Improvements to shear-deformational models of glacier dynamics through a longitudinal stress factor

Abstract

In a two-dimensional (plane strain) glacier domain, gravity-driven ice flow is balanced by basal drag and the resistance associated with longitudinal stress gradients. The plane strain Stokes model accommodates both these resistances, whereas several simpler models only account for basal drag. Solving the Stokes equations is numerically challenging and computationally expensive, but simpler models may lead to unrealistic dynamical behaviour. Here, we propose a factor which can be introduced in shear-deformational flow models to yield results comparable to those from the plane strain Stokes model. As this factor adapts simpler models to capture the effects of missing dynamics, i.e. longitudinal stress gradients, we refer to it as the longitudinal stress (L L-)factor. We assess the usefulness of this factor for idealized domains with complex basal topography and evolving geometry. We apply the model to Haig Glacier, Canadian Rockies, in order to present an illustration of how simulations of glacier response to climate forcing can be improved through the introduction of the L-factor in a shear-deformational flow model.

Modelling Dynamics of Valley Glaciers

“…Without adding the numerical complexity, the dynamical reach of such models can be extended through the introduction of parameterized correction factors. The effects of longitudinal stress gradients can be accounted for by embedding L-factors (Adhikari & Marshall, 2011); the lateral drag associated with the valley walls (Nye, 1965) and stick/slip basal interface (Adhikari & Marshall, in preperation) can also be captured via analogous correction factors. This offers a pragmatic middle ground for simulating glacier response to climate change.…”

“…In the SD model, τ xz (x, y, b) characterizes τ b (e.g. Adhikari & Marshall, 2011), which is the sole resistance to the gravitational driving stress, τ d ; it follows that τ xz (x, y, b) ≈ τ d . Therefore, we calculate the errors as the difference between the SD and FS/PS models with respect to the former one.…”

“…We validate SIA2 model by comparing results with the corresponding analytical solutions (Eq. 8; see Adhikari & Marshall, 2011).…”

“…Several attempts have therefore been made to capture high-order dynamics in ice flow models; effects of longitudinal stress gradients (e.g. Adhikari & Marshall, 2011;Shoemaker & Morland, 1984;Souček & Martinec, 2008) and lateral drag (e.g. Adhikari & Marshall, in preperation;Nye, 1965) are particularly accounted via physically-based or numerical/empirical parameterizations.…”

A JavaScript API for the Ice Sheet System Model (ISSM) 4.11: towards an online interactive model for the cryosphere community

“…The first simulations pertain to the simulation of glacier flow, mainly from work on the Haig Glacier Marshall, 2011) andColumbia Glacier (A. Gardner, M. Fahnestock, andE. Larour, personal communication, 2016).…”