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The Cryosphere An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/tc-2020-229
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/tc-2020-229
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  31 Aug 2020

31 Aug 2020

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This preprint is currently under review for the journal TC.

Inferring the basal sliding coefficient field for the Stokes ice sheet model under rheological uncertainty

Olalekan Babaniyi1, Ruanui Nicholson2, Umberto Villa3, and Noémi Petra4 Olalekan Babaniyi et al.
  • 1School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA
  • 2Department of Engineering Science, University of Auckland, Auckland 1010, New Zealand
  • 3Electrical & Systems Engineering, Washington University in St. Louis, St. Louis, MO 63130, USA
  • 4Department of Applied Mathematics, University of California, Merced, Merced, CA 95343, USA

Abstract. We consider the problem of inferring the basal sliding coefficient field for an uncertain Stokes ice sheet forward model from surface velocity measurements. The uncertainty in the forward model stems from unknown (or uncertain) auxiliary parameters (e.g., rheology parameters). This inverse problem is posed within the Bayesian framework, which provides a systematic means of quantifying uncertainty in the solution. To account for the associated model uncertainty (error), we employ the Bayesian Approximation Error (BAE) approach to approximately premarginalize simultaneously over both the noise in measurements and uncertainty in the forward model. We also carry out approximative posterior uncertainty quantification based on a linearization of the parameter-to-observable map centered at the maximum a posteriori (MAP) basal sliding coefficient estimate, i.e., by taking the Laplace approximation. The MAP estimate is found by minimizing the negative log posterior using an inexact Newton conjugate gradient method. The gradient and Hessian actions to vectors are efficiently computed using adjoints. Sampling from the approximate covariance is made tractable by invoking a low-rank approximation of the data misfit component of the Hessian. We study the performance of the BAE approach in the context of three numerical examples in two and three dimensions. For each example the basal sliding coefficient field is the parameter of primary interest, which we seek to infer, and the rheology parameters (e.g., the flow rate factor, or the Glen's flow law exponent coefficient field) represent so called nuisance (secondary uncertain) parameters. Our results indicate that accounting for model uncertainty stemming from the presence of nuisance parameters is crucial. Namely our findings suggest that using nominal values for these parameters, as is often done in practice, without taking into account the resulting modeling error, can lead to overconfident and heavily biased results. We also show that the BAE approach can be used to account for the additional model uncertainty at no additional cost at the online stage.

Olalekan Babaniyi et al.

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Olalekan Babaniyi et al.

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