The path over a surface with complex topography that a snow avalanche will take is usually not known in advance. To predict avalanche paths over such terrain, we propose a model for the motion of the mass centre of an avalanche over an arbitrary surface. The numerical solution for this model shows that avalanche paths over complex topography are very sensitive to small differences in the avalanche velocity.

The authors of this paper have previously, in 1987, outlined the development of a set of constitutive equations representing the behaviour of avalanching snow, and the resulting equations for fully developed steady shear flow. The present paper considers the development of non-steady two-dimensional shear flow together with the use of a finite-difference programme to calculate snow-avalanche velocities and flow heights in the run-out zone. The numerical results thus obtained are compared with full-scale experimental data. These comparisons indicate that front velocity and run-out distance are simulated well by the model, and that the predicted snow deposits are fairly well in agreement with those actually observed.

Questionnaires concerning slush flows were distributed globally. The purpose of the questionnaire was to determine the geographic distribution of slush-flow activity and also to collect information concerning the most commonly used nomenclature, release conditions, the season of occurrence, the type of terrain most susceptible to slush-flow occurrences, the characteristics of starting zones, paths and run-out zones, geomorphic activity, type of damage likely to result, and hazard control.

Individuals having first-hand experience of the slush-flow process have been identified. The answers to the questionnaire established that slush flows definitely occur in lower latitudes as well as in the Arctic, and that the slush-flow hazard has not yet received the emphasis that it deserves. Heavy rainfall may cause slush flows at any time during winter, especially in areas with a marine west-coast type of climate. Stream channels and shallow depressions are the most common locations of starting zones, while slush-flow frequency seems to be closely related to the permeability of the substratum. Slush flows are a significant geomorphic agent, and it is noteworthy that there has been an increasing encroachment into potential slush-flow zones as a consequence of human activity.

Walking tracks which cross relatively rugged avalanche-prone terrain are becoming increasingly popular in New Zealand. Consequently, there exists the need to develop a methodology by which it will be possible objectively to assess the avalanche hazard in the vicinity of the tracks. This paper outlines some procedures that have been used to map avalanche paths, and introduces modifications to an internationally used highway hazard index employed to quantify the danger to walkers. The Fiordland region of south-west New Zealand is an area of spectacular scenic beauty, made famous by the Milford Track which has been walked by large numbers of tourists since the late nineteenth century. In recent years, avalanches have killed one person on the track, severely damaged a lodge, and destroyed several small bridges. Other walking tracks have been opened to tourists in this century and one of these, the Routeburn Track, is included in this study. Avalanche paths which affected the Milford and Routeburn Tracks were mapped in the field using well-established techniques and applying the results of previous research on the Milford Road, where historical records are available for a period of 50 years. The risk to walkers was assessed with a hazard index which depends on frequency of avalanches, numbers of paths, time taken to traverse each path, and numbers of walkers using the track. Results indicate that the avalanche hazard is low to moderate on the Milford Track and moderate on the Routeburn Track. The management implications of these findings are outlined.

This physics-based two-phase flow model of the mass balance of drifting snow calculates the transport of snow through saltation and suspension, and recognizes the important role of in-transit sublimation on surface-erosion rates. Measurements of the vertical gradient of drifting snow-mass flux and wind speed in the surface-boundary layer indicate the total flux of saltating snow increases linearly with wind speed and is sensitive to the transport threshold. The total flux of suspended snow requires saltation to become established, and increases with the cube of both the total flux of saltating snow and the wind speed. The total suspended flux quickly becomes the dominant transport mode as wind speeds increase beyond threshold levels, and comprises more than 90% of the total flux for wind speeds greater than 15 ms−1. Sublimation rates estimated from wind speed, temperature, and humidity are sufficiently balanced by snow-surface erosion rates to ablate completely snow-packs with depths of the order 200 mm, a typical value for steppe and prairie environments.

The avalanche-hazard index is a numerical expression of damage and loss as the result of an interaction between snow avalanches and vehicles on a road. The index is determined by multiplying the frequencies of moving and waiting vehicles being hit by various types of avalanches by a weighting which indicates the severity of the consequences. The avalanche-hazard index has proved to be a useful decision-making tool for identification of those avalanche paths where control would be most beneficial, for evaluation of options for control measures, and for comparison of the risks for different roads.

The shapes of equilibrium lee drifts formed by snow fences are scaled in proportion to height of snow fences independent of the snow and weather conditions, even in small-scale models, but those of up-wind drifts are not.

Field studies have been made of the snow-collection mechanisms of a snow fence. It has been observed that particles of saltated snow piled up to windward, and that it was the previously suspended particles that were heaped up in the lee drift. It can be shown that the shapes of up-wind drifts vary in different snow and weather conditions because threshold shear stress and drift-snow saltation depend on the physical properties of the surface snow.

Equilibrium lee drifts are scaled in proportion to fence height, because snow and weather conditions have less effect on threshold wind speed for suspension, and the sheltering effect of a fence is scaled in proportion to the height of the fence.

The dimensions of the equilibrium drifts at snow fences were measured, and maximum snow-retention capacity and lee-drift length presented as a function of fence height, fence density, and depth of snow cover.

Twelve years of observation at Austre Okstindbreen, Norway, have demonstrated that the drainage systems of glaciers change with time, both between and within seasons. Random events indicative of instability have been recorded, and disruption of the glacier systems has preceded some outbursts from Kalvtjørna, the glacier-dammed lake. The results of dye-tracer tests suggest that, although discrete systems exist within the glacier, these vary between years. They also demonstrate that some of the water entering the glacier is stored temporarily as the capacities of the systems change. The chemical composition of river water emerging from Austre Okstindbreen differs from year to year, and it is found that both systematic patterns of variation and random deviations from them occur. Although waters of different origin mix within drainage systems, not all systematic patterns of isotopie composition are eliminated by this mixture; diurnal variations are superimposed on longer-term trends, which sheds light on drainage conditions. Between-year differences of within-season trends probably reflect changing spatial patterns of drainage. The general level of oxygen-isotope (δ18O) values of bulk glacier river water in a particular summer is much lower than the values of δ18O for old snow and glacier ice, and indicates the relative contribution of the base-flow component, which may be sustained either by accumulation-area sources or by water release from storage.

Glaciological investigations were carried out on the Greenland ice sheet to help develop plans for a hydro-electric power station to supply energy to Ilulissat/Jakobshavn. The investigations required research on supraglacial and subglacial melt-water drainage in order to delineate water-drainage basins. This involved repeated detailed photogrammetric mapping, radio echo-sounding, hot-water drilling, and mathematical modelling of subglacial drainage. Repeated mappings combine to show an overall stability in the supraglacial drainage pattern, while model calculations for the subglacial conditions show a limited sensitivity in the predicted drainage areas to changes in hydraulic conditions. The investigations provide the basis for setting safer limits for planning hydro-electric power in the area, and give a general understanding of glacier hydrology for a continuous ice cover such as the Greenland ice sheet.

The River Londalselva drains a part of the Søndre Folgefonni ice cap. On maps showing the topography of the basin, two potentially glacier-dammed lakes can be identified, the lakes of Blomsterskardvatn and Sauavatn. Four large floods occurred in the late summer or early autumn periods of the years 1938, 1944, 1948, and 1962, resulting in great damage to the farms in the settlement of Mosnes. After each of the earlier floods, river-protection work was carried out, but after the 1962 flood further protection efforts were considered too expensive and so the settlement was abandoned by its farmers in the mid-1960s. Originally, the floods were believed to result from the emptying of Blomsterskardvatn. However, field studies have revealed that in fact the floods actually orginated in Sauavatn. This paper suggests a possible flood-prevention measure, based on the construction of a 400 m long tunnel from Sauavatn, which would keep water levels low. The cost is estimated at approximately 5 million Norwegian kroner (NOK.) based on an exchange rate of 6.9 NOK = 1 $US in September 1988. The paper also stresses the importance of making proper hydrological investigations in other cases of flood.

A two-dimensional, finite-element calculation was performed to simulate the development of a snowdrift. The underlying two-dimensional topography was taken as the lower boundary, and this changed as the drift developed. The two-dimensional wind field was calculated from the Navier–Stokes equations. The calculation was performed until a quasi-steady state was reached, and the pattern of erosion and deposition was estimated by computing the divergence of snowdrift transport. Considering a snowdrift as a new surface, the wind field was then recalculated. Simulated results were compared with outdoor observations of the wind field and snowdrifts. The results were in fairly good agreement with each other, but more detailed research is regarded as being necessary.

Located south of Grenoble, in the French Alps, Glacier de Sarennes is a small cirque glacier whose mass balance has been measured since 1948.

Field measurements are made after the accumulation period (from October to May) and during the ablation period (from June to September). The main variables for snow are depth, density, and water equivalent for accumulation, together with ice depth and water equivalent for ablation which are used to calculate mass balance and regime. We present an example of the data collected on the glacier during the 1986–87 season, the evolution of the mass balance during the summer of 1987, and the main variables followed during the 40 years of observation, 1948–88. Mass balance, accumulation, and ablation are directly related to precipitation and temperature. Glacier de Sarennes is a simple glacier which has no tongue and no ice movement, and is like a gigantic rain gauge. The evolution of its mass balance is simply related to the meteorological variables of the year. For more significant and complex glaciers, it is necessary to take account of past as well as present meteorological variables.

Lake Arsine, a pro-glacial lake in the French Alps, first appeared 30 years ago and has since been growing steadily. In 1985, it reached an area of 5.9 ha, a maximum depth of 39 m, and a volume of 0.8 × 106 m3. This lake is dammed partially by a glacial moraine and partially by a tongue of dead ice covered by a moraine 1–2 m thick. The glacier calves into the lake, which collects all the melt water from the surrounding glacial area of 250 ha. No open outlet exists and seepage reaches a value of 5 × 106 m3 year−1. A 1 year water balance shows that seepage increases rapidly with water level, from less than 0.03 m3 s−1to more than 0.75 m3 s−l for a rise in water level of 10 m. The seasonal lake-volume fluctuations of 0.5 × 106 m3 are small compared with the inflow volume of 5 × 106 m3.

Progressive clogging of the bottom by glacial flour has led to a gradual rise of 8 m in 16 years in the summer level, while at the same time the height of the dam has decreased by 10 m due to the melting of dead ice. Consequently, by the end of July 1985 the freeboard was only 2 m and overflow on to the dead ice was thought likely to occur in the very near future. To eliminate this flood hazard, a 250 m long channel was dug in an ice-free zone which had been profiled by geophysical prospecting. This work was carried out between 14 April and 13 June 1986, in order to benefit from the low winter water level.

Geotechnical studies of the moraine have shown that no large landslide is to be feared. A crude model of the waves created by calving shows that the new water level is safe and the channel is capable of handling the maximum likely discharge of 15 m3 s−1 resulting from the highest possible wave of 3.5 m.

Between 70 and 80% of the total annual run-off from the Upper Indus Basin originates from heavy snowfall and glacierized basins at elevations greater than 3500 m a.s.l. However, very little is known concerning the mountainous headwaters of the Indus. This is especially true with respect to the amount of snowfall in the major source area, the high Karakoram. Recent studies of high-altitude alpine glaciers indicate that geochemical dating techniques can accurately and confidently identify seasonal and annual stratigraphy within snow pits and ice cores, and thus can be used to determine the seasonal and annual rate of snow accumulation. In addition, chemical records can usually be employed to determine sources of precipitation. Six snow pits, each 5–10 m deep, were investigated in the accumulation zones of the Biafo and Khurdopin Glacier basins. Both accumulation zones are characterized by broad, open basins separated by steep, narrow ridges in which direct precipitation is the dominant form of nourishment. Seasonal stratigraphy is delineated through an analysis of the seasonal variation in the chemical and physical characteristics of the snow-pack. Annual snow accumulation in the Biafo Glacier basin ranges from 0.9 to 1.9 m water equivalent; maximum accumulation occurs in the elevation band 4900–5400 m a.s.l. Roughly one-third of this snow accumulation occurs during the summer.

Source areas of snow-melt run-off vary spatially and temporally, with corresponding changes in chemistry of the snow-pack, and influence both timing and quality of snow-pack run-off. In the the alpine basin of Emerald Lake, located in the southern Sierra Nevada, California, U.S.A., we have found that nitrate ion and sulphate ion concentrations in streams were correlated with the amount of snow melt in each sub-basin. Inflows to Emerald Lake had elevated concentrations of , and , which corresponded temporally with the initiation of snow melt in each sub-basin. Concentrations of both anions then decreased as snow melt progressed. The onset of snow melt shifted temporally from sub-basins with a south-westerly aspect to basins with a progressively more northerly aspect. The and pulses also moved, with time, from the sub-basins with south-westerly aspects to those with more northerly aspects. The time span over which the basin experienced these anionic pulses was longer than that for any single sub-basin. Maximum concentrations of and in the lake outflow, which also occurred at the onset of snow melt, were elevated by 100 and 40%, respectively, above their January concentrations in line with increases in inflow, but were sustained for a longer period than that of any inflow increase.

One of the main aims of the Snow and Ice Hydrology Project, a joint Canada-Pakistan endeavour, is to estimate ice loss in the ablation areas of glaciers in order to predict with greater confidence stream flow in the headwaters of the Indus River. To this end, Miar Glacier, located in the central Karakoram Range, north of Gilgit, was intensively studied during the summers of 1986 and 1987.

Measurements of glacier mass balance by the monitoring of accumulation and ablation at stake locations is very difficult in the Himalyan environment. It is usually almost impossible to reach elevations above the equilibrium line without major effort, and always very difficult once there to make meaningful measurements; the ablation areas are often heavily crevassed and/or debris-covered, and this poses difficult sampling problems.

The method used in this study was to monitor annual surface movement on a cross-profile as near as possible to the equilibrium line. The measurements, obtained in conjunction with depth soundings made on the same profile, allow the annual ice flux through the cross-profile to be calculated. If an approximately steady-state glacier is assumed, it would be expected that this flux would be roughly equivalent to the rate of ice loss below the profile.

The movements of wooden stakes drilled into the glacier were monitored throughout each of the summers and, since two of the stakes survived the intervening winter, this allowed calculation of annual movement. Distances between the crests of ogives were also surveyed, providing an independent assessment of glacier movement. Depth measurements by radio-echo sounder were successfully made in the summer of 1987, showing maximum ice depths of 550 m. The annual ice flux through the transverse profile was estimated as 5.67 × 107 m3, which corresponds to a mean annual ice loss from the glacier surface below the profile of 8.10 m of ice.