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A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models
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Atmosphere 2018, 9(6), 213; https://doi.org/10.3390/atmos9060213

Cluster Sampling Filters for Non-Gaussian Data Assimilation

1,†
,
2,†
and
2,†,*
1
Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, USA
2
Computational Science Laboratory, Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 20 March 2018 / Revised: 2 May 2018 / Accepted: 2 May 2018 / Published: 31 May 2018
(This article belongs to the Special Issue Efficient Formulation and Implementation of Data Assimilation Methods)
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Abstract

This paper presents a fully non-Gaussian filter for sequential data assimilation. The filter is named the “cluster sampling filter”, and works by directly sampling the posterior distribution following a Markov Chain Monte-Carlo (MCMC) approach, while the prior distribution is approximated using a Gaussian Mixture Model (GMM). Specifically, a clustering step is introduced after the forecast phase of the filter, and the prior density function is estimated by fitting a GMM to the prior ensemble. Using the data likelihood function, the posterior density is then formulated as a mixture density, and is sampled following an MCMC approach. Four versions of the proposed filter, namely C MCMC , C HMC , MC- C HMC , and MC- C HMC are presented. C MCMC uses a Gaussian proposal density to sample the posterior, and C HMC is an extension to the Hamiltonian Monte-Carlo (HMC) sampling filter. MC- C MCMC and MC- C HMC are multi-chain versions of the cluster sampling filters C MCMC and C HMC respectively. The multi-chain versions are proposed to guarantee that samples are taken from the vicinities of all probability modes of the formulated posterior. The new methodologies are tested using a simple one-dimensional example, and a quasi-geostrophic (QG) model with double-gyre wind forcing and bi-harmonic friction. Numerical results demonstrate the usefulness of using GMMs to relax the Gaussian prior assumption especially in the HMC filtering paradigm. View Full-Text
Keywords: data assimilation; ensemble filters; markov chain monte-carlo sampling; hamiltonian monte-carlo; gaussian mixture models data assimilation; ensemble filters; markov chain monte-carlo sampling; hamiltonian monte-carlo; gaussian mixture models
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Attia, A.; Moosavi, A.; Sandu, A. Cluster Sampling Filters for Non-Gaussian Data Assimilation. Atmosphere 2018, 9, 213.

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