Sliding of temperate basal ice on a rough, hard bed: creep mechanisms, pressure melting, and implications for ice streaming
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Abstract. Basal ice motion is crucial to ice dynamics of ice sheets. The classic Weertman model for basal sliding over bedrock obstacles proposes that sliding velocity is controlled by pressure melting and/or ductile flow, whichever is the fastest; it further assumes that pressure melting is limited by heat flow through the obstacle and ductile flow is controlled by standard power-law creep. These last two assumptions, however, are not applicable if a substantial basal layer of temperate (T ∼ Tmelt) ice is present. In that case, frictional melting can produce excess basal meltwater and efficient water flow, leading to near-thermal equilibrium. High-temperature ice creep experiments have shown a sharp weakening of a factor 5–10 close to Tmelt, suggesting standard power-law creep does not operate due to a switch to melt-assisted creep with a possible component of grain boundary melting. Pressure melting is controlled by meltwater production, heat advection by flowing meltwater to the next obstacle and heat conduction through ice/rock over half the obstacle height. No heat flow through the obstacle is required. Ice streaming over a rough, hard bed, as possibly in the Northeast Greenland Ice Stream, may be explained by enhanced basal motion in a thick temperate ice layer.Keywords:
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As ice flows over a subglacial lake, the drop in bed resistance leads to an increase in ice velocity and a subsequent lowering of the ice surface in the vicinity of the upstream lake edge. Conversely, at the downstream end of the lake a small hump is observed as the ice velocity decreases near the point of contact with land. There are two contributions arising from the ice/lake interaction: (1) changes in the thermal regime that propagate downwards with the advection of ice and (2) the increase in flow speeds caused by basal sliding over the lake surface. Sediment transport from upstream areas into subglacial lakes changes their size, thus reducing the area of the ice/lake interface. Here, we aim to study the effect that this reduction in size has on the flow dynamics and the surface elevation of an artificial ice stream and the temporal evolution of this effect. To this end, we use a full-Stokes, polythermal ice flow model, implemented into the commercial finite element software COMSOL Multiphysics. An enthalpy gradient method is used in order to account for the evolution of temperature and water content within the ice. This conceptual model uses prescribed boundary velocity and temperature profiles and a Weertman-type sliding law with a fixed parameter combination. In order to separate the effect of the slow thermal contribution from the fast mechanical one, we will present sensitivity tests that additionally involve a thermally-constant flow.
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Abstract. Basal ice motion is crucial to ice dynamics of ice sheets. The classic Weertman model for basal sliding over bedrock obstacles proposes that sliding velocity is controlled by pressure melting and/or ductile flow, whichever is the fastest; it further assumes that pressure melting is limited by heat flow through the obstacle and ductile flow is controlled by standard power-law creep. These last two assumptions, however, are not applicable if a substantial basal layer of temperate (T ∼ Tmelt) ice is present. In that case, frictional melting can produce excess basal meltwater and efficient water flow, leading to near-thermal equilibrium. High-temperature ice creep experiments have shown a sharp weakening of a factor 5–10 close to Tmelt, suggesting standard power-law creep does not operate due to a switch to melt-assisted creep with a possible component of grain boundary melting. Pressure melting is controlled by meltwater production, heat advection by flowing meltwater to the next obstacle and heat conduction through ice/rock over half the obstacle height. No heat flow through the obstacle is required. Ice streaming over a rough, hard bed, as possibly in the Northeast Greenland Ice Stream, may be explained by enhanced basal motion in a thick temperate ice layer.
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A geometrical force balance that links stresses to ice bed coupling along a flow band of an ice sheet was developed in 1988 for longitudinal tension in ice streams and published 4 years later. It remains a work in progress. Now gravitational forces balanced by forces producing tensile, compressive, basal shear, and side shear stresses are all linked to ice bed coupling by the floating fraction ϕ of ice that produces the concave surface of ice streams. These lead inexorably to a simple formula showing how ϕ varies along these flow bands where surface and bed topography are known: ϕ = h O / h I with h O being ice thickness h I at x = 0 for x horizontal and positive upslope from grounded ice margins. This captures the basic fact in glaciology: the height of ice depends on how strongly ice couples to the bed. It shows how far a high convex ice sheet (ϕ = 0) has gone in collapsing into a low flat ice shelf (ϕ = 1). Here ϕ captures ice bed coupling under an ice stream and h O captures ice bed coupling beyond ice streams.
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When a strong, cold wind blows over open polar leads, ice grows in the form of small crystals which are herded downwind by both wind waves and a wind‐driven surface current to pile up at the downwind edge of the lead. As this process continues, the piled‐up ice, called ‘grease ice,’ advances upwind until the entire lead is ice covered. In a numerical model of ice growth in a horizontally one‐dimensional lead with a wind blowing along its length we use the heat flux taken from existing formulations to determine the ice production rate. Similarly, we use the wave field and surface current, which are functions of wind speed and fetch, to calculate the ice pileup depth and the ice cover advance rate. Because this ice growth mechanism allows water at its freezing point to remain in contact with the cold air, high heat and salt fluxes are maintained. The ice growth predicted from this model is an order of magnitude greater than one‐dimensional vertical growth.
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The plasticity of the Arctic ice pack depends on its granular nature, in particular on the size and distribution of areas of thin ice and open water surrounding multiyear ice floes. The paper begins with construction of a mesoscale (10–100 km) granular model of the central Arctic ice pack. The mesoscale model is based on a dynamic particle simulation in which individual multiyear ice floes and surrounding parcels of first‐year ice are explicitly modeled as discrete, convex polygons in a two‐dimensional domain. Deformation of the domain produces areas of localized failure and areas of open water. The areas of localized failure are modeled as pressure ridging events using the results of numerical experiments performed with a computer simulation of the ridging process. The paper focuses on the results of numerical experiments performed with the mesoscale model. In the experiments the model ice pack is biaxially deformed at constant strain rates. The principal strain rates are varied to create deformation states ranging from pure shear to uniform compression. The results define the shape and magnitude of the plastic yield surface, the strain rate vectors associated with points on the yield surface, the partition of energy dissipation between ridging and in‐plane sliding, and the changes in the ice thickness distribution associated with various deformation states.
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The West Antarctic region from which ice drains into the Ross Sea is described and analyzed on a twenty km grid with the assumption that the ice is in a steady state of zero overall mass balance. The most striking features of the basin are five major ice streams moving in their lower reaches with velocities two orders of magnitude larger than the ice in which they are embedded. These high velocities are produced by driving stresses which markedly decrease downstream; this suggests that basal sliding takes over from internal deformation as dominant mode of flow. Algebraic expressions for both velocity components are given in terms of the downslope driving (or basal shear) stress, the ice thickness excess above the maximum thickness that can float on rock below mean sea level (''thickness above buoyancy''), and the basal temperature. Thus computed the velocities agree broadly with those derived directly from the condition of steady-state mass conservation (''balance velocities'') but there remain large local discrepancies. The latter fully define the three-dimensional strain rate fields and permit the residence times and ages of the ice to be estimated. They also enter into solutions of thermodynamic energy balance equations which give the temperatures inmore » the ice and define regions where basal melting can be expected to occur for different values of the geothermal heat flux. The associated melt water layer is the key feature for a deeper understanding of the sliding and surging processes in ice streams and for improving the agreement between modeled and observed ice velocities.« less
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Abstract. Basal ice motion is crucial to ice dynamics of ice sheets. The Weertman sliding model for basal sliding over bedrock obstacles proposes that sliding velocity is controlled by pressure melting and/or ductile flow, whichever is the fastest; it further assumes that stoss-side melting is limited by heat flow through the obstacle and ductile flow is controlled by Power Law Creep. These last two assumptions, it is argued here, are invalid if a substantial basal layer of temperate (T ~ Tmelt) ice is present. In that case, frictional melting results in excess basal meltwater and efficient water flow, leading to near-thermal equilibrium. Stoss-side melting is controlled by melt water production, heat advection by flowing meltwater to the next obstacle, and heat conduction through ice/rock over half the obstacle height. No heat flow through the obstacle is required. High temperature ice creep experiments have shown a sharp weakening of a factor 5–10 close to Tmelt, implying breakdown of Power Law Creep and probably caused by a deformation-mechanism switch to grain boundary pressure melting. Ice streaming over a rough, hard bed, as likely in the Northeast Greenland Ice Stream, may be explained by enhanced basal motion in a thick temperate ice layer.
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