Journal cover Journal topic
Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
Journal topic

Journal metrics

IF value: 5.240
IF5.240
IF 5-year value: 5.768
IF 5-year
5.768
CiteScore value: 8.9
CiteScore
8.9
SNIP value: 1.713
SNIP1.713
IPP value: 5.53
IPP5.53
SJR value: 3.18
SJR3.18
Scimago H <br class='widget-line-break'>index value: 71
Scimago H
index
71
h5-index value: 51
h5-index51
Preprints
https://doi.org/10.5194/gmd-2020-58
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-2020-58
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: development and technical paper 09 Apr 2020

Submitted as: development and technical paper | 09 Apr 2020

Review status
This preprint is currently under review for the journal GMD.

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

Anna Wirbel1 and Alexander Helmut Jarosch2 Anna Wirbel and Alexander Helmut Jarosch
  • 1Department of Atmospheric and Cryospheric Sciences, Universität Innsbruck, Innsbruck, Austria
  • 2Independent Researcher, Hörfarterstrasse 14, Kufstein, Austria

Abstract. Like any gravitationally driven flow that is not constrained at the upper surface, glaciers and ice sheets feature a free-surface, which becomes a free boundary problem within simulations. A kinematic boundary condition is often used to describe the evolution of this free-surface. However, in the case of glaciers and ice sheets, the naturally occurring constraint that the ice surface elevation (S) can not fall below the bed topography (B), (S-B > = 0) in combination with a non-zero mass balance rate complicates the matter substantially. We present an open-source numerical simulation framework to simulate the free-surface evolution of glaciers that directly incorporates this natural constraint. It is based on the finite element software package FEniCS solving the Stokes equations for ice flow and a suitable transport equation, i.e. 'kinematic boundary condition', for the free-surface evolution. The evolution of the free--surface is treated as a variational inequality, constrained by the bedrock underlying the glacier or the topography of the surrounding ground. To solve this problem, the 'constrained' non--linear problem solving capabilities of PETSc's SNES interface are used. As the constraint is considered in the solving process, this approach does not require any ad-hoc post-processing steps to enforce no--negativity of ice thickness as well as mass conservation. The simulation framework provides the possibility to partition the computational domain so that individual forms of the relevant equations can be solved for different subdomains all at once. In the presented setup, this is used to distinguish between glacierized and ice-free regions. The option to chose different time discretizations, spatial stabilisation schemes and adaptive mesh refinement make it a versatile tool for glaciological applications.

We present a set of benchmark tests that highlight the simulation framework is able to reproduce the free-surface evolution of complex geometries under different conditions for which it is mass conserving and numerically stable. Real--world glacier examples demonstrate high resolution change in glacier geometry due to fully-resolved 3D velocities and spatially variable mass balance rate, whereby realistic glacier recession and advance states can be simulated. Additionally, we provide a thorough analysis of different spatial stabilisation techniques as well as time discretization methods. We discuss their applicability and suitability for different glaciological applications.

Anna Wirbel and Alexander Helmut Jarosch

Interactive discussion

Status: final response (author comments only)
Status: final response (author comments only)
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
[Login for Authors/Topical Editors] [Subscribe to comment alert] Printer-friendly Version - Printer-friendly version Supplement - Supplement

Anna Wirbel and Alexander Helmut Jarosch

Model code and software

evolve_glacier v1.1 A. Wirbel and A. H. Jarosch https://doi.org/10.5281/zenodo.3734021

Anna Wirbel and Alexander Helmut Jarosch

Viewed

Total article views: 425 (including HTML, PDF, and XML)
HTML PDF XML Total BibTeX EndNote
273 122 30 425 37 38
  • HTML: 273
  • PDF: 122
  • XML: 30
  • Total: 425
  • BibTeX: 37
  • EndNote: 38
Views and downloads (calculated since 09 Apr 2020)
Cumulative views and downloads (calculated since 09 Apr 2020)

Viewed (geographical distribution)

Total article views: 295 (including HTML, PDF, and XML) Thereof 295 with geography defined and 0 with unknown origin.
Country # Views %
  • 1
1
 
 
 
 

Cited

Saved

No saved metrics found.

Discussed

No discussed metrics found.
Latest update: 28 Sep 2020
Publications Copernicus
Download
Short summary
We present an open-source numerical tool to simulate the free-surface evolution of gravity driven flows (e.g glaciers) constrained by bed topography. No ad-hoc post-processing is required to enforce positive ice thickness and mass conservation. We utilize finite elements, define benchmark tests, and showcase glaciological examples. In addition we provide a thorough analysis of the applicability and robustness of different spatial stabilisation- and time discretization methods.
We present an open-source numerical tool to simulate the free-surface evolution of gravity...
Citation