[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.

Surges are common in all the major ice caps in Iceland, and historical reports of surge occurrence go back several centuries. Data collection and regular observation over the last several decades have permitted a detailed description of several surges, from which it is possible to generalize on the nature of surging in Icelandic glaciers. Combining the historical records of glacier-front variations and recent field research, we summarize the geographic distribution of surging glaciers, their subglacial topography and geology, the frequency and duration of surges, changes in glacier surface geometry during the surge cycle, and measured velocity changes compared to calculated balance velocities. We note the indicators of surge onset and describe changes in ice, water and sediment fluxes during a surge. Surges accomplish a significant fraction of the total mass transport through the main outlet glaciers of ice caps in Iceland and have important implications for their hydrology. Our analysis of the data suggests that surge-type glaciers in Iceland are characterized by gently sloping surfaces and that they move too slowly to remain in balance given their accumulation rate. Surge frequency is neither regular nor clearly related to glacier size or mass balance. Steeply sloping glaciers, whether hard- or soft-bedded, seem to move sufficiently rapidly to keep in balance with the annual accumulation.

Recent observations of dynamic water systems beneath the Greenland and Antarctic ice sheets have sparked renewed interest in modelling subglacial drainage. The foundations of today's models were laid decades ago, inspired by measurements from mountain glaciers, discovery of the modern ice streams and the study of landscapes evacuated by former ice sheets. Models have progressed from strict adherence to the principles of groundwater flow, to the incorporation of flow 'elements' specific to the subglacial environment, to sophisticated twodimensional representations of interacting distributed and channelized drainage. Although presently in a state of rapid development, subglacial drainage models, when coupled to models of ice flow, are now able to reproduce many of the canonical phenomena that characterize this coupled system. Model calibration remains generally out of reach, whereas widespread application of these models to large problems and real geometries awaits the next level of development.

A hydrologically coupled flowband model of 'higher order' ice dynamics is used to explore perturbations in response to supraglacial water drainage and subglacial flooding. The subglacial drainage system includes interacting 'fast' and 'slow' drainage elements. The fast drainage system is assumed to be composed of ice-walled conduits and the slow system of a macroporous water sheet. Under high subglacial water pressures, flexure of the overlying ice is modelled using elastic beam theory. A regularized Coulomb friction law describes basal boundary conditions that enable hydrologically driven acceleration. We demonstrate the modelled interactions between hydrology and ice dynamics by means of three observationally inspired examples: (i) simulations of meltwater drainage at an Alpine-type glacier produce seasonal and diurnal variability, and exhibit drainage evolution characteristic of the so-called 'spring transition'; (ii) horizontal and vertical diurnal accelerations are modelled in response to summer meltwater input at a Greenlandtype outlet glacier; and (iii) short-lived perturbations to basal water pressure and ice-flow speed are modelled in response to the prescribed drainage of a supraglacial lake. Our model supports the suggestion that a channelized drainage system can form beneath the margins of the Greenland ice sheet, and may contribute to reducing the dynamic impact of floods derived from supraglacial lakes.

[1] Basal hydrology is acknowledged as a fundamental control on glacier dynamics, especially in cases where surface meltwater reaches the bed. For many glaciers at midlatitudes, basal drainage is influenced by subaerial, englacial, and subsurface water flow. One of the major shortcomings of existing basal hydrology models is the treatment of the glacier bed as an isolated system. We present theoretical and computational models that couple glacier surface runoff, englacial water storage and transport, subglacial drainage, and subsurface groundwater flow. Each of the four model components is represented as a two-dimensional, vertically integrated layer that communicates with its neighbors through water exchange. Governing equations are derived from the law of mass conservation and are expressed as a balance between the internal distribution of water and external sources. The numerical exposition of this theory is a time-dependent finite difference model that can be used to simulate glacier drainage. In this paper we outline the theory and conduct simple tests using an idealized glacier geometry. In the companion paper, the model is tailored to Trapridge Glacier, Yukon Territory, Canada, where results are compared with measurements of subglacial water pressure.