Bayesian Inversion for the Basal Sliding Parameter Field in a Nonlinear Stokes Ice Sheet Model Under Uncertain Rheology
Abstract
Modeling the dynamics of polar ice sheets is critical for projections of future sea level rise. Yet, there remain large uncertainties in the basal boundary conditions and in the non-Newtonian constitutive relations employed within ice sheet models. In this presentation, we considered the problem of inferring the distributed basal sliding coefficient field from surface flow observations under an unknown random rheological exponent parameter field. When there are multiple unknown (or uncertain) parameters in a model, a common approach would be to invert for these parameter fields separately or simultaneously. While the latter would in principle result in less model error/discrepancy, a joint inversion is typically highly ill-posed and potentially an untractable inverse problem. To avoid the need for a joint inversion, we premarginalize over the rheological exponent parameter field, and invert only for the basal sliding coefficient. To account for model errors, stemming from ``ignoring" the uncertain rheology, we use the Bayesian approximation error (BAE) approach, which has the ability to approximately premarginalize over parameters which are not of primary interest.
The uncertainty analysis presented here relies on a local linearization of the parameter-to-observable map at the maximum a posteriori (MAP) estimates, which leads to a normal (Gaussian) approximation of the parameter posterior density. To compute the MAP point we apply an inexact Newton conjugate gradient approach based on the adjoint methodology. The construction of the covariance is made tractable by invoking a low-rank approximation of the data misfit component of the Hessian. The results indicate that fixing the rheological exponent parameter as an incorrect but otherwise well justified (distributed parameter) field can result in infeasible and misleading posterior estimates in the sense that the true parameter is not supported by the posterior model. In addition, we demonstrate that the BAE approach is approximately as computationally expensive (measured in the number of PDE solves) as the conventional error approach.- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2018
- Bibcode:
- 2018AGUFM.S31E0551P
- Keywords:
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- 1873 Uncertainty assessment;
- HYDROLOGYDE: 1990 Uncertainty;
- INFORMATICSDE: 3260 Inverse theory;
- MATHEMATICAL GEOPHYSICSDE: 3275 Uncertainty quantification;
- MATHEMATICAL GEOPHYSICS