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

The specific surface area (SSA), defined as the surface area of ice per unit mass, is an important variable characterizing the complex microstructure of snow. Its application range covers the physical evolution of snow (metamorphism), photochemistry and optical and microwave remote sensing. This paper presents a new device, POSSSUM (Profiler Of Snow Specific Surface area Using SWIR reflectance Measurement), designed to allow the rapid acquisition of SSA profiles down to ∼20 m depth and with an effective vertical resolution of 10–20 mm. POSSSUM is based on the infrared (IR) reflectance technique: A laser diode operating at 1310 nm illuminates the snow at nadir incidence angle along the face of a drilled hole. The reflected radiance is measured at three zenith angles (20°, 40° and 60°) each for two azimuth angles (0° and 180°). A second laser operating at a shorter wavelength (635 nm), which is almost insensitive to SSA, allows the distance to the snow face to be estimated. The reflected IR radiance and the distance are combined to estimate bidirectional reflectances. These reflectances are converted into hemispherical reflectances and in turn into SSA using a theoretical formulation based on an asymptotic solution of the radiative transfer equation. The evaluation and validation of POSSSUM’s SSA measurements took place in spring 2009 in the French Alps. The new method was compared with the methane adsorption technique and DUFISSS, another well-validated instrument based on the IR technique. The overall measurement error is in the range 10–15%.

The diffusion of stable water isotopes in snow was measured in two controlled laboratory experiments. Two batches of snow of different isotopic composition were stacked alternately with varying layer thicknesses. The stack was stored in a freezer room at constant temperature for several months, and sampled at regular intervals to analyse the diffusion. Measured isotope profiles were fitted to a theoretical model with diffusion length as the fit parameter. In the first experiment, we observed a difference in diffusion rates between layers of different thicknesses, which is likely caused by layers of snow not being in proper contact with each other. In the second experiment we found very good agreement between measurements and model results. The measured diffusivity is compared with theory, in which we mainly focus on the temperature dependence of the ice–vapour fractionation factors. This temperature dependence is slightly different for the different isotopes of water, which leads to a difference in diffusion rates. We illustrate how our set-up can be used to measure the ratio between ice–vapour fractionation factors of oxygen-18 and deuterium, which determine the relation between the difference in diffusion and the firn temperature.

We used observations and modeling of Siple Dome, West Antarctica, a ridge ice divide, to infer the importance of linear deformation mechanisms in ice-sheet flow. We determined the crossover stress (a threshold value of the effective deviatoric stress below which linear flow mechanisms dominate over nonlinear flow mechanisms) by combining measurements of ice properties with in situ deformation rate measurements and a finite-element ice flow model that accounts for the effects of viscous anisotropy induced by preferred crystal-orientation fabric. We found that a crossover stress of 0.18 bar produces the best match between predicted and observed deformation rates. For Siple Dome, this means that including a linear term in the flow law is necessary, but generally the flow is still dominated by the nonlinear (Glen; n = 3) term. The pattern of flow near the divide at Siple Dome is also strongly affected by crystal fabric. Measurements of sonic velocity, which is a proxy for vertically oriented crystal fabric, suggest that a bed-parallel shear band exists several hundred meters above the bed within the Ice Age ice.

We report measurements using a portable real aperture radar (Gamma Portable Radar Interferometer (GPRI)) for interferometric imaging of the surface ice motion on Gornergletscher, Switzerland, during the drainage of the adjacent ice-marginal lake Gornersee. The GPRI tracked the surface ice motion in line of sight over an area of ∼3 km2 down-glacier of Gornersee almost continuously during the drainage event. The displacement maps derived from the acquired interferograms capture the spatial distribution of the surface ice motion. Due to fast acquisition times of the microwave images, the GPRI was able to record sub-daily variations of the ice displacements, most likely caused by the impact of the Gornersee drainage on the ice motion of Gornergletscher. In situ point measurements of the ice displacement agree reasonably well with the results obtained by the GPRI and highlight the use of the GPRI for high-resolution measurements of glacier surface ice motion.

We have measured the in situ average electric field attenuation length, 〈Lα〉, for radio-frequency signals broadcast vertically through the Ross Ice Shelf, Antarctica. We chose a location, Moore Embayment, south of Minna Bluff, known for its high reflectivity at the ice–sea interface. We confirmed specular reflection and used the return pulses to measure the average attenuation length from 75–1250 MHz over the round-trip distance of 1155 m. We find 〈Lα〉 to vary from ∼500 m at 75 MHz to ∼300 m at 1250 MHz, with an experimental uncertainty of 55–15 m.

We assess basal roughness beneath Pine Island Glacier (PIG), West Antarctica, based on a recent airborne radio-echo sounding dataset. We identify a clear relationship between faster ice flow and decreased basal roughness in significant parts of PIG. The central portion and two of its tributaries are particularly smooth, but the majority of the tributaries feeding the main trunk are rougher. We interpret the presence of a smooth bed as being a consequence of the deposition of marine sediments following disappearance of the West Antarctic ice sheet in the Pliocene or Pleistocene, and, conversely, a lack of marine sedimentation where the bed is rough. Importantly, we also identify a patchy distribution of marine sediments, and thus a bed over which the controls on flow vary. While there is a notable correspondence between ice velocity and bed roughness, we do not assume a direct causal relationship, but find that an indirect one is likely. Where low basal roughness results in low basal resistance to flow, a lower driving stress is required to produce the flux required to achieve mass balance. This, in turn, means that the surface in that area will be lower than surrounding areas with a rougher bed, and this will tend to draw flow into the area with low bed roughness. Since our studies shows that bed roughness beneath the tributaries of the trunk varies substantially, there is a strong likelihood that these tributaries will differ in the rate at which they transmit current velocity changes on the main trunk into the interior of the glacier basin.

The cold-based termini of polythermal glaciers are usually assumed to adhere strongly to an immobile substrate and thereby supply significant resistance to the flow of warm-based ice up-glacier. This compressive environment is commonly thought to uplift basal sediment to the surface of the glacier by folding and thrust faulting. We present model and field evidence from the terminus of Storglaciären, Sweden, showing that the cold margin provides limited resistance to flow from up-glacier. Ice temperatures indicate that basal freezing occurs in this zone at 10−1 −10−2 m a−1, but model results indicate that basal motion at rates greater than 1 m a−1 must, nevertheless, persist there for surface and basal velocities to be consistent with measurements. Estimated longitudinal compressive stresses of 20–25 kPa within the terminus further indicate that basal resistance offered by the cold-based terminus is small. These results indicate that where polythermal glaciers are underlain by unlithified sediments, ice-flow trajectories and sediment transport pathways may be affected by subglacial topography and hydrology more than by the basal thermal regime.

We derive mass changes of the Greenland ice sheet (GIS) for 2003–07 from ICESat laser altimetry and compare them with results for 1992–2002 from ERS radar and airborne laser altimetry. The GIS continued to grow inland and thin at the margins during 2003–07, but surface melting and accelerated flow significantly increased the marginal thinning compared with the 1990s. The net balance changed from a small loss of 7 ± 3 Gt a−1 in the 1990s to 171 ± 4 Gt a−1 for 2003–07, contributing 0.5 mm a−1 to recent global sea-level rise. We divide the derived mass changes into two components: (1) from changes in melting and ice dynamics and (2) from changes in precipitation and accumulation rate. We use our firn compaction model to calculate the elevation changes driven by changes in both temperature and accumulation rate and to calculate the appropriate density to convert the accumulation-driven changes to mass changes. Increased losses from melting and ice dynamics (17–206 Gt a−1) are over seven times larger than increased gains from precipitation (10–35 Gt a−1) during a warming period of ∼2 K (10 a)−1 over the GIS. Above 2000 m elevation, the rate of gain decreased from 44 to 28 Gt a−1, while below 2000 m the rate of loss increased from 51 to 198 Gt a−1. Enhanced thinning below the equilibrium line on outlet glaciers indicates that increased melting has a significant impact on outlet glaciers, as well as accelerating ice flow. Increased thinning at higher elevations appears to be induced by dynamic coupling to thinning at the margins on decadal timescales.

Ice crystal orientation fabric data from ice cores contain important information concerning the internal structure and the flow behaviour of ice sheets. When ice cores are recovered from the Antarctic and Greenland ice sheets, crystal orientation measurements are performed immediately to obtain fundamental physical property information. In the past, we have measured the c-axis orientation of ice crystals by a manual optical method using a universal stage. This method is very time-consuming, involving tedious work in a cold laboratory. Recently, automated systems have been developed that enable measurement of c-axis orientation, grain size and other microstructures. However, in order to detect the full crystal orientation of an ice crystal, we also need information on its a-axis orientation. A variety of other crystal orientation measurement methods have previously been discussed, but some shortcomings for ice-core studies cannot be neglected. We have developed a crystal-orientation analysing device using the Laue X-ray diffraction method. As this device can measure the orientations of all crystal axes with high accuracy, it is possible to obtain new microstructure information on natural ice crystals. For the first time, we are able to quantify very low subgrain misorientation angles in polar ice-core samples, allowing us to investigate micro-deformation features of individual crystals. Here we discuss the analysis process, which is customized to measure standard ice thin sections, and show preliminary results.

Ice in polar ice sheets undergoes deformation during its flow towards the coast. Deformation and recrystallization microstructures such as subgrain boundaries can be observed and recorded using high-resolution light microscopy of sublimation-edged sample surfaces (microstructure mapping). Subgrain boundaries observed by microstructure mapping reveal characteristic shapes and arrangements. As these arrangements are related to the basal plane orientation, full crystallographic orientation measurements are needed for further characterization and interpretation of the subgrain boundary types. X-ray Laue diffraction measurements validate the sensitivity of different boundary types with sublimation used by microstructure mapping for the classification. X-ray Laue diffraction provides misorientation values of all four crystal axes. Line scans across a subgrain boundary pre-located by microstructure mapping can determine the rotation axis and angle. Together with the orientation of the subgrain boundary this yields information on the dislocation types. Tilt and twist boundaries composed of dislocations lying in the basal plane, and tilt boundaries composed of nonbasal dislocations were found. A statistical analysis shows that nonbasal dislocations play a significant role in the formation of all subgrain boundaries.

We apply a point-scale energy-balance model to a small polythermal glacier in the St Elias Mountains of Canada in order to investigate the applicability and limitations of different treatments of the glacier surface temperature and subsurface heat flux. These treatments range in complexity from a multilayer subsurface model that simulates snowpack evolution, to the assumption of a constant glacier surface temperature equal to 0°C. The most sophisticated model includes dry densification of the snowpack, penetration of shortwave radiation into the subsurface, internal melting, refreezing of percolating meltwater and generation of slush layers. Measurements of subsurface temperature and surface lowering are used for model validation, and highlight the importance of including subsurface penetration of shortwave radiation in the model. Using an iterative scheme to solve for the subsurface heat flux as the residual of the energy-balance equation results in an overestimation of total ablation by 18%, while the multilayer subsurface model underestimates ablation by 6%. By comparison, the 0°C surface assumption leads to an overestimation of ablation of 29% in this study where the mean annual air temperature is about −8°C.

Temporal trends related to recent climatic fluctuations are extracted from the longest glacier-wide winter and summer mass-balance series recorded in the Alps, at Glacier de Sarennes, France. For this, all point balances measured at the glacier surface are used, and different statistical models are developed and tested. First, Lliboutry’s linear variance analysis model is extended to the two seasonal components of the balance. The explicit modelling of variability sources and correlations is proved useful for appropriately quantifying uncertainties in the different components of the balance and estimating missing data. Next, a non-exchangeable structure is added to model the winter and summer balance time series. Two change points separating different underlying trends are thus detected. The first change was in 1976, with a shift of +23% in the winter balance. The second was in 1982 for the summer balance series. These systematic changes explain 20–30% of the variability of the different components of the balance, the rest being made up of random interannual fluctuations. Simplified and/or less physically based models are less efficient in capturing data variability. As a result, the cumulative glacier-wide balance shows systematic parabolic trends, which result in an accelerated mass loss for Glacier de Sarennes over the last 25 years.

Little quantitative information is available concerning the size of ice particles in the turbulent clouds of powder-snow avalanches. To quantify particle size distributions, we have developed an experimental device that collects particles in real-scale powder avalanches. The device was placed on the concrete bunker of the Swiss Vallée de la Sionne avalanche dynamics test site. On 31 January 2003, a large powder-snow avalanche struck the bunker and we were able to collect particle samples. The collected particles have been photographed and the pictures digitized. An image analysis tool allows us to determine an equivalent particle radius. The captured particles have a geometric mean of 0.16 mm; the largest particles were 0.8 mm in size and the smallest particles 0.03 mm.

An approximation to the first-order momentum balance with consistent boundary conditions is derived using variational methods. Longitudinal and lateral stresses are treated as depth-independent, but vertical velocity gradients are accounted for both in the nonlinear viscosity and in the treatment of basal stress, allowing for flow over a frozen bed. A numerical scheme is presented that is significantly less computationally expensive than that of a fully three-dimensional (3-D) solver. The numerical solver is subjected to the ISMIP-HOM experiments and experiments involving nonlinear sliding laws, and results are compared with those of 3-D models. The agreement with first-order surface velocities is favorable down to length scales of 10 km for flow over a flat bed with periodic basal traction, and ∼40 km for flow over periodic basal topography.

Time series of observed microwave brightness temperatures at Dome C, East Antarctic plateau, were modeled over 27 months with a multilayer microwave emission model based on dense-medium radiative transfer theory. The modeled time series of brightness temperature at 18.7 and 36.5 GHz were compared with Advanced Microwave Scanning Radiometer–EOS observations. The model uses in situ high-resolution vertical profiles of temperature, snow density and grain size. The snow grain-size profile was derived from near-infrared (NIR) reflectance photography of a snow pit wall in the range 850–1100 nm. To establish the snow grain-size profile, from the NIR reflectance and the specific surface area of snow, two empirical relationships and a theoretical relationship were considered. In all cases, the modeled brightness temperatures were overestimated, and the grain-size profile had to be scaled to increase the scattering by snow grains. Using a scaling factor and a constant snow grain size below 3 m depth (i.e. below the image-derived snow pit grain-size profile), brightness temperatures were explained with a root-mean-square error close to 1 K. Most of this error is due to an overestimation of the predicted brightness temperature in summer at 36.5 GHz.

Imaging spectroscopy is emerging as a critical tool in our ability to move beyond simple detection of changes in cryosphere–climate interactions to attribution of these changes to forcings by changes in greenhouse gases and absorbing impurities (Dozier and others, 2009; Singh and others, 2010). Fresh in the growing literature related to imaging spectroscopy of snow and ice, Singh and others (2010) have explored the impact of dust on the hyperspectral reflectance of snow with the intent of understanding the capacity of imaging spectroscopy to quantify snow properties. The paper reaches relatively robust conclusions about the impact of soil on snow reflectance. As such, the efforts of the authors and the importance of their paper in providing foundational work on imaging spectroscopy of the cryosphere should be appreciated.

Isvand is an ice-dammed lake situated on the western flank of Kangiata Nunaata Sermia, a large ice stream from the Inland Ice, producing calf ice into Kangersuneq fjord at the head of Godtha˚bsfjord (Nuup Kangerlua), West Greenland (Fig. 1). This outlet of the Inland Ice is the only significant calving outlet of the ice sheet met with between 628 and 698 N.