A theory of glacier dynamics and instabilities Part 1: Topographically confined glaciers

Abstract

We present a theoretical framework that integrates the dynamics of glaciers with and without the topographic confinement. This Part 1 paper concerns the former, which may exhibit surge cycles when subjected to thermal switches associated with the bed condition. With the topographic trough setting the glacier width and curbing the lateral drainage of the meltwater, the problem falls under the purview of the undrained plastic bed (UPB) formalism. Employing the UPB, we shall examine the external controls of the glacial behavior and test them against observations. Through our non-dimensionalization scheme, we construct a 2-D regime diagram, which allows a ready prognosis of the glacial properties over the full range of the external conditions, both climate- and size-related. We first discern the boundaries separating the glacial regimes of steady-creep, cyclic-surging and steady-sliding. We then apply the regime diagram to observed glaciers for quantitative comparisons. These include the Svalbard glaciers of both normal and surge types, Northeast Greenland Ice Stream characterized by steady-sliding, and Hudson Strait Ice Stream exhibiting cyclic surges. The quantitative validation of our model containing no free parameters suggests that the thermal switch may unify the dynamics of these diverse glaciers.

Complementary Approaches Towards a Universal Model of Glacier Surges

“…Basal processes are difficult to observe during an active phase (Harrison and Post, 2003), and the physics of basal drag are generally simplified or circumvented altogether in numerical models of surging (e.g. Van Pelt and Oerlemans, 2012;Benn et al, 2019a;Ou, 2021). This gap in understanding makes basal mechanics an obvious avenue for identifying a fundamental mechanism regulating all surge motion.…”

“…Down-glacier surge propagation is then simply driven by the increase in compressive longitudinal stress induced by fast upstream motion, and up-glacier propagation is caused by longitudinal stretching (e.g. Halfar, 2020;Ou, 2021). Incorporating the new theories describing transient basal drag solves the problematic dependence of ice motion, and more importantly surge propagation, on water pressure at the base.…”

A theory of glacier dynamics and instabilities Part 2: Flatbed ice streams

“…With the above, we discern the needed expansion of the theoretical framework presented in Part 1 (Ou, 2021) to address the ice stream problem, as expounded next. First of all, without the topographic trough confining the glacial mass flux, we must allow inflowing ice flux from the adjacent ridge (termed 'entrainment'), which indeed is comparable to the upper-glacier catchment in observations (Shabtaie and others, 1988).…”

“…In Part 1 (Ou, 2021), we have considered the dynamics of a glacier confined in a topographic trough, which may exhibit cyclic surges when the bed becomes temperate. We establish that a prognostic model of the phenomenon must entail global momentum balance and subglacial hydrology in its closure.…”

“…In addition, the streams exhibit surge cycle, much like that observed for a topography-confined glacier when it is sufficiently wide (Part 1). The modeled variability, thus, is due to the thermal switch considered in Part 1 (Ou, 2021), and the stream width is essentially that divides the cyclic-surge and steady-sliding regimes. In other words, the additional degree of freedom associated with the unknown stream width can be countered by the Hopf bifurcation when the unstable stationary state vaults into a stable limit cycle (Robel and others, 2013).…”