We use simple numerical and analytical models of ice flow and heat flow to characterize the shape of isochrones and isotherms beneath moving ice divides. Both nonlinear ice flow and reduced accumulation (wind scouring) at a divide can cause reduced downward flow in a region about one ice thickness wide under a divide. Greater downward velocities on the flanks cause isochrones and isotherms to become arched at depth. The magnitudes and shapes of these arches depend on the history of divide position. Arch amplitudes decrease by approximately e−1 for each increase in migration rate of 3–5 times the accumulation rate, the arches become asymmetric, with steeper leading edges and more gentle trailing edges, and the arch apex lags behind the divide. Isochrone and isotherm shapes can be used to infer past divide motions. In advection-dominated ice sheets, isochrone shapes record a longer history of divide position than do isotherm shapes. The opposite is true for diffusion-dominated ice sheets, in which a spatial array of ice-temperature measurements might extend the recorded history of divide position.

Catchment-wide information on glacier snow-cover depth, surface albedo and surface roughness is important input data for distributed models of glacier energy balance. In this study, we investigate the small-scale (mm to 100 m) spatial variability in these properties, with a view to better simulating this variability in such models. Data were collected on midre Lovénbreen, a 6 km2 valley glacier in northwest Svalbard. The spatial variability of all three properties was found to be self-similar over the range of scales under investigation. Snow depth and albedo exhibit a correlation length within which measurements were spatially autocorrelated. Late-winter and summer properties of snow depth differed, with smaller depths in summer due to melt, and shorter correlation lengths. Similar correlation lengths for snow depth and surface albedo may suggest that snow-depth variation is an important control on the small-scale spatial variability of glacier surface albedo. For surface roughness, the data highlight a possible problem in energy-balance studies which use microtopographic surveys to calculate aerodynamic roughness, in that the scale of the measurements made affects the calculated roughness value. This suggests that further investigations of the relationships between surface form and aerodynamic roughness of glacier surfaces are needed.

Increased summer ice velocities on the Greenland ice sheet are driven by meltwater input to the subglacial environment. However, spatial patterns of surface input and partitioning of meltwater between different pathways to the base remain poorly understood. To further our understanding of surface drainage, we apply a supraglacial hydrology model to the Paakitsoq region, West Greenland for three contrasting melt seasons. During an average melt season, crevasses drain ~47% of surface runoff, lake hydrofracture drains ~3% during the hydrofracturing events themselves, while the subsequent surface-to-bed connections drain ~21% and moulins outside of lake basins drain ~15%. Lake hydrofracture forms the primary drainage pathway at higher elevations (above ~850 m) while crevasses drain a significant proportion of meltwater at lower elevations. During the two higher intensity melt seasons, model results show an increase (~5 and ~6% of total surface runoff) in the proportion of runoff drained above ~1300 m relative to the melt season of average intensity. The potential for interannual changes in meltwater partitioning could have implications for how the dynamics of the ice sheet respond to ongoing changes in meltwater production.

The roughness of the snow-free surface of the glacier midre Lovénbreen, Svalbard, has been investigated on scales between 1 mm and 300 m. It is shown that the roughness is reasonably well described by scale-free (fractal) models for scales longer than a few metres and shorter than about 100 mm. However, there is a break in the behaviour between these scales which can be characterized by a definite scale length of 70–500 mm and a root-mean-square height variation between around 6 and 70 mm. The aerodynamic roughness length contributed by these features is estimated to be 0.3–1.5 mm. Features on this scale are consistent with the observed microwave backscattering properties of the glacier.

Suspended-sediment concentrations in melt waters from the Gornera, Gornergletscher, Switzerland, were determined at hourly intervals for periods during the ablation seasons of 1974 and 1975. Rapid erratic fluctuations of suspended-sediment concentration produced peaks which occurred both before and after highest daily flows. Clockwise daily hysteresis rating loops between sediment concentration and discharge included many involutions. Suspended-sediment-concentration-discharge rating curves were different for rising and falling limbs of individual diurnal hydrographs and varied from day to day. Close-interval measurements of sediment concentration and discharge records allow interpretation of the nature of ice–water–sediment interactions at the bed of an Alpine glacier. At Gornergletscher, subglacial sediment is delivered to melt waters flowing in the smaller basal conduits, which often change course suddenly, entraining unworked sediment stored at the bed. During diurnal discharge maxima, sediment concentration in the Gornera is reduced because the rate of increase of water volume outstrips the rate of supply of sediment. The drainage of the ice-dammed lake Gornersee, producing exceptionally high flows, extended the drainage network over large areas of the glacier bed, and evacuated much sediment.

The evaluation of avalanche release depths constitutes a great challenge for risk assessment in mountainous areas. This study focuses on slab avalanches, which generally result from the rupture of a weak layer underlying a cohesive slab. We use the finite-element code Cast3M to build a mechanical model of the slab/weak-layer system, taking into account two key ingredients for the description of avalanche release: weak-layer heterogeneity and stress redistribution via slab elasticity. The system is loaded by increasing the slope angle until rupture. We first examine the cases of one single and two interacting weak spots in the weak layer, in order to validate the model. We then study the case of heterogeneous weak layers represented through Gaussian distributions of the cohesion with a spherical spatial covariance. Several simulations for different realizations of weak-layer heterogeneity are carried out and the influence of slab depth and heterogeneity correlation length on avalanche release angle distributions is analyzed. We show, in particular, a heterogeneity smoothing effect caused by slab elasticity. Finally, this mechanically based probabilistic model is coupled with extreme snowfall distributions. A sensitivity analysis of the predicted distributions enables us to determine the values of mechanical parameters that provide the best fit to field data.

The retreat of glaciers since 1927 in Cordillera Blanca has produced dangerous lakes at the front of many glaciers. All the known data, most of them unpublished, are reviewed. The known aluviones are listed, and those of Chavin, Quebrada Los Cedros and Artesoncocha described in full. In these three cases a breach in the front moraine came from big ice falls into the lake. The protective devices made on the outlets are described, as well as the effects of the big earthquake on 31 May 1970. In the case of Laguna Parón, which keeps its level thanks to infiltrations, the fluctuations of the discharge of the springs as related to the level of the lake from 1955 to 1969 are reported. The projects for lowering the level of Laguna Parón and for emptying Safuna Alta are described. The latter partially emptied in fact by piping after the earthquake, allowing a final solution.

Knowledge of the spatial snow distribution and its interannual persistence is of interest for a broad spectrum of issues in cryospheric sciences. In this study, snow depths derived from airborne laser scanning are analyzed for interannual persistence of the seasonal snow cover in a partly glacierized mountain area (~36 km2). At the end of five accumulation periods, the snow-covered area varied by 16% of its temporal mean. Mean snow depth of the total area ranged by a factor of two (1.31–2.58 m), with a standard deviation of 0.42 m. Interannual correlation coefficients of snow depth distribution were in the range 0.68–0.84. Of the investigated area, 75% was found to be interannually persistent. The remaining area showed variable snow cover from year to year, caused by occasional avalanches and changes in surface topography as a result of glacier retreat. Snow cover underwent a change from a homogeneous distribution on the former glacier surface to a more heterogeneous snow cover in the recently deglaciated terrain. A geostatistical analysis shows interannual persistence in scaling behavior of snow depth in ice-free terrain with scale break distances at 20 m. Scale-invariant behavior of snow depth is indicated over >100 m on smooth glacier surfaces.

The microstructure and stratigraphy of a snowpack determine its physical behaviour. Weak layers or weak interfaces buried under a slab are prerequisites for the formation of dry-snow slab avalanches, and a precise characterization of weak layers or interfaces is essential to assess stability. Yet their exact geometry and micromechanical properties are poorly known. We cast weak layers and their adjacent layers in the field during two winters and reconstructed their three-dimensional microstructure using X-ray microcomputer tomography. The high resolution of 10–20 μm allowed us to study snow stratigraphy at the microstructural scale. We quantified the microstructural variability for 32 centimetre-sized layered samples and we calculated Young’s modulus and Poisson’s ratio by tomography-based finite-element simulations. Layers in a sample could therefore be differentiated not only by a change in morphology or microstructure, but also by a change in mechanical properties. We found a logarithmic correlation of Young’s modulus with density for two different density ranges, consistent with previous studies. By calculating the relative microstructural changes within our samples, we showed that a large change could indicate a potential weak layer, but only when the weak layer and both adjacent layers, i.e. the sandwich, were considered.

Bore-hole photography demonstrates that the glacier bed was reached by cable-tool drilling in five bore holes in Blue Glacier, Washington. Basal sliding velocities measured by bore-hole photography, and confirmed by inclinometry, range from 0.3 to 3.0 cm/d and average 1.0 cm/d, much less than half the surface velocity of 15 cm/d. Sliding directions deviate up to 30° from the surface flow direction. Marked lateral and time variations in sliding velocity occur. The glacier bed consists of bedrock overlain by a ≈ 10 cm layer of active subsole drift, which intervenes between bedrock and ice sole and is actively involved in the sliding process. It forms a mechanically and visibly distinct layer, partially to completely ice-free, beneath the zone of debris-laden ice at the base of the glacier. Internal motions in the subsole drift include rolling of clasts caught between bedrock and moving ice. The largest sliding velocities occur in places where a basal gap, of width up to a few centimeters, intervenes between ice sole and subsole drift. The gap may result from ice—bed separation due to pressurization of the bed by bore-hole water. Water levels in bore holes reaching the bed drop to the bottom when good hydraulic connection is established with sub-glacial conduits; the water pressure in the conduits is essentially atmospheric. Factors responsible for the generally low sliding velocities are high bed roughness due to subsole drift, partial support of basal shear stress by rock friction, and minimal basal cavitation because of low water pressure in subglacial conduits. The observed basal conditions do not closely correspond to those assumed in existing theories of sliding.

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.

We show results from a positive degree-day (PDD) model of Greenland ice sheet (GrIS) surface mass balance (SMB), 1870–2012, forced with reanalysis data. The model includes an improved daily temperature parameterization as compared with a previous version and is run at 1 km rather than 5 km resolution. The improvements lead overall to higher SMB with the same forcing data. We also compare our model with results from two regional climate models (RCMs). While there is good qualitative agreement between our PDD model and the RCMs, it usually results in lower precipitation and lower runoff but approximately equivalent SMB: mean 1979–2012 SMB (± standard deviation), in Gt a−1, is 382 ± 78 in the PDD model, compared with 379 ± 101 and 425 ± 90 for the RCMs. Comparison with in situ SMB observations suggests that the RCMs may be more accurate than PDD at local level, in some areas, although the latter generally compares well. Dividing the GrIS into seven drainage basins we show that SMB has decreased sharply in all regions since 2000. Finally we show correlation between runoff close to two calving glaciers and either calving front retreat or calving flux, this being most noticeable from the mid-1990s.

Satellite imagery has been used to acquire seasonal terminus positions of tidewater Hubbard Glacier, Alaska, USA, from 1992 to 2006. During this 15 year time period, the width-averaged advance of the entire terminus has been ∼620 m at a mean rate of 35 m a−1. Seasonal fluctuation of the terminus ranges from 150 to 200 m on average and varies spatially. A section of the terminus, near a narrow gap where the glacier has now twice closed off 40 km long Russell Fiord, exhibited little to no mean advance during this time period but displayed seasonal fluctuations of 300–500 m. Seasonal variability in surface ice speeds and surface sea-water temperatures was also observed; both are potential forcing mechanisms for terminus fluctuations. Seasonal changes in sea-water temperature of 10–12°C, as well as seasonal changes in subglacial freshwater discharge, are inferred to influence calving and submarine melting at the terminus, driving seasonal variations. Displacements of the medial moraine separating Hubbard and Valerie Glaciers at the terminus suggest surge-like pulses of the latter, with a periodicity of several years. The timing of these pulses suggests they may influence the Hubbard terminus near Gilbert Point and have implications for future closures of Russell Fiord.

In nature, when hazardous geophysical granular flows (e.g. a snow avalanche) impact on an obstacle as they stream down a slope, rapid changes in flow depth, direction and velocity will occur. It is important to understand how granular material flows around such obstacles in order to enhance the design of defense structures. In this study, a three dimensional (3-D) Smoothed Particle Hydrodynamics (SPH) model is developed to simulate granular flow past different types of obstacles. The elastic–perfectly plastic model with implementation of the Mohr–Coulomb failure criterion is applied to simulate the material behavior, which describes the stress states of soil in the plastic flow regime. The model was validated by simulating the collapse of a 3-D column of sand with two different aspect ratios; the results showed that the SPH method is capable of simulating granular flow. The model is then applied to simulate the gravity-driven granular flow down an inclined surface obstructed by a group of columns with different spacing, a circular cylinder and a tetrahedral wedge. The numerical results are then compared with experimental results and two different numerical solutions. The good agreements obtained from these comparisons demonstrate that the SPH method may be a powerful method for simulating granular flow and can be extended to design protective structures.

Ice-marginal Hidden Creek Lake, Alaska, USA, outbursts annually over the course of 2–3 days. As the lake fills, survey targets on the surface of the ‘ice dam’ (the glacier adjacent to the lake) move obliquely to the ice margin and rise substantially. As the lake drains, ice motion speeds up, becomes nearly perpendicular to the face of the ice dam, and the ice surface drops. Vertical movement of the ice dam probably reflects growth and decay of a wedge of water beneath the ice dam, in line with established ideas about jökulhlaup mechanics. However, the distribution of vertical ice movement, with a narrow (50–100 m wide) zone where the uplift rate decreases by 90%, cannot be explained by invoking flexure of the ice dam in a fashion analogous to tidal flexure of a floating glacier tongue or ice shelf. Rather, the zone of large uplift-rate gradient is a fault zone: ice-dam deformation is dominated by movement along high-angle faults that cut the ice dam through its entire thickness, with the sense of fault slip reversing as the lake drains. Survey targets spanning the zone of steep uplift gradient move relative to one another in a nearly reversible fashion as the lake fills and drains. The horizontal strain rate also undergoes a reversal across this zone, being compressional as the lake fills, but extensional as the lake drains. Frictional resistance to fault-block motion probably accounts for the fact that lake level falls measurably before the onset of accelerated horizontal motion and vertical downdrop. As the overall fault pattern is the same from year to year, even though ice is lost by calving, the faults must be regularly regenerated, probably by linkage of surface and bottom crevasses as ice is advected toward the lake basin.

The ice streams feeding the Ross Ice Shelf, Antarctica, have large tidally modulated (sinusoidal and stick–slip) flow, but the interaction with the ice shelf is poorly understood. We show that the flow of the Ross Ice Shelf front, up to ∼650 km from the ice streams, exhibits smooth, sinusoidal motions corresponding to tidal modulation. These observations suggest a possible linking of the ice shelf with the ice streams to form a unified system that responds to small perturbations in stresses associated with ocean tides. If this is the case, the presence of the sinusoidal motion but the absence of stick–slip motion suggests there is damping of very high-frequency signals. The dissimilar signatures of the motions observed in the ice streams and at the front of the ice shelf present challenges to model development aimed at understanding the dynamics of coupled ice-stream/ice-shelf flow and the movement of ice across grounding lines.

Interferometric synthetic aperture radar (InSAR) observations of ice-shelf tidal deformation reveal the wide transition between grounded and floating ice as well as local areas where the ice shelf is only grounded at low tide, a condition that we call ephemeral grounding. Ephemeral grounding creates a subtle, local disturbance on the vertical motion field of the ice-shelf surface in response to changes in oceanic tide which is detected with millimetric precision using InSAR. These ice-shelf features are, however, not expected to produce a noticeable disturbance on the ice-shelf velocity field. To illustrate the influence of ephemeral grounding on ice-shelf creep flow, we use a finite-element model in which ephemeral grounding is incorporated through a variable basal friction coefficient. The results show that while ice rises (permanently grounded areas) have a pronounced influence on the ice-shelf velocity field, areas of ephemeral grounding have a vanishingly small influence. What is thus of most interest is the capacity for observations of ephemeral grounding to reveal subtle changes in ice-shelf thickness over time. We discuss an example in the Thwaites Glacier area, West Antarctica, where multi-year data show how ice rises become ephemeral grounding and subsequently disappear. This result is consistent with the grounding-line retreat and ice thinning of Thwaites Glacier.

Small mountain glaciers are an important part of the cryosphere and tend to respond rapidly to climate warming. Historically, mapping very small glaciers (generally considered to be <0.5 km2) using satellite imagery has often been subjective due to the difficulty in differentiating them from perennial snowpatches. For this reason, most scientists implement minimum size-thresholds (typically 0.01–0.05 km2). Here, we compare the ability of different remote-sensing approaches to identify and map very small glaciers on imagery of varying spatial resolutions (30–0.25 m) and investigate how operator subjectivity influences the results. Based on this analysis, we support the use of a minimum size-threshold of 0.01 km2 for imagery with coarse to medium spatial resolution (30–10 m). However, when mapping on high-resolution imagery (<1 m) with minimal seasonal snow cover, glaciers <0.05 km2 and even <0.01 km2 are readily identifiable and using a minimum threshold may be inappropriate. For these cases, we develop a set of criteria to enable the identification of very small glaciers and classify them as certain, probable or possible. This should facilitate a more consistent approach to identifying and mapping very small glaciers on high-resolution imagery, helping to produce more comprehensive and accurate glacier inventories.

There is growing recognition of the significance of biologically active supraglacial dust (cryoconite) for glacial mass balance and ecology. Nonetheless, the processes controlling the distribution, transport and fate of cryoconite particles in the glacial system remain somewhat poorly understood. Here, using a 216 hour time series of plot-scale (0.04 m2) images, we quantify the small-scale dynamics of cryoconite on Longyearbreen, Svalbard. We show significant fluctuations in the apparent cryoconite area and dispersion of cryoconite over the plot, within the 9 day period of observations. However, the net movement of cryoconite across the ice surface averaged only 5.3 mm d−1. High-resolution measurements of cryoconite granule motion showed constant, random motion but weak correlation with meteorological forcing factors and no directional trends for individual particle movement. The high-resolution time-series data suggest that there is no significant net transport of dispersed cryoconite material across glacier surfaces. The areal coverage and motion of particles within and between cryoconite holes appears to be a product of differential melting leading to changes in plot-scale microtopography, local meltwater flow dynamics and weather-dependent events. These subtle processes of cryoconite redistribution may be significant for supraglacial albedo and have bearing on the surface energy balance at the glacier scale.

The relationship between velocity field and isochrone geometry along a steady flowline of an ice sheet is examined. The method is analytical and based upon the stream function and its vertically normalized form, the normalized stream function (NSF). We show that the slope of the isochrones is the slope of the iso-NSF lines, plus a path term which is the cumulative result of the past trajectory of the ice particles. We illustrate this path term in three different examples: varying basal melting, varying basal sliding (Weertman effect) and varying velocity profile around a divide (Raymond effect). The path term generally counteracts the slope of the iso-NSF lines. In the case of the Raymond effect, it can even lead to depressions surrounding the bumps if the transition from dome to flank velocity profile is sufficiently abrupt.