Ice sheet flow with thermally activated sliding. Part 1: the role of advection

Abstract

Flow organization into systems of fast-moving ice streams is a well-known feature of ice sheets. Fast motion is frequently the result of sliding at the base of the ice sheet. Here, we consider how this basal sliding is first initiated as the result of changes in bed temperature. We show that an abrupt sliding onset at the melting point, with no sliding possible below that temperature, leads to rapid drawdown of cold ice and refreezing as the result of the increased temperature gradient within the ice, and demonstrate that this result holds regardless of the mechanical model used to describe the flow of ice. Using this as a motivation, we then consider the possibility of a region of 'subtemperate sliding' in which sliding at reduced velocities occurs in a narrow range of temperatures just below the melting point. We confirm that this prevents the rapid drawdown of ice and refreezing of the bed, and construct a simple numerical method for computing steady-state ice sheet profiles that include a subtemperate region. The stability of such an ice sheet is analysed in a companion paper.

The role of sliding in ice stream formation

“…Note that previous work on subtemperate sliding in [11] explicitly considered the limit δ ≪ 1 of strong temperate sensitivity, which is however fraught with instabilities [27]. Here, we retain δ as a nominally O (1) parameter, although we will be concerned primarily with the case of small δ eventually: as we will show, taking the limit δ ≪ 1 in the confines of our already reduced model will be valid provided ε ≪ δ 2 , where ε is the ice sheet aspect ratio.…”

“…Consider a part of the free boundary at y m ( x , t ), and suppose without loss of generality that the cold subdomain lies to the left of the boundary y = y m . For a growing temperate region, we have V = ∂ y m /∂ t < 0, we assume that migration occurs only when heat flux is non-singular at y = y m (so there is no singular freezing rate false[−false(∂T/∂zfalse)false]−+) as previously studied in [11,12,16,19]: limyfalse→ym+(false|ym−y|1/2[∂T∂z]−+)≥01em if V<0. Note that the local analysis around the transition point y = y m in [19] is applicable here, which shows freezing will in general occur near the margin, but we can insist that freezing rates not be singular if the ice stream is expanding (in which case the left-hand side of (2.25) is zero, see also §2 of the electronic supplementary material). The condition (2.25) is mathematically analogous to prescribing a vanishing fracture toughness in crack propagation problems [36], although applied to the thermal rather than the mechanical problem.…”

“…Motivated by recent work [11] demonstrating that the transition from cold to temperate bed must involve a region of subtemperate sliding, we revisit the possibility of pattern formation in such a region. We abandon Hindmarsh’s [10] use of a depth-integrated model with no vertical shear.…”

“…As Mantelli et al [11] show in two dimensions, vertical advection of cold ice is key in suppressing the feedback between sliding and a warming bed. As sliding gets faster in the downstream direction, mass conservation dictates that ice higher in the ice column is drawn down towards the bed.…”

Topographic Correction of Geothermal Heat Flux in Greenland and Antarctica

“…While any topographic dependence of geothermal heat flux is not expected to influence its regional value at larger spatial scales (≳ 10 km), because of the constrained self‐affinity of subglacial topography (Jordan et al., 2017), it may have significant implications for subglacial hydrology and basal conditions at smaller scales (≲ 10 km). Local reorganizations of water or ice flow can instigate larger‐scale downstream changes (Fahnestock et al., 2001; Mantelli et al., 2019; Pittard et al., 2016). Spatial variability in geothermal heat flux can also be a consideration when reconstructing the subglacial hydrology of paleo‐ice sheets (Näslund et al., 2005).…”