2.1. Morphology and ice dynamics

Topographic characteristics of ice cliffs across the globe vary due to their genesis. Ice cliffs on Kilimanjaro range between 3 and 50 m (Winkler and others, Reference Winkler2010, Fig. 1c), and like the ice margins along ice sheets (Weidick, Reference Weidick1968; Abermann and others, Reference Abermann, Steiner, Prinz, Wecht and Lisager2020) can span distances of several 100 m. They are generally near-vertical, with slopes of at least 60°. Cliffs in Antarctica were reported to be ~20 m high (Chinn, Reference Chinn1987; Lewis and others., Reference Lewis, Fountain and Dana1999), observations in Greenland suggest heights of 20–30 m (Weidick, Reference Weidick1968; Abermann and others, Reference Abermann, Steiner, Prinz, Wecht and Lisager2020, Fig. 1a). No comprehensive assessment of the terrestrial ice margin of the Greenland Ice Sheet exists, but field observations suggest many sections with near-vertical portions (Weidick, Reference Weidick1968; Kjær and others, Reference Kjær2018; Abermann and others, Reference Abermann, Steiner, Prinz, Wecht and Lisager2020). In all cases the transition from vertical to shallow ramps happens within a few 10 s of metres of the margin (Fig. 1a, left part of the margin), and an understanding of what causes the margin to be vertical or a shallow slope is lacking. Ice mass changes have been consistently negative on Kilimanjaro, without indicative direct coupling to local climate variability over time (Kaser and others, Reference Kaser, Mölg, Cullen, Hardy and Winkler2010). There is no definite explanation how the ice cliffs formed in the first place, however some explanations exist for their persistence. With relatively stable air temperatures below the melting point throughout the year on the horizontal ice surface, ice temperatures fluctuate with changing solar radiation along the cliff face, resulting in stronger melting and sublimation, compared to the horizontal glacier surface. Maintaining the vertical wall is further supported by near constant longwave radiation emitted from the surrounding terrain (Fig. 2b, Kaser and others, Reference Kaser, Mölg, Cullen, Hardy and Winkler2010). Ice dynamics on the glaciers inside the flat Kilimanjaro crater can be neglected due to the horizontal bedrock and glaciers not being thick enough for significant ice deformation. Thus, once formed, the cliffs must inevitably retreat due to a lacking accumulation component (Kaser and others, Reference Kaser, Mölg, Cullen, Hardy and Winkler2010). For the ice sheet margin Goldthwait (Reference Goldthwait1971) hypothesized that (a) ice cliffs are the product of the advancing ice margin, possibly surging initially in response to kinetic waves down the ice surface (Fig. 2a); (b) the vertical edge develops only where basal motion is much slower than upper ice motion, i.e. with a strong plastic shear zone near the base, overriding itself; and (c) no ice cliff will maintain itself more than 30 to 50 m high, inasmuch as the plausible stresses of forward motion cannot exceed the rate of vertical closure due to the creep rate in thick ice. Dry calving becomes a potent factor limiting cliff height.

Figure 1. (a) Cliffs along the land-terminating ice margin in North Greenland (photo: Jakob Steiner). (b) The terminus of surging Crusoe glacier on Axel Heiberg Island (photo: Juerg Alean). (c) The vertical northern cliffs on Kibo, Kilimanjaro (photo: Lindsey Nicholson). (d) Ice cliff with adjacent pond on a debris-covered glacier in the Himalaya, person next to the main boulder on top of the cliff for scale (photo: Pascal Buri).

Figure 2. Conceptual examples of cliff development. The size and number of arrows for radiation and glacier flow indicate their relative magnitude. Dashed ice or debris surfaces represent past or future surfaces. Depending on the type of cliff these surface changes happen within months or years (ice margin) or days (debris-covered glaciers). The conceptual sun in the top left corner shows its approximate position around noon and the associated illumination of an idealized cliff at different latitudes. (a) The vertical ice margin in the Arctic/Antarctica is advancing or retreating and due to low temperatures receives relatively little longwave radiation from the terrain. The role of ice dynamics remains uncertain. (b) Cliffs on Kilimanjaro receive solar radiation at steeper angles and more longwave radiation, but ice dynamics play a minor or no role. (c) Persistence of cliffs on debris-covered glaciers is often defined by their aspect. Cliffs shaded from direct radiation potentially persist longer and develop complex patterns. (d) Cliffs on debris mounds facing the sun disappear faster and as a result are often also smaller. (e) Cliffs at termini recede rapidly but persist as more ice is supplied continuously.

Cliffs on debris-covered glaciers occur from ~1 m up to 20–30 m high and >100 m wide, but rarely are steeper than 60°. Exceptions are vertical and even overhanging sections at the cliff foot, caused by subaqueous or waterline melt, stream erosion or differential melt due to varying energy fluxes (Figs. 1d and 2c; Steiner and others, Reference Steiner2015; Watson and others, Reference Watson2017; Mölg and others, Reference Mölg, Ferguson, Bolch and Vieli2020). Their aspect can vary widely within a single cliff and between different cliffs on a single glacier (Steiner and others, Reference Steiner, Buri, Miles, Ragettli and Pellicciotti2019). Ice cliffs cover $< 15\%$ of the area of the debris-covered tongue of glaciers (Steiner and others, Reference Steiner, Buri, Miles, Ragettli and Pellicciotti2019; Anderson and others, Reference Anderson, Armstrong, Anderson and Buri2021; Kneib and others, Reference Kneib2021a; Loriaux and Ruiz, Reference Loriaux and Ruiz2021). Their genesis has been hypothesized to be related to spatially heterogeneous debris thicknesses leading to differential melt and debris mobilization (Nicholson and others, Reference Nicholson, McCarthy, Pritchard and Willis2018; Moore, Reference Moore2021), subglacial streams or ponds leading to debris remobilization and undercutting (Sakai and others, Reference Sakai, Takeuchi, Fujita and Nakawo2000; Mölg and others, Reference Mölg, Bolch, Walter and Vieli2019), collapsing englacial channels (Benn and others, Reference Benn2012; Reid and Brock, Reference Reid and Brock2014) or crevasses (Reid and Brock, Reference Reid and Brock2014; Steiner and others, Reference Steiner, Buri, Miles, Ragettli and Pellicciotti2019). However, the wide variety of cliff types and their varied behaviour in melt, is not conclusively explored, and their formation mechanisms have not been entirely understood to date.

Ice cliffs provide a window into the geomorphology around glacier ice. Their presence has been interpreted as an indicator of debris thickness around their edges, a variable that is crucial to estimate sub-debris ice melt (Nicholson and others, Reference Nicholson, McCarthy, Pritchard and Willis2018). Debris transport has been a long standing discussion, with the main transport path likely being englacial (Kirkbride and Deline, Reference Kirkbride and Deline2013), but evidence of the commonly coarse surface debris within ice is rare (Miles and others, Reference Miles2021), matching observations along cliff faces. Englacial debris is likely concentrated along medial moraine bands. Cliff surfaces can provide some insight into englacial processes, including foliation and basal thrusting (Fig. 1b, Hooke and Hudleston, Reference Hooke and Hudleston1978; Fitzsimons and Colhoun, Reference Fitzsimons and Colhoun1995). This potential is also true for the ice margin, where distinctive stratigraphies hold a potential window into the past (see Fig. 1a). MacGregor and others (Reference MacGregor2020) showed that sediment bands on the much shallower margin match with data taken from ice cores further up the ice sheet. Hooke (Reference Hooke1970) used foliation patterns and samples on steep sections of the margin in Northern Greenland to indicate past ice dynamics.

2.2. Melt and energy balance

Ice cliffs on the Greenland Ice Sheet (Fig. 1a) were initially studied for reasons of access to the ice sheet with heavy vehicles under a military purpose (Goldthwait, Reference Goldthwait1971). A peculiarity that remains not completely solved, is an apparent stability or even advance of the margin, during times of otherwise negative mass balance (Abermann and others, Reference Abermann, Steiner, Prinz, Wecht and Lisager2020). Similar observations were made in Antarctica, where any margin change was found to be an ambiguous indicator for mass balance conditions (Fitzsimons and Colhoun, Reference Fitzsimons and Colhoun1995), assuming there to be a not yet explored dynamic connection.

In the Dry Valleys ice cliffs have been identified as important sources of local meltwater due to the high zenith angles at high latitude and hence the relatively strong solar irradiation onto the near-vertical cliff (Chinn, Reference Chinn1987). While on the horizontal ice surface more mass is lost due to sublimation, mass loss along the cliff face is melt dominated, driven by solar radiation, due to their favourable equatorward aspect (Lewis and others., Reference Lewis, Fountain and Dana1999). Melt rates in the Dry Valleys were reported to be much higher along the cliff (~8 mm w.e. day⁻¹) than on the horizontal surface (~1 mm w.e. day⁻¹) over a three week period (Chinn, Reference Chinn1987). Similarly, during 41 days in the same region ablation rates on the vertical cliff face were ~7 mm w.e. day⁻¹ (6$\%$ sublimation) and ~2 mm w.e. day⁻¹ (42$\%$ sublimation) on the horizontal surface (Lewis and others., Reference Lewis, Fountain and Dana1999, according to 1995–1996 data), suggesting mass wasting to be four to eight times higher along the cliff face. Initial unpublished readings from stake measurements along a south facing ice cliff in Greenland (see Abermann and others, Reference Abermann, Steiner, Prinz, Wecht and Lisager2020, for details on the field site) suggest ablation is strongly controlled by solar irradiance. During clear-sky conditions, frontal ablation is up to six times higher than on the rather flat glacier surface. In contrast, during overcast conditions frontal ablation is about 30$\%$ less than on the flat surface.

At Kilimanjaro, close to the equator at 3°S, the radiative forcing is considerably different. Ice cliff aspect on the Northern Ice Field of Kibo Glacier is north or south only, allowing a minimum of solar irradiance at high zenith angles in the morning and evening and at low zenith angles during the day. Solar irradiance on the horizontal surface is very high, but snow accumulation, sublimation and refreezing of melt water inhibits ablation. The vertical south-facing ice cliff retreats only during the half year when solar radiation reaches the cliff face (13 cm month⁻¹ or ~0.5 cm w.e. day⁻¹), reduced to just 1.4 cm month⁻¹ between March and October when the cliff is permanently shaded due to the solar geometry (Winkler and others, Reference Winkler2010).

On mid-latitude debris-covered glacier tongues similar processes are observed. Solar radiation is higher in the horizontal than along a poleward facing cliff (Fig. 3b) but melt on cliffs between 2 and 90 mm w.e. day⁻¹ (Steiner and others, Reference Steiner2015; Watson and others, Reference Watson2017) is much higher than below the surrounding debris (2 to 8 mm w.e. day⁻¹ Steiner and others, Reference Steiner, Kraaijenbrink and Immerzeel2021). This is largely due to insulation of ice below the debris, and the very low albedo of cliffs, that receive dust loading from the debris cover above.

Figure 3. Incoming solar radiation measured at a horizontal AWS (I ₀ AWS) and a station located on a north-facing cliff (I ₀ meas.) on the debris-covered Lirung Glacier in the Central Himalaya (from Steiner and others (Reference Steiner2015)). I _s mod. refers to the modelled radiation on the cliff. The radiation sensor is mounted parallel to the cliff face.

The aspect of ice cliffs on debris-covered glaciers in the northern hemisphere was reported to be dominantly north facing, i.e. away from direct solar radiation (Sakai and others, Reference Sakai, Nakawo and Fujita2002; Thompson and others, Reference Thompson, Benn, Mertes and Luckman2016; Watson and others, Reference Watson2017; Steiner and others, Reference Steiner, Buri, Miles, Ragettli and Pellicciotti2019). A study investigating this hypothesis confirmed that the angle at which a cliff faces the sun likely plays an important role in ice cliff persistence (Buri and Pellicciotti, Reference Buri and Pellicciotti2018). This can be compared to a similar phenomenon on Kilimanjaro, where vertical cliffs are predominately orientated towards the north and south (Winkler and others, Reference Winkler2010). The processes involved in cliff morphodynamics on debris-covered tongues are however more complex and include radiative fluxes from the surrounding terrain, the dynamics of supraglacial ponds and streams and the glacier itself as well as constant rearrangement of debris across the cliff face (Figs. 2c–d).

To date no studies exist modelling the dynamic component of land-terminating ice cliffs or cliffs on debris-covered glaciers in conjunction with the frontal energy and mass balance. For ice cliffs on debris-covered glaciers, energy balance studies with an incorporation of the dynamic change of the surrounding debris surface (Buri and others, Reference Buri2016a) exist, however not accounting for glacier dynamics.

3.1. High resolution datasets

There is no comprehensive understanding of the distribution of supraglacial ice cliffs in all mountain regions in time and space. Specifically, debris-covered mountain glaciers in the high Arctic as well as the Karakoram, should be a priority for more detailed assessments. The potential of increasingly high resolution satellite imagery combined with automated mapping (Kneib and others, Reference Kneib2021b) has already been shown on the catchment scale, providing a basis for upscaling. The Greenland ice sheet and ice cap margin has already been mapped at great spatial detail (Citterio and Ahlstrøm, Reference Citterio and Ahlstrøm2013), for Antarctica a number of ice masks exist (Hansen and others, Reference Hansen2022), however in both cases without a characterisation of the margin's morphology. Given the nature of cliffs, with steep sections not adequately represented in most available topographic data, more high resolution DEMs able to capture (near-)vertical slopes (resolution <1 m) should be collected to validate the suitability of already available regional elevation data (>1 m, e.g. the ArcticDEM, Porter and others, Reference Porter2022).

3.2. Cliff genesis and numerical modelling

Due to their slow evolution we have very limited documentation on how steep sections of the ice sheet margins develop (Abermann and others, Reference Abermann, Steiner, Prinz, Wecht and Lisager2020), and why the transition from steep to shallow occurs. Building on high resolution data mentioned above, an analysis across the complete margin of shallow versus steep sections compared to the respective ice dynamics (i.e. velocity fields) as well as the bed topography would help to test some of the hypotheses developed in individual field sites. Additionally, ice temperature measurements and documentation of their long term change would be required to better constrain high-resolution dynamical models along the margin. Collecting more evidence on linkages between ice dynamics and margin morphology would then allow for the refinement of ice dynamic models that concern themselves with margin evolution (e.g. Leysinger Vieli and Gudmundsson, Reference Leysinger Vieli and Gudmundsson2010). A high resolution representation of the ice margin could also help to resolve micro climate in the complex transition between ice and non-glaciated terrain or steep and near-horizontal ice, applying numerical simulations as has been done for cliffs on debris-covered glaciers (Bonekamp and others, Reference Bonekamp, Heerwaarden, Steiner and Immerzeel2020).

For debris-covered glaciers the full life cycle of cliffs has been documented on single glaciers, limited to the Himalaya. Debris-covered surfaces exist across all glacier-covered mountain ranges (Scherler and others, Reference Scherler, Wulf and Gorelick2018), on many of which cliffs have been observed but not documented (e.g. the Karakoram or peripheral glaciers in Greenland). Comparing cliff inventories with climate, mass change and ice dynamic data would allow us to establish more generalized concepts of ice cliff genesis and general occurrence. Combining numerical models for debris-covered glaciers (e.g. Scherler and Egholm, Reference Scherler and Egholm2020) with concepts of cliff melt models (e.g. Buri and others, Reference Buri2016a), would allow us to investigate the link between mass change and cliff occurrence over long time scales. A systematic comparison to data on ice mass change as well as numerical models could in turn elucidate if cliff occurrence or morphology provide an indication for ice sheet or glacier health.

3.3. Dry calving

Dry calving has been reported for all types of cliffs, along the polar ice sheets, on Kilimanjaro and debris-covered tongues, but no large scale estimates on its magnitude exist and how it is linked to ice dynamics. This process has been discussed for grounded lake-terminating cliffs (Kirkbride and Warren, Reference Kirkbride and Warren1997), but could be equally monitored for ice cliffs without a connection to water bodies. Development in employing SfM from timelapse imagery for change detection used on more rapidly changing sections of the ice sheet margin (Mallalieu and others, Reference Mallalieu, Carrivick, Quincey, Smith and James2017), would allow for quantification of dry calving.