Modelling debris transport within glaciers by advection in a full-Stokes ice flow model

Abstract

Abstract. Glaciers with extensive surface debris cover respond differently to climate forcing than those without supraglacial debris. In order to include debris-covered glaciers in projections of glaciogenic runoff and sea-level rise, and to understand the paleoclimate proxy recorded by such glaciers it is necessary to understand the manner and timescales over which a supraglacial debris cover develops. As debris is delivered to the glacier by processes that are heterogeneous in space and time, and these debris inclusions are altered during englacial transport through the glacier system, correctly determining where, when, and how much, debris is delivered to the glacier surface requires that the englacial transport pathways and deformation can be known. To achieve this, we present a model of englacial debris transport in which we couple an advection scheme to a full-Stokes ice flow model. The model performs well in numerical benchmark tests, and we present both 2D and 3D steady-state glacier test cases that, for a set of prescribed debris inputs, reproduce the englacial features, deformation thereof, and patterns of surface emergence predicted by theory and observations of structural glaciology. In a future step, coupling this model to a (i) debris-aware surface mass-balance scheme and (ii) supraglacial debris transport scheme will enable the co-evolution of debris-cover and glacier geometry to be modelled.

Heterogeneous Influence of Glacier Morphology on the Mass Balance Variability in High Mountain Asia

“…Our results show that debris‐covered tongues can be generally characterized as flatter and located at lower elevations than debris‐free tongues. Moreover, the avalanche contributing area correlates strongly with the percentage of debris cover, hinting that large part of the debris supply originates from the glacier upper reaches (e.g., Wirbel et al, ). These conclusions are in line with those of Scherler et al (), even though, contrary to them, we do not include ice surface velocity in our analysis.…”

Free–Surface Flow as a Variational Inequality (<i>evolve_glacier v1.1</i>): Numerical Aspects of a Glaciological Application

“…The setup presented here has been developed to be fully compatible with an existing glacial debris transport model debadvect (Wirbel, 2018), with the wider aim of developing a full debris-covered glacier system model (Wirbel et al, 2018). Nevertheless our treatment of the free-surface evolution is widely applicable to geophysical flows.…”

“…Velocities for the slow, gravity-driven flow of ice are computed with the stationary incompressible Stokes equations (see Wirbel et al (2018) for details). We treat the surface of a glacier as stress-free for which:…”

“…Ice velocities are computed on a three-dimensional (3D) mesh using icetools, an open-source full-Stokes model for ice flow (Jarosch, 2008;Wirbel et al, 2018). As the free-surface evolves on ∂Ω top , the problem has one dimension less than the ice flow problem itself (defined on Ω).…”

“…Elmer/Ice imposes Dirichlet conditions on the constrained boundaries that are iteratively released by a criterion based on residuals (Gagliardini et al, 2013), whereas instead we here utilize reduced-space methods (Benson and Munson, 2006). Our novel approach combines an existing finiteelement Stokes flow model (Jarosch, 2008;Wirbel et al, 2018) with highly efficient, existing variational inequality solving numerical libraries (PETSc, Balay et al, 2018aBalay et al, , b, 1997 that have been successfully applied to SIA ice flow (Bueler, 2016).…”