Large‐scale ice flow over a viscous basal sediment: Theory and application to ice stream B, Antarctica

Abstract

Recent seismic studies of ice stream B, Antarctica and field analysis of mid‐latitude glacial deposits suggest that deformable basal sediments (e.g., water‐saturated till) are important in determining ice sheet flow. If the ratio of till viscosity to effective ice viscosity is small, vertical shear associated with horizontal flow is confined to the deforming bed alone. Ice flow over a deformable bed is thus akin to that of floating ice shelves, because ice shelves flow over inviscid seawater. For some Antarctic ice streams, and possibly for portions of the late Wisconsin ice sheets in North America and Eurasia, basal drag associated with deforming basal sediment does not induce significant vertical gradients of horizontal velocity. Instead, basal drag affects the flow as if it were a horizontal body force balanced by longitudinal and transverse deviatoric stress gradients. Comparison of the observed flow of ice stream B to finite element simulations incorporating a viscous basal till suggest that a simple till rheology is sufficient to explain the current velocity profile. These simulations also highlight the importance of horizontal deviatoric stress in regions where driving stress and basal stress do not locally balance. While bed deformation is critical to ice stream existence, sensitivity tests suggest that ice shelf back pressure is still a crucial control affecting ice stream response to atmospheric and oceanic climate.

Basal sliding of Ice Stream B, West Antarctica

“…Alley and others, 1989;MacAyeal, 1989MacAyeal, , 1992Kamb, 1991). This affects formulation of the basal boundary condition (relation between basal shear stress and basal flow velocity) and the longitudinal transport of till, including the continuity condition on sources and sinks of till.…”

“…In the discussion of the cause of this rapid movement the main current focus is on shear deformation of unfrozen, water-saturated subglacial till (Alley and others, 1986(Alley and others, ,1987(Alley and others, ,1989MacAyeal, 1989MacAyeal, , 1992Kamb, 1991). The alternative possibility of rapid basal sliding, proposed originally by Rose (1979), has been discounted theoretically (Alley, 1989).…”

Similitude of ice dynamics against scaling of geometry and physical parameters

“…with constant friction coefficient C. The exponent m determines the particular type of the sliding law, including plastic (m = 0, magnitude of basal shear stress independent of velocity; Tulaczyk et al, 2000) and linear-viscous (m = 1, basal shear stress proportional to ice velocity; MacAyeal, 1989) behaviors. A value of m = 1/n = 1/3 is commonly assumed to represent sliding over rough bed (Schoof, 2007a;Joughin et al, 2009;Cuffey and Paterson, 2010).…”

“…Here we apply the concept of similitude to the dynamics of idealized ice sheets based on the shallow-shelf approximation (SSA; Morland, 1987;MacAyeal, 1989;Greve and Blatter, 2009). In particular we assume isothermal ice and a spatially uniform basal friction coefficient, conditions that have been used to analyze ice-sheet dynamics in a number of previous studies (e.g., Dupont and Alley, 2005;Goldberg et al, 2009;Gudmundsson et al, 2012;Pattyn et al, 2013;AsayDavis et al, 2015).…”

“…A dimensional analysis of the ice-dynamic equations is often carried out to compare the magnitudes of the different acting forces and thus to derive physically motivated approximations, as done when deriving the SSA from the full Stokes stress balance (MacAyeal, 1989;Greve and Blatter, 2009). The non-dimensionalized form of the SSA itself and the involved dimensionless coefficients that result from the introduction of typical scales for, e.g., ice-sheet thickness and velocity, have been used to consider asymptotic limits of SSA ice flow in previous work (Schoof, 2007a;Dupont and Alley, 2005;Tsai et al, 2015;Haseloff et al, 2015).…”