Though someone pointed out that most of the items are focused on land based glaciers, rather than on the WAIS which is a marine ice sheet. However, i welcome all contribution in the comment section which helps to better understand marine ice sheets and particular Antarctic ice sheet integrity/stability.

Flotation and free surface flow in a model for subglacial drainage. Part I: Distributed drainage (2012)

By Christian Schoof, Ian J. Hewitt and Mauro A. Werder | Source

Abstract

We present a continuum model for melt water drainage through a spatially distributed system of connected subglacial cavities, and consider in this context the complications introduced when effective pressure or water pressure drops to zero. Instead of unphysically allowing water pressure to become negative, we model the formation of a partially vapour-or air-filled space between ice and bed. Likewise, instead of allowing sustained negative effective pressures, we allow ice to separate from the bed at zero effective pressure. The resulting model is a free boundary problem in which an elliptic obstacle problem determines hydraulic potential, and therefore also determines regions of zero effective pressure and zero water pressure. This is coupled with a transport problem for stored water, and the coupled system bears some similarities with Hele-Shaw and squeeze film models.

We present a numerical method for computing time-dependent solutions, and find close agreement with semi-analytical travelling wave and steady state solutions. As may be expected, we find that ice-bed separation is favoured by high fluxes and low ice surface slopes and low bed slopes, while partially filled cavities are favoured by low fluxes and high slopes. At the boundaries of regions with zero water or effective pressure, discontinuities in water level are frequently present, either in the form of propagating shocks or as stationary hydraulic jumps accompanied by discontinuities in potential gradient.

Significant sliding typically occurs when the base of the ice reaches the melting point.Spatial as well as temporal variability in glacier sliding can therefore be caused by temperature changes at the bed (Clarke 1976; MacAyeal 1993; Cueyet al.1999; Fowleret al.2001). However, there is strong field evidence that sliding is not controlled purely by the presence or absence of liquid water at the ice-bed interface, but that subglacial water pressure plays a crucial role (Iken & Bindschadler 1986; Jansson 1995; Howatet al.2008; van de Walet al.2008; Shepherdet al.2009; Bartholomewet al.2010). Consequently, most parameterizations of glacier sliding postulate that there is a relationship between friction, sliding velocity and effective pressure at the glacier bed, where effective pressure is defined as normal stress at the bed minus water pressure (Buddet al.1979).

Theory and experiment indicate two primary ways in which effective pressure can affect friction at the base of a glacier. If the bed is composed of a granular material, then a low effective pressure will correspond to weakened grain contacts. This facilitates slip between grains and hence basal ice motion (Iversonet al.1999). Where larger asperities on the bed rather than the strength of subglacial sediments control drag on the base of the glacier, effective pressure controls the degree of contact between ice and bed. At low effective pressure, water filled cavities can form in the lee of asperities, and their size increases with decreasing effective pressure. Larger cavities correspond to reduced contact, and hence to less drag (Lliboutry 1968; Fowler 1986; Schoof 2005; Gagliardini et al.2007).

In both cases, where friction is controlled by mechanical failure in sediment and by larger asperities, friction increases with effective pressure. In models of glacier and ice sheet dynamics, it can therefore be important to be able to predict effective pressure (see e.g. Flowerset al.2004, 2005; Flowers 2008; Hewitt & Fowler 2008; Pimentel & Flowers 2010). This must be done through a model component that describes the flow of water. There are numerous complications that make this task difficult. While direct observations of the glacier bed are difficult, there is evidence that drainage can generically occur in two distinct styles: through a spatially distributed, effectively porous system that can consist at least in part of the cavities described above, and through a few individual channels(Kambet al.1985; Iken & Bindschadler 1986; Hubbardet al.1995; Lappegardet al.2006). Modelling the interactions between cavities and channels has been challenging,especially in two dimensions, with recent progress relying on discrete descriptions of channels with prescribed locations coupled either to discrete cavities or a continuum porous model (Schoof 2010; Hewitt 2011).

In addition to the possibility of different styles of drainage, models also have to contend with channels and cavities that may only be partially filled with water, or even with no water at all (see e.g. Fowler 1987, for a discussion). This is most likely when melt water input is low or under thin ice, and is commonly observed near glacier termini. Most current models do not describe partially filled channels and cavities, and instead unphysically predict negative water pressures, a notable exception being the partially filled channel model of Schuler & Fischer (2009). At the opposite extreme, existing models often predict large negative effective pressures in response to increases in water input, corresponding to water pressure significantly exceeding overburden (e.g. Pimentel & Flowers 2010; Schoof 2010). The physics built into these models is however not intended to capture the rapid opening of an ice-water gap that should ensue, which has been modelled as an elastic hydrofracture problem in Tsai & Rice (2010).

In this paper, we consider only a distributed drainage system whose mathematical description is motivated by the dynamics of subglacial cavities. We then focus on the complications introduced by predictions of negative water pressures or negative effective pressures. In particular, we fashion a free boundary model that prevents either situation from occurring, and instead allows for partial filling of the drainage system at zero water pressure (which we refer to as `under pressure’) as well as for the opening of an ice-bed gap at zero eective pressure (or `overpressure’). In the companion paper (Hewittetal., 2011, submitted), we then extend the ideas developed here to a model that includes a description of subglacial channels coupled to the subglacial cavities (see also Hewitt2011).

Subglacial Drainage

Drainage through subglacial water sheets (2009)

Timothy T. Creyts, Christian G. Schoof | Source

Abstract

Subglacial drainage plays an important role in controlling coupling between glacial ice and underlying bed. Here, we study the flow of water in thin, macroporous sheets between ice and bed. Previous work shows that small perturbations in depth of a nearly parallel-sided water film grow unstably because these areas have enhanced viscous dissipation that leads to enhanced melting of an ice roof. We argue that in the presence of bed protrusions bridging a water sheet, downward motion of the ice roof can stabilize this sheet. Stability results when the rate of roof closure increases faster with water depth than the rate of viscous dissipation. We therefore modify existing theory to include protrusions that partially support the overlying glacier. Differences in the pressure on protrusions relative to water pressure drive roof closure.

The mechanisms of both regelation and creep normal to the bed close the overlying ice roof and decrease the ice-bed gap. In order to account for multiple protrusion sizes along the bed (for instance, resulting from an assortment of various-sized sediment grains), we incorporate a method of partitioning overburden pressure among different protrusion size classes and the water sheet. Partitioning is dependent on the amount of ice protrusion contact and, therefore, water depth. This method allows prediction of roof closure rates. We then investigate stable, steady sheet configurations for reasonable parameter choices and find that these steady states can occur for modest water depths at very low effective pressures, as is appropriate for ice streams. Moreover, we find that multiple steady sheet thicknesses exist, raising the possibility of switches between low and high hydraulic conductivity regimes for the subglacial water system.

Friction at the glacier bed is deter- mined in large part by effective pressure, usually deØned as the diÆerence between ice overburden and subglacial water pressure. This is the case for both deformable and rigid glacier beds [ e.g., Paterson , 1994, Chaps. 7,8]. For glaciers and ice sheets with water at the bed, any predictive theory of ice dynamics requires a component that describes evolu- tion of eÆective pressure, that is, a theory for drainage at the ice{bed interface. To determine the distribution of eÆective pressure at the glacier bed requires an understanding of the morphology of the subglacial drainage system and of the relationship between water discharge, eÆective pressure, and hydraulic gradient in individual drainage elements. A drainage sys- tem can consist of diÆerent types of individual elements: for instance, channels, linked cavities, canals, englacial or groundwater ∞ow, or a combination of any of these [ e.g., Fountain and Walder , 1998; Hubbard and Nienow , 1997]. While theories exist for the behavior of individual drainage elements, interactions between any of these elements are not to grow. Consequently, linked cavity systems tend to form a distributed drainage network.

Subglacial drainage is one of the main controls on glacier sliding and erosion. Friction at the glacier bed is determined in large part by effective pressure, usually defined as the difference between ice overburden and subglacial water pressure. This is the case for both deformable and rigid glacier beds [e.g., Paterson, 1994, Chaps. 7,8]. For glacier sand ice sheets with water at the bed, any predictive theory of ice dynamics requires a component that describes evolution of effective pressure, that is, a theory for drainage at the ice-bed interface. To determine the distribution of effective pressure at the glacier bed requires an understanding of the morphologyof the subglacial drainage system and of the relationship between water discharge, effective pressure, and hydraulic gradient in individual drainage elements. A drainage system can consist of different types of individual elements: for instance, channels, linked cavities, canals, englacial or groundwater flow, or a combination of any of these [e.g.,Fountain and Walder, 1998; Hubbard and Nienow, 1997]. While theories exist for the behavior of individual drainage elements, interactions between any of these elements are not to grow. Consequently, linked cavity systems tend to form a distributed drainage network.

Once a drainage system is established subglacially, its response to water input is determined by the relationship between flux on one hand and effective pressure and hydraulic gradient on the other. Usually, systems such as R-channels that contain more water at high rather than low effective pressure will also transmit higher fluxes at high rather than low effective pressure. Conversely, distributed drainage systems such as linked cavities, in which water storage is facilitated by low effective pressures, need not have such a simple, monotonic relationship between effective pressure and flux. For instance, the linked cavity theory of Fowler [1987] predicts increasing flux with increasing effective pressure (as Rchannel theory does) while the canal theory of Walder and Fowler [1994] predicts the opposite.

To model a drainage system thus requires the physics that determines water flux at a given effective pressure to be understood. In short, a theory for subglacial drainage must incorporate two fundamental pieces: a functional relationship between water storage and effective pressure, and a means of determining water flux in terms of effective pressure and hydraulic gradient.
Sheet-like drainage elements have been considered previously, for instance by Weertman [1972] and Walder [1982].The main difference between their notion of a water film and our notion of a water sheet is that we consider an ice roof that is partially supported by contact with the bed – as is also the case in a linked cavity system – while in Weertman’s and Walder’s cases, ice and bed are everywhere separated by water, so the ice is effectively afoat on a thin water film. In general, we expect complete flotation of the ice on a thin water film not to occur, but unevenness in the bed to lead to partial contact. As we shall outline next, this is a crucial difference which allows our water sheet to remain stable while Walder’s film configuration necessarily leads to channelization.

We make the distinction that a watersheet has partial contact between the ice roof and sediment floor. On the contrary, a water film everywhere supports the overlying ice as described by Walder [1982] and Weertman[1972].

If the ice is at the pressure melting point throughout, then a pressure difference in the ice near the contact with the bed protrusion will cause a temperature gradient that leads to a melt/freeze pattern that allows the ice to move downward [ Paterson , 1994, Chap. 7].

Conclusions
Here, we have extended previous work [ e.g., Walder , 1982; Weertman , 1972] to show that distributed water sheets can be stable to much greater depth than previously quantified. The presence of protrusions that bridge the ice-bed gap can stabilize distributed sheets. Stabilization occurs because areas of greater water depth (and therefore those areas that are actively increasing water depth due to ice melt from enhanced viscous dissipation) can be offset by enhanced downward closure of an ice roof. This mechanism relies on a finite difference between overburden and water pressure ( i.e., a finite effective pressure) driving downward closure. This feature stands in contrast to water films with- out bed protrusions Walder [ e.g., 1982] where only water pressure balances ice overburden.

In constructing our theory, we have developed a recursive formulation for computing the partition of stresses between different protrusion sizes that exist at the bed and related these stresses to the downward motion of the ice through both viscous creep and regelation mechanisms. As a result, we are able to relate the closure velocity of the ice roof above the water sheet to effective pressure and sheet thickness. A steady state water sheet can then be formed if the melt rate of the ice roof due to viscous dissipation in the sheet balances the closure velocity. Steady state sheets of this form can, however, only persist if they are also stable , that is, if a small departure from steady state thickness leads to a negative feedback that returns thickness to its steady state value. This requires that a small thickening of the sheet from steady state should lead to a larger increase in down- ward ice velocity than the corresponding increase in melt rate. In turn, this is the case if a thickening of the sheet leads to a significant loss of contact between ice and bed protrusions.

Our theory predicts that such stable steady states do exist, and in fact, for beds with multiple protrusion sizes, multiple stable steady states can exist. Switches between these steady states can then lead to abrupt switches in water dis- charge in the drainage system. Future work will extend our theory to take account of spatial variations in effective pressure and hydraulic gradient, and to understand the effects of potential hydraulic switches.

Hydraulics of subglacial outburst floods: new insights from the Spring-Hutter formulation

Clarke, Garry K.C. | Source

Abstract:

Using a slightly modified form of the Spring-Hutter equations, glacial outburst floods are simulated from three classic sites, “Hazard Lake”, Yukon, Canada, Summit Lake, British Columbia, Canada, and Grímsvötn, Iceland, in order to calibrate the hydraulic roughness associated with subglacial conduits. Previous work has suggested that the Manning roughness of the conduits is remarkably high, but the new calibration yields substantially lower values that are representative of those for natural streams and rivers.The discrepancy can be traced to a poor assumption about the effectiveness of heat transfer at the conduit walls. The simulations reveal behaviour that cannot be inferred from simplified theories: (1) During flood onset, water pressure over much of the conduit can exceed the confining pressure of surrounding ice. (2) Local values of fluid potential gradient can differ substantially from the value averaged over the length of the conduit, contradicting an assumption of simple theories. (3) As the flood progresses, the location of flow constrictions that effectively control the flood magnitude can jump rapidly over large distances. (4) Predicted water temperature at the conduit outlet exceeds that suggested by measurements of exit water temperature.

Twenty-first-century warming of a large Antarctic ice-shelf cavity by a redirected coastal current (2012)
Hartmut H. Hellmer, Frank Kauker, Ralph Timmermann, Jürgen Determann & Jamie Rae | Source Nature

Abstract

The Antarctic ice sheet loses mass at its fringes bordering the Southern Ocean. At this boundary, warm circumpolar water can override the continental slope front, reaching the grounding line^{1, 2}through submarine glacial troughs and causing high rates of melting at the deep ice-shelf bases^{3, 4}. The interplay between ocean currents and continental bathymetry is therefore likely to influence future rates of ice-mass loss. Here we show that a redirection of the coastal current into the Filchner Trough and underneath the Filchner–Ronne Ice Shelf during the second half of the twenty-first century would lead to increased movement of warm waters into the deep southern ice-shelf cavity. Water temperatures in the cavity would increase by more than 2 degrees Celsius and boost average basal melting from 0.2 metres, or 82 billion tonnes, per year to almost 4 metres, or 1,600 billion tonnes, per year. Our results, which are based on the output of a coupled ice–ocean model forced by a range of atmospheric outputs from the HadCM3⁵ climate model, suggest that the changes would be caused primarily by an increase in ocean surface stress in the southeastern Weddell Sea due to thinning of the formerly consolidated sea-ice cover. The projected ice loss at the base of the Filchner–Ronne Ice Shelf represents 80 per cent of the present Antarctic surface mass balance⁶. Thus, the quantification of basal mass loss under changing climate conditions is important for projections regarding the dynamics of Antarctic ice streams and ice shelves, and global sea level rise.

Inland thinning of West Antarctic Ice Sheet steered along subglacial rifts (2012)

Robert G. Bingham, Fausto Ferraccioli, Edward C. King, Robert D. Larter, Hamish D. Pritchard, Andrew M. Smith & David G. Vaughan | Source Nature

Abstract

Current ice loss from the West Antarctic Ice Sheet (WAIS) accounts for about ten per cent of observed global sea-level rise¹. Losses are dominated by dynamic thinning, in which forcings by oceanic or atmospheric perturbations to the ice margin lead to an accelerated thinning of ice along the coastline^{2, 3, 4, 5}. Although central to improving projections of future ice-sheet contributions to global sea-level rise, the incorporation of dynamic thinning into models has been restricted by lack of knowledge of basal topography and subglacial geology so that the rate and ultimate extent of potential WAIS retreat remains difficult to quantify. Here we report the discovery of a subglacial basin under Ferrigno Ice Stream up to 1.5 kilometres deep that connects the ice-sheet interior to the Bellingshausen Sea margin, and whose existence profoundly affects ice loss. We use a suite of ice-penetrating radar, magnetic and gravity measurements to propose a rift origin for the basin in association with the wider development of the West Antarctic rift system. The Ferrigno rift, overdeepened by glacial erosion, is a conduit which fed a major palaeo-ice stream on the adjacent continental shelf during glacial maxima⁶. The palaeo-ice stream, in turn, eroded the ‘Belgica’ trough, which today routes warm open-ocean water back to the ice front⁷ to reinforce dynamic thinning. We show that dynamic thinning from both the Bellingshausen and Amundsen Sea region is being steered back to the ice-sheet interior along rift basins. We conclude that rift basins that cut across the WAIS margin can rapidly transmit coastally perturbed change inland, thereby promoting ice-sheet instability.

Related

Depositional model in subglacial cavities, Killiney Bay, Ireland. Interactions between sedimentation, deformation and glacial dynamics

Sylvain Clerca, Jean-François Buoncristiania, Michel Guirauda, Guy Desaubliauxb, Eric Portierb | Source ScienceDirect

Abstract
Subglacial meltwater drainage and sedimentary processes play a major role in ice-sheet dynamic but there is a lack of study of subglacial environment because modern ice-sheet beds remain inaccessible. Previous authors already intended to provide diagnostic criterion and recent investigations suggest that fluid pressure variations are a key factor in subglacial environment. This paper investigated the late Devensian sedimentary record in order to describe subglacial sedimentological facies associations and deformation features related to fluid overpressures. We used an integrated approach, based on stratigraphy, sedimentology and deformations styles to demonstrate a subglacial depositional model. The studied interval is composed of stratified gravel and sand interbedded with diamicton and boulder pavement, deposited in depressions formed by irregularity of the upper surface of diamicton. Deformation structures include convolutes, dykes and normal micro-faulting. Dykes show different dip directions from vertical, oblique to subhorizontal from which both directions of shortening and extension can be determined. Vertical dykes are formed under pure shear strain related to ice weight only.

Oblique dykes imply both ice-bed coupling and simple shear strain between ice and substrate induced by flowing ice related to progressively increasing meltwater drainage intensity. Horizontal dykes are formed when minimum strain is vertical and therefore the overpressure exceeds the weight of overburden. They are associated with high meltwater drainage intensity and ice-bed uncoupling and refer to hydrofracturing. Overall, depositional and deformation sequence also illustrates the increasing intensity of meltwater drainage in small cavity as high energy channelised deposits, and in large cavities where subaqueous fan are deposited under hydraulic jump conditions. Moreover, large cavities represent lee-side cavities formed by fast-flowing ice over an obstacle. Hydrofracturing is likely to occur when a dense fluid, potentially associated with catastrophic drainage of an upstream cavity enters the low-pressure confined environment of a downstream cavity and is injected under pressure in the soft substrate.

The studied glacial sequence represents a regional pattern probably related to an allocyclic control on sedimentation linked to long-term glacial dynamics rather than local depositional conditions. Based on these results, we provided a synthetic model linking depositional and deformation processes during ice-sheet growth and decay, but also valid at different timescales from annual to seasonal scale. Source

• Hydraulics of sub glacial cavities 1986, Walder
• Subglacial water pressures and the shape of subglacial conduits (1990)
• Detection of a subglacial lake in Glacier de Teˆte Rousse (Mont Blanc area) 2012, Example for hydrostatic water pressure exceeds the ice pressure at the bottom of the cavity.
• Teaser image by http://homepages.ulb.ac.be/~desamyn/Tsanfleuron%20Glacier%2006.html