marine ice sheets is influenced by ice-shelf properties, in contrast to unconfined configurations where grounding line stability is solely determined by the local slope of the bed. Consequently, the marine ice-sheet instability hypothesis may not apply to buttressed marine ice sheets.

Snowpack base temperatures vary during accumulation and diurnally. Their measurement provides insight into physical, biological and chemical processes occurring at the snow/soil interface. Recent advances in Raman-spectra instruments, which use the scattered light in a standard telecommunications fiber-optic cable to infer absolute temperature along the entire length of the fiber, offer a unique opportunity to obtain basal snow temperatures at resolutions of 1 m, 10 s and 0.1°C. Measurements along a 330 m fiber over 24 hours during late-spring snowmelt at Mammoth Mountain, California, USA, showed basal snow temperatures of 0 ± 0.2°C using 10 s averages. Where the fiber-optic cable traversed bare ground, surface temperatures approached 40°C during midday. The durability of the fiber optic was excellent; no major damage or breaks occurred through the winter of burial. Data from the Dry Creek experimental watershed in Idaho across a small stream valley showed little variability of temperature on the northeast-facing, snow-covered slope, but clearly showed melting patterns and the effects of solar heating on southwest-facing slopes. These proof-of-concept experiments show that the technology enables more detailed spatial and temporal coverage than traditional point measurements of temperature.

One of the questions still unanswered concerning the surge behavior of glaciers concerns their quasi-periodic occurrence. Some results on the phenomenological connection between local cumulative balance and surge initiation of Variegated Glacier, Alaska, U.S.A., are discussed here. Based on climate data from neighboring weather stations, an empirical relation between precipitation, temperature and local mass balance is established and used to reconstruct the annual balance at a location in the accumulation area back to 1905. Between the last four surges in 1946/47, 1964/65, 1982/83 and 1994/95, the ice-equivalent cumulative balance was 43.5 m on average, with a 1σ error of 1.2 m. Although the existence of a surge level cannot be directly interpreted in physical terms, it explains the variable length of the quiescent periods of Variegated Glacier by variations in the accumulation rate prior to the surge. We use the surge level to hindcast former unobserved surges, to compare the results with other surge datings obtained from photographs and to establish a complete surge history for Variegated Glacier for the 20th century.

To investigate the internal accumulation on Storglaciären, Sweden, we couple a multi-layer snow model to a distributed energy- and mass-balance model. The snow model describes the temperature, density and water-content evolution of the snow/ice pack and includes the processes of percolation and refreezing of water. The model is run for the period 9 May–2 September 1999 and validated against weather station and mass-balance observations on the glacier. The model performs reasonably well, with an average summer mass balance for the location of stake observations of –1.56 m w.e. compared to –1.59 m w.e. observed. However, the amount of melt is overestimated in the higher parts of the accumulation area and underestimated in the lower parts of the ablation area. The modelled mass balance is most sensitive to the albedo parameterization, the chosen momentum and scalar roughness lengths and all parameters related to snowfall. The modelled internal accumulation is +0.25 m w.e., which amounts to about 20% of the winter accumulation and results in a positive net balance for 1999 of +0.23 m w.e. The modelled internal accumulation is most sensitive to the initial subsurface temperature profile and the irreducible water content.

We propose an infinite-dimensional adjoint-based inexact Gauss-Newton method for the solution of inverse problems governed by Stokes models of ice sheet flow with nonlinear rheology and sliding law. The method is applied to infer the basal sliding coefficient and the rheological exponent parameter fields from surface velocities. The inverse problem is formulated as a nonlinear least-squares optimization problem whose cost functional is the misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. Our findings show that the inexact Newton method is significantly more efficient than the nonlinear conjugate gradient method and that the number of Stokes solutions required to solve the inverse problem is insensitive to the number of inversion parameters. The results also show that the reconstructions of the basal sliding coefficient converge to the exact sliding coefficient as the observation error (here, the noise added to synthetic observations) decreases, and that a nonlinear rheology makes the reconstruction of the basal sliding coefficient more difficult. For the inversion of the rheology exponent field, we find that horizontally constant or smoothly varying parameter fields can be reconstructed satisfactorily from noisy observations.

In most models of the flow of glaciers on till beds, it has been assumed that till behaves as a viscoplastic fluid, despite contradictory evidence from laboratory studies. In accord with this assumption, displacement profiles measured in subglacial till have been fitted with viscoplastic models by estimating the stress distribution. Here we present a model that illustrates how observed displacement profiles can result from till deformation resisted solely by Coulomb friction. Motion in the till bed is assumed to be driven by brief departures from static equilibrium caused by fluctuations in effective normal stress. These fluctuations result from chains of particles that support intergranular forces that are higher than average and that form and fail at various depths in the bed during shearing. Newton’s second law is used to calculate displacements along slip planes and the depth to which deformation extends in the bed. Consequent displacement profiles are convex upward, similar to those measured by Boulton and colleagues at Breidamerkurjökull, Iceland. The model results, when considered together with the long-term and widespread empirical support for Coulomb models in soils engineering, indicate that efforts to fit viscoplastic flow models to till displacement profiles may be misguided.

Precise measurements of basal melting have been made at a series of 14 sites lying within a few kilometres of the grounding line of the Ronne Ice Shelf, Antarctica, where the ice thickness ranges from 1570 to 1940 m. The study was conducted over the course of 1 year and included a detailed survey of the horizontal deformation, as well as phase-sensitive radar measurements of the vertical displacement of both internal reflecting horizons and the ice-shelf base. Results from the surface survey show that the long-term viscous strain rate is modulated at tidal frequencies by (probably) elastic strains of order 10−5 per metre of tidal elevation. The radar measurements show a similar modulation of the long-term thinning/thickening of the ice shelf, with thickness oscillations up to a few centimetres in range. The long-term trends in ice thickness determined at points moving with the ice-shelf flow are consistent with a steady-state thickness profile. Vertical strain rates within the ice shelf were determined from the relative motion of internal reflectors. At two sites the observations were sufficient to discern the effect of tidal bending about a neutral surface 60% of the way down the ice column. Coincident measurements of horizontal and vertical strain imply a Poisson’s ratio of 0.5, and this combined with the asymmetric bending gives rise to the observed oscillations in thickness. At a number of sites the longterm viscous strain rates were found to be a linear function of depth. For an ice shelf this is an unexpected result. It can be attributed to the presence of significant vertical shear stresses set up close to the grounding line where the ice is still adjusting to flotation. Additional vertical motion arising from firn compaction was observed within the upper layers of the ice shelf. The additional motion was consistent with the assumption that firn density is a function only of the time since burial by steady surface accumulation. With both spatial and temporal fluctuations in the vertical strain rate accurately quantified it was possible to estimate the vertical motion of the ice-shelf base in response. Differences between the calculated and observed motion of the basal reflector arise because of basal melting. Derived melt rates at the 14 sites ranged from −0.11 ±0.31 to 2.51 ±0.10 m a−1, with a mean of 0. 85 m a−1 and a standard deviation of 0.69 m a−1, and showed no signs of significant sub-annual temporal variability. There was no obvious global correlation with either ice thickness or distance from the grounding line, although melt rates tended to decrease downstream along each of the flowlines studied. Previous estimates of basal melting in this region have been obtained indirectly from an assumption that the ice shelf is locally in equilibrium and have included a broad range of values. Only those at the lower end of the published range are consistent with the directly measured melt rates reported here.

The length of time TM over which a glacier responds to a prior change in climate is investigated with reference to the linearized theory of kinematic waves and to results from numerical models. We show the following: TM may in general be estimated by a volume time-scale describing the time required for a step change in mass balance to supply the volume difference between the initial and final steady states. The factor f in the classical estimate of τM = ƒl/u, where I is glacier length and u is terminus velocity, has a simple geometrical interpretation. Ft is the ratio of thickness change averaged over the full length I to the change at the terminus. Although both u and f relate to dynamic processes local to the terminus zone, the ratio f/u and, therefore, Tm are insensitive to details of the terminus dynamics, in contrast to conclusions derived from some simplified kinematic wave models. A more robust estimate of Tm independent of terminus dynamics is given by TM= h/(–b) where h is a thickness scale for the glacier and –b is the mass-balance rate (negative) at the terminus. We suggest that Tm for mountain glaciers can be substantially less than the 1O2–103 years commonly considered to be theoretically expected.

A structural glaciological description and analysis of surface morphological features of the Larsen C ice shelf, Antarctic Peninsula, is derived from satellite images spanning the period 1963–2007. The data are evaluated in two time ranges: a comparison of a 1963 satellite image photomosaic with a modern digital mosaic compiled using 2003/04 austral summer data; and an image series since 2003 showing recent evolution of the shelf. We map the ice-shelf edge, rift swarms, crevasses and crevasse traces, and linear longitudinal structures (called ‘flow stripes’ or ‘streak lines’). The latter are observed to be continuous over distances of up to 200 km from the grounding line to the ice-shelf edge, with little evidence of changes in pattern over that distance. Integrated velocity measurements along a flowline indicate that the shelf has been stable for ∼560 years in the mid-shelf area. Linear longitudinal features may be grouped into 12 units, each related to one or a small group of outlet feeder glaciers to the shelf. We observe that the boundaries between these flow units often mark rift terminations. The boundary zones originate upstream at capes, islands or other suture areas between outlet glaciers. In agreement with previous work, our findings imply that rift terminations within such suture zones indicate that they contain anomalously soft ice. We thus suggest that suture zones within the Larsen C ice shelf, and perhaps within ice shelves more generally, may act to stabilize them by reducing regional stress intensities and thus rates of rift lengthening.

Substantial ice loss has occurred in the Russian High Arctic during the past decade, predominantly on Novaya Zemlya, yet the region has been studied relatively little. Consequently, the factors forcing mass loss and the relative contribution of ice dynamics versus surface melt are poorly understood. Here we evaluate the influence of atmospheric/oceanic forcing and variations in fjord width on the behaviour of 38 glaciers on the northern ice cap, Novaya Zemlya. We compare retreat rates on land- versus marine-terminating outlets and on the Kara versus Barents Sea coasts. Between 1992 and 2010, 90% of the study glaciers retreated and retreat rates were an order of magnitude higher for marine-terminating outlets (52.1 ma-1) than for land-terminating glaciers (4.8ma-1). We identify a post-2000 acceleration in marine-terminating glacier retreat, which corresponded closely to changes in sea-ice concentrations. Retreat rates were higher on the Barents Sea coast, which we partly attribute to lower sea-ice concentrations, but varied dramatically between individual glaciers. We use empirical data to categorize changes in along-flow fjord width, and demonstrate a significant relationship between fjord width variability and retreat rate. Results suggest that variations in fjord width exert a major influence on glacier retreat.

Scientific observations of sea ice began more than a century ago, but detailed sea-ice models appeared only in the latter half of the last century. The high albedo of sea ice is critical for the Earth’s heat balance, and ice motion across the ocean’s surface transports fresh water and salt. The basic components in a complete sea-ice model must include vertical thermodynamics and horizontal dynamics, including a constitutive relation for the ice, advection and deformational processes. This overview surveys topics in sea-ice modeling from the global climate modeling perspective, emphasizing work that significantly advanced the state of the art and highlighting promising new developments.

For three field seasons (2002/03, 2004/05, 2005/06) we have deployed a network of GPS receivers and seismometers around the tip of a propagating rift on the Amery Ice Shelf, East Antarctica. During these campaigns we detected seven bursts of episodic rift propagation. To determine whether these rift propagation events were triggered by short-term environmental forcings, we analyzed simultaneous ancillary data such as wind speeds, tidal amplitudes and sea-ice fraction (a proxy variable for ocean swell). We find that none of these environmental forcings, separately or together, correlated with rift propagation. This apparent insensitivity of ice-shelf rift propagation to short-term environmental forcings leads us to suggest that the rifting process is primarily driven by the internal glaciological stress. Our hypothesis is supported by order-of-magnitude calculations that the glaciological stress is the dominant term in the force balance. However, our calculations also indicate that as the ice shelf thins or the rift system matures and iceberg detachment becomes imminent, short-term stresses due to winds and ocean swell may become more important.

During the snow-melt season of 1982, basal water pressure was recorded in 11 bore holes communicating with the subglacial drainage system. In most of these holes the water levels were at approximately the same depth (around 70 m below surface). The large variations of water pressure, such as diurnal variations, were usually similar at different locations and in phase. In two instances of exceptionally high water pressure, however, systematic phase shifts were observed; a wave of high pressure travelled down-glacier with a velocity of approximately 100 m/h.

The glacier-surface velocity was measured at four lines of stakes several times daily. The velocity variations correlated with variations in subglacial water pressure. The functional relationship of water pressure and velocity suggests that fluctuating bed separation was responsible for the velocity variations. The empirical functional relationship is compared to that of sliding over a perfectly lubricated sinusoidal bed. On the basis of the measured velocity-pressure relationship, this model predicts a reasonable value of bed roughness but too high a sliding velocity and unstable sliding at too low a water pressure. The main reason for this disagreement is probably the neglect of friction from debris in the sliding model.

The measured water pressure was considerably higher than that predicted by the theory of steady flow through straight cylindrical channels near the glacier bed. Possible reasons are considered. The very large disagreement between measured and predicted pressure suggests that no straight cylindrical channels may have existed.

A climate–glacier model was used to reconstruct Late-glacial climate conditions from two case-study glaciers at 18° and 22° S in the arid (sub)tropical western Andes of northern Chile. The model uses (i) the geometry of the Late-glacial maximum glaciation, (ii) modern diurnal and annual cycles, amplitudes and lapse rates of the climate, (iii) empirical–statistical sublimation, melt and accumulation models developed for this area, and (iv) dynamic ice flow through two known cross-sections for steady-state conditions. The model is validated with modern conditions and compares favorably with the glaciological features of today. The mass-balance model calculates the modern equilibrium-line altitude at 18° S as high as 5850 m (field data 5800 m), whereas no glaciers exist in the fully arid southern area at 22° S despite altitudes above 6000 m and continuous permafrost. For Late-glacial times, the model results suggest a substantial increase in tropical summer precipitation (ΔP = +840 (− 50/+ 10) mm a−1 for the northern test area; +1000 (− 10/+ 30) mm a−1 for the southern test area) and a moderate temperature depression (ΔT = −4.4 (− 0.1/+ 0.2) °C at 18° S; −3.2 (±0.1) °C at 22° S). Extratropical frontal winter precipitation (June–September) was <15% of the total annual precipitation. A scenario with higher winter precipitation from the westerlies circulation belt does not yield a numerical solution which matches the observed geometry of the glaciers. Therefore, we conclude that an equatorward displacement of the westerlies must be discarded as a possible explanation for the late Pleistocene glaciation in the Andes of northern Chile.

The growth of single crystals of ice for the study of plasticity has to be done with care, since a disturbing lineage structure is easily generated. The orientation of specimens can be found from growth figures (dendrites) and Tyndall’s “flowers”; these give the a-axis, as the branches in both cases point in the [1120] direction. Slip occurs on the basal plane without following a definite glide direction. In pure shear two stages of creep exist, the first for a glide of 10–20 per cent in an undeformed crystal, the second for greater shears having a higher creep velocity. Both stages obey the law , n being 2.3–4 in the first case and 1.3–1.8 in the second. The deformed state above the transition remains stable and no recrystallization takes place in pure shear. Restoration of the undeformed state by recrystallization occurs only in inhomogeneously deformed parts. This observation may have an influence in interpreting measurements of glacier movements and tests on polycrystalline specimens in the laboratory.

Glacier runoff from the Yangtze River source region (YRSR), China, is estimated for the period 1961–2000 using a degree-day approach. In the investigation area, glacier runoff accounts for 11.0% of the total river runoff during the period 1961–2000. In the 1990s its contribution to river runoff rises to 17.0%. Due to the current rate of glacier decline, the impact of glacier runoff on river runoff has recently increased in the source region. Based on two different climate-change scenarios derived from ECHAM5/MPI-OM, future glacier runoff is assessed for the period 2001–50. In all climate-change scenarios, annual glacier runoff shows a significant increase due to intensified ice melting. There is an increase in glacier runoff during spring and early summer, yet a significant decrease in late summer. This study highlights the current and future impact of glacier runoff on river runoff in the YRSR.

Petermann Gletscher, northwest Greenland, drains 4% of the Greenland ice sheet into Nares Strait. Its floating ice shelf retreated from 81 to 48 km in length during two large calving events in 2010 and 2012. We document changes in the three-dimensional ice-shelf structure from 2000 to 2012, using repeated tracks of airborne laser altimetry and ice radio-echo sounding, ICESat laser altimetry and MODIS visible imagery. The recent ice-shelf velocity, measured by tracking surface features between flights in 2010 and 2011, is ~1.25 km a−1, ~15–30% faster than estimates made before 2010. The steady- state along-flow ice divergence represents 6.3 Gta−1 mass loss through basal melting (~5Gta−1) and surface melting and sublimation (~1.0Gta−1). Airborne laser altimeter data reveal thinning, both along a thin central channel and on the thicker ambient ice shelf. From 2007 to 2010 the ice shelf thinned by ~5 m a−1, which represents a non-steady mass loss of ~4.1 Gta−1. We suggest that thinning in the basal channels structurally weakened the ice shelf and may have played a role in the recent calving events.

We investigate the transferability of an enhanced temperature-index melt model that was developed and tested on Haut Glacier d’Arolla, Switzerland, in the 2001 season. The model’s empirical parameters (temperature factor, TF, and shortwave radiation factor, SRF) are recalibrated for: (1) other locations on Haut Glacier d’Arolla; (2) subperiods of distinct meteorological conditions; (3) different years on Haut Glacier d’Arolla; and (4) other glaciers in different years. The model parameters are optimized against simulations of an energy-balance model validated against ablation observations. Results are compared with those obtained with the original parameters. The model works very well when applied to other sites, seasons and glaciers, with the exception of overcast conditions. Differences are due to underestimation of high melt rates. The parameter values are associated with the prevailing energy-balance conditions, showing that high SRF are obtained on clear-sky days, whereas higher TF are typical of locations where glacier winds prevail and turbulent fluxes are high. We also provide a range of parameters clearly associated with the site’s location and its meteorological characteristics that could help to assign parameter values to sites where few data are available.