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Investigations of the time-dependent behavior of marine ice sheets and their sensitivity to basal conditions require numerical models because existing theoretical analyses focus only on steady-state configurations primarily with a power-law basal shear stress. Numerical results indicate that the choice of the sliding law strongly affects ice-sheet dynamic behavior. Although observed or simulated grounding-line retreat is typically interpreted as an indication of marine ice sheet instability introduced by Weertman (1974), this (in)stability is a characteristic of the ice sheet's steady states – not time-variant behavior. To bridge the gap between theoretical and numerical results, we develop a framework to investigate grounding line dynamics with generalized basal and lateral stresses (i.e. the functional dependencies are not specified). Motivated by observations of internal variability of the Southern Ocean conditions we explore the grounding-line response to stochastic variability. We find that adding stochastic variability to submarine melt rates that produced stable steady-state configurations leads to intermittently advancing and retreating grounding lines. They can also retreat in an unstoppable manner on time-scales significantly longer than the stochastic correlation time-scales. These results suggest that at any given time of their evolution, the transient behavior of marine ice sheets cannot be described in terms of 'stable' or 'unstable'. [ABSTRACT FROM AUTHOR]

Temperate ice (ice at the melting point) is expected to form in the margins of fast moving ice streams. Experimental data suggest that water in the ice matrix changes the mechanical properties of ice by decreasing its viscosity. However, the implications of this weakening for ice sheet dynamics are poorly understood. Here, we investigate how the coupling between temperate ice properties, ice mechanics, and drainage of excess melt water from the ice stream margin to the bed alters the energy balance of ice streams. We model the steady-state ice flow, temperature, water content, and subglacial water drainage in the ice stream cross-section. Temperate ice dynamics are modelled as a coupled two-phase flow, with gravity-driven water transport in the compacting ice matrix according to Darcy's law. We find that the dependence of ice viscosity on melt water content leads to a strong focusing of the temperate ice region in ice stream margins, thereby strengthening heat dissipation there. This increases the amount of melt water delivered to the ice stream bed, and consequently elevates the water content in the bed. Our results demonstrate that the strength of these processes is controlled by the permeability of the temperate ice region and the dependence of the ice viscosity on the melt water content, both of which are poorly constrained properties. [ABSTRACT FROM AUTHOR]