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Title: Cluster Sampling Filters for Non-Gaussian Data Assimilation

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 ℓ MCMC , C ℓ HMC , MC- C ℓ HMC , and MC- C ℓ HMC are presented. C ℓ MCMC uses a Gaussian proposal density to sample the posterior, and C ℓ HMC is an extension to the Hamiltonian Monte-Carlo (HMC) sampling filter. MC- C ℓ MCMC and MC- C ℓ HMC are multi-chain versions of the cluster sampling filters C ℓ MCMC and C ℓ 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 aremore » tested using a simple one-dimensional example, and a quasi-geostrophic (QG) model with double-gyre wind forcing and bi-harmonic friction. Here, numerical results demonstrate the usefulness of using GMMs to relax the Gaussian prior assumption especially in the HMC filtering paradigm.« less

Authors:
 [1];  [2];  [2]
  1. Argonne National Lab. (ANL), Argonne, IL (United States)
  2. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
Air Force Research Laboratory (AFRL), Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF); Virginia Polytechnic Institute, Dept of Computer Science; USDOE
OSTI Identifier:
1463676
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
Atmosphere (Basel)
Additional Journal Information:
Journal Name: Atmosphere (Basel); Journal Volume: 9; Journal Issue: 6; Journal ID: ISSN 2073-4433
Publisher:
MDPI
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; data assimilation; ensemble filters; gaussian mixture models; hamiltonian monte-carlo; markov chain monte-carlo sampling

Citation Formats

Attia, Ahmed, Moosavi, Azam, and Sandu, Adrian. Cluster Sampling Filters for Non-Gaussian Data Assimilation. United States: N. p., 2018. Web. doi:10.3390/atmos9060213.
Attia, Ahmed, Moosavi, Azam, & Sandu, Adrian. Cluster Sampling Filters for Non-Gaussian Data Assimilation. United States. doi:10.3390/atmos9060213.
Attia, Ahmed, Moosavi, Azam, and Sandu, Adrian. Thu . "Cluster Sampling Filters for Non-Gaussian Data Assimilation". United States. doi:10.3390/atmos9060213. https://www.osti.gov/servlets/purl/1463676.
@article{osti_1463676,
title = {Cluster Sampling Filters for Non-Gaussian Data Assimilation},
author = {Attia, Ahmed and Moosavi, Azam and Sandu, Adrian},
abstractNote = {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 ℓ MCMC , C ℓ HMC , MC- C ℓ HMC , and MC- C ℓ HMC are presented. C ℓ MCMC uses a Gaussian proposal density to sample the posterior, and C ℓ HMC is an extension to the Hamiltonian Monte-Carlo (HMC) sampling filter. MC- C ℓ MCMC and MC- C ℓ HMC are multi-chain versions of the cluster sampling filters C ℓ MCMC and C ℓ 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. Here, numerical results demonstrate the usefulness of using GMMs to relax the Gaussian prior assumption especially in the HMC filtering paradigm.},
doi = {10.3390/atmos9060213},
journal = {Atmosphere (Basel)},
number = 6,
volume = 9,
place = {United States},
year = {2018},
month = {5}
}

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