Flow speed within the Antarctic ice sheet and its controls inferred from satellite observations

Abstract

Accurate dynamical models of the Antarctic ice sheet with carefully specified initial conditions and well-calibrated rheological parameters are needed to forecast global sea level. By adapting an inverse method previously used in electric impedance tomography, we infer present-day flow speeds within the ice sheet. This inversion uses satellite observations of surface velocity, snow accumulation rate, and rate of change of surface elevation to estimate the basal drag coefficient and an ice stiffness parameter that influences viscosity. We represent interior ice motion using a vertically integrated approximation to incompressible Stokes flow. This model represents vertical shearing within the ice and membrane stresses caused by horizontal stretching and shearing. Combining observations and model, we recover marked geographical variations in the basal drag coefficient. Relative changes in basal shear stress are smaller. No simple sliding law adequately represents basal shear stress as a function of sliding speed. Low basal shear stress predominates in central East Antarctica, where thick insulating ice allows liquid water at the base to lubricate sliding. Higher shear stress occurs in coastal East Antarctica, where a frozen bed is more likely. Examining Thwaites glacier in more detail shows that the slowest sliding often coincides with elevated basal topography. Differences between our results and a similar adjoint-based inversion suggest that inversion or regularization methods can influence recovered parameters for slow sliding and finer scales; on broader scales we recover a similar pattern of low basal drag underneath major ice streams and extensive regions in East Antarctica that move by basal sliding.

Incorporating modelled subglacial hydrology into inversions for basal drag

“…The ice-sheet model implemented is based on the hybrid formulation described in Goldberg (2011) and Arthern et al (2015) and uses the numerical implementation of Arthern et al (2015). This formulation is derived from the Stokes equations using variational principles (Dukowicz et al, 2010;Goldberg, 2011) and is a hybrid of the shallow ice approximation (Cuffey and Paterson, 2010) and the shallow shelf approximation (MacAyeal, 1989;Morland, 1987).…”

“…Following Goldberg (2011) and Arthern et al (2015), the conservation of momentum equations for depth-averaged velocities are…”

“…A variety of inversion methodologies have been applied in glaciology. These include iterative methods (Arthern et al, 2015), automatic differentiation (AD; Goldberg and Heimbach, 2013;Heimbach and Bugnion, 2009;Martin and Monnier, 2014), and Lagrangian multiplier methods based on control theory (MacAyeal, 1993;Morlighem et al, 2013).…”

“…The ice-sheet model uses the hybrid formulation of Arthern et al (2015) and Goldberg (2011) and is numerically similar to Arthern et al (2015). The inversion procedure is based on AD (Goldberg and Heimbach, 2013).…”

How dynamic are ice-stream beds?

“…Models of basal drag inverted from satellite-imaged surface properties (e.g. Joughin et al, 2009;Arthern et al, 2015) offer the 35 best opportunities to guide site selection.…”