A brief description of the resistivity method is given, stressing the points which are of particular importance when working on glaciers. The literature is briefly reviewed.

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.

A number of improvements have been made to an existing two-dimensional ice-flow model applied to an alpine glacier. Analysis of the results of the existing model revealed several shortcomings. The first concerns the lack of mass conservation of the applied alternating-direction-implicit (ADI) scheme. A semi-implicit (SI) scheme is therefore proposed and the effects on mass conservation assessed by a comparison with the ADI scheme. The comparison is first carried out with a simple theoretical glacier for which the improvement is significant. Concerning the real case of Glacier de Saint-Sorlin, France, the initial deviation in mass conservation was much less pronounced such that the new scheme, although improving mass conservation, does not significantly change the modelled dynamics. However, other shortcomings that have a more profound impact on the modelling of glacier behaviour have been identified. The ice thickness may become negative over some gridpoints, leading to an inconsistency. The problem is partly resolved by incorporating extra checks on critical gridpoints at the glacier border. Finally, with the help of ice particle tracking, unrealistic ice settlement above the bergschrund has been identified as the main reason for spurious dynamic effects and has been corrected.

Seasonal variations in sodium concentrations have been measured on surface-pit snow samples and on firn and ice core samples from the Ross Ice Shelf, Antarctica. Site locations include J-9 (82° 22’ S., 168° 40’ W.), Roosevelt Island dome (79° 22’ S, 161° 40’ W), C-7-1 (78° 30’ S., 177° 00’ W.), and C-7-3 (78° 20’S., 179° 51’ E.). The predominant source for the Na is sea salt, indicated by greater concentration levels at seaward sites. Al concentrations of the order of only 10–9 g/g show that the input of continental dust is comparable to that at inland Antarctic locations, and that dust contributes only a negligibly small fraction of the Na on the shelf. Maximum Na concentrations occur in the winter or early spring, as is the case for Greenland ice. The annual accumulation-rate at J-9, determined by counting Na concentration peaks with depth, is 90 kg m–2 year–1, in agreement with rates determined radiometrically. Annual cycles in Na concentration are also detectable at depth in the J-9 ice core. It is suggested that Na concentration is a useful diagnostic criterion for distinguishing between East Antarctic ice (10–8 g Na/g), West Antarctic ice (30 × 10–9 g Na/g), and ice that fell as snow on the shelf itself (> 30 × 10–9g Na/g). The transition between snow that is chemically characteristic of the ice-shelf regime to snow of an inland regime is expected to occur near the 500 m elevation contour. This position is up to 200 km inland of the grounding line. A model is presented for the large-scale decrease in Na concentration with distance inland within the ice-shelf regime. Since deeper ice in Ross Ice Shelf cores originated generally further from the ocean, the up-stream origin of shelf ice may be estimated from the chemical profile. The Little America V ice-core chemistry profile shows no discontinuity as would be expected if a recent surge of West Antarctic ice had occurred.

Water-pressure fluctuations beneath glaciers may accelerate rock fracture by redistributing stresses on subglacial bedrock and changing the pressure of water in bedrock cracks. To study the potential influence of water-pressure fluctuations on the fracture of subglacial bedrock, ice flow over a small bedrock step with a water-filled cavity in its lee is numerically modeled, and stresses on the bedrock surface are calculated as a function of transient water pressures in the cavity. Stresses on the bed are then used to calculate principal stress differences within the step. Rapid reductions in cavity water pressure increase principal stress differences in the bed, increasing the likelihood of crack growth in the step and the formation of predominantly vertical fractures. Relatively impermeable bedrock may be most susceptible to fracturing during water-pressure reductions because high water pressure in cracks within the rock can be maintained, as water pressure decreases in cavities. These results, when considered in conjunction with the strong likelihood that increases in water pressure accelerate the removal of rock fragments loosened from the bed, suggest that in zones of ice-bed separation where water-pressure fluctuations typically are large, rates of quarrying may be higher than along other parts of glacier beds.

In a series of papers, Bartelt and co-workers developed novel snow-avalanche models in which random kinetic energy (RKE) RK (a.k.a. granular temperature) is a key concept. The earliest models were for a single, constant density layer, using a Voellmy model but with RK-dependent friction parameters. This was then extended to variable density, and finally a suspension layer (powder-snow cloud) was added. The physical basis and mathematical formulation of these models are critically reviewed here, with the following main findings: (i) Key assumptions in the original RKE model differ substantially from established results on dense granular flows; in particular, the effective friction coefficient decreases to zero with velocity in the RKE model. (ii) In the variable-density model, non-canonical interpretation of the energy balance leads to a third-order evolution equation for the flow depth or density, whereas the stated assumptions imply a first-order equation. (iii) The model for the suspension layer neglects gravity and disregards well-established theoretical and experimental results on particulate gravity currents. Some options for improving these aspects are discussed.

A degree-day glacier mass-balance model is coupled to a dynamic glacier model for temperate glaciers. The model is calibrated for two outlet glaciers from the Hofsjökull ice cap in central Iceland. It is forced with a climate scenario that has recently been defined for the Nordic countries for the purpose of outlining the hydrological consequences of future greenhouse warming. The scenario for Iceland specifies a warming rate of 0.25°C per decade in mid-summer and 0.35°C per decade in mid-winter with a sinusoidal variation through the year. The volume of the glaciers is predicted to decrease by approximately 40% over the next century, and the glaciers essentially disappear during the next 200 years. Runoff from the area that is presently covered by the glaciers is predicted to increase by approximately 0.5 m a−1 30 years from now due to the reduction in the volume of the glaciers. The runoff increase reaches a flat maximum of 1.5–2.0 m a−1 100–150 years from now and levels off after that. The predicted runoff increase leads to a significant increase in the discharge of rivers fed by meltwater from the outlet glaciers of the ice cap and may have important consequences for the operation and planning of hydroelectric power plants in Iceland.

We investigate the errors caused by neglecting the crystal-orientation fabric when inferring the basal friction coefficient field, and whether such errors can be alleviated by inferring an isotropic enhancement factor field to compensate for missing fabric information. We calculate the steady states that arise from ice flowing over a sticky spot and a bedrock bump using a vertical-slab numerical ice-flow model, consisting of a Weertman sliding law and the anisotropic Johnson flow law, coupled to a spectral fabric model of lattice rotation and dynamic recrystallisation. Given the steady or transient states as input for a canonical adjoint-based inversion, we find that Glen's isotropic flow law cannot necessarily be used to infer the true basal drag or friction coefficient field, which are obscured by the orientation fabric, thus potentially affecting vertically integrated mass fluxes. By inverting for an equivalent isotropic enhancement factor, a more accurate mass flux can be recovered, suggesting that joint inversions for basal friction and the isotropic flow-rate factor may be able to compensate for mechanical anisotropies caused by the fabric. Thus, in addition to other sources of rheological uncertainty, fabric might complicate attempts to relate subglacial conditions to basal properties inferred from an inversion relying on Glen's law.

Dirty snow avalanches have been observed to carry considerable amounts of rock debris on to lake ice at the foot of scree slopes. As ice breaks up in the spring thaw, this material is carried back and forth on ice floes and is gradually deposited in the lake. In some areas this produces typical drop stones of rock debris in predominantly fine-grained deposits. Most avalanche debris is very angular which enables avalanche drop stones to be differentiated from those of glacial or other drift-ice origins. However, where avalanches incorporate glacial debris, such deposits may be indistinguishable from those formed by floating glacier ice.

Arches in stratigraphic layers directly under a flow divide (Raymond bumps) are predicted by models of steady ice-sheet flow, and have been observed in several ice domes. Here, we model the evolution of these layers when a formerly stationary divide migrates rapidly to a new position, then again becomes stationary, leaving the arched layers in a flank position. As they are then carried downstream with the flow, these abandoned arches can develop into recumbent folds. These folds can occur over a wide range of divide migration speeds. The shearing flow that produces these recumbent folds also distributes the folded layers over a wide distance downstream from the original divide location. If the divide offset is abrupt, ‘pre-cores’, or material lines comprising core-relative isochrones, can be used to quickly identify portions of an abandoned Raymond bump that would be overturned at any future ice-core site downstream. If, as appears to be the case in Greenland, the divide is never stable long enough to produce a mature arch, folds of this type would not occur. The most likely place to find such folds might be the flank of an ice ridge bounded by unsteady ice streams.

We address the usefulness of the unstable manifold correction (UMC) in a Picard iteration for the solution of the velocity field in higher-order ice-flow models. We explain under- and overshooting and how one can remedy them. We then discuss the rationale behind the UMC, initially developed to remedy overshooting, and how it was previously introduced in a Picard iteration to calculate the velocity field in higher-order models. Using a laminar-flow experiment with two higher-order model implementations, we demonstrate that it is not overshooting, but undershooting, that is the main problem when using a proper implementation for the calculation of the velocity field in higher-order models. We also consider a variant of the original UMC algorithm that often enables a relatively fast solution, but is theoretically less sound. Therefore, neither the variant nor the original algorithm is suited for these problems. We present a more appropriate, stable and simple relaxed Picard algorithm and demonstrate that, compared to the true Picard iteration and the variant of the original UMC algorithm, it results in a faster solution of the velocity field in higher-order models for problems with real data.

During the North Water Project of the late F. Müller, glaciological studies were carried out on Laika ice cap. In addition to the main climatological investigations, surveying, mapping, mass-balance studies, and englacial temperature measurements were carried out. The mass-balance distribution is strongly determined by the orography. Strong westerly winds erode and transport snow from exposed surfaces, whereas prevailing easterly winds, during precipitation, deposit snow on lee slopes. The balance is negative under the present climate. The history of the glacier-tongue geometry is reconstructed using geomorphological observations and photogrammetric mapping for 1959 and 1971. Englacial temperature measurements revealed a finite layer of temperate basal ice in the ablation zone. The temperature distribution in the accumulation area around the summit of the ice cap is not stationary.

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.

A simple model uses once-daily meteorological values in the U.S. National Centers for Environmental Prediction and U.S. National Center for Atmospheric Research (NCEP–NCAR) re-analysis database to estimate summer balance of South Cascade Glacier, Washington, U.S.A., each year over 1959–99. The rms error, 0.30 m w.e. (r2 = 0.71), is comparable to measurement error. The model relates summer balance linearly to temperature T > 0°C at 2000 m andto snow flux at 1650 m, the altitudes in recent years of the equilibrium line and terminus. The snow flux is the product of the humidity and westerly wind component at 850 hPa when temperature T <+2°C at 1650 m. Temperatures are interpolated linearly between the 850 and 700 hPa levels. Both the positive 2000 m temperature and the snow flux are summed from 26 April to 4 October. When the summer estimates are combined with those from a winter balance model using the same database, the rms error in estimating net balance is 0.40 m (r2 = 0.81). The indicated sensitivities of balance to warming of 1°C are −0.51 m for summer and −0.24 m for winter. On the assumption that the total −0.75 m °C−1 sensitivity exists at all altitudes, a warming of only 0.7°C would be sufficient to overcome the 1986–98 average net balance +0.5 m at the top of the glacier.

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.

Accurately estimating winter surface mass balance on glaciers is central to assessing glacier health and predicting glacier run-off. However, measuring and modelling snow distribution is inherently difficult in mountainous terrain. Here, we explore rigorous statistical methods of estimating winter balance and its uncertainty from multiscale measurements of snow depth and density. In May 2016, we collected over 9000 manual measurements of snow depth across three glaciers in the St. Elias Mountains, Yukon, Canada. Linear regression, combined with cross-validation and Bayesian model averaging, as well as ordinary kriging are used to interpolate point-scale values to glacier-wide estimates of winter balance. Elevation and a wind-redistribution parameter exhibit the highest correlations with winter balance, but the relationship varies considerably between glaciers. A Monte Carlo analysis reveals that the interpolation itself introduces more uncertainty than the assignment of snow density or the representation of grid-scale variability. For our study glaciers, the winter balance uncertainty from all assessed sources ranges from 0.03 to 0.15 m w.e. (5–39%). Despite the challenges associated with estimating winter balance, our results are consistent with a regional-scale winter-balance gradient.

We use a simple energy-conservation model and a model based on Röthlisberger’s theory for steady-state water flow in a subglacial conduit to model water movement between lakes in the Adventure subglacial trench region of East Antarctica during a 1996–98 jökulhlaup. Using available field evidence to constrain the models suggests that water flow would likely be accommodated in a tunnel with a cross-sectional area of 36 m2 and a value for k (the reciprocal of Manning’s roughness parameter) larger than the 12.5 m1/3 s−1 previously calculated. We also use Nye’s theory for time-dependent conduit water flow to model the temporal evolution of conduit discharge, cross-sectional area, water pressure and lake draining and filling during the flood. We initially assume one source and one sink lake. We perform sensitivity tests on the input parameter set, matching modeled source- and sink-lake depth changes with measured surface elevation data. Using a simple function for vertical ice deformation in which surface deformation scales linearly to the lake depth change, we find the scaling factor is of the order 4 × 10−3 of the ice thickness. The most likely value of k lies in the range 55–68 m1/3 s−1, and the ratio of source to sink-lake radii is approximately 1 : 1.4. Finally, we experiment using Nye’s theory to model water movement between one source and three sink lakes. The model fails to produce the observed patterns of water movement as indicated by the surface deformation data.