We present the first simulations of Jakobshavn Isbrae (Sermeq Kujalleq), west Greenland, using a 3D Stokes calving model that permits unrestricted advance and retreat. Using the position-based crevasse-depth calving law, the model is applied to simulate the calving dynamics of 2016–2017 season when Jakobshavn Isbrae is assumed to be stable because of the presence of a strong proglacial ice mélange. The calving law needs to be adjusted to avoid an underestimation of calving, but once adjusted the calving model simulates seasonal calving dynamics that reflect observed calving-driven retreat very well. We find that a crevasse penetration threshold of 94.5% best matches observations from satellite imagery. Additional, 2-year transient simulations show that although ice mélange is essential to the glacier's winter readvance, when removed, the glacier only retreats a couple of kilometres before reaching a stable position. While the backstress provided by the ice mélange allows the glacier to advance beyond this point, the retreated terminus position is determined by a combination of bed geometry and glacier dynamics. Ultimately, while the ice mélange allows winter readvance, cessation of the well-documented rapid retreat of Jakobshavn Isbrae will be influenced by the bed geometry.

We investigate the physical basis of the crevasse-depth (CD) calving law by analysing relationships between glaciological stresses and calving behaviour at Sermeq Kujalleq (Store Glacier), Greenland. Our observations and model simulations show that the glacier has a stable position defined by a compressive arch between lateral pinning points. Ice advance beyond the arch results in calving back to the stable position; conversely, if melt-undercutting forces the ice front behind the stable position, it readvances because ice velocities exceed subaqueous melt rates. This behaviour is typical of self-organising criticality, in which the stable ice-front position acts as an attractor between unstable super-critical and sub-critical regimes. This perspective provides strong support for a ‘position-law’ approach to modelling calving at Sermeq Kujalleq, because any calving ‘rate’ is simply a by-product of how quickly ice is delivered to the critical point. The CD calving law predicts ice-front position from the penetration of surface and basal crevasse fields, and accurately simulates super-critical calving back to the compressive arch and melt-driven calving into the sub-critical zone. The CD calving law reflects the glaciological controls on calving at Sermeq Kujalleq and exhibits considerable skill in simulating its mean position and seasonal fluctuations.

Close-range sensors are employed to observe glaciological processes that operate over short timescales (e.g. iceberg calving, glacial lake outburst floods, diurnal surface melting). However, under poor weather conditions optical instruments fail while the operation of radar systems below 17 GHz do not have sufficient angular resolution to map glacier surfaces in detail. This letter reviews the potential of millimetre-wave radar at 94 GHz to obtain high-resolution 3-D measurements of glaciers under most weather conditions. We discuss the theory of 94 GHz radar for glaciology studies, demonstrate its potential to map a glacier calving front and summarise future research priorities.

It is commonly asserted that there are two distinct classes of glacier surges: slow, long-duration ‘Svalbard-type’ surges, triggered by a transition from cold- to warm-based conditions (thermal switching), and fast, shorter-duration ‘Alaska-type’ surges triggered by a reorganisation of the basal drainage system (hydraulic switching). This classification, however, reflects neither the diversity of surges in Svalbard and Alaska (and other regions), nor the fundamental dynamic processes underlying all surges. We argue that enthalpy balance theory offers a framework for understanding the spectrum of glacier surging behaviours while emphasising their essential dynamic unity. In this paper, we summarise enthalpy balance theory, illustrate its potential to explain so-called ‘Svalbard-type’ and ‘Alaska-type’ surges using a single set of principles, and show examples of a much wider range of glacier surge behaviour than previously observed. We then identify some future directions for research, including strategies for testing predictions of the theory against field and remote sensing data, and priorities for numerical model development.

Recent speleological surveys of meltwater drainage systems in cold and polythermal glaciers have documented dynamic englacial and in some cases subglacial conduits formed by the ‘cut-and-closure’ mechanism. Investigations of the spatial distribution of such conduits often require a combination of different methods. Here, we studied the englacial drainage system in the cold glacier Longyearbreen, Svalbard by combining speleological exploration of a 478 m long meltwater conduit with a high-resolution ground penetrating radar (GPR) survey with two different centre-frequencies (25 and 100 MHz). The results yielded a 3-D documentation of the present englacial drainage system. The study shows that the overall form of englacial conduits can be detected from velocity−depth converted GPR data, and that the 3-D model can facilitate a method to pinpoint the reflections in a radargram corresponding with the englacial drainage system, although fine detail cannot be resolved. Visible reflections approximately parallel to the mapped englacial water drainage system likely result from sediment incorporated in the ice or from abandoned parts of the englacial drainage system.

Analysis of a recent surge of Morsnevbreen, Svalbard, is used to test predictions of the enthalpy balance theory of surging. High-resolution time series of velocities, ice thickness and crevasse distribution allow key elements of the enthalpy (internal energy) budget to be quantified for different stages of the surge cycle. During quiescence (1936–1990), velocities were very low, and geothermal heat slowly built-up enthalpy at the bed. Measurable mass transfer and frictional heating began in 1990–2010, then positive frictional heating-velocity feedbacks caused gradual acceleration from 2010 to 2015. Rapid acceleration occurred in summer 2016, when extensive crevassing and positive air temperatures allowed significant surface to bed drainage. The surge front reached the terminus in October 2016, coincident with a drop in velocities. Ice plumes in the fjord are interpreted as discharge of large volumes of supercooled water from the bed. Surge termination was prolonged, however, indicating persistence of an inefficient drainage system. The observations closely match predictions of the theory, particularly build-up of enthalpy from geothermal and frictional heat, and surface meltwater, and the concomitant changes in ice-surface elevation and velocity. Additional characteristics of the surge reflect spatial processes not represented in the model, but can be explained with respect to enthalpy gradients.

We present a highly detailed study of calving dynamics at Tunabreen, a tidewater glacier in Svalbard. A time-lapse camera was trained on the terminus and programmed to capture images every 3 seconds over a 28-hour period in August 2015, producing a highly detailed record of 34 117 images from which 358 individual calving events were distinguished. Calving activity is characterised by frequent events (12.8 events h−1) that are small relative to the spectrum of calving events observed, demonstrating the prevalence of small-scale calving mechanisms. Five calving styles were observed, with a high proportion of calving events (82%) originating at, or above, the waterline. The tidal cycle plays a key role in the timing of calving events, with 68% occurring on the falling limb of the tide. Calving activity is concentrated where meltwater plumes surface at the glacier front, and a ~ 5 m undercut at the base of the glacier suggests that meltwater plumes encourage melt-under-cutting. We conclude that frontal ablation at Tunabreen may be paced by submarine melt rates, as suggested from similar observations at glaciers in Svalbard and Alaska. Using submarine melt rate to calculate frontal ablation would greatly simplify estimations of tidewater glacier losses in prognostic models.

We evaluate the variability in basal friction for Kronebreen, Svalbard, a fast-flowing tidewater glacier. We invert 3 years (2013–15) of surface velocities at high temporal resolution (generally 11 days), to estimate the changing basal properties of the glacier. Our results suggest that sliding behaviour of Kronebreen within a year is primarily influenced by changes in water input patterns during the meltwater season and basal friction is highly variable from a year to another. At present, models usually employ parameterisations to encompass the complex physics of glacier sliding by mathematically simulate their net effect. For such ice masses with strong seasonal variations of surface melt, the spatio-temporal patterns of basal friction imply that it is neither possible nor appropriate to use a parameterisation for bed friction that is fixed in space and/or time, at least in a timescale of a few years. Basal sliding may not only be governed by local processes such as basal topography or summer melt, but also be mediated by factors that vary over a larger distance and over a longer time period such as subglacial hydrology organisation, ice-thickness changes or calving front geometry.

Glacier surges tend to be initiated in relatively small regions, then propagate down-glacier, up-glacier and/or across-glacier. The processes controlling patterns and rates of surge propagation, however, are incompletely understood. In this paper, we focus on patterns of surge propagation in two confluent glaciers in Svalbard, and examine possible causes. One of these glaciers, Bakaninbreen, surged in 1985–95. The surge propagated ∽7 km down-glacier, but did not cross the medial moraine onto the other glacier, Paulabreen. When Paulabreen surged between 2003 and 2005, the surge wave travelled several km down-glacier, but its lateral boundary stayed very close to the medial moraine. The confluent glaciers formerly extended into a fjord, and bathymetric mapping and historical observations show that an active subglacial conduit has existed between Bakaninbreen and Paulabreen since at least the early 20th century. The existence of a persistent subglacial conduit below the medial moraine was confirmed when we entered and mapped a Nye channel at the confluence of Bakaninbreen and Paulabreen. We argue that the conduit acts as a barrier to surge propagation. If pressurized water below one branch of the glacier system reaches the conduit, water can be readily evacuated, preventing its propagation into the other branch.

A new calving criterion is introduced, which predicts calving where the depth of surface crevasses equals ice height above sea level. Crevasse depth is calculated from strain rates, and terminus position and calving rate are therefore functions of ice velocity, strain rate, ice thickness and water depth. We couple the calving criterion with three ‘sliding laws’, in which velocity is controlled by (1) basal drag, (2) lateral drag and (3) a combination of the two. In model 1, velocities and strain rates are dependent on effective pressure, and hence ice thickness relative to water depth. Imposed thinning can lead to acceleration and terminus retreat, and ice shelves cannot form. In model 2, ice velocity is independent of changes in ice thickness unless accompanied by changes in surface gradient. Velocities are strongly dependent on channel width, and calving margins tend to stabilize at flow-unit widenings. Model 3 exhibits the combined characteristics of the other two models, and suggests that calving glaciers are sensitive to imposed thickness changes if basal drag provides most resistance to flow, but stable if most resistance is from lateral drag. Ice shelves can form if reduction of basal drag occurs over a sufficiently long spatial scale. In combination, the new calving criterion and the basal–lateral drag sliding function (model 3) can be used to simulate much of the observed spectrum of behaviour of calving glaciers, and present new opportunities to model ice-sheet response to climate change.

Numerous field and theoretical studies have pointed to an important role for subaqueous and waterline melting in the dynamics of calving glaciers. These processes remain unquantified because of the dangerous nature of the environment, a data gap which hampers both theoretical and numerical modelling studies. Here we report laboratory experiments designed to quantify waterline and subaqueous ice-melt rates in saline and fresh water. Experiments were conducted at temperatures of 1–10°C, a range typical of ice-contact environments, and at salinities of 0,17.5 and 35 ppt. Results indicate that melt rates are slightly faster under fresh-water conditions, and that different thermohaline combinations can produce contrasting ice-front geometries. Thermo-notches develop quickly at higher temperatures ( >4°C), and form most rapidly and to a greater extent in saline water. Contrasts in melt rates and ice-front geometry are controlled by temperature-driven density contrasts and circulation patterns. Rates of up to 0.8 md–1 suggest that mass loss by subaqueous melting is a significant process at calving termini.

The subaqueous margins of calving glaciers have the potential to make significant contributions to glacier mass loss. However, to date, very little is known about the morphology and development of subaqueous margins. A unique combination of sub-bottom profile and bathymetric data collected between 2008 and 2010 in proglacial lakes at Mueller, Hooker and Tasman glaciers in New Zealand’s Southern Alps reveal subaqueous ice ramps extending up to 510 m from the terminus of each glacier. Ice ramp surfaces are undulating and covered with a thick layer (up to 10 m) of unsorted sediment derived from supraglacial and englacial debris, lateral moraines and deltaic deposits. A cyclic calving pattern, relatively stable lake level and the debris cover appear to control the development and maintenance of these ice ramps. High subaerial retreat rates generally correspond to high subaqueous calving rates, although the highest subaerial retreat rates are not associated with the largest ice ramp. Debris mantling the subaqueous ice ramp surfaces insulates the ice from melting and also reduces buoyant forces acting on the terminus. Comparisons with previous studies show that the ice ramps evolve over time with changes in glacier dynamics and water-body properties.

Generalized numerical models of sub-debris ice ablation are preferable to empirical approaches for predicting runoff and glacier response to climate change, as empirical methods are site-specific and strongly dependent upon the conditions prevailing during the measurement period. We present a modified surface energy-balance model to calculate melt beneath a surface debris layer from daily mean meteorological variables. Despite numerous simplifications, the model performs well and modelled melt rates give a good match to observed melt rates, suggesting that this model can produce reliable estimates of ablation rate beneath debris layers several decimetres thick. This is a useful improvement on previous models which are inappropriate for thick debris cover.

Interest in crevasses and associated ice-fracture processes has recently increased due to recognition of the importance of calving glaciers to the mass balance of the cryosphere, as well as the importance of fractures in glacier hydrology. Recently developed calving criteria make use of models which predict crevasse depth from surface strain rates, but these models have rarely been tested against observations. In this study, we present data on crevasse depth and surface strain rates, and compare the measured values with results of two crevasse-depth models: a simple function proposed by Nye and a linear elastic fracture mechanics (LEFM) model developed by Van der Veen. Our results indicate that both models predict crevasse depths within the correct order of magnitude. The LEFM model, incorporating measured values of crevasse spacing and tuned for fracture toughness, performs better in predicting crevasse depths, but where lack of input data precludes such tuning, the results are similar to Nye’s model predictions. We conclude that both models may be used to calculate crevasse depths in calving models, although the Nye function is undoubtedly much simpler to implement within an ice-dynamics model.

The simple calving laws currently used in ice-sheet models do not adequately reflect the complexity and diversity of calving processes. To be effective, calving laws must be grounded in a sound understanding of how calving actually works. Here, we develop a new strategy for formulating calving laws, using (a) the Helsinki Discrete Element Model (HiDEM) to explicitly model fracture and calving processes, and (b) the continuum model Elmer/Ice to identify critical stress states associated with HiDEM calving events. A range of observed calving processes emerges spontaneously from HiDEM in response to variations in ice-front buoyancy and the size of subaqueous undercuts. Calving driven by buoyancy and melt under-cutting is under-predicted by existing calving laws, but we show that the location and magnitude of HiDEM calving events can be predicted in Elmer/Ice from characteristic stress patterns. Our results open the way to developing calving laws that properly reflect the diversity of calving processes, and provide a framework for a unified theory of the calving process continuum.

Large numbers of small valley glaciers on Svalbard were thicker and more extensive during the Little Ice Age (LIA), demonstrated by prominent ice-cored moraines up to several kilometres beyond present-day margins. The majority of these glaciers have since experienced a long period of strongly negative mass balance during the 20th century and are now largely frozen to their beds, indicating they are likely to have undergone a thermal transition from a polythermal to a cold-based regime. We present evidence for such a switch by reconstructing the former flow dynamics and thermal regime of Tellbreen, a small cold-based valley glacier in central Spitsbergen, based on its basal sequence and glaciological structures. Within the basal sequence, the underlying matrix-supported diamict is interpreted as saturated subglacial traction till which has frozen at the bed, indicating that the thermal switch has resulted in a cessation of subglacial sediment deformation due to freezing of the former deforming layer. This is overlain by debris-poor dispersed facies ice, interpreted to have formed through strain-induced metamorphism of englacial ice. The sequential development of structures includes arcuate fracture traces, interpreted as shear planes formed in a compressive/transpressive stress regime; and fracture traces, interpreted as healed extensional crevasses. The formation of these sediment/ice facies and structures is indicative of dynamic, warm-based flow, most likely during the LIA when the glacier was significantly thicker.

Controls on the global distribution of surge-type glaciers hold the keys to a better understanding of surge mechanisms. We investigate correlations between the distribution of surge-type glaciers and climatic and glacier geometry variables, using a new global geodatabase of 2317 surge-type glaciers. The highest densities of surge-type glaciers occur within an optimal climatic envelope bounded by temperature and precipitation thresholds. Across all regions with both surge-type and normal glaciers, the former are larger, especially at the cold, dry end of the climatic spectrum. A species distribution model, Maxent, accurately predicts the major clusters of surge-type glaciers using a series of climatic and glacier geometry variables, but under-predicts clusters found outside the climatically optimal surge zone. We interpret the results in terms of a new enthalpy cycle model. Steady states require a balance between enthalpy gains generated by the balance flux and losses via heat conduction and meltwater discharge. This condition can be most easily satisfied in cold, dry environments (thin, low-flux glaciers, efficient conductive heat losses) and warm, humid environments (high meltwater discharges). Intermediate conditions correspond to the optimal surge zone, where neither heat conduction nor runoff can effectively discharge enthalpy gains, and dynamic cycling can result.

Glacial sediments and landforms preserved beside the Strait of Magellan record repeated advances of an outlet of the Patagonian Icefield during and following the last glacial maximum (LGM; ∼25,000–14,000 14C yr B.P.). Ice-marginal landform assemblages consist of thrust moraine complexes, kame and kettle topography, and lateral meltwater channels, very similar to those found at the margins of modern subpolar glaciers. Taken together with other forms of paleoenvironmental evidence, the landform assemblages show that, during the LGM and late-glacial time, permafrost occurred near sea level in southernmost South America. This finding implies that mean annual temperatures were ∼7–8°C lower than at present, somewhat lower than those reconstructed by current glacier–climatic models. Comparison with precipitation–temperature relationships for modern glaciers suggests, in addition, that precipitation levels were lower than today. Reduced glacial-age precipitation may have resulted from a precipitation shadow induced by the Patagonian Icefield, an equatorward migration of the average position of westerly cyclonic storm tracks in the southern midlatitudes, or both these factors.

Hydraulic roughness exerts an important but poorly understood control on water pressure in subglacial conduits. Where relative roughness values are <5%, hydraulic roughness can be related to relative roughness using empirically-derived equations such as the Colebrook–White equation. General relationships between hydraulic roughness and relative roughness do not exist for relative roughness >5%. Here we report the first quantitative assessment of roughness heights and hydraulic diameters in a subglacial conduit. We measured roughness heights in a 125 m long section of a subglacial conduit using structure-from-motion to produce a digital surface model, and hand-measurements of the b-axis of rocks. We found roughness heights from 0.07 to 0.22 m and cross-sectional areas of 1–2 m2, resulting in relative roughness of 3–12% and >5% for most locations. A simple geometric model of varying conduit diameter shows that when the conduit is small relative roughness is >30% and has large variability. Our results suggest that parameterizations of conduit hydraulic roughness in subglacial hydrological models will remain challenging until hydraulic diameters exceed roughness heights by a factor of 20, or the conduit radius is >1 m for the roughness elements observed here.

The ablation areas of debris-covered glaciers typically consist of a complex mosaic of surface features with contrasting processes and rates of mass loss. This greatly complicates glacier response to climate change, and increases the uncertainty of predictive models. In this paper we present a series of high-resolution DEMs and repeat lake bathymetric surveys on Ngozumpa Glacier, Nepal, to study processes and patterns of mass loss on a Himalayan debris-covered glacier in unprecedented detail. Most mass loss occurs by melt below supraglacial debris, and melt and calving of ice cliffs (backwasting). Although ice cliffs cover only ~5% of the area of the lower tongue, they account for 40% of the ablation. The surface debris layer is subject to frequent re-distribution by slope processes, resulting in large spatial and temporal differences in debris-layer thickness, enhancing or inhibiting local ablation rates and encouraging continuous topographic inversion. A moraine-dammed lake on the lower glacier tongue (Spillway Lake) underwent a period of rapid expansion from 2001 to 2009, but later experienced a reduction of area and volume as a result of lake level lowering and sediment redistribution. Rapid lake growth will likely resume in the near future, and may eventually become up to 7 km long.