The dependence of oxygen isotope fractionation on ice growth rate during the freezing of sea water is investigated based on laboratory experiments and field observations in McMurdo Sound, Antarctica. The laboratory experiments were performed in a tank filled with sea water, with sea ice grown under calm conditions at various room temperatures ranging from −5°C to −20°C. In McMurdo Sound, the ice growth rate was monitored using thermistor probes for first-year landfast ice that grew to ∼2 m in thickness. Combining these datasets allows, for the first time, examination of fractionation at a wide range of growth rates from 0.8 × 10−7 to 9.3 × 10−7 m s−1. In the analysis a stagnant boundary-layer model is parameterized using these two independent datasets. As a result, the optimum values of equilibrium pure-ice fractionation factor and boundary-layer thickness are estimated. It is suggested that a regime shift may occur at a growth rate of ∼2.0 × 10−7 m s−1. A case study on sea ice in the Sea of Okhotsk, where the growth rate is modeled by coupling the thermodynamic properties of the sea ice with meteorological data, demonstrates the utility of the fitted models.

Taylor Glacier, an outlet of the East Antarctic ice sheet, flows through the Transantarctic Mountains and terminates in the Dry Valleys. Understanding how this glacier fluctuates is important for studies of glacial geology, paleoclimate, ice dynamics and ecology. Sublimation is the primary mass-loss process for most of the glacier. Four years of specific balance measurements from the ablation zone show sublimation rates up to 40 cm a−1. We used data from an array of weather stations as inputs to a model for latent heat flux and hence sublimation rate. Calculated and measured ablation rates agree to within uncertainties, indicating that wind speed and vapour pressure gradient (a function of temperature and humidity) are the governing variables, as expected from theory. Measurements and model results together allowed us to examine the spatial and temporal variations of sublimation on the glacier. On average, sublimation is about two times faster in summer than winter. Rapid sublimation occurs during storms and katabatic wind events, but such periods contribute less to the annual total than do slow, persistent losses. Spatially, sublimation reaches a maximum midway along the glacier, where descending surface air currents are focused by the topography of the aptly named tributary, Windy Gully.

Knowledge of glacier volume is crucial for ice flow modelling and predicting the impacts of climate change on glaciers. Rugged terrain, harsh weather conditions and logistic costs limit field-based ice thickness observations in the Himalaya. Remote-sensing applications, together with mathematical models, provide alternative techniques for glacier ice thickness and volume estimation. The objective of the present research is to assess the application of artificial neural network (ANN) modelling coupled with remote-sensing techniques to estimate ice thickness on individual glaciers with direct field measurements. We have developed two ANN models and estimated the ice thickness of Chhota Shigri Glacier (western Himalaya) on ten transverse cross sections and two longitudinal sections. The ANN model estimates agree well with ice thickness measurements from a ground-penetrating radar, available for five transverse cross sections on Chhota Shigri Glacier. The overall root mean square errors of the two ANN models are 24 and 13 m and the mean bias errors are ±13 and ±6 m, respectively, which are significantly lower than for other available models. The estimated mean ice thickness and volume for Chhota Shigri Glacier are 109 ± 17 m and 1.69 ± 0.26 km3, respectively.

A newly developed hammer was used to insert two autonomous probes 0.8 m and 2.1 m into clast-rich subglacial till under Black Rapids Glacier, Alaska, USA. Both probes were instrumented with a dual-axis tilt sensor and a pore-water pressure transducer. The data are compared to a 75 day record of surface velocities. Till deformation at depth was found to be highly seasonal: it is significant during an early-season speed-up event, but during long periods thereafter measured till deformation rates are negligible. Both tilt records show rotation around the probe axis, which indicates a change in tilt direction of about 30°. The tilt records are very similar, suggesting spatial homogeneity on the scale of the probe separation (4 m horizontal and 3.3 m vertical). There is evidence that during much of the year sliding of ice over till or deformation of a thin till layer (<20 cm) accounts for at least two-thirds of total basal motion. Basal motion accounts for 50–70% of the total surface motion. The inferred amount of ice–till sliding is larger than that found at the same location in a previous study, when surface velocities were about 10% lower. We suggest that variations in ice–till coupling account for the observed variations in mean annual speed.

Recent observations and modeling studies emphasize the crucial role of fracture mechanics for the stability of ice shelves and thereby the evolution of ice sheets. Here we introduce a macroscopic fracture-density field into a prognostic continuum ice-flow model and compute its evolution incorporating the initiation and growth of fractures as well as their advection with two dimensional ice flow. To a first approximation, fracture growth is assumed to depend on the spreading rate only, while fracture initiation is defined in terms of principal stresses. The inferred fracture-density fields compare well with observed elongate surface structures. Since crevasses and other deep-reaching fracture structures have been shown to influence the overall ice-shelf dynamics, we propose the fracture- density field introduced here be used as a measure for ice softening and decoupling of the ice flow in fracture-weakened zones. This may yield more accurate and realistic velocity patterns in prognostic simulations. Additionally, the memory of past fracture events links the calving front to the upstream dynamics. Thus the fracture-density field proposed here may be employed in fracture-based calving parameterizations. The aim of this study is to introduce the field and investigate which of the observed surface structures can be reproduced by the simplest physically motivated fracture source terms.

Long-term ice-core records of Alpine glaciers are usually taken from cold-firn areas at high altitudes, as on Mont Blanc and Monte Rosa. Perennial ice bodies at lower altitudes, however, also bear information about the past. Recent findings from the remains of such ice (the Oetztal iceman found in Austria; wooden bows at Lötschen Pass, Switzerland) clearly indicate the hitherto little-recognized fact that small, more-or-less static perennial ice bodies which are cold and frozen to the underlying bedrock may contain very old ice and, hence, important palaeoclimatic information about warm periods with minimum ice extent in the Alps. Since autumn 1998, investigations have been initiated on a crest-type location or “miniature ice cap” at Piz Murtèl, Engadine, Swiss Alps. First results from shallow drilling, temperature data-logging, geodetic surveying, visual observation, finite-element modelling of simplified basic two-dimensional configurations and comparison to earlier measurements at similar sites provide promising perspectives concerning a little-studied phenomenon with considerable scientific-environmental research potential. Specific characteristics of the investigated site, and probably of many other comparable mountain sites, are: cold ice (about –4°C at 10 m depth), no basal sliding, small mass turnover, striking lack of a firn zone, accumulation mainly by superimposed ice, and direct access to old layers (centuries, millennia?) at the ice/bedrock interface.

Accurate knowledge of the ice thickness distribution and glacier bed topography is essential for predicting dynamic glacier changes and the future developments of downstream hydrology, which are impacting the energy sector, tourism industry and natural hazard management. Using AIR-ETH, a new helicopter-borne ground-penetrating radar (GPR) platform, we measured the ice thickness of all large and most medium-sized glaciers in the Swiss Alps during the years 2016–20. Most of these had either never or only partially been surveyed before. With this new dataset, 251 glaciers – making up 81% of the glacierized area – are now covered by GPR surveys. For obtaining a comprehensive estimate of the overall glacier ice volume, ice thickness distribution and glacier bed topography, we combined this large amount of data with two independent modeling algorithms. This resulted in new maps of the glacier bed topography with unprecedented accuracy. The total glacier volume in the Swiss Alps was determined to be 58.7 ± 2.5 km3 in the year 2016. By projecting these results based on mass-balance data, we estimated a total ice volume of 52.9 ± 2.7 km3 for the year 2020. Data and modeling results are accessible in the form of the SwissGlacierThickness-R2020 data package.

Uncertainties in estimates of glacier and ice-cap contribution to sea-level rise exist in part due to poor quantification of mass-balance errors, particularly those resulting from extrapolation of sparse measurements. Centre-line data are often assumed to be representative of the glacier as a whole, with little attention paid to extrapolation errors or their effect on mass-balance estimates. Here we present detailed digital elevation model (DEM) measurements of glacier-wide elevation changes over the last ~40 years at two glaciers on Svalbard, Norwegian Arctic. Austre Br0ggerbreen and Midtre Lovenbreen are shown to have lost 27.54 ± 0.98 and 9.65 ± 0.76 × 107m3 of ice, respectively, between 1966 and 2005, findings that we relate to trends in average summer air temperatures and winter accumulation. These volume losses correspond to geodetic balances of -0.58 ± 0.03 and -0.41 ± 0.03 mw.e. a-1, respectively. Our analysis revealed high spatial complexity in patterns of elevation change, varying between glaciers, between measurement intervals and within and between elevation bins. Balances from extrapolated centre-line geodetic data were the same (within errors) as those from full-coverage DEM differencing in the majority of comparisons, yet significantly underestimated balance in three instances. Additionally, field mass balance from centre-line ablation stake data underestimated balances from full-coverage geodetic measurements during three of six measurement periods. These findings may support the hypothesis that field measurements underestimate Svalbard glacier mass loss, at least partly as a result of the failure of centre-line measurements to account for glacier-wide variations in ablation. Our results demonstrate the importance of deriving accurate interpolation functions and constraining extrapolation errors from sparse measurements.

The quality of the ice core from Siple Dome, West Antarctica, varied widely, with significant fracturing below 400 m. Bubbly ice persisted to the ice–rock interface at 1004 m and constituted the brittle zone. The core has undergone minimal relaxation and has remained brittle and prone to fracturing more than 5 years after it was drilled. This behavior is attributed to unrelieved stresses from Kamb and Bindschadler Ice Streams (former Ice Streams C and D) flanking the dome. Melt layers were identified sporadically throughout the core, as were inclined layers tilted at angles that occasionally exceeded 10°. Structurally, the ice was characterized by extensive recrystallization including grain-size changes from 0.074 cm2 at 59 m to >50 cm2 at 992 m, and major transitions in c-axis fabrics. Unusual fabrics included vertical c-axis clusters superimposed on vertical girdles that may reflect vertical compression acting in conjunction with horizontal tension. The sudden appearance of a shear-type fabric at 700–800 m appears closely linked to the occurrence of abundant tephra particles embedded in the ice. The occurrence of dispersed sediment in the bottom 2 m is attributed to freeze-on of basal meltwater.

This study investigates the processes of ice-marginal sedimentation in Vestfold Hills, Antarctica. Most debris is released from the ice when basal and englacial debris bands become warped and reach the surface of the glacier and where the debris bands are exposed by ablation of the ice surface. Once released, the debris is redistributed in the ice-marginal area by depositional processes that are controlled by the availability of water. During the short summer, melt water from snow and ice saturates the newly released debris and causes sediment flows and other mass-movement deposits. Melt-out and sublimation tills form after the layer of debris on the moraines is consolidated and melting rates decrease. When the thickness of deposits on the surface of ice-cored moraines reaches or exceeds the depth of summer thawing, the ice core no longer melts and the moraines become semi-permanent features. The sediments and land forms of the ice-marginal area closely resemble those formed by sub-polar glaciers with a complex thermal regime and are unlike those that form at the margins of dry-based polar glaciers. Although glacier thermal regime is understood to be a major control on debris dispersal and processes of glacial sedimentation, the evidence from Vestfold Hills suggests that the primary control is the climate of the glacier terminus area.

Towards accounting for the dynamic response of glaciers and ice caps in the estimation of their contribution to sea-level rise due to global warming, a mass-balance degree-day model is coupled to a geometric glacier model. The ice dynamics are treated implicitly in the geometric model by using scaling parameters that have been extensively investigated in the literature. The model is tested by presenting a case-study of the glacier Hintereisferner, Austrian Alps. The results are compatible with geomorphological data and other modelling studies. An estimate is made of the volume decrease due to initial disequilibrium. An extensive sensitivity study using generalized glacier shapes and sizes allows a comparison of results with dynamic theory. According to the geometric model, glaciers with a narrowing channel change more with a change in mass balance than glaciers with a widening channel, due to their shape and the way in which that shape changes with a changing climate. Also their response time is longer. As time progresses after a mass-balance perturbation, the longer response time for continental glaciers compared to glaciers with larger mass turnover offsets the effect of their smaller static sensitivity. Thus, although for the next century we may expect greater changes in volume from alpine glaciers, the equilibrium or committed change is greater for the continental glaciers.

An indirect methodology for determining the distribution of mass balance at high spatial resolution using remote sensing and ice-flow modelling is presented. The method, based on the mass-continuity equation, requires two datasets collected over the desired monitoring interval: (i) the spatial pattern of glacier surface-elevation change, and (ii) the mass-flux divergence field. At Haut Glacier d’Arolla, Valais, Switzerland, the mass-balance distribution between September 1992 and September 1993 is calculated at 20 m resolution from the difference between the pattern of surface-elevation change derived from analytical photogrammetry and the mass-flux divergence field determined from three-dimensional, numerical flow modelling constrained by surface-velocity measurements. The resultant pattern of mass balance is almost totally negative, showing a strong dependence on elevation, but with large localized departures. The computed distribution of mass balance compares well (R2 = 0.91) with mass-balance measurements made at stakes installed along the glacier centre line over the same period. Despite the highly optimized nature of the flow-modelling effort employed in this study, the good agreement indicates the potential this method has as a strategy for deriving high spatial and temporal-resolution estimates of mass balance.

Observations of surface elevation (s) and horizontal velocity components (u and v) are inverted to infer the topography (b) and lubrication (c) at the bed of an ice stream, based on a linearized perturbation theory of the transmission of flow disturbances through the ice thickness. Synthetic data are used to illustrate non-uniqueness in the inversion, but also demonstrate that effects of b and c can be separated when s, u and v are specified, even with added noise to simulate measurement errors. We have analyzed prominent short-horizontal-scale (∼2 km) features in topography and velocity pattern in a local 64 km by 32 km area of the surface of Ice Stream E,West Antarctica. Our preferred interpretation of bed conditions beneath the most prominent features on the surface identifies a deep trough in the basal topography with low lubrication in the base of the trough.

The transition from inland- to streaming-style ice flow near to and upstream from the onset to Ice Stream D, West Antarctica, is investigated using the force-balance technique. Basal drag provides the majority of the flow resistance over the study area but is substantially modified by non-local stress gradients. Lateral drag increases with distance downstream, balancing ∼50–100% of the driving stress at the onset. Longitudinal stress gradients (LSG) are also found to be significant, an observation that distinguishes ice flow in this region from the inland- and streaming-flow regimes that bound it, in which LSG are usually negligible. LSG decrease the spatial variability in basal drag and sliding speed and increase the area of the bed over which frictional melting occurs. Overall, LSG decrease the resistive influence of basal stress concentrations and increase the spatial uniformity of basal sliding. These observations suggest that streaming flow develops as an integrated response to the physical interaction between the ice and its bed over an extended region upstream from the onset, rather than being solely due to changes in basal characteristics at the onset. An implication is that non-steady-flow behavior upstream from the onset may ultimately propagate downstream and result in non-steady behavior at the onset.

This paper presents a simple model to estimate ice ablation under a thick supraglacial debris cover. The key method employed in the model is to establish a link between the debris heat flux and the debris temperature at a certain depth when the heat transfer in the debris is described by a diffusion process. Given surface temperature, debris thermal properties and relevant boundary conditions, the proposed model can estimate mean debris temperature at interfaces of different debris layers using an iterative procedure, and then the heat flux for ice ablation. The advantage of the proposed model is that it only requires a few parameters to conduct the modeling, which is simpler and more applicable than others. The case study on Koxkar glacier, west Tien Shan, China, shows, in general, that the proposed model gives good results for the prediction of debris temperatures, except for an apparent phase shift between modeled and observed values. We suggest that this error is mainly due to complex phase relations between debris temperature and debris heat flux. The modeled ablation rates at three experimental sites also show good results, using a direct comparison with observed data and an indirect comparison with a commonly used energy-balance model.

To obtain information on changes in glacier mass balance in the central Nyainqentanglha Range, a comprehensive study was carried out based on digital-elevation models derived from the 1968 topographic maps, the Shuttle Radar Topography Mission DEM (2000) and TerraSAR-X/TanDEM-X (2013). Glacier area changes between 1968 and 2016 were derived from topographic maps and Landsat OLI images. This showed the area contained 715 glaciers, with an area of 1713.42 ± 51.82 km2, in 2016. Ice cover has been shrinking by 0.68 ± 0.05% a−1 since 1968. The glacier area covered by debris accounted for 11.9% of the total and decreased in the SE–NW directions. Using digital elevation model differencing and differential synthetic aperture radar interferometry, a significant mass loss of 0.46 ± 0.10 m w.e. a−1 has been recorded since 1968; mass losses accelerated from 0.42 ± 0.20 m w.e. a−1 to 0.60 ± 0.20 m w.e. a−1 between 1968–2000 and 2000–2013, with thinning noticeably greater on the debris-covered ice than the clean ice. Surface-elevation changes can be influenced by ice cliffs, as well as debris cover and land- or lake-terminating glaciers. Changes showed spatial and temporal heterogeneity and a substantial correlation with climate warming and decreased precipitation.

We propose a novel Eulerian algorithm to compute the changes of a glacier geometry for given mass balances. The surface of a glacier is obtained by solving a transport equation for the volume of fluid (VOF). The surface mass balance is taken into account by adding an interfacial term in the transport equation. An unstructured mesh with standard stabilized finite elements is used to solve the non-linear Stokes problem. The VOF function is computed on a structured grid with a high resolution. The algorithm is stable for Courant numbers larger than unity and conserves mass to a high accuracy. To demonstrate the potential of the algorithm, we apply it to reconstructed Late-glacial states of a small valley glacier, Vadret Muragl, in the Swiss Alps.

Two Eppley pyrheliometers were used to measure incoming and reflected sun and sky radiation over a saturated, melting snowpack. Albedo values computed from these measurements varied strongly, not only with snow surface conditions, but also diurnally with the angle of the sun, and from clear to cloudy skies. On clear days minimum albedo in the afternoon was approximately 35 per cent less than the maximum in early morning; a secondary maximum occurred at sunset. Also, midday albedos were higher under cloudy skies than under clear skies. These variations appear to relate primarily to changes in angle of incident radiation, and secondarily to changes in the physical structure of the snow surface. Spectral changes in incident radiation are also a possible factor.

A model for the isotopic composition in δD and δ 18O of ice formed by refreezing at the glacier sole is developed. This model predicts relatively well the distribution of points representing samples from basal layers of an Arctic and an Alpine glacier on a δD–δ 18O diagram. The frozen fraction which is the part of the liquid that refreezes can be determined for each basal ice layer. This may have implications on the study of the ice–water system at the ice–rock interface.

We assess basal roughness beneath Pine Island Glacier (PIG), West Antarctica, based on a recent airborne radio-echo sounding dataset. We identify a clear relationship between faster ice flow and decreased basal roughness in significant parts of PIG. The central portion and two of its tributaries are particularly smooth, but the majority of the tributaries feeding the main trunk are rougher. We interpret the presence of a smooth bed as being a consequence of the deposition of marine sediments following disappearance of the West Antarctic ice sheet in the Pliocene or Pleistocene, and, conversely, a lack of marine sedimentation where the bed is rough. Importantly, we also identify a patchy distribution of marine sediments, and thus a bed over which the controls on flow vary. While there is a notable correspondence between ice velocity and bed roughness, we do not assume a direct causal relationship, but find that an indirect one is likely. Where low basal roughness results in low basal resistance to flow, a lower driving stress is required to produce the flux required to achieve mass balance. This, in turn, means that the surface in that area will be lower than surrounding areas with a rougher bed, and this will tend to draw flow into the area with low bed roughness. Since our studies shows that bed roughness beneath the tributaries of the trunk varies substantially, there is a strong likelihood that these tributaries will differ in the rate at which they transmit current velocity changes on the main trunk into the interior of the glacier basin.