Articles | Volume 10, issue 4
The Cryosphere, 10, 1477–1494, 2016
The Cryosphere, 10, 1477–1494, 2016

Research article 13 Jul 2016

Research article | 13 Jul 2016

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

Hongyu Zhu et al.

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Cited articles

Bangerth, W.: A Framework for the Adaptive Finite Element Solution of Large-Scale Inverse Problems, SIAM J. Scient. Comput., 30, 2965–2989,, 2008.
Borzì, A. and Schulz, V.: Computational Optimization of Systems Governed by Partial Differential Equations, SIAM, Philadelphia, PA, 3–26, 2012.
Brooks, A. N. and Hughes, T. J. R.: Streamline Upwind/Petrov–Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on the Incompressible Navier–Stokes Equations, Comput. Meth. Appl. Mech. Eng., 32, 199–259, 1982.
Collis, S. S. and Heinkenschloss, M.: Analysis of the Streamline Upwind/Petrov Galerkin Method Applied to the Solution of Optimal Control Problems, Tech. Rep. TR02-01, Department of Computational and Applied Mathematics, Rice University, Houston, (last access: July 2016), 2002.
Dahl-Jensen, D.: Steady thermomechanical flow along two-dimensional flow lines in large grounded ice sheets, J. Geophys. Res., 94, 10355–10362, 1989.
Short summary
We study how well the basal geothermal heat flux can be inferred from surface velocity observations using a thermomechanically coupled nonlinear Stokes ice sheet model. The prospects and limitations of this inversion is studied in two and three dimensional model problems. We also argue that a one-way coupled approach for the adjoint equations motivated by staggered solvers for forward multiphysics problems can lead to an incorrect gradient and premature termination of the optimization iteration.