ALBERT

Description: Application of thermal convection theory to polar ice sheets (Hughes, 1970, 1971. 1972[a],[c]) is reviewed and expanded. If it occurs, thermal convection is mainly concentrated near the bed of the ice sheet; resulting in active and passive convective flow, respectively below and above the ice density inversion. Convection begins as transient creep when a stress-independent critical Rayleigh number is exceeded, and stabilizes as steady-state creep when a stress-dependent critical Rayleigh number is exceeded. Transient- creep convection begins as unstable ripples in isotherms near the bed, with some ripples becoming upward bulges of basal ice which rapidly shrink laterally and grow vertically to become ascending dikes of recrystallized basal ice during steady-state creep. Sills of basal ice are injected horizontally between weakly coupled layers in the strata of cold ice slowly sinking en masse between dikes. Convection begins under domes of thick ice toward the ice-sheet center and a stable polygonal array of dikes may form if frictional heat creates hot ice at the bed as rapidly as convection flow redistributes hot basal ice in dikes and sills, Advective flow transports the converting ice toward the margin of the ice sheet where dikes converge at the heads of ice streams. Dike—sill convection then becomes ice-stream convection in which the entire ice stream behaves like a dike, uncoupling from the bed, and rising en masse. This would help explain why ice streams flow at surge velocities.

Description: Using simple Fourier transform techniques and extensions to stationary-phase methods, the behaviour of surface gravity waves is determined near triply coalescing roots of the dispersion relation. It is shown that the amplitude of the surface wave is proportional to (∂U/∂x)−¼ at the location of the triple root. Far from the triple root it satisfies conservation of action. The internal wave is modelled simply by its surface current U. Asymptotic orders of magnitude are also given for the case ∂U/∂x = 0 at the triple root. © 1976, Cambridge University Press. All rights reserved.

Description: Late-Wisconsin ice sheets were reconstructed for the CLIMAP 18000 years b.p. experiment. This experiment modeled the ice-age steady-state climate using boundary conditions that differed from present ones mainly in Earth-surface albedos, sea-surface areas, and land-surface topography. These required determinations of the area, volume, and elevation of Late Wisconsin ice sheets. An initial-value finite-difference numerical model for ice-sheet reconstruction was developed from a recursive formula which gave ice thickness for known variations of bed topography and theoretical variations of basal shear stress. Ice thicknesses were calculated in 50 km to 100 km steps along flow lines from margins to domes of late-Wisconsin ice sheets. We assumed that terrestrial margins were along the furthermost moraines, marine margins were along the present 500 m bathymetric contour, domes were centers of maximum post-glacial isostatic rebound, and flow lines were along glacial lineations (eskers, striations, drumlins, etc.) connecting margins to domes. At various locations ice-sheet margins were verified by dated moraines for terrestrial margins and Egga-type moraines for marine margins. Ice-sheet elevations and thicknesses were contoured from profiles reconstructed for 40 Antarctic flow lines and 137 Northern Hemisphere flow lines for a maximum ice-sheet extent, and 86 Northern Hemisphere flow lines for a minimum ice-sheet extent.

Description: The CLIMAP 18000 years b.p. experiment required reconstructing late-Wisconsin-Weichselian ice sheets. In the Northern Hemisphere, the greatest uncertainty in these reconstructions is the area covered by ice sheets. Two schools of thought exist (Hughes and others, in press). The minimum-ice-sheet school holds that ice sheets originated from present ice caps in the High Arctic islands, but the northern seaward margins of these ice sheets retreated as the southern landward margins advanced. This occurred because northern margins became isolated from sources of precipitation as Arctic seas became permanently ice-covered and the advancing southern margin changed atmospheric circulation patterns. In this view, these ice sheets stay about the same size and migrate southward during an ice age. Northern margins rarely reach sea-level during the later stage of the ice age so no marine portions form and ablation is by melting or sublimation. Marine portions formed only when the ice sheets migrated across shallow seas between the High Arctic islands and the mainland. At the end of the ice age, huge amounts of heat had to be transferred from the tropics to the ice sheets in order to account for late-Wisconsin-Weichselian and Holocene retreat-rates by melting along ice-sheet margins.

Description: The CLIMAP 18000 years b.p. experiment required reconstructing late-Wisconsin-Weichselian ice sheets. In the Northern Hemisphere, the greatest uncertainty in these reconstructions is the area covered by ice sheets. Two schools of thought exist (Hughes and others, in press). The minimum-ice-sheet school holds that ice sheets originated from present ice caps in the High Arctic islands, but the northern seaward margins of these ice sheets retreated as the southern landward margins advanced. This occurred because northern margins became isolated from sources of precipitation as Arctic seas became permanently ice-covered and the advancing southern margin changed atmospheric circulation patterns. In this view, these ice sheets stay about the same size and migrate southward during an ice age. Northern margins rarely reach sea-level during the later stage of the ice age so no marine portions form and ablation is by melting or sublimation. Marine portions formed only when the ice sheets migrated across shallow seas between the High Arctic islands and the mainland. At the end of the ice age, huge amounts of heat had to be transferred from the tropics to the ice sheets in order to account for late-Wisconsin-Weichselian and Holocene retreat-rates by melting along ice-sheet margins.

Description: Application of thermal convection theory to polar ice sheets (Hughes, 1970, 1971. 1972[a],[c]) is reviewed and expanded. If it occurs, thermal convection is mainly concentrated near the bed of the ice sheet; resulting in active and passive convective flow, respectively below and above the ice density inversion. Convection begins as transient creep when a stress-independent critical Rayleigh number is exceeded, and stabilizes as steady-state creep when a stress-dependent critical Rayleigh number is exceeded. Transient- creep convection begins as unstable ripples in isotherms near the bed, with some ripples becoming upward bulges of basal ice which rapidly shrink laterally and grow vertically to become ascending dikes of recrystallized basal ice during steady-state creep. Sills of basal ice are injected horizontally between weakly coupled layers in the strata of cold ice slowly sinking en masse between dikes. Convection begins under domes of thick ice toward the ice-sheet center and a stable polygonal array of dikes may form if frictional heat creates hot ice at the bed as rapidly as convection flow redistributes hot basal ice in dikes and sills, Advective flow transports the converting ice toward the margin of the ice sheet where dikes converge at the heads of ice streams. Dike—sill convection then becomes ice-stream convection in which the entire ice stream behaves like a dike, uncoupling from the bed, and rising en masse. This would help explain why ice streams flow at surge velocities.

Description: Most numerical models of present ice-sheet dynamics predict basal thermal conditions for an assumed geothermal heat flux and measured ice thickness, surface temperature, and snow precipitation. These models are not ideally suited for reconstructing former ice sheets because what is known for present ice sheets is unknown for former ones, and vice versa. In particular, geothermal heat fluxes are immeasurable at an ice-sheet bed but can be measured after the ice sheet is gone, and the thermal conditions predicted at an ice-sheet bed can be inferred from the glacial-geological–topographic record after the ice sheet is gone. The Maine CLIMAP ice-sheet reconstruction model uses these inferred basal thermal conditions to compute ice thicknesses from basal shear stresses. Basal shear stress is assumed to reflect the degree of ice–bed coupling which, in turn, is assumed to reflect the amount and distribution of basal water under the ice sheet. Under the ice-sheet interior, basal water exists in a thin film of constant thickness covering the low places on the bed. This film expands for a melting bed and contracts for a freezing bed. Along the ice-sheet margin, basal water exists in narrow channels of varying thickness corresponding to troughs on the bed. These water channels become deeper for a melting bed and shallower for a freezing bed. In areas covered by the Laurentide and Scandinavian ice sheets, myriads of interconnected lakes in regions of greatest postglacial rebound are interpreted as evidence suggesting the interior basal water distribution, whereas eskers pointed toward terminal moraines and troughs across continental shelves are interpreted as evidence suggesting the basal water distribution toward the margins. Continental-shelf troughs were assumed to correspond to former ice streams, by analogy with observations in Greenland and Antarctica. Three modes of glacial erosion are considered to be responsible for the lakes, eskers, troughs, and associated topography. Quarrying is by a freeze-thaw mechanism which occurs where the melting-point isotherm intersects bedrock, so it is important only for freezing or melting beds because high places on the bed are frozen, low places are melted, and minor basal temperature fluctuations shift the isotherm separating them. Crushing results when rocks at the ice-bed interface are ground against each other and the bed by glacial sliding, so it occurs where the bed is melted and is most important when the entire bed is melted. Abrasion of bedrock occurs when rock cutting tools imbedded in the ice at the ice–rock interface are moved across the interface by glacial sliding, so it is also most important when the entire bed is melted. If basal melting continued after the entire bed is melted, abrasion-rates drop because the basal water layer thickens and drowns bedrock projections otherwise subjected to abrasion. Basal freezing reduces both crushing and abrasion-rates by coating quarried rocks with a sheath of relatively soft ice and transporting them upward from the ice–rock interface. An initially flat subglacial topography will develop depressions where glacial erosion is greatest and deposition is least, and ridges where the opposite conditions prevail. We interpret the central depressions represented today by Hudson Bay and the Gulf of Bothnia as caused by erosion on a melting bed under the Laurentide and Scandinavian ice sheets, respectively. The arc of lakes, gulfs, and shallow seas surrounding these depressions are interpreted as resulting from a freezing bed under the former ice sheets. The present watershed separating the depressions from the arcs marks the approximate former basal equilibrium line where the bed was melted. The Canadian and Baltic continental shields beyond these arcs are blanketed by material eroded from within the arcs, and represent areas having a frozen bed where evidence for abrasion is missing and a second zone having a melting bed where evidence for abrasion is present. This basic pattern was assumed to be imprinted on the bed during the steady-state period of maximum ice-sheet extent, and maintained in varying degrees during growth and shrinkage of these ice sheets.

Description: Size, shape, and surface albedo of former ice sheets are needed in order to model atmospheric circulation for the CLIMAP 18000 years B.P. experiment. Both the size and shape of an ice sheet depend on the hardness of ice and its coupling to bedrock. Ice hardness is controlled by ice temperature and fabric, which are not adequately described by any ice flow law. Ice–bed coupling is controlled by bed roughness and basal melt water, which are not adequately described by any ice sliding law. With these inadequacies in mind, we assumed equilibrium ice-sheet conditions 18000 years ago and combined the standard steady-state flow and sliding laws of ice with the equation of mass balance to obtain separate basal shear-stress variations along ice-sheet flow lines for a frozen bed when the flow law dominates and for a melted bed when the sliding law dominates. Theoretical basal shear-stress variations were then derived for freezing and melting beds on the assumption that separate melted areas of the bed had water films of constant thickness which expanded and merged for a melting bed but contracted and separated for a freezing bed. Theoretical basal shear-stress variations were also derived for ice streams along marine ice-sheet margins and ice lobes along terrestrial ice-sheet margins on the assumption that the entire area of their bed was wet so that further melting increased the water-layer thickness, which would then be decreased by freezing. Melting was assumed to continue to the grounding line of an ice stream and the minimum-slope surface inflection line of an ice lobe, where freezing began and continued to the ice-lobe terminus. Ice–bed uncoupling is complete at an ice-stream grounding line and maximized at an ice-lobe minimum-slope inflection line, so ice velocity and consequent generation of frictional heat were assumed to reach maxima across these lines. Theoretical basal shear-stress variations were derived for the zone of converging flow at the heads of ice streams and ice lobes, and from domes to saddles along the ice divide for both frozen and melted beds.