A one-dimensional avalanche dynamics model accounting for vertical density and velocity distributions is presented. Mass and momentum flux distribution factors are derived to incorporate the effect of density and velocity variations within the framework of depth-integrated models. Using experiments of avalanche flows on an inclined snow chute at Dhundhi, Manali, India, we conceptualize snow flow rheology as a Voellmy fluid where the distribution of internal shearing is given by a Newtonian fluid (NF) or Criminale–Ericksen–Filbey fluid (CEFF). Then the generalized mass and momentum distribution factors are computed for these two fluid models for different density stratifications. Numerical solutions are obtained using a total variation diminishing Lax–Friedrichs (TVDLF) finite-difference method. The model is validated with the experimental results. We find that the flow features of the chute experiments are simulated well by the model. The velocities and runout distances are obtained for the Voellmy model with both NF and CEFF extensions for various input volumes, and the optimum values of the model parameters, namely, coefficients of dynamic and turbulent friction, are determined.

Recent advances in the measurement of bedforms beneath active ice streams have been made using ground-based grid profiling using impulse radar systems operating with centre frequencies in the 3–5 MHz range. Surveys of Rutford Ice Stream and Pine Island Glacier have shown that features such as mega-scale glacial lineations with topographic relief of as little as 3 m can be traced for many kilometres downstream under more than 2 km of fast-moving ice. In the discussion of these data, it is often asked ‘How is it possible to map such fine-scale topography with such a low-frequency radar’. In answering that question, the key point is the distinction between the precision of a radar range measurement to a single, isolated reflective interface and the ability to resolve the presence of two closely-spaced interfaces of similar reflectivity (commonly referred to as the vertical resolution). This paper will discuss and illustrate this distinction and use the case study of data acquired over Pine Island Glacier to examine the limits of precision of the radar range measurement.

Stable-isotope (δD and δ18O) data from the Vostok (East Antarctica) ice core are used to explore whether or not subglacial Vostok lake is in isotopic steady state. A simple box model shows that the lake is likely to be in steady state on time-scales of the order of 104–105 years (three to four residence times of the water in the lake), given our current knowledge of north–south and east–west gradients in the stable-isotopic composition of precipitation in the vicinity of Vostok station and Ridge B. However, the lake may not be in perfect steady state depending on the precise location of the melting area, which determines the source region of inflowing ice, and on the magnitude of the east–west gradient in isotopic compositions in the vicinity of Vostok station and Ridge B.

Field measurements on maximum runout from two different mountain ranges in Canada are presented and compared: the Coast Mountains in British Columbia and the Rocky Mountains. We include a statistical analysis of topographic terrain parameters such as starting zone catchment area, horizontal reach, vertical drop and relevant slope angles. Following McClung and Mears (1991), we derived a dimensionless parameter which is a measure of runout for each avalanche and we found that the runout ratios (defined below) for a given mountain range obey a Gumbel distribution consistent with previous results. In addition, we found that the runout ratios for both mountain ranges have a length-scale dependence which is potentially very important for land-use planning procedures: the mean value of the runout ratio decreases significantly as the horizontal reach increases. Together with data from other mountain ranges, our results show that path length effects will have to be incorporated when using statistical prediction methods for engineering zoning purposes.

The runout ratio is defined as the quotient of two lengths, Δx/Xβ, where Δ is the horizontal distance from the 10° point to the maximum runout position, and Xβ is the horizontal distance from the start position to the point where slope angle first declines to 10°.

The ERS-1 satellite has delivered altimetric data since 1992, enabling us to map most of the Antarctic ice-sheet topography south to 82° S with better precision than all previous techniques. An algorithm has been developed such that the accuracy of the height data reaches the sub-metre level. As a first step, an inverse method has been designed to map the large-scale global topography, which is of interest to the study of the ice-sheet flow dynamics. As a second step, an adapted inverse algorithm displays precisely the short-scale undulations which are controlled by the bedrock below the ice. Finally, variations in the back-scattered altimetric signal allow us to map directly the kilometre-scale roughness that is related to the basal-flow conditions. Together, these maps constitute an important data base for modelling the ice sheet.

The Asian–Pacific Oscillation (APO) is a climate pattern related to the thermal differences between the Asian continent and the north Pacific. We present a 1000 year record of the major ions in a 108.83 m ice core from east Rongbuk glacier (28°01′ N, 86°58′ E; 6518ma.s.l.) on the northeast slope of Qomolangma (Mount Everest), and discuss its relationship with a 993 year time series of the summer APO index that has been reconstructed from Beijing’s summer temperature (recorded by a stalagmite) and the Pacific Decadal Oscillation (PDO) index. Empirical orthogonal function (EOF) analysis shows that crustal major ions (Mg2+, Ca2+, SO42– and NO3–) are highly loaded on EOF1, whereas marine major ions (Cl– and Na+) are highly loaded on EOF2. Higher EOF1 is associated with lower upper-troposphere temperature (UTT) over Mongolia, corresponding to a lower APO index and higher surface pressure. Higher EOF2 is associated with higher UTT over Mongolia, corresponding to a higher APO index and lower surface pressure. The higher burden of major ions and higher summer APO index during the period AD 1000–1323 may be due to drought and warm climate of the major-ion source regions. From AD1323 to 1900, EOF1 and EOF2 do not show a consistent correlation with summer APO index, indicating the complex mechanisms of ion transport over the southern Tibetan Plateau (TP) during this period. After AD 1900, the summer APO index is correlated negatively with EOF1 and positively with EOF2, indicating that ion transport over the southern TP during this period is influenced significantly by the APO. Our examinations of the PDO index and major-ion record show that higher PDO corresponds to higher EOF1 and lower EOF2. This suggests that the correlation between the recorded major-ion concentration and the APO index originates in the seesaw relationship in temperature between the Asian continent and the north Pacific.

The seasonal progression of snow melt on the Arctic pack ice is mapped from satellite shortwave imagery (0.4–1.1 micrometers) for four spring/summer seasons (1977, 1979, 1984 and 1985). This provides the first detailed information on the temporal change of the ice surface albedo in summer and of its year-to-year variability. The average surface albedo of the Arctic Basin for the years investigated falls from between 0.75 and 0.80 in early May to between 0.35 and 0.45 in late July and early August. In the central Arctic, where ice concentration remains high and ponding on the ice is limited, the July albedo ranges from 0.50 to 0.60. Overall, melt progresses poleward from the Kara and Barents Seas and from the southern Beaufort and Chukchi Seas, with the melt fronts meeting on the American side of the Pole. There are substantial year-to-year differences in the timing, duration and extent of the melt interval. The progression of melt in May and June of the earliest melt year (1977) was about 3 weeks ahead of the latest year (1979). By late July, the central Arctic was essentially snow free in 1977 and 1979, but more than 50% snow covered in 1984. Although limited in extent, our data base suggests relationships between snow melt and Arctic surface air temperatures in spring, spring cloudiness and the extent of late summer ice.

An explosive detonation in snow produces high intensity shock waves that are rapidly attenuated by momentum spreading as the snow is compacted. Our experimental measurements and numerical calculations indicate that the maximum shock-wave attenuation in seasonal snow (250 kgm−3) is proportional to between x−1.6 and x−3 for plane waves and x−3 for spherical waves (x is the propagation distance). Outside the region of shock-compacted snow or in air over snow, stresses are transmitted as acoustic/seismic waves. Attenuation of these waves depends on snow permeability and the effective modulus of the ice frame and is proportional to about x−0.7 for plane waves in seasonal snow and to about x−1 for spherical waves in air over seasonal snow. Increasing the scaled detonation height of an explosive up to 2mkgf−1/3 above a snow cover increases the far field (scaled distances greater than about 8m kgf−1/3 snow surface pressures. Scaled detonation heights greater than about 2mkgf−1/3 have little additional effect.

Lichenometry was used to date “Little Ice Age” moraines in the Kamchatka peninsula, northeastern Russia. The Rhizocarpon geographicum growth-rate curve was based on seven data points from lava flows and moraines, dated using historical records or tephrochronology (15–300 BP). No reduction in growth rate due to decreasing lichen age was observed, so a linear approximation was used. Accuracy test results yield differences between real and calculated dates up to, but not exceeding, five years. From eight “Little Ice Age” (LIA) moraines it was established that Kamchatka glaciers advanced in the 1690s, 1850–70 and 1910–20. Only one moraine clearly corresponded to the 1690s advance. The maximum stage of the LIA was during the mid- to late 19th century when glacier fronts were generally 100–200 m lower than at present. Glacier termini with ash and moraine layers, covered by lichens and vascular plants, have been preserved for 150–300 years, judging by the lichen sizes.

Results examining variations in the ice extent along the Norwegian coastline based on the analysis of Moderate Resolution Imaging Spectroradiometer (MODIS) images from 2001 to 2019, February through May, are presented. A total of 386 fjords and coastal areas were outlined and grouped into ten regions to assess seasonal and long-term trends in ice extent. In addition, three fjords were examined to investigate how ice extent may vary over short distances (<100 km). Of the 386 outlined, 47 fjords/coastal areas held >5 km2 of ice at least once between 2001 and 2019. Over this span of time, no statistically significant trend in ice extent is found for all ten regions; however, variations between regions and years are evident. Ice extent is assessed through comparison to three weather variables – freezing degree days (FDD), daily new snowfall and daily freshwater supply from rainfall plus snowmelt. Six out of ten regions are significantly positively correlated (p < 0.05) to FDD. In addition, ice in two regions is significantly positively correlated to daily new snowfall, and in one region negatively correlated to rainfall plus snowmelt. The importance of fjord geometry and bathymetry as well as other weather variables including wind is discussed.

This study links two models, one that simulates changes in snow microstructure and one that recovers microstructure properties from measurements of snow reflectance. An energy and mass transfer model, SNTHERM.89, was used to calculate snow grain growth. Grain-sizes from the model and measurements of grain bond areas provided estimates of the surface-to-volume ratio of the bulk snow, which were transformed to geometrically-equivalent sphere sizes. An inversion technique based on a discrete-ordinate model of the directional reflectance recovered optically-equivalent sphere sizes from reflectance measurements at 1.075 μm. The predictions of equivalent sphere sizes from the snow model and the recovered optical sphere sizes from the inversion method were compared with stereological measurements from snow sections. The geometrically-equivalent and optically-equivalent grain-sizes showed good agreement with each other and with stereological measurements from snow a few days old. The predictions of the reflectance inversion method also compared favorably with geometrically-equivalent grain-sizes measured from a melt-freeze surface crust. This investigation showed the potential for fully coupling snow property simulations with models to predict the spectral reflectance of snow.

Glaciofluvial ridges, several hundred kilometres long, are commonly referred to as interlobate moraines because they appear to have formed at the convergence of two distinct ice lobes. Flow convergence is indicated by patterns of striations, streamlined forms and eskers. The so-called interlobate moraines are also thought to have formed asynchronously as the ice margin retreated. By contrast, we argue that the Harricana moraine of northern Quebec, Canada, formed following flow convergence in a regional-scale subglacial outburst flood. Flowlines constructed from streamlined bedforms mapped on the glacial map of Canada, reinterpretation of these streamlined forms as products of meltwater erosion, and field records of erosional marks (S-forms) in bedrock and glaciofluvial deposits to the lee of bedrock highs support this model. The effects of this flow convergence on the ice-sheet topography and drainage controlled the location of the broad conduit in which the Harricana moraine was deposited. Continued flow in this conduit and melting of the conduit walls explain the local patterns of striae, the supply of debris to the conduit, and the morphological and sedimentary characteristics of the moraine itself. From these characteristics, we conclude that the moraine was formed synchronously. This conclusion, if correct, is instructive regarding the deglacial hydrological organization of a large sector of the Laurentide ice sheet.

The impact energy of an avalanche on the flat surface of an instrumented structure has been quantified by full-scale experiments performed at the Lautaret avalanche test site, France. The deformation and acceleration of the structure were measured during the avalanche. The impact energy of the avalanche was calculated from an energy balance via the mechanical energy theorem. First the elastic potential energy and kinetic energy of the structure were calculated from the measured deformations and an adequate mechanical model of the structure. Internal energy dissipation due to material damping and potential plastic deformation was calculated. Finally the mechanical work done on the structure by the avalanche forces was deduced from the energy balance. Results show that the elastic energy is the main component of the energy injected in the structure. The kinetic and viscous components are negligible because of the very low displacement rate of the structure during the impact. Another important result is that the maximum of the mechanical power (work rate) is done when the head of the avalanche impacts the structure. This occurs before the pressure reaches its nominal value, approximately when the product of the pressure by the pressure rate is maximum.

This paper explores the potential of using satellite-derived albedos to estimate the surface mass balance of the Kangerlussuaq transect (K-transect; Greenland ice sheet). We first retrieved surface albedos from Advanced Very High Resolution Radar data by using, among other techniques, a new cloud detection algorithm based on the relation between brightness temperature and surface elevation. We then computed the ‘satellite-derived mass balance’ (bsat) from the mean albedo for the transect, by taking fixed values for atmospheric transmissivity and the longwave and turbulent fluxes. We found that bsat explains 7 1% of the variance in 13 years of stake mass-balance measurements (bm). Our method also provides good estimates of the magnitude of the interannual variability in bm. The performance of the method degrades considerably without correction for anisotropic reflection at the surface and recalibration of the satellite sensors with dry snow at the top of the ice sheet. Sensitivity tests indicate that the method’s performance is hardly sensitive to uncertainties in parameters. Therefore, we expect that the method could be successfully applied on other glaciers and parts of ice sheets and ice caps, especially where accumulation rates are relatively small. We show that the investigated method performs best just below the mean equilibrium-line altitude.

Uniaxial and biaxial compression tests were carried out on ice samples from the 2040 m Vostok ice core. It is shown that the ice viscosity does not significantly change with depth. As a result the high impurity content in glacial ice does not seem to influence the mechanical behavior of the Vostok ice core. The measured enhancement factor, smaller than 1, is caused by the particular orientation of c-axes in this polar ice. It is deduced that the viscosity of Vostok ice for horizontal shear is high compared with that of other ice cores.

Data assimilation techniques are one method by which to improve the quality of model Simulations of Sea ice. The availability of daily gridded fields of Sea-ice motion makes this field one that can be readily assimilated. These fields are generally of higher resolution than forcing values Such as atmospheric wind which are used to drive the model, and on any given day may depict ice circulation that is dramatically different than what the model Solution represents. Typically, a blending method Such as optimal interpolation (OI) is used and corrections are applied to the initial modeled velocity field Such that the new Solution corresponds better with actual observations. However, care must be taken in Such a technique, as the corrections are not applied directly to the model physics, and the underlying physical assumptions in the ice dynamics may be violated. Previous Studies have Shown that improvements in the ice-motion Solution come at the cost of the quality of other modeled fields. The Strength parameterization in Sea-ice models controls the ice velocity in the model, and is obtained in part by comparison with observed motions. Here we investigate the Sensitivity of the Sea-ice model to variations in the Strength parameterization, and determine the effect of using data assimilation to impose observed velocities. We find that the alternation of the frictional loss parameter has limited effect on model performance. Rather, it is the assimilated data that overwhelm and degrade the Solution, bringing into question whether underlying physical assumptions in the model may be compromised.

We have conducted short-term pump experiments with pump pressures exceeding ice overburden to study the seasonality of the subglacial hydraulic system of Engabreen, Norway. Data were collected from load cells installed flush with the ice–bedrock interface and pressure transducers installed in boreholes leading from bedrock tunnels underneath the glacier to the ice–bedrock interface. The water-pressure recordings, seen in relation with the load-cell record, show the existence of hydraulically connected vs unconnected bed areas. Monitored boreholes have been used to inject water at high pressures. Each experiment led to the growth of a high-pressure water cavity whose spatial extent could be inferred from load-cell and pressure transducer records. Post-pump pressures were low after summer pump tests and close to ice-overburden level after winter pump experiments. We conclude that drainage takes place in a fast-flow, low-pressure, channel-based drainage system during summer, and a low-flow, high-pressure, linked-cavity drainage system during winter.

In order to clarify the metamorphic process of snow particles immersed in water, distributions of grain size were examined as functions of time (0.1 to 1 000 hrs) and impurity concentrations. When disaggregated snow particles were immersed in water kept at 0°C, each particle became spherical and grain coarsening took place with time. The average diameter increased with cube root of time and the average volume increased in proportion to time. Grain coarsening was not detected in a kerosene environment.

In solutions of glucose, NaCl, HC1 and dextran, the growth rate was controlled by the concentration and the diffusivity of the solute. The higher concentration and the lower diffusivity, the grain coarsening was controlled. The grain coarsening is explained by the disappearance of relatively small particles and growth of relatively large ones, caused by differences of the equilibrium temperature of each particle if the total ice mass is conserved.

The currently adopted approach for avalanche-hazard mapping in Switzerland includes avalanche-dynamics modelling coupled with estimation of the greatest annual 3 day snowfall depth, H72, for high-return periods, used as the release depth. New advances in avalanche dynamics show that this approach can be improved using models with mass entrainment, requiring in turn a statistical definition of the erodible snow cover. We propose a regional approach, based on index value, to evaluate release depth and erodible snow cover for large-return periods. The territory of Switzerland is divided into seven climatologically homogeneous regions. Generalized extreme value (GEV) distributions for the growth factors coupled with index-value estimation based on altitude provide an accurate estimate of snow depths, also for large-return periods. RAMMS, a two-dimensional avalanche-dynamics model including snow entrainment, is used for hazard mapping for a site used as an example of the Swiss procedure. The regional approach allows the boundary conditions for hazard mapping to be set using an entrainment model, and also provides statistical uncertainty of the design release and erosion depth, thus aiding in applying uncertainty analysis to hazard-mapping procedure.

Using a dynamic-thermodynamic numerical sea-ice model, external oceanic and atmospheric forcings on sea ice in the Weddell Sea are examined to identify physical processes associated with the seasonal cycle of pack ice, and to identify further the parameters that coupled models need to consider in predicting the response of the pack ice to climate and ocean-circulation changes. In agreement with earlier studies, the primary influence on the winter ice-edge maximum extent is air temperature. Ocean heat flux has more impact on the minimum ice-edge extent and in reducing pack-ice thickness, especially in the eastern Weddell Sea. Low relative humidity enhances ice growth in thin ice and open-water regions, producing a more realistic ice edge along the coastal areas of the western Weddell Sea where dry continental air has an impact. The modeled extent of the Weddell summer pack is equally sensitive to ocean heat flux and atmospheric relative humidity variations with the more dynamic responses being from the atmosphere. Since the atmospheric regime in the eastern Weddell is dominated by marine intrusions from lower latitudes, with high humidity already, it is unlikely that either the moisture transport could be further raised or that it could be significantly lowered because of its distance from the continent (the lower humidity source). Ocean heat-transport variability is shown to lead to overall ice thinning in the model response and is a known feature of the actual system, as evidenced by the occurrence of the Weddell Polynya in the mid 1970s.