To better understand the recent wide-scale changes in glacier coverage, we created and compared two glacier inventories covering eastern Nepal, based on aerial photographs (1992) and high-resolution Advanced Land Observing Satellite (ALOS) imagery (2006–10). The ALOS-derived inventory contained 1034 debris-free and 256 debris-covered glaciers with total and average areas of 440.2 ± 33.3 and 0.42 km2 and 1074.4 ± 206.4 and 4.19 km2, respectively. We found that the debris-free glaciers have lost 11.2% (0.7 ± 0.1% a−1) of their area since 1992, whereas the number of glaciers increased by 5% because of fragmentation. The area change was significantly correlated by simple linear regression with minimum elevation (r = 0.30), maximum elevation (r = −0.18), altitudinal range (r = −0.50), glacier area (r = −0.62) and mean slope (r = 0.16), confirming that larger glaciers tended to lose a larger area (but a smaller percentage) than smaller glaciers. The intra-regional analysis of the glacier changes clearly showed higher shrinkage rates in the western massifs compared with the eastern massifs. In addition, 61 small glaciers covering an area of 2.4 km2 have completely disappeared since 1992.

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.

Finely resolved geodetic data provide an opportunity to assess the extent and morphology of crevasses and their change over time. Crevasses have the potential to bias geodetic measurements of elevation and mass change unless they are properly accounted for. We developed a framework that automatically maps and extracts crevasse geometry and masks them where they interfere with surface mass-balance assessment. Our study examines airborne light detection and ranging digital elevation models (LiDAR DEMs) from Haig Glacier, which is experiencing a transient response in its crevassed upper regions as the glacier thins, using a self-organizing map algorithm. This method successfully extracts and characterizes ~1000 crevasses, with an overall accuracy of 94%. The resulting map provides insight into stress and flow conditions. The crevasse mask also enables refined geodetic estimates of summer mass balance. From differencing of September and April LiDAR DEMs, the raw LiDAR DEM gives a 9% overestimate in the magnitude of glacier thinning over the summer: −5.48 m compared with a mean elevation change of −5.02 m when crevasses are masked out. Without identification and removal of crevasses, the LiDAR-derived summer mass balance therefore has a negative bias relative to the glaciological surface mass balance.

A record of volumes of jökulhlaups from the subglacial Grímsvötn lake, Vatnajökull, Iceland, has been derived for the period 1934–91. The change in lake volume during jökulhlaups is estimated from the lake area, ice-cover thickness and the drop in lake level. The jökulhlaup volumes have decreased gradually during this period of low volcanic activity and declining geothermal power. The two jökulhlaups in the 1930s each discharged about 4.5 km3 (peak discharge 25-30 × 103m3s−1). In the 1980s, jökulhlaup volumes were 0.6.-1.2 km3 (peak discharge 2 × 103 m3 s−1). The lake level required to trigger a jökulhlaup has risen as an ice dam east of the lake has thickened. Water flow in a jökulhlaup ceases when the base of a floating ice shelf covering Grímsvötn settles to about 1160 m a.s.l. Apparently, the jökulhlaups are cut off when the base of the ice shelf collapses on to a subglacial ridge bordering the lake on its eastern side. The decline in melting rates has resulted in a positive mass balance of the 160-170 km2 Grímsvötn ice-drainage basin. Comparison of maps shows that the average positive mass-balance rate was 0.12 km3 a−1 (25% of the total accumulation) in the period 1946-87. A gradually increasing positive mass balance has prevailed since 1954, reaching 0.23 km3 a−1 in 1976-86 (48% of total accumulation).

Measurements of natural and artificial radioisotopes (32Si, 210Pb and 137Cs) and oxygen isotopes (δ18O) have been carried out on surface snow and ice, shallow snow pits and an ice core collected from Dokriani Bamak glacier, central Himalaya, to study the dynamics of glacier ice and short-term climatic changes. Based on the 32Si and 210Pb activities in the meltwaters, the age of the snout ice is 400 years and the flow rate of ice along the glacier length is ∼14 m a−1. The specific activity of 137Cs, corresponding to 1963 fallout, in the surface ice at the equilibrium line yields a flow rate of 32 m a−1, a factor of two higher than that derived for the snout ice. The depth variation of 137Cs concentration in a shallow ice core yields a mean accumulation rate of 0.43 m a−1 for the glacier ice over the past decade. The δ18O of snout ice (−13.4‰) is significantly depleted compared to the average value of −9.2‰ in the shallow ice core, indicating that cooler climatic conditions prevailed around AD 1600. Based on the oxygen isotopic ratios in the shallow pits, an “altitude effect” of 0.9‰ per 100 m in δ18O variation is documented for this glacier.

We analyse ice flow and structural glaciology of Shackleton Glacier, a dendritic glacier with multiple icefalls in the Canadian Rockies. A major tributary-trunk junction allows us to investigate the potential of tributaries to alter trunk flow and structure, and the formation of bedrock steps at confluences. Multi-year velocity-stake data and structural glaciology up-glacier from the junction were assimilated with glacier-wide velocity derived from Radarsat-2 speckle tracking. Maximum flow speeds are 65 m a−1 in the trunk and 175 m a−1 in icefalls. Field and remote-sensing velocities are in good agreement, except where velocity gradients are high. Although compression occurs in the trunk up-glacier of the tributary entrance, glacier flux is steady state because flow speed increases at the junction due to the funnelling of trunk ice towards an icefall related to a bedrock step. Drawing on a published erosion model, we relate the heights of the step and the hanging valley to the relative fluxes of the tributary and trunk. It is the first time that an extant glacier is used to test and support such model. Our study elucidates the inherent complexity of tributary/trunk interactions and provides a conceptual model for trunk flow restriction by a tributary in surge-type glaciers.

Ice-sheet modelers tend to be more familiar with the Newtonian, vectorial formulation of continuum mechanics, in which the motion of an ice sheet or glacier is determined by the balance of stresses acting on the ice at any instant in time. However, there is also an equivalent and alternative formulation of mechanics where the equations of motion are instead found by invoking a variational principle, often called Hamilton’s principle. In this study, we show that a slightly modified version of Hamilton’s principle can be used to derive the equations of ice-sheet motion. Moreover, Hamilton’s principle provides a pathway in which analytic and numeric approximations can be made directly to the variational principle using the Rayleigh–Ritz method. To this end, we use the Rayleigh–Ritz method to derive a variational principle describing the large-scale flow of ice sheets that stitches the shallow-ice and shallow-shelf approximations together. Numerical examples show that the approximation yields realistic steady-state ice-sheet configurations for a variety of basal tractions and sliding laws. Small parameter expansions show that the approximation reduces to the appropriate asymptotic limits of shallow ice and shallow stream for large and small values of the basal traction number.

A transverse profile of velocity was measured across Ice Stream B, West Antarctica, in order to determine the role of the margins in the force balance of an active ice stream. The profile extended from near the ice-stream center line, through a marginal shear zone and on to the slow-moving ice sheet. The velocity profile exhibits a high degree of shear deformation within a marginal zone, where intense, chaotic crevassing occurs. Detailed analysis of the profile, using analytical and numerical models of ice flow, leads to the following conclusions regarding the roles of the bed and the margins in ice-stream dynamics:

• (i) The overall resistive drag on the ice stream is partitioned nearly equally between the margins and the bed and, thus, both are important in the force balance of the ice stream.

• (ii) The ice within the chaotic zone must be about 10 times softer than the ice in the central part of the ice stream.

• (iii) The average basal shear stress is 0.06 × 105 Pa. This implies that the entire bed cannot be blanketed by the weak, deformable till observed by Engelhardt and others (1990) near the center of the ice stream — there must be regions of increased basal drag.

• (iv) High strain rates and shear stresses in the marginal zones indicate that strain heating in the margins may be significant.

While the exact quantitative values leading to these conclusions are somewhat model and location-dependent, the overall conclusions are robust. As such, they are likely to have importance for ice-stream dynamics in general.

Historical records are valuable for assessing glacier change in the Canadian High Arctic. Ommanney’s (1969) detailed inventory of Axel Heiberg Island glaciers, based on photography from 1958–59, has been revisited, converted into digital format and compared to glacier extents mapped from 1999–2000 satellite imagery. Our results show that the island-wide ice coverage decreased by 15.92 km2 in the 42 year period, a loss of <1%. However, two trends are apparent: one of advance or minor retreat from basins hosting outlet glaciers from Müller and Steacie Ice Caps, and one of significant retreat, on the order of 50–80%, for independent ice masses, which include valley glaciers, mountain glaciers, glacierets, and ice caps smaller than 25 km2. If the contributions to ice advance of only three surging glaciers are removed, then the island-wide ice loss approaches 60 km2. Furthermore, it is notable that 90% of ice masses smaller than 0.2 km2 disappeared entirely during the 42 year study period, an observation confirmed by field studies. Successful predictions from the original inventory are highlighted and the likely mechanisms driving the observed advances and retreats are discussed.

The temporal and spatial variation in the surface albedo of the Greenland ice sheet during the ablation season of 1991 is investigated. The study focuses on an area east of Søndre Strømfjord measuring 200 km by 200 km and centred at 67°5′ N, 48° 13′W. The analysis is based on satellite radiance measurements carried out by the Advanced Very High Resolution Radiometer (AVHRR). The broad-band albedo is estimated from the albedos in channel 1 (visible) and channel 2 (near-infrared). The results are calibrated with the surface albedo of sea and dry snow.

Satellite-derived albedos are compared with GIMEX ground measurements at three stations. There is a high degree of consistency in temporal variation at two of the three stations. Large systematic differences are attributed to albedo variations on sub-pixel scale.

In the course of the ablation season four zones appear, each parallel to the ice edge. It is proposed that these are, in order of increasing altitude: (I) clean and dry ice, (II) ice with surface water, (III) superimposed ice, and (IV) snow. An extensive description of these zones is given on the basis of the situation on 25 July 1991. Zones I, III and IV reveal fairly constant albedos (0.46, 0.65 and 0.75 on average), whereas zone II is characterised by an albedo minimum (0.34). Survey of the western margin of the Greenland ice sheet (up to 71° N) shows that the zonation occurs between 66° and 70° N.

Devon Ice Cap, Nunavut, Canada, has been losing mass since at least 1960. Laser-altimetry surveys, however, suggest that the high-elevation region (>1200 m) of the ice cap thickened between 1995 and 2000, perhaps because of anomalously high accumulation rates during this period. We derive an independent estimate of thickness change in this region by comparing ∼40 year mean annual net accumulation rates to mean specific outflow rates for 11 drainage basins. The area-averaged rate of thickness change across the whole region is within error of zero (0.01 ± 0.12 m w.e. a−1), but two drainage basins in the northwest are thickening significantly, and two basins in the south are thinning significantly. The laser-altimetry observations are biased towards the drainage basins where we find thickening. Recent changes in the rate of accumulation or the rate of firnification cannot explain the observed thickening, but decreased ice outflow, due to the penetration of Neoglacial cooling to, and subsequent stiffening of, the basal ice, may provide an explanation. Thinning in the south may result from increased ice outflow from basins in which fast flow and basal sliding extend above 1200 m.

Measured subglacial water pressures are frequently higher than theoretical values calculated by assuming that subglacial conduits are straight and either circular or semi-circular in shape. While this may be attributed to errors in the estimates of conduit roughness or ice viscosity, we suggest here an alternative explanation: namely, that the conduits are actually broad and low rather than semi-circular. Good agreement between measured and calculated pressures can be obtained by assuming that the cross-sectional shape of conduits resembles the space between the arc of a circle and its chord. The angle subtended by the arc, θ, is treated as an adjustable parameter. In four cases studied, θ ranged from 2° to 36°.

During the summers of 1987 and 1988, 15 dye-tracer tests from a total of eight injection points were conducted in the ablation area of Midtdalsbreen, a northern outlet of Hardangerjokulen, southern Norway. The spatial and temporal patterns of water discharge, shapes of the dye-return curves, through-flow velocities, dye-recovery rates, dispersivities, and velocity/discharge relationships suggest the existence of distinct catchments beneath the eastern and western halves of the glacier which are characterized by different types of drainage sytem. Experiments on the eastern side were associated with high melt-water discharges and produced short-lived and highly peaked dye-return curves, fast through-flow velocities, high dye-recovery rates, low dispersivity values which decreased through the melt season, and a velocity/discharge relationship with an exponent of 1.0. Experiments on the western side were associated with low melt-water discharges and produced flat, extended dye-return curves which often displayed secondary peaks, slow through-flow velocities, low dye-recovery rates, high dispersivity values which increased during the melt season, and a velocity/discharge relationship with an exponent of 0.6. Comparison of observed through-flow velocities with values calculated theoretically using various hypothetical drainage-system structures suggests that water flows in a major sinuous conduit beneath the eastern half of the glacier and in a system of linked cavities beneath the western half. A model for the seasonal evolution of the whole drainage network is postulated which has important implications for temporal variations in subglacial water pressures and glacier-sliding velocity.

Hydraulic roughness exerts an important but poorly understood control on water pressure in subglacial conduits. Where relative roughness values are <5%, hydraulic roughness can be related to relative roughness using empirically-derived equations such as the Colebrook–White equation. General relationships between hydraulic roughness and relative roughness do not exist for relative roughness >5%. Here we report the first quantitative assessment of roughness heights and hydraulic diameters in a subglacial conduit. We measured roughness heights in a 125 m long section of a subglacial conduit using structure-from-motion to produce a digital surface model, and hand-measurements of the b-axis of rocks. We found roughness heights from 0.07 to 0.22 m and cross-sectional areas of 1–2 m2, resulting in relative roughness of 3–12% and >5% for most locations. A simple geometric model of varying conduit diameter shows that when the conduit is small relative roughness is >30% and has large variability. Our results suggest that parameterizations of conduit hydraulic roughness in subglacial hydrological models will remain challenging until hydraulic diameters exceed roughness heights by a factor of 20, or the conduit radius is >1 m for the roughness elements observed here.

Experimental and theoretical studies on the growth rate of an icicle were carried out as a function of temperature, water-supply rate and wind speed; the relative humidity was also taken into account. The length of an icicle increases by the downward growth of thin dendritic crystals into the supercooled pendant water drop at the tip, and thus the growth is in the crystallographic a-axis direction. The diameter, on the other hand, increases by the freezing of a water film flowing down along the icicle wall. The ratio of measured length-and diameter-growth rates was large, namely 8–32.

Both growth rates increased with decreasing temperature and increasing wind speed. The increase in water-supply rate led to the decrease in the length-growth rate but no significant change in the diameter-growth rate. These results could be well described by a numerical model of icicle growth which takes account of the dendritic growth at the tip and the wall and the effective heat transfer within the turbulent boundary layer around the icicle. A formation mechanism of ribs and hollows is discussed in relation to the flowing and freezing process of water on an icicle wall.

Dispersed facies basal ice – massive (i.e. structureless) ice with dispersed debris aggregates – is present at the margins of many glaciers and, as a product of internal glacial processes, has the potential to provide important information about the mechanisms of glacier flow and the nature of the subglacial environment. The origin of dispersed facies is poorly understood, with several hypotheses having been advanced for its formation, and there is disagreement as to whether it is largely a sedimentary or a tectonic feature. We test these established hypotheses at the temperate glacier Svínafellsjökull, Iceland, and find that none fully account for dispersed facies characteristics at this location. Instead, dispersed facies physical, sedimentological and stable-isotope (δ18O, δD) characteristics favour a predominantly tectonic origin that we suggest comprises the regelation and strain-induced metamorphism of debris-rich basal ice that has been entrained into an englacial position by tectonic processes operating at the base of an icefall. Further thickening of the resultant dispersed facies may also occur tectonically as a result of ice flow against the reverse bed slope of a terminal overdeepening. Lack of efficient subglacial drainage in the region of the overdeepening may limit basal melting and thus favour basal ice preservation, including the preservation of dispersed facies. Despite the relatively low sediment content of dispersed facies ( ∼1.6% by volume), its thickness (up to 25 m) and ubiquity at Svínafellsjökull results in a significant contribution to annual sediment discharge (1635–3270 m3 a−1) that is ∼6.5 times that contributed by debris-rich stratified facies basal ice.

Glacier basal motion is responsible for the majority of ice flux on fast-flowing glaciers, enables rapid changes in glacier motion and provides the means by which glaciers shape alpine landscapes. In an effort to enhance our understanding of basal motion, we investigate the evolution of glacier velocity and ice-marginal lake stage on Kennicott Glacier, Alaska, during the spring–summer transition, a time when subglacial drainage is undergoing rapid change. A complicated record of > 50 m fill-and-drain sequences on a hydraulically-connected ice-marginal lake likely reflects the punctuated establishment of efficient subglacial drainage as the melt season begins. The rate of change of lake stage generally correlates with diurnal velocity maxima, both in timing and magnitude. At the seasonal scale, the up-glacier progression of enhanced summer basal motion promotes uniformity of daily glacier velocity fluctuations throughout the 10 km study reach, and results in diurnal velocity patterns suggesting increasingly efficient meltwater delivery to and drainage from the subglacial channel system. Our findings suggest the potential of using an ice-marginal lake as a proxy for subglacial water pressure, and show how widespread basal motion affects bulk glacier behavior.

Ice-stream dynamics are strongly controlled by processes taking place at the ice/bed interface where subglacial water both lubricates the base and saturates any existing, underlying sediment. Large parts of the former Eurasian ice sheet were underlain by thick sequences of soft, marine sediments and many areas are imprinted with geomorphological features indicative of fast flow and wet basal conditions. Here, we study the effect of subglacial water on past Eurasian ice-sheet dynamics by incorporating a thin-film model of basal water flow into the ice-sheet model SICOPOLIS and use it to better represent flow in temperate areas. The adjunction of subglacial hydrology results in a smaller ice-sheet building up over time and generally faster ice velocities, which consequently reduces the total area fraction of temperate basal ice and ice streaming areas. Minima in the hydraulic pressure potential, governing water flow, are used as indicators for potential locations of past subglacial lakes and a probability distribution of lake existence is presented based on estimated lake depth and longevity.

For the construction of a hydro-electric power station in western Norway, a diversion tunnel was made to collect subglacial melt water under an outlet glacier from the Folgefonni ice cap. Many investigations were carried out by glaciologists and engineers before the project could begin, and several unexpected problems arose during the completion of the project. This paper deals with some of the problems and how they were solved.

To avoid coarse glacier-carried material from being flushed into the water-collecting tunnel system, a large sedimentation chamber was constructed in the bedrock under the glacier. The dimensions of this huge chamber were decided from sediment-transport studies in the glacier stream and from studies of old bottom deposits in a lake close to the glacier front.

Ice-velocity measurements were made on the glacier surface and similar studies were attempted in sub-glacial ice caves made by spraying hot water near the glacier bed, where the ice is 170 m thick.

The subglacial water-drainage system was studied from a horizontal tunnel constructed in the bedrock under the glacier. Some preliminary conclusions are drawn from these studies.

In future, it will still be possible to undertake subglacial studies because inspection tunnels have been left in the bedrock, and the accessibility is relatively good.

The depths and diameters of 158 cryoconite holes were measured at ten positions in the ablation zone of Sermikavsak, West Greenland. It was found that the depths increased on going up the glacier in agreement with other measurements made earlier on polar glaciers. There was no significant correlation of depth with diameter. The relative importance of the combined short- and long-wavelength radiation balances and the transfer of heat by convectional mixing in water-filled holes is discussed. The variations in depth are attributed to changes in the albedo and the bulk extinction coefficient of the surface ice layers on the glacier.