Fritz Müller (1926–80) was the leader of the Jacobsen-McGill Arctic Research Expeditions to Axel Heiberg Island, Nunavut, Canada. He was a faculty member at McGill University, Montreal, Canada, from 1959 to 1970. Thereafter, he was Chair of Geography at Eidgenossische Techmsche Hochschule, Zürich, Switzerland. He conducted research on Axel Heiberg Island, mainly in the vicinity of Expedition Fiord, from 1959 until his death in 1980. This paper is a personal account of Müller’s work by one of his students, with a commentary on his contributions to Arctic science. The personal account focuses on the early years of the expeditions. The commentary includes discussion of glacier mass-balance records and lake-ice break-up from 1959 to the present, glacier-terminus records from 1948 to the present and other research focused on the region.

The Axel Heiberg Island Expedition of McGill University, Montreal, Canada, led by the late Fritz Müller was the cradle for a number of scientific investigations, not all of them glaciological. During the four years 1969–72, the tundra climate was investigated in the Expedition Area, encompassing about 100 km2 on the mid-west coast of Axel Heiberg Island, Nunavut, Canada. This series of studies identified the main features of the tundra climate, clarified its causal processes and contributed to an understanding of the differences between tundra climates and those of the neighboring regions with glaciers, ocean surfaces and boreal forests. A fundamental consideration of climate processes on a global scale was conceived during this time. Some significant results are recorded here to commemorate Fritz Müller’s contributions as a polar scientist and a university educator.

A hydrometeorological model designed for climatological applications with monthly time-steps and 100 m altitude intervals was calibrated with runoff and climate data on five small, glacierized basins in the Silvretta mountains, Austria (46°55’ N, 10° 10’ E). These basins are exposed to similar synoptic weather conditions but differ in their altitude ranges and glacier covers, enabling the model to be tested for a variety of physical conditions. The structure of the model, the data input and the calibration and tuning procedures are described. Sensitivities of the model to temperature and precipitation changes are derived and applied to annual and decadal values of T and P, respectively. Judged by the difference between observed and calculated sums of runoff, simulation of decadal values is satisfactory, while annual simulations and measurements have rms differences of the order of 200 mm.

The water balance of Alpine regions is strongly determined by the storage of water in the form of snow and ice On the basis of long time series of daily precipitation, air temperature and discharge, the conceptual runoff model HBV3–ETH9 was applied to various basins of the eastern Alps showing a glacierization of 0–80%. Using the results of regional climate modelling under the assumption of doubling of C02 , the meteorological input data files were altered taking into account more frequent hot days and additional connective precipitation events during the summer months, and the consequences of these changes for daily discharge were evaluated. The results show that in regions with insignificant glacierization, runoff reacts primarily to changes in precipitation, and less so to rising summer air temperature. In highly glacierized basins, however, the same scenarios suggest strongly enhanced water yields in an initial phase. Higher flood peaks will result when high melt rates and heavy summer rains coincide. If glacier mass losses continue in the more distant future, the glacierized area will diminish and summer discharge will be gradually reduced, resulting in drastic water shortages in hot, dry summers once the glaciers have disappeared.

Analysis of aerial photographs of about 1000 glaciers located in the mountain ranges of the former Soviet Union –Caucasus, Polar Urals, Pamir-Alay, Tien Shan, Altay, Kodar, Cherskiy range, Suntar-Khayata, Koryakskoye Nagorye, Kamchatka–shows that variations in the magnitude of glacier retreat since the Little Ice Age maximum are significant and probably connected to climatic continentality. On average, the scale of glacier shrinkage is much smaller in continental Siberia than in central Asia and along the Pacific margins.

A carefully homogenized climate dataset is used to interpret glacier behaviour in the Austrian Alps. Periods of glacier advance are generally more maritime and cooler, with reduced sunshine duration and increased precipitation sum during the ablation period. Periods of retreat are associated with a more continental, warmer climate, with increased sunshine duration and reduced precipitation sum. Three recent sub-periods of Austrian glacier behaviour are documented by direct measurement of glacier mass balance (before 1965 more negative; 1965–81 more positive; since 1982 more negative). A long-term mass-balance series in the eastern part of the Austrian Alps parameterized by snow-depth measurements indicates very clearly that periods of more negative mass balance have a higher correlation to summer air temperature and a lower correlation to winter accumulation. Periods of more positive mass balance are highly correlated to winter accumulation and only slightly correlated to summer temperature. The positive mass-balance period 1965–81 is also characterized by negative North Atlantic Oscillation index values which caused an increased meridional circulation mode, resulting in a northwesterly to northerly precipitation regime during winter.

Most glaciers in the Northern Hemisphere reached their postglacial maximum in recent times, that is, after the medieval period. During the last 100 or 150 years a significant retreat has taken place, and there is little sign that this is coming to an end. The current worldwide shrinkage of glaciers is considered to be a strong indication of global warming. However, glacier retreat should be judged against the natural variability of glacier systems. Numerical glacier models can be used to quantify this variability. I have studied the natural variability of three glaciers for which long historic records of glacier length exist: Nigardsbreen, Norway; Rhonegletscher, Switzerland; and Franz Josef Glacier, New Zealand. Integrations for a 10 000 year period, driven by random forcing of a realistic strength, show that the current retreat cannot be explained from natural variability in glacier length and must be due to external forcing.

The kinematic boundary condition at the glacier surface can be used to provide glacier mass balance at individual points if changes in surface elevation, horizontal and vertical surface velocities and surface slope are known. Vertical ice velocity can in turn be estimated from basal slope, basal ice velocity and surface strain. This relation is applied to reconstruct a 20 year mass-balance curve of Grubengletscher, Swiss Alps, largely using repeated aerial photogrammetry, with only a minimum of fieldwork For individual years the mass-balance distribution on the glacier tongue was modelled with an accuracy of about ±0.9 m a"1. Ice-mechanical assumptions and errors in glacier bed geometry markedly affect discrete mass-balance patterns but are largely eliminated in the calculation of year-to-year mass-balance changes The resulting 1973–92 curve for the Grubengletscher tongue shows reasonable consistency with meteorological data and other glaciologically derived mass-balance series. Large changes in measured ice speed on the glacier tongue (±50%) significantly governed the long-term variability of ice thickness over the observational period.

The impact of spatial and temporal variations in the surface albedo and aerodynamic roughness length on the surface energy balance of Haut Glacier d’Arolla, Switzerland, was examined using a semi-distributed surface energy-balance model (Arnold and others, 1996). The model was updated to incorporate the glacier-wide effects of albedo and aerodynamic roughness-length variations using parameterizations following Brock (1997). After the model’s performance was validated, the glacier-wide patterns of the net shortwave, turbulent and melt energy fluxes were examined on four days, representative of surface conditions in late May, June July and August. In the model, meteorological conditions were held constant on each day in order that the impact of albedo and aerodynamic roughness-length variations could be assessed independently. A late-summer snowfall event was also simulated. Albedo and aerodynamic roughness-length variations, particularly those associated with the migration of the transient snowline and the decay of the winter snowpack, were found to exert a strong influence on the magnitude of the surface energy fluxes The importance of meteorological conditions in suppressing the surface energy fluxes and melt rate following a fresh snowfall was highlighted

Data from automated in situ measurements of surface displacements on Unteraargletscher, Bernese Alps, Switzerland, made a few times a day from late June until late October 1998 are presented. Two short-term speed-up events were observed, and partial evidence for a third motion event was seen. Short-term motion events are thus not limited to the start of the melting season. Strong correlation between the timing of the motion events and periods of heavy rainfall, in conjunction with the large size of the area of the glacier which becomes activated during the events, both point towards an external triggering mechanism. In the time periods between two motion events, surface velocities do not vary significantly with time. After a motion event, surface velocities do not return to previous values, suggesting that the events have a lasting effect on the structure of the subglacial drainage system.

A flow model for cold firn proves to be very successful in calculating the age-depth relation of several deep ice cores drilled on Colle Gnifetti, Monte Rosa, Swiss Alps. The compressibility of firn is taken into account by an appropriate constitutive equation, first employed in glaciology by Gagliardini and Meyssonnier (1997), which is implemented in a finite-element code. Flow models of the Colle Gnifetti saddle glaciation in two and three dimensions are based on digital elevation maps of the surface σnd the bedrock, based on radio-echo soundings of the ice thickness. Firn density and the englacial temperature fields are either prescribed or calculated in coupled models. Measured surface velocities, density profiles, the ages of chemically dated layers in ice cores and the closure of a 100 m deep borehole provide benchmarks for the models. The good agreement of modeled and measured quantities confirms that the model includes the relevant physical processes and particularly that the firn flow law is well suited for this type of glacier. The study provides new constraints on the age of the ice near the base as well as the source regions of the ice in the cores.

An exceptional flow behavior of the basal ice layer was detected in measurements of borehole closure and inclination. Measurtxl6ed deformation rates exceed upper bounds derived from the flow models, and are thus attributed to altered rheological properties.

Moraines of the Younger Dryas ˚Egesen Stadial", which are widespread features in the Alps, are a valuable terrestrial data source for quantitative palaeoclimatic studies. The depression of the early Younger Dryas (Egesen-I) equilibrium-line altitude (ELA) shows a distinct spatial pattern. It was greatest (about –450 to –500 m vs present day) m areas exposed towards the west and northwest. In the central, more sheltered valleys it was on the order of –300 m or less. Summer temperature depression, which can be derived from the Younger Dryas timberline depression, was on the order of –3.5 K. The stochastic glacier-climate model of Ohmura and others (1992), which relates summer temperature and precipitation at the ELA, is used to infer precipitation change. Results are compared with those obtained from the glacial-meteorological approach of Kuhn (1981a). The two models produce highly similar results. During the early Younger Dryas, climate in the central valleys of the Alps seems to have been considerably drier than today In areas open to the west and northwest, precipitation seems to have been the same as today or even slightly higher. These results, which are based on a rather dense network of data points, agree well with results from permafrost-climate studies and the more qualitative information from palaeobotanical research. They also support the results from atmospheric general circulation models for the Younger Dryas in Europe, which point towards a more zonal type of circulation.

To obtain more reliable information about the focal-depth distribution of icequakes, in April 1997 we operated an array of seven portable digital seismographs on Unteraargletscher, central Swiss Alps. Over 5000 events were detected by at least two instruments during the 9 day recording period. P-wave velocities (3770 m f) were determined from several calibration shots detonated at the glacier surface as well as in a 49 m deep borehole, whereas S-wave velocities (1860 ms–1) were derived from a simultaneous inversion for Vp/Vs6 applied to 169 icequakes. So far, hypocentral locations have been calculated for over 300 icequakes. Besides confirming the occurrence of shallow events associated with the opening of crevasses, our results show that a small but significant fraction of the hypocenters are located at or near the glacier bed. One event was found at an intermediate depth of about 120 m. Three-dimensional particle-motion diagrams of both explosions and icequakes clearly demonstrate that all vertical component seismograms from shallow sources are dominated by the Rayleigh wave. On the other hand, for events occurring at depths greater than about 40 m, the Rayleigh wave disappears almost entirely. Therefore, a qualitative analysis of the signal character provides direct information on the focal depth of an event and was used as an independent check of the locations obtained from traditional arrival-time inversions. Thus, our results demonstrate that deep icequakes do occur and that simple rheological models, according to which brittle deformation is restricted to the uppermost part of a glacier, may need revision.

Measurements of summer and winter mass balances have been carried out over the past 53 years on Storglaciären, northern Sweden. Repeated surveys of the glacier have resulted in several maps of surface topography as well as a map of the bed topography A new time-dependent ice flow model allows us to compare the observed surface evolution of the glacier with that computed by the model using measured mass-balance maps as input. The computed volume change compares well with the measured change: the model replicates the distribution of surface elevation to within ±10 m over 30 years of integration. On the model side, these deviations can be attributed to the low-resolution discretization of the model domain as well as to the limited accuracy of the ice rheology and omitted basal sliding. On the other hand, the uncertainties of the topography and mass-balance maps match the model uncertainties. In this sense, the experiments are a validation of both model and observations.

In glacier-dominated catchments, glaciers have an important effect on the water balance. It is important to understand the glacier control on inflow in order to assess historic trends and future scenarios. The mass balance of a 100 km2 glacier sub-basin of Svartisen ice cap, northern Norway, was reconstructed for 1917 to 1995. The reconstruction was carried out using three different methods, the hydrological method, the correlation between mass balance and meteorological observations and a precipitation-degree-day model. Calibration data were derived from field observations, map comparisons and correlation of observations at different glaciers. The reconstructed series showed a total loss of ∼3 × 109 m3 of water, most of which occurred between 1920 and 1950. After 1950, the net balance increased gradually and is currently near equilibrium with the present climate. Suggested climate scenarios for this region gave a loss between zero and 5 ×109 m3 of water until the year 2050.

In the course of a tremendous outburst flood (jökulhlaup) following the subglacial eruption in Vatnajökull, Iceland, in October 1996, a depression in the surface of the ice cap was created as a result of ice melting from the walls of a subglacial tunnel. The surface depression was initially approximately 6 km long, 800 m wide and 100 m deep. This ˚canyon" represents a significant perturbation in the geometry of the ice cap in this area where the total ice thickness is about 200–400 m. We present results of repeated measurements of flow velocities and elevation changes in the vicinity of the canyon made over a period of about 2 years. The measurements show a reduction in the depth of the canyon and a concomitant decrease in surface flow towards it over time. By calculating the transient evolution of idealized surface depressions using both analytical zeroth- and first-order theories, as well as the shallow-ice approximation (SIA) and a finite-element model incorporating all the terms of the momentum equations we demonstrate the importance of horizontal stress gradients at the spatial scale of this canyon. The transient evolution of the canyon is calculated with a two-dimensional time-dependent finite-element model with flow parameters (the parameters A and n of Glen’s flow law) that are tuned towards an optimal agreement with measured flow velocities. Although differences between measured and calculated velocities are comparable to measurement errors, the differences are not randomly distributed. The model is therefore not verified in detail. Nevertheless the model reproduces observed changes in the geometry over a 15 month time period reasonably well The model also reproduces changes in both velocities and geometry considerably better than an alternative model based on the SIA.

Nioghalvfjerdsfjorden glacier is a >60 km long and 20 km wide floating outlet glacier located at 79°30’ N, 22° W, draining a large area of the northeast Greenland ice sheet. Climate, mass-balance and dynamics studies were carried out on the glacier in three field seasons in 1996, 1997 and 1998. As part of this work, tidal-movement observations were carried out by simultaneous differential global positioning system (GPS) measurements at several locations distributed on the glacier surface. The GPS observations were performed continuously over several tidal cycles. At the same time, tiltmeter measurements were carried out in the grounding zones along the glacier margins and upstream, where the glacier leaves the main ice sheet A tide gauge installed in the sea immediately in front of the glacier front recorded the tide in the open sea during the field seasons. The observations show that the main part of the glacier tongue responds as a freely floating plate to the phase and amplitude of the local tide in the sea. However, kilometre-wide flexure zones exist along the marginal and upstream grounding lines. Attempts to model the observed tidal deflection and tilt patterns in the flexure zone by elastic-beam theory are unsuccessful, in contrast to previous findings by other investigators. The strongest disagreement between our measurements and results derived from elastic-beam theory is a significant variation of the phase of the tidal records with distance from the grounding line (most clearly displayed by the tilt records). We suggest that the viscous properties of glacier ice must be taken into account, and consequently that a viscoelastic-beam model must be used to adequately describe tidal bending of floating glaciers.

Gridded distributions of the annual mean temperature and annual total accumulation for Greenland are presented. They are objectively derived by deterministic and statistical interpolation from measurements at coastal stations and at locations on the ice sheet. They can be used not only for driving cryospheric models, but also for verifying atmospheric simulations.

Three methods to calculate summer snow- and ice melt are combined with a simplified climate model to estimate past, present and future values of accumulation and ablation on the Greenland ice sheet. This allows the reliability of the computationally efficient temperature-based parameterizations of melting to be compared to that of a more complicated physical model of the snow cover which calculates explicitly the formation of meltwater, refreezing and runoff. Six runs are subject to the same observed climatic forcing over the 20th century with different model parameters chosen. The range of change in sea level which accompanies these six runs is ωlcm. Because of a near-perfect cancellation between increases in accumulation and runoff, for a reference climate scenario similar to the Intergovernmental Panel on Climate Change’s IS92a, the Greenland ice sheet is not expected to contribute significantly to changes in the ocean level over the 21st century. The uncertainty in these predictions is estimated by repeating the calculation for a range of climate-change scenarios.