[1] We present a two-dimensional Glacier Drainage System model (GlaDS) that couples distributed and channelized subglacial water flow. Distributed flow occurs through linked cavities that are represented as a continuous water sheet of variable thickness. Channelized flow occurs through Röthlisberger channels that can form on any of the edges of a prescribed, unstructured network of potential channels. Water storage is accounted for in an englacial aquifer and in moulins, which also act as point sources of water to the subglacial system. Solutions are presented for a synthetic topography designed to mimic an ice sheet margin. For low discharge, all the flow is accommodated in the sheet, whereas for sufficiently high discharge, the model exhibits a channelization instability which leads to the formation of a self-organized channel system. The random orientation of the network edges allows the channel system geometry to be relatively unbiased, in contrast to previous structured grid-based models. Under steady conditions, the model supports the classical view of the subglacial drainage system, with low pressure regions forming around the channels. Under diurnally varying input, water flows in and out of the channels, and a rather complex spatiotemporal pattern of water pressures is predicted. We explore the effects of parameter variations on the channel system topology and mean effective pressure. The model is then applied to a mountain glacier and forced with meltwater calculated by a temperature index model. The results are broadly consistent with our current understanding of the glacier drainage system and demonstrate the applicability of the model to real settings.

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-filled 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-film 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.

Gornersee, Switzerland, is an ice-marginal lake, which drains almost every year, subglacially, within a few days. We present an analysis of the lake outburst events between 1950 and 2005, as well as results of detailed field investigations related to the lake drainage in 2004 and 2005. The latter include measurements of lake geometry, water pressure in nearby boreholes and glacier surface motion. A distributed temperature-index melt model coupled to a linear-reservoir runoff model is used to calculate hourly discharge from the catchment of Gornergletscher in order to distinguish between the melt/precipitation component and the outburst component of the discharge hydrograph. In this way, drainage volume and timing are determined. From 1950 there is a clear trend for the outburst flood to occur earlier in the melt season, but there is no trend in lake discharge volumes. Peak discharges from the lake lie significantly below the values obtained using the empirical relation proposed by Clague and Mathews (1973). The shapes of the 2004 and 2005 lake outflow hydrographs differ substantially, suggesting different drainage mechanisms. From water balance considerations we infer a leakage of the glacier-dammed lake in 2005, starting 1 week prior to the lake outburst. During the drainage events, up to half of the lake water is temporarily stored in the glacial system, causing substantial uplift of the glacier surface.

We present a new model of subglacial drainage incorporating flow in a network of channels and a porous sheet, with water exchange between the two determined by pressure gradients. The sheet represents the average effect of many linked cavities, whilst the channels emerge from individual cavities that enlarge due to dissipation-induced melting. The model distinguishes cases when the water pressure drops to zero, in which case it allows for the drainage space to be only partially filled with water (free surface flow), and when the pressure reaches the ice overburden pressure, in which case it allows for uplift of the ice to whatever extent is needed to accommodate the water (flotation). Numerical solutions are found for a one-dimensional flow-line version of the model. The results capture typically observed or inferred features of subglacial drainage systems, including open channel flow at the ice margin, seasonal channel evolution, and high water pressures and uplift of the ice surface driven by rapid changes in water supply.

Subglacial hydrology plays a key role in many glaciological processes, including ice dynamics via the modulation of basal sliding. Owing to the lack of an overarching theory, however, a variety of model approximations exist to represent the subglacial drainage system. The Subglacial Hydrology Model Intercomparison Project (SHMIP) provides a set of synthetic experiments to compare existing and future models. We present the results from 13 participating models with a focus on effective pressure and discharge. For many applications (e.g. steady states and annual variations, low input scenarios) a simple model, such as an inefficient-system-only model, a flowline or lumped model, or a porous-layer model provides results comparable to those of more complex models. However, when studying short term (e.g. diurnal) variations of the water pressure, the use of a two-dimensional model incorporating physical representations of both efficient and inefficient drainage systems yields results that are significantly different from those of simpler models and should be preferentially applied. The results also emphasise the role of water storage in the response of water pressure to transient recharge. Finally, we find that the localisation of moulins has a limited impact except in regions of sparse moulin density.

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ABSTRACT. Over recent decades, Greenland ice sheet surface melt has shown an increase both in intensity and spatial extent. Part of this water probably reaches the bed and can enhance glacier speed, advecting a larger volume of ice into the ablation area. In the context of a warming climate, this mechanism could contribute to the future rate of thinning and retreat of land-terminating glaciers of Greenland. These changes in ice flow conditions will in turn influence surface crevassing and thus the ability of water to reach the bed at higher elevations. Here, using a coupled basal hydrology and prognostic ice flow model, the evolution of a Greenland-type glacier subject to increasing surface melt is studied over a few decades. For different scenarios of surface melt increase over the next decades, the evolution of crevassed areas and the ability of water to reach the bed is inferred. Our results indicate that the currently observed crevasse distribution is likely to extend further upstream which will allow water to reach the bed at higher elevations. This will lead to an increase in ice flux into the ablation area which, in turn, accelerates the mass loss of land-terminating glaciers.

We investigate the dynamics of Bose-Einstein condensates in a tilted one-dimensional periodic lattice within the mean-field (Gross-Pitaevskii) description. Unlike in the linear case the Bloch oscillations decay because of nonlinear dephasing. Pronounced revival phenomena are observed. These are analyzed in detail in terms of a simple integrable model constructed by an expansion in Wannier-Stark resonance states. We also briefly discuss the pulsed output of such systems for stronger static fields.