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The choice of the prior model can have a large impact on the ability to assimilate data. In standard applications of ensemble-based data assimilation, all realizations in the initial ensemble are generated from the same covariance matrix with the implicit assumption that this covariance is appropriate for the problem. In a hierarchical approach, the parameters of the covariance function, for example the variance, the orientation of the anisotropy and the ranges in two principal directions, may all be uncertain. Thus, the hierarchical approach is much more robust against model misspecification. In this paper, three approaches to sampling from the posterior for hierarchical parameterizations are discussed: an optimization-based sampling approach (RML), an iterative ensemble smoother (IES), and a novel hybrid of the previous two approaches (hybrid IES). The three approximate sampling methods are applied to a linear-Gaussian inverse problem for which it is possible to compare results with an exact "marginal-then-conditional" approach. Additionally, the IES and the hybrid IES methods are tested on a two-dimensional flow problem with uncertain anisotropy in the prior covariance. The stan

Author

Oliver, Dean S.

Published

2022

Language

EN