Ice-shelf basal melting is tightly coupled to ice-shelf morphology. Ice shelves, in turn, are coupled to grounded ice via their influence on compressive stress at the grounding line (‘ice-shelf buttressing’). Here, we examine this interaction using a local parameterization that relates the basal melt rate to the ice-shelf thickness gradient. This formulation permits a closed-form solution for a steady-state ice tongue. Time-dependent numerical simulations reveal the spatial and temporal evolution of ice-shelf/ice-stream systems in response to changes in ocean temperature, and the influence of morphology-dependent melting on grounding-line retreat. We find that a rapid (<1 year) re-equilibration in upstream regions of ice shelves establishes a spatial pattern of basal melt rates (relative to the grounding line) that persists over centuries. Coupling melting to ice-shelf shape generally, but not always, increases grounding-line retreat rates relative to a uniform distribution with the same area- average melt rate. Because upstream ice-shelf thickness gradients and retreat rates increase nonlinearly with thermal forcing, morphology-dependent melting is more important to the response of weakly buttressed, strongly forced ice streams grounded on beds that slope upwards towards the ocean (e.g. those in the Amundsen Sea).

Mathematical modeling of ice sheets is complicated by the nonlinearity of the governing equations and boundary conditions. Standard grid-based methods require complex front-tracking techniques and have a limited capability to handle large material deformations and abrupt changes in bottom topography. Consequently, numerical methods are usually restricted to shallow ice-sheet and ice-shelf approximations. We propose a new smoothed-particle hydrodynamics (SPH) model for coupled ice-sheet and ice-shelf dynamics. SPH, a fully Lagrangian particle method, is highly scalable and its Lagrangian nature and meshless discretization are well suited to the simulation of free surface flows, large material deformation and material fragmentation. In this paper, we use the SPH model to study ice-sheet/ice-shelf behavior, and the dynamics of the grounding line. The steady-state position of the grounding line obtained from SPH simulations is in good agreement with laboratory observations for a wide range of simulated bedrock slopes and density ratios, similar to those of ice and sea water. The numerical accuracy of the SPH algorithm is verified by simulating the plane-shear flow of two immiscible fluids and the propagation of a highly viscous blob of fluid along a horizontal surface. In the experiment, the ice was represented with a viscous Newtonian fluid. For consistency, in the described SPH model the ice is also modeled as a viscous Newtonian fluid. Typically, ice sheets are modeled as a non-Newtonian fluid, accounting for the changes in the mechanical properties of the ice. Implementation of a non-Newtonian rheology in the SPH model is the subject of our ongoing research.

Observations of the water level in Beaver Lake, an epishelf lake in East Antarctica, show a regular tidal signal that is lagged and attenuated from the tides beneath the adjacent Amery Ice Shelf. The phase lag and amplitude attenuation can be created by a narrow inlet connection between Beaver Lake and the cavity beneath the Amery Ice Shelf. A forced linear damped oscillator is used to determine the inlet dimensions that are required to produce the observed phase lag and amplitude attenuation. The model shows that the observations are consistent with a tidal flow that is restricted by the drag created by flow in the narrow inlet. Analysis shows that the phase lag and amplitude attenuation of the tides in Beaver Lake has increased over the years 1991-2002, probably due to a thickening of the overlying ice shelf. The response is sensitive to subtle variations in the dimensions of the inlet.

This study assesses the impact of a large 2010 calving event on the current and future stability of Petermann Glacier, Greenland, and ascertains the glacier’s interaction with different components of the climate and ocean system. We use a numerical ice-flow model that captures the major aspects of the glacier’s mass budget, the resistive forces controlling glacier flow, and includes dynamic calving. Satellite observations and model results show that the recent break-off of 25% of the floating tongue did not result in a significant glacier speed-up due to the low lateral resistance of this relatively wide and thin ice tongue. We demonstrate that seasonal speed-up at Petermann Glacier is mainly driven by meltwater lubrication rather than freeze-up conditions in the fjord. Results also show that sub-shelf ocean melt may have a profound effect on the future stability of Petermann Glacier, emphasizing the urgent need for more observations, and a better understanding of fjord temperature variability and circulation.

Unconformable firn stratigraphy exists throughout a 650 km long radar profile that we recorded down-flow of megadune fields in the Byrd Glacier (East Antarctica) catchment. Profile segments reveal cosets of prograding bedding sequences up to 90 m thick and with lateral, along-crest dimensions up to tens of kilometers. We profiled them in oblique section and nearly parallel to the prevailing wind. The prograding snow accumulates on broad, low windward slopes located above ice-bed depressions, which implies long-term slope stability. The apparent subglacial control implies that the accumulation progrades in balance with ice velocity, which we measured at ~30 ma”1. The sequences prograde over intensely modified and recrystallized wind-glaze firn, visible in the profiles as unstratified layers and zones up to several tens of meters thick. The intense recrystallization eliminates density stratification, and the altered layers appear to thicken into a connected network. Modeling of coset formation using wind and ice flow reproduces their dimensions and morphology. However, accumulation rates well above current regional estimates and existing data for megadunes are required because of the measured ice speed and required slope stability. The consistent unconformable strata along our traverse show that coset and recrystallized morphology extend far beyond the megadune fields.

Complex unconformable englacial stratigraphy, including a segment of distinctive cosets of bed sequences, occurs throughout the thickness of a 3.2 MHz ice-sheet radar profile we acquired across the upper Byrd Glacier (East Antarctica) catchment. Some cosets span >10 km, are >100 m thick and are delineated by distinct horizons. At 40-90 m depth in firn, comparisons between 200 MHz and specially processed 3.2 MHz profiles reveal that the delineating horizons result from density-modified layers produced by decades to millennia of subaerial exposure, as detailed in our related paper (Part I). These comparisons, together with reflected waveforms at depth, also reveal that the modified layers retain their chemical stratification, and therefore the original unconformable surface. Two profile segments show high-amplitude transverse folds spanning much of the ice-sheet thickness. The parallel nature of most of them suggests basal sliding beneath long-term up-ice-flow accumulation zones, which we identify in satellite images as the likely sources for the cosets. The unconformable stratigraphy at depths greater than 2000 m shows that antidunal deposition and intense firn recrystallization zones have persisted for tens of thousands of years in this region of East Antarctica.

Interferometric synthetic aperture radar (InSAR) observations of ice-shelf flow contain ocean-tide and atmospheric-pressure signals. A model-based correction can be applied, but this method is limited by its dependency upon model accuracy, which in remote regions can be uncertain. Here we describe a method to determine two-dimensional ice-shelf flow vectors independently of model predictions of tide and atmospheric pressure, by stacking conventional and multiple aperture InSAR (MAI) observations of the Dotson Ice Shelf, West Antarctica. In this way we synthesize a longer observation period, which enhances long-period (flow) displacement signals, relative to rapidly varying (tide and atmospheric pressure) signals and noise. We estimate the error associated with each component of the velocity field to be ~22 ma-1, which could be further reduced if more images were available to stack. With the upcoming launch of several satellite missions, offering the prospect of regular short-repeat SAR acquisitions, this study demonstrates that stacking can improve estimates of ice-shelf flow velocity.

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.

Fluxes of atmospheric CO2 have been reported over sea ice during winter and spring. These fluxes are partly driven by the gradient of the CO2 concentration between sea ice and the atmosphere. We present a new non-destructive method to measure the pCO2 of bulk sea ice at its in situ temperature. This method is based on an equilibration procedure between sea ice and a standard gas of known CO2 concentration. The concentration is measured by gas chromatography with a precision of 5%. Tests were performed on artificial standard sea ice and confirmed the reproducibility of the technique in the range of precision of the gas chromatograph. To test the accuracy of this method, the first profiles of pCO2 measured in bulk sea ice are reported and compared with direct in situ measurements of brine pCO2 over depth-integrated intervals.

Laboratory creep deformation experiments have been conducted on initially isotropic laboratory-made samples of polycrystalline ice. Steady-state tertiary creep rates, , were determined at strains exceeding 10% in either uniaxial-compression or simple-shear experiments. Isotropic minimum strain rates, , determined at ˜1 % strain, provide a reference for comparing the relative magnitude of tertiary creep rates in shear and compression through the use of strain-rate enhancement factors, E, defined as the ratio of corresponding tertiary and isotropic minimum creep rates, i.e. . The magnitude of strain-rate enhancement in simple shear was found to exceed that in uniaxial compression by a constant factor of 2.3. Results of experiments conducted at octahedral shear stresses of to = 0.040.80 MPa indicate a creep power-law stress exponent of n = 3 for isotropic minimum creep rates and n = 3.5 for tertiary creep rates. The difference in stress exponents for minimum and tertiary creep regimes can be interpreted as a t0 stress-dependent level of strain-rate enhancement, i.e. .The implications of these results for deformation in complex multicomponent stress configurations and at stresses below those used in the current experiments are discussed.

Mass-balance and dynamic behaviour of Chhota Shigri glacier, western Himalaya, India, has been investigated between 2002 and 2010 and compared to data collected in 1987-89. During the period 2002-10, the glacier experienced a negative glacier-wide mass balance of -0.67 ± 0.40 m w.e. a-1. Between 2003 and 2010, elevation and ice-flow velocities slowly decreased in the ablation area, leading to a 24-37% reduction in ice fluxes, an expected response of the glacier dynamics to its recent negative mass balances. The reduced ice fluxes are still far larger than the balance fluxes calculated from the 2002-10 average surface mass balances. Therefore, further slowdown, thinning and terminus retreat of Chhota Shigri glacier are expected over the next few years. Conversely, the 2003/04 ice fluxes are in good agreement with ice fluxes calculated assuming that the glacier-wide mass balance is zero. Given the limited velocity change between 1987−89 and 2003/04 and the small terminus change between 1988 and 2010, we suggest that the glacier has experienced a period of near-zero or slightly positive mass balance in the 1990s, before shifting to a strong imbalance in the 21st century. This result challenges the generally accepted idea that glaciers in the Western Himalaya have been shrinking rapidly for the last few decades.

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.

Scale-invariant phenomena are common in nature and fractals represent a suitable mathematical tool to describe them. Snow avalanche flow is made up of a mixture of grains and aggregates (granules) which can be broken or sintered together. The granular properties and interactions are important in understanding how avalanches flow. In this paper a fractal model for describing the grain-size distribution in the deposit of a snow avalanche is formulated by introducing the concept of aggregation probability. Although the model is two-dimensional, an extension to the three-dimensional case is proposed in the conclusions. The cumulative size distribution law is extrapolated from the model, and a physical discussion on fractal parameters is conducted. Finally, an experimental application to a real avalanche event is considered to confirm the predictions of the model and to present an extension to multifractality.

Numerical experiments are conducted on a synthetic topography with a three-dimensional thermomechanically coupled ice-sheet model, the Parallel Ice Sheet Model (PISM). Within the model, combined stress balances are connected to evolving thermodynamics and hydrology. The sensitivity of cyclic behaviour to changes in sliding-law parameters and the climate input is studied. Multiple types of oscillations were found, with strong variations in both amplitude and frequency. A physical description is given, in which these variations and transitions from one oscillation type to another are linked to the interplay of stresses, heat transport and hydrological processes. High-frequency oscillations (period 114-169 years), which are shown to have a major impact on ice velocities and a small effect on the ice volume, are related to variations in the water distribution at the base. Low-frequency cycles (period 1000+ years), which have a major impact on both velocities and ice volume, are linked to changes in the thermal regime. Oscillation characteristics are shown to be strongly sensitive to changes in sliding-law parameters and the prescribed surface temperature and mass balance. Incorporating a surface-height dependence of the mass balance is shown to provide an additional feedback, which may induce long- period oscillations.

The transfer of surface-generated meltwater to the subglacial drainage system through full ice thickness crevassing may lead to accelerated glacier velocities, with implications for ice motion under future climatic scenarios. Accurate predictions of where surface meltwater accesses the ice/bed interface are therefore needed in fully coupled hydrodynamic ice-sheet models. We present a spatially distributed modelling routine for predicting the location and timing of delivery of surface-derived meltwater to the ice/bed interface through moulins and supraglacial lake drainage. The model is explained as it is applied to the Croker Bay glacial catchment of Devon Ice Cap, Canada. The formation of moulins, drainage of lakes, and the transfer of meltwater through the full ice thickness are modelled for the 2004 and 2006 ablation seasons. Through this case study we assess the model’s sensitivity to degree-day factors, fracture toughness, tensile strength and crevasse width, and confirm that parameters influencing the rate at which water fills a crevasse are the most significant controls on the ability of a crevasse to reach the bed. Increased surface melt production, therefore, has the potential to significantly influence the spatial and temporal transfer of meltwater through surface-to-bed connections in a warmer climate

An analytical theory is developed for ice flow velocity in a boundary layer couplet at the calving front. The theory has simple quantitative characteristics that relate ice front velocity to thickness, strain rate and shelf width, matching one set of empirically derived relationships (Alley and others, 2008) and implying that these relationships predict ice velocity rather than calving rate. The two boundary layers are where longitudinal and transverse flow fields change from the interior flow to patterns consistent with the calving-front stress condition. Numerical simulations confirm the analytical theory. The quantitative predictions of the theory have low sensitivity to unmeasured parameters and to shelf plan aspect ratio, while its robustness arises from its dependence on the scale invariance of the governing equations. The theory provides insights into calving, the stability of ice-shelf calving fronts, the stability of the grounding line of laterally resisted ice streams, and also suggests that the calving front is an instructive dynamical analogue to the grounding line.

A combination of remotely sensed data, field mapping, bathymetric survey and geophysical soundings is used to describe the recent changes in the terminal area of Petrov glacier, the largest glacier in the Akshiirak massif, central Tien Shan. According to our results, three periods of accelerated glacier retreat (1977-80, 1990-95 and 2008-09) can be distinguished since 1977. The largest recession occurred in 1990-95 when the glacier retreated by 54 ± 8ma-1. Accelerated glacier retreat affected the enlargement rate of Petrov lake, which increased by 0.04-0.1 km2 a-1 and by 1.3-2.2 × 106m3a-1 in the last three decades. Since 1995, the mean annual retreat rate of the lake-calving northern glacier section has been up to three times higher than the retreat rate of the land-terminating southern section. The calving flux ranged from 2.5 to 4.6 × 106m3a-1 in 2003-09, resulting in a total glacier mass loss of (17.7 ± 0.4) × 106m3. The calving terminus of Petrov glacier was >65 m thick in 2009 according to ground-penetrating radar measurements.

We present a new surface-balance and ice-motion dataset derived from high-precision GPS measurements from a network of steel poles within three icefields of the Allan Hills blue-ice area, Antarctica. The surveys were conducted over a 14 year time period. Ice-flow velocities and mass- balance estimates for the main icefield (MIF) are consistent with those from pre-GPS era measurements but have much smaller uncertainties. The current study also extends these measurements through the near-western icefield (NWIF) to the eastern edge of the mid-western icefield (MWIF). The new dataset includes, for the first time, well-constrained evidence of upward motion within the Allan Hills MIF, indicating that old ice should be present at the surface. These data and terrestrial meteorite ages suggest that paleoclimate reconstructions using the surface record within the Allan Hills MIF could potentially extend the ice-core-based record beyond the 800 000 years currently available in the EPICA Dome C core.

The propagation saw test (PST) is a recently developed snowpack test that enables assessment of the fracture propagation propensity of selected persistent weak-layer and slab combinations, which are known to release dry-slab avalanches. In this paper, we assess the slope- scale accuracy of the standard PST method at validated sites of observed weak-layer fracture initiation, with or without propagation. We also report on experiments with alternative test methods and varying saw thicknesses. Results show the standard PST method is comparably accurate to other common snowpack tests in predictive skill when predicting propagation propensity on the slope scale. Although a slight but significant dependence on saw thickness was found, it did not affect the interpretation in our validation study. Alternative methods such as scaling the test column length with weak-layer depth or leaving the upslope end of the column attached to the surrounding snowpack did not improve slope- scale accuracy and these tests were often more difficult to interpret.