Measurements of the mechanical properties of snow are essential for improving our understanding and the prediction of snow failure and hence avalanche release. We performed fracture mechanical experiments in which a crack was initiated by a saw in a weak snow layer underlying cohesive snow slab layers. Using particle tracking velocimetry (PTV), the displacement field of the slab was determined and used to derive the mechanical energy of the system as a function of crack length. By fitting the estimates of mechanical energy to an analytical expression, we determined the slab effective elastic modulus and weak layer specific fracture energy for 80 different snowpack combinations, including persistent and nonpersistent weak snow layers. The effective elastic modulus of the slab ranged from 0.08 to 34 MPa and increased with mean slab density following a power-law relationship. The weak layer specific fracture energy ranged from 0.08 to 2.7 J m−2 and increased with overburden. While the values obtained for the effective elastic modulus of the slab agree with previously published low-frequency laboratory measurements over the entire density range, the values of the weak layer specific fracture energy are in some cases unrealistically high as they exceeded those of ice. We attribute this discrepancy to the fact that our linear elastic approach does not account for energy dissipation due to non-linear parts of the deformation in the slab and/or weak layer, which would undoubtedly decrease the amount of strain energy available for crack propagation.

This is the first (Paper I) of three companion papers focused respectively, on the estimates of the errors in ice thickness retrieved from pulsed ground-penetrating radar (GPR) data, on how to estimate the errors at the grid points of an ice-thickness DEM, and on how the latter errors, plus the boundary delineation errors, affect the ice-volume estimates. We here present a comprehensive analysis of the various errors involved in the computation of ice thickness from pulsed GPR data, assuming they have been properly migrated. We split the ice-thickness error into independent components that can be estimated separately. We consider, among others, the effects of the errors in radio-wave velocity and timing. A novel aspect is the estimate of the error in thickness due to the uncertainty in horizontal positioning of the GPR measurements, based on the local thickness gradient. Another novel contribution is the estimate of the horizontal positioning error of the GPR measurements due to the velocity of the GPR system while profiling, and the periods of GPS refreshing and GPR triggering. Their effects are particularly important for airborne profiling. We illustrate our methodology through a case study of Werenskioldbreen, Svalbard.

This paper is the second (Paper II) in a set of studies concerning the errors involved in the estimate of ice thickness and ice volume. Here we present a detailed analysis of the errors involved in the generation of ice-thickness DEMs constructed, most often, from GPR data, complemented by boundary data and sometimes, additional synthetic data arising from estimates based on theoretical considerations supported by independent data. We describe a complete methodology of error analysis that, starting from the errors in the data, propagates them to the grid nodes. In turn, the interpolation error at the grid nodes is calculated using a novel procedure that also provides an estimate of the bias introduced by the interpolation process. Finally, both errors are combined at the grid nodes to produce a gridpoint-dependent error estimate, which is complemented by an overall error estimate providing an assessment of the quality of the DEM. This methodology is illustrated with the case study of Werenskioldbreen, a land-terminating polythermal glacier in Svalbard.

This paper is the third (Paper III) in a set of studies of the errors involved in the estimate of ice thickness and ice volume. Here we present a methodology to estimate the error in the calculation of the volume of an ice mass from an ice-thickness DEM. We consider the two main error sources: the ice-thickness error at each DEM grid point and the uncertainty in the boundary delineation. To accurately estimate the volume error due to the error in thickness of the DEM, it is crucial to determine the degree of correlation among the ice-thickness errors at the grid points. We find that the two-dimensional integral range, which represents the equivalent area of influence of each independent value, allows estimation of the equivalent number of independent values of error within the DEM. Hence, it provides an easy way to obtain the volume error resulting from the uncertainty in ice thickness of a DEM. We show that the volume error arising from the uncertainty in boundary delineation, often neglected in the literature, can be of the same order of magnitude as the volume error resulting from ice-thickness errors. We illustrate our methodology through the case study of Werenskioldbreen, Svalbard.

Documenting past changes in the East Antarctic surface mass balance is important to improve ice core chronologies and to constrain the ice-sheet contribution to global mean sea-level change. Here we reconstruct past changes in the ratio of surface mass balance (SMB ratio) between the EPICA Dome C (EDC) and Dome Fuji (DF) East Antarctica ice core sites, based on a precise volcanic synchronization of the two ice cores and on corrections for the vertical thinning of layers. During the past 216 000 a, this SMB ratio, denoted SMBEDC/SMBDF, varied between 0.7 and 1.1, being small during cold periods and large during warm periods. Our results therefore reveal larger amplitudes of changes in SMB at EDC compared with DF, consistent with previous results showing larger amplitudes of changes in water stable isotopes and estimated surface temperature at EDC compared with DF. Within the last glacial inception (Marine Isotope Stages, MIS-5c and MIS-5d), the SMB ratio deviates by up to 0.2 from what is expected based on differences in water stable isotope records. Moreover, the SMB ratio is constant throughout the late parts of the current and last interglacial periods, despite contrasting isotopic trends.

A new Rapid Access Ice Drill (RAID) will penetrate the Antarctic ice sheets in order to create borehole observatories and take cores in deep ice, the glacial bed and bedrock below. RAID is a mobile drilling system to make multiple long, narrow boreholes in a single field season in Antarctica. RAID is based on a mineral exploration-type rotary rock-coring system using threaded drill pipe to cut through ice using reverse circulation of a non-freezing fluid for pressure-compensation, maintenance of temperature and removal of ice cuttings. Near the bottom of the ice sheet, a wireline latching assembly will enable rapid coring of ice, the glacial bed and bedrock below. Once complete, boreholes will be kept open with fluid, capped and available for future down-hole measurement of temperature gradient, heat flow, ice chronology and ice deformation. RAID is designed to penetrate up to 3300 m of ice and take cores in <200 hours, allowing completion of a borehole and coring in ~10 d at each site. Together, the rapid drilling capability and mobility of the system, along with ice-penetrating imaging methods, will provide a unique 3-D picture of interior and subglacial features of the Antarctic ice sheets.

Microwave radar amplitude within a snowpack can be strongly influenced by spatial variability of internal layer boundaries. We quantify the impact of spatial averaging of snow stratigraphy and physical snowpack properties on surface scattering from near-nadir frequency-modulated continuous-wave radar at 12–18 GHz. Relative permittivity, density, grain size and stratigraphic boundaries were measured in-situ at high resolution along the length of a 9 m snow trench. An optimal range of horizontal averaging (4–6 m) was identified to attribute variations in surface scattering at layer boundaries to dielectric contrasts estimated from centimetre-scale measurements of snowpack stratigraphy and bulk layer properties. Single vertical profiles of snowpack properties seldom captured the complex local variability influencing near-nadir radar surface scattering. We discuss implications of scaling in-situ measurements for snow radiative transfer modelling and evaluation of airborne microwave remote sensing of snow.

Englacial temperature is a major control on ice rheology and flow. However, it is difficult to measure at the glacier to ice-sheet scale. As a result, ice-sheet models must make assumptions about englacial temperature and rheology, which affect sea level projections. This is problematic if fundamental processes are not captured by models due to a lack of observationally constrained ice temperature values. Although radar sounding data have been exploited to constrain the temperature structure of the Greenland ice sheet using englacial layers, this approach is limited to areas and depths where these layers exist intact. In order to extend empirical radar-based temperature estimation beyond this limitation, we present a new technique for estimating englacial attenuation rates for the entire ice column using adaptive fitting of unfocused radar bed echoes based on the correlation of ice thickness and corrected bed echo power. We apply this technique to an airborne survey of Thwaites Glacier in West Antarctica and compare the results with temperatures and attenuation rates from a numerical ice-sheet model. We find that the estimated attenuation rates reproduce modelled patterns and values across the catchment with the greatest differences near steeply sloping bed topography.

To quantify recent thinning of marine-terminating outlet glaciers in northwestern Greenland, we carried out field and satellite observations near the terminus of Bowdoin Glacier. These data were used to compute the change in surface elevation from 2007 to 2013 and this rate of thinning was then compared with that of the adjacent land-terminating Tugto Glacier. Comparing DEMs of 2007 and 2010 shows that Bowdoin Glacier is thinning more rapidly (4.1 ± 0.3 m a−1) than Tugto Glacier (2.8 ± 0.3 m a−1). The observed negative surface mass-balance accounts for <40% of the elevation change of Bowdoin Glacier, meaning that the thinning of Bowdoin Glacier cannot be attributable to surface melting alone. The ice speed of Bowdoin Glacier increases down-glacier, reaching 457 m a−1 near the calving front. This flow regime causes longitudinal stretching and vertical compression at a rate of −0.04 a−1. It is likely that this dynamically-controlled thinning has been enhanced by the acceleration of the glacier since 2000. Our measurements indicate that ice dynamics indeed play a predominant role in the rapid thinning of Bowdoin Glacier.

Glacier mass balance is a key variable for the monitoring strategies of the Earth climate system, but the continuation of long-term observations is now endangered by the impending extinction of several monitored glaciers. It is therefore advisable to start new observations on neighbouring glaciers that are more likely to survive into the next few decades. These glaciers will be located at higher altitude, have larger elevation range, thus preserving an accumulation area and have good spatial representativeness. Glaciers with these characteristics may pose some problems and are more demanding for mass-balance measurements and calculations, due to their size and presence of remote and inaccessible areas, further complicated by the complex morphology and high-lateral gradients of mass balance. I present the new mass-balance series for La Mare Glacier, started in 2003 to replace the long-term monitored and rapidly vanishing Careser Glacier in the Ortles-Cevedale Group (Eastern Italian Alps). Direct glaciological mass-balance observations have been complemented by measurements with the hydrological method and, as recommended by the World Glacier Monitoring Service, validated using the geodetic method. The collected data are useful for testing and optimising two techniques proposed in the literature for extrapolating measurements to inaccessible areas.

We use satellite radar interferometry to investigate changes in the location of the Petermann Glacier grounding line between 1992 and 2011. The grounding line location was identified in 17 quadruple-difference interferograms produced from European Remote Sensing (ERS)-1/2 data – the most extensive time series assembled at any ice stream to date. There is close agreement (20.6 cm) between vertical displacement of the floating ice shelf and relative tide amplitudes simulated by the Arctic Ocean Dynamics-based Tide Model 5 (AODTM-5) Arctic tide model. Over the 19 a period, the groundling line position varied by 470 m, on average, with a maximum range of 7.0 km observed on the north-east margin of the ice stream. Although the mean range (2.8 km) and variability (320 m) of the grounding line position is considerably lower if the unusually variable north-east sector is not considered, our observations demonstrate that large, isolated movements cannot be precluded, thus sparse temporal records should be analysed with care. The grounding line migration observed on Petermann Glacier is not significantly correlated with time (R2 = 0.22) despite reported ice shelf thinning and episodes of large iceberg calving, which suggests that unlike other ice streams, on the south-west margin of the Greenland ice sheet, Petermann Glacier is dynamically stable.

Thinning rates for the debris-covered Gangotri Glacier and its tributary glaciers during the period 1968–2014, length variation and area vacated at the snout from 1965 to 2015, and seasonal variation of ice-surface velocity for the last two decades have been investigated in this study. It was found that the mass loss of Gangotri and its tributary glaciers was slightly less than those reported for other debris-covered glaciers in the Himalayan regions. The average velocity during 2006–14 decreased by ~6.7% as compared with that during 1993–2006. The debris-covered area of the main trunk of Gangotri Glacier increased significantly from 1965 until 2015 with the maximum rate of increase (0.8 ± 0.2 km2 a−1) during 2006–15. The retreat (~9.0 ± 3.5 m a−1) was less in recent years (2006–2015) but the down-wasting (0.34 ± 0.2 m a−1) in the same period (2006–2014) was higher than that (0.20 ± 0.1 m a−1) during 1968–2006. The study reinforced the established fact that the glacier length change is a delayed response to climate change and, in addition, is affected by debris cover, whereas glacier mass balance is a more direct and immediate response. Therefore, it is recommended to study the glacier mass balance and not only the glacier extent, to conclude about a glacier's response to climate change.

Time-varying elevations near the calving front of Jakobshavn Isbræ, Greenland were observed with a terrestrial radar interferometer (TRI) in June 2015. An ice block with surface dimensions of 1370 m × 290 m calved on 10 June. TRI-generated time series show that ice elevation near the calving front began to increase 65 h prior to the event, and can be fit with a simple block rotation model. We hypothesize that subsurface melting at the base of the floating terminus breaks the gravity-buoyancy equilibrium, leading to slow subsidence and rotation of the block, and its eventual failure.

Accurate modeling of calving glaciers relies on knowledge of many processes (ice flow, surface/submarine melting, calving, mélange interaction) and glacier-specific factors (air temperature, ocean circulation, precipitation rate, glacier geometry) that remain challenging to assess. Iceberg calving, especially, is important to glacier mass loss and difficult to resolve in currently-available models. Given these challenges facing even the most sophisticated models, there is value in simple, computationally-efficient models that can capture first-order effects. In this study we derive a simple model, extending Nye's perfect plastic approximation to include a yield surface at the calving front. With one climate-related input—either an upstream glacier thinning rate or glacier-wide accumulation—this model is able to simulate the advance and retreat of marine-terminating glaciers on annual to decadal scales. Our model requires knowledge of only two glacier-specific factors: glacier bed topography and basal shear strength, both reasonably constrained by laboratory and field observations. We apply the model to a case study of Columbia Glacier, Alaska and show that, despite its simplicity, the model succeeds in reproducing observed centerline profiles and rates of terminus retreat up to 2007.

Remote sensing is a powerful method to reconstruct annual mass-balance series over past decades by exploiting archives of available images, as well as to study glaciers in inaccessible regions. We present the application of a methodological framework based only on optical satellite images to retrieve glacier-wide annual mass balances for 30 glaciers in the French Alps. The glacier-wide annual mass balance for the period 1983–2014 was reconstructed by combining changes in glacier volumes computed from remote-sensing derived DEMs with annual measurements of the snow line altitude on satellite images. Data from direct observations on two of the glaciers confirmed the accuracy of the annual mass balances quantified by remote sensing with an average difference of ~0.3 m w.e., within the uncertainty range of the methods. Our results confirm the significant increase in mass loss since the early 2000s, with a difference >1 m w.e. a−1 between the periods 1983–2002 and 2003–14. The region-wide mass balance for the French Alps over the period 1979–2011 was −0.66 ± 0.27 m w.e. a−1, close to that of the European Alps. We also show that changes in glacier surface area or length are not representative of changes in mass balance at the scale of a few decades.

Greenland's marine-terminating glaciers may be sensitive to oceanic heat, but the fjord processes controlling delivery of this heat to glacier termini remain poorly constrained. Here we use a three-dimensional numerical model of Kangerdlugssuaq Fjord, East Greenland, to examine controls on fjord/shelf exchange. We find that shelf-forced intermediary circulation can replace up to ~25% of the fjord volume with shelf waters within 10 d, while buoyancy-driven circulation (forced by subglacial runoff from marine-terminating glaciers) exchanges ~10% of the fjord volume over a 10 d period under typical summer conditions. However, while the intermediary circulation generates higher exchange rates between the fjord and shelf, the buoyancy-driven circulation is consistent over time hence more efficient at transporting water along the full length of the fjord. We thus find that buoyancy-driven circulation is the primary conveyor of oceanic heat to glaciers during the melt season. Intermediary circulation will however dominate during winter unless there is sufficient input of fresh water from subglacial melting. Our findings suggest that increasing shelf water temperatures and stronger buoyancy-driven circulation caused the heat available for melting at Kangerdlugssuaq Glacier to increase by ~50% between 1993–2001 and 2002–11, broadly coincident with the onset of rapid retreat at this glacier.

If a series of glacial advances occurs over the same pathway, the moraines that are now present may constitute an incomplete record of the total history. This is because a given advance can destroy the moraine left by a previous one, if the previous advance was less extensive. Gibbons, Megeath and Pierce (GMP) formulated an elegant stochastic model for this process; the key quantity in their analysis is $\bi P(n\vert N)$, the probability that n moraines are preserved after N glacial advances. In their paper, GMP derive a recursion formula satisfied by $\bi P(n\vert N)$, and use this formula to compute values of P for a range of values of n and N. In the present paper, we derive an explicit general answer for $\bi P(n\vert N)$, and show explicit, exact results for the mean value and standard deviation of n. We use these results to develop more insight into the consequences of the GMP model; for example, to a good approximation, 〈n〉 increases as ln(N). We explain how a Bayesian approach can be used to analyze $\bi P(N\vert n)$, the probability that there were N advances, given that we now observe n moraines.