Title: An improved framework for the dynamic likelihood filtering approach to data assimilation

Abstract

We propose improvements to the Dynamic Likelihood Filter (DLF), a Bayesian data assimilation filtering approach, specifically tailored to wave problems. The DLF approach was developed to address the common challenge in the application of data assimilation to hyperbolic problems in the geosciences and in engineering, where observation systems are sparse in space and time. When these observations have low uncertainties, as compared to model uncertainties, the DLF exploits the inherent nature of information and uncertainties to propagate along characteristics to produce estimates that are phase aware as well as amplitude aware, as would be the case in the traditional data assimilation approach. Along characteristics, the stochastic partial differential equations underlying the linear or nonlinear stochastic dynamics are differential equations. This study focuses on developing the explicit challenges of relating dynamics and uncertainties in the Eulerian and Lagrangian frames via dynamic Gaussian processes. It also implements the approach using the ensemble Kalman filter (EnKF) and compares the DLF approach to the conventional one with respect to wave amplitude and phase estimates in linear and nonlinear wave problems. Numerical comparisons show that the DLF/EnKF outperforms the EnKF estimates, when applied to linear and nonlinear wave problems. This advantage is particularly noticeable whenmore » sparse, low uncertainty observations are used.« less

Authors:

Foster, Dallas  ^[1];

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• Search DOE PAGES for ORCID "0000-0001-8459-9767"

Restrepo, Juan M.  ^[2]

• Search DOE PAGES for author "Restrepo, Juan M."
• Search DOE PAGES for ORCID "0000-0003-2609-2882"

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+ Show Author Affiliations

1. Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)
2. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); University of Tennessee, Knoxville, TN (United States)

Publication Date:

Tue May 10 00:00:00 EDT 2022

Research Org.:

Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:

USDOE

OSTI Identifier:

1906631

Alternate Identifier(s):

OSTI ID: 1867319

Grant/Contract Number:  

AC05-00OR22725

Resource Type:

Accepted Manuscript

Journal Name:

Chaos: An Interdisciplinary Journal of Nonlinear Science

Additional Journal Information:

Journal Volume: 32; Journal Issue: 5; Journal ID: ISSN 1054-1500

Publisher:

American Institute of Physics (AIP)

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING