Cluster Sampling Filters for Non-Gaussian Data Assimilation
| dc.contributor.author | Attia, Ahmed | en |
| dc.contributor.author | Moosavi, Azam | en |
| dc.contributor.author | Sandu, Adrian | en |
| dc.contributor.department | Computer Science | en |
| dc.date.accessioned | 2018-06-25T12:22:02Z | en |
| dc.date.available | 2018-06-25T12:22:02Z | en |
| dc.date.issued | 2018-05-31 | en |
| dc.date.updated | 2018-06-25T07:43:33Z | en |
| dc.description.abstract | This paper presents a fully non-Gaussian filter for sequential data assimilation. The filter is named the “<i>cluster sampling filter</i>”, 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 <math display="inline"> <semantics> <mrow> <mi mathvariant="script">C</mi> <mi>ℓ</mi> <mi>MCMC</mi> </mrow> </semantics> </math> , <math display="inline"> <semantics> <mrow> <mi mathvariant="script">C</mi> <mi>ℓ</mi> <mi>HMC</mi> </mrow> </semantics> </math> , MC- <math display="inline"> <semantics> <mrow> <mi mathvariant="script">C</mi> <mi>ℓ</mi> <mi>HMC</mi> </mrow> </semantics> </math> , and MC- <math display="inline"> <semantics> <mrow> <mi mathvariant="script">C</mi> <mi>ℓ</mi> <mi>HMC</mi> </mrow> </semantics> </math> are presented. <math display="inline"> <semantics> <mrow> <mi mathvariant="script">C</mi> <mi>ℓ</mi> <mi>MCMC</mi> </mrow> </semantics> </math> uses a Gaussian proposal density to sample the posterior, and <math display="inline"> <semantics> <mrow> <mi mathvariant="script">C</mi> <mi>ℓ</mi> <mi>HMC</mi> </mrow> </semantics> </math> is an extension to the Hamiltonian Monte-Carlo (HMC) sampling filter. MC- <math display="inline"> <semantics> <mrow> <mi mathvariant="script">C</mi> <mi>ℓ</mi> <mi>MCMC</mi> </mrow> </semantics> </math> and MC- <math display="inline"> <semantics> <mrow> <mi mathvariant="script">C</mi> <mi>ℓ</mi> <mi>HMC</mi> </mrow> </semantics> </math> are multi-chain versions of the cluster sampling filters <math display="inline"> <semantics> <mrow> <mi mathvariant="script">C</mi> <mi>ℓ</mi> <mi>MCMC</mi> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <mi mathvariant="script">C</mi> <mi>ℓ</mi> <mi>HMC</mi> </mrow> </semantics> </math> 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. | en |
| dc.description.version | Published version | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Attia, A.; Moosavi, A.; Sandu, A. Cluster Sampling Filters for Non-Gaussian Data Assimilation. Atmosphere 2018, 9, 213. | en |
| dc.identifier.doi | https://doi.org/10.3390/atmos9060213 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/83719 | en |
| dc.language.iso | en | en |
| dc.publisher | MDPI | en |
| dc.rights | Creative Commons Attribution 4.0 International | en |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | en |
| dc.subject | data assimilation | en |
| dc.subject | ensemble filters | en |
| dc.subject | markov chain monte-carlo sampling | en |
| dc.subject | hamiltonian monte-carlo | en |
| dc.subject | gaussian mixture models | en |
| dc.title | Cluster Sampling Filters for Non-Gaussian Data Assimilation | en |
| dc.title.serial | Atmosphere | en |
| dc.type | Article - Refereed | en |
| dc.type.dcmitype | Text | en |