Cluster Sampling Filters for Non-Gaussian Data Assimilation

TR Number

Date

2018-05-31

Journal Title

Journal ISSN

Volume Title

Publisher

MDPI

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.

Description

Keywords

data assimilation, ensemble filters, markov chain monte-carlo sampling, hamiltonian monte-carlo, gaussian mixture models

Citation

Attia, A.; Moosavi, A.; Sandu, A. Cluster Sampling Filters for Non-Gaussian Data Assimilation. Atmosphere 2018, 9, 213.