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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 25, issue 2 | Copyright
Nonlin. Processes Geophys., 25, 355-374, 2018
https://doi.org/10.5194/npg-25-355-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 03 May 2018

Research article | 03 May 2018

Feature-based data assimilation in geophysics

Matthias Morzfeld, Jesse Adams, Spencer Lunderman, and Rafael Orozco Matthias Morzfeld et al.
  • Department of Mathematics, University of Arizona, 617 N. Santa Rita Ave., P.O. Box 210089, Tucson, Arizona 85721, USA

Abstract. Many applications in science require that computational models and data be combined. In a Bayesian framework, this is usually done by defining likelihoods based on the mismatch of model outputs and data. However, matching model outputs and data in this way can be unnecessary or impossible. For example, using large amounts of steady state data is unnecessary because these data are redundant. It is numerically difficult to assimilate data in chaotic systems. It is often impossible to assimilate data of a complex system into a low-dimensional model. As a specific example, consider a low-dimensional stochastic model for the dipole of the Earth's magnetic field, while other field components are ignored in the model. The above issues can be addressed by selecting features of the data, and defining likelihoods based on the features, rather than by the usual mismatch of model output and data. Our goal is to contribute to a fundamental understanding of such a feature-based approach that allows us to assimilate selected aspects of data into models. We also explain how the feature-based approach can be interpreted as a method for reducing an effective dimension and derive new noise models, based on perturbed observations, that lead to computationally efficient solutions. Numerical implementations of our ideas are illustrated in four examples.

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Many applications in science require that computational models and data be combined. In a Bayesian framework, this is usually done by defining likelihoods based on the mismatch of model outputs and data. However, matching model outputs and data in this way can be unnecessary or impossible. This issue can be addressed by selecting features of the data, and defining likelihoods based on the features, rather than by the usual mismatch of model output and data.
Many applications in science require that computational models and data be combined. In a...
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