Feature-based data assimilation in geophysics
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 e...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2018-05-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | https://www.nonlin-processes-geophys.net/25/355/2018/npg-25-355-2018.pdf |
| _version_ | 1818110433392852992 |
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| author | M. Morzfeld J. Adams S. Lunderman R. Orozco |
| author_facet | M. Morzfeld J. Adams S. Lunderman R. Orozco |
| author_sort | M. Morzfeld |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T02:47:04Z |
| format | Article |
| id | doaj.art-30dba950f9f44159881166430641a937 |
| institution | Directory Open Access Journal |
| issn | 1023-5809 1607-7946 |
| language | English |
| last_indexed | 2024-12-11T02:47:04Z |
| publishDate | 2018-05-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Nonlinear Processes in Geophysics |
| spelling | doaj.art-30dba950f9f44159881166430641a9372022-12-22T01:23:24ZengCopernicus PublicationsNonlinear Processes in Geophysics1023-58091607-79462018-05-012535537410.5194/npg-25-355-2018Feature-based data assimilation in geophysicsM. Morzfeld0J. Adams1S. Lunderman2R. Orozco3Department of Mathematics, University of Arizona, 617 N. Santa Rita Ave., P.O. Box 210089, Tucson, Arizona 85721, USADepartment of Mathematics, University of Arizona, 617 N. Santa Rita Ave., P.O. Box 210089, Tucson, Arizona 85721, USADepartment of Mathematics, University of Arizona, 617 N. Santa Rita Ave., P.O. Box 210089, Tucson, Arizona 85721, USADepartment of Mathematics, University of Arizona, 617 N. Santa Rita Ave., P.O. Box 210089, Tucson, Arizona 85721, USAMany 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.https://www.nonlin-processes-geophys.net/25/355/2018/npg-25-355-2018.pdf |
| spellingShingle | M. Morzfeld J. Adams S. Lunderman R. Orozco Feature-based data assimilation in geophysics Nonlinear Processes in Geophysics |
| title | Feature-based data assimilation in geophysics |
| title_full | Feature-based data assimilation in geophysics |
| title_fullStr | Feature-based data assimilation in geophysics |
| title_full_unstemmed | Feature-based data assimilation in geophysics |
| title_short | Feature-based data assimilation in geophysics |
| title_sort | feature based data assimilation in geophysics |
| url | https://www.nonlin-processes-geophys.net/25/355/2018/npg-25-355-2018.pdf |
| work_keys_str_mv | AT mmorzfeld featurebaseddataassimilationingeophysics AT jadams featurebaseddataassimilationingeophysics AT slunderman featurebaseddataassimilationingeophysics AT rorozco featurebaseddataassimilationingeophysics |