Attia, AhmedMoosavi, AzamSandu, Adrian2018-06-252018-06-252018-05-31Attia, A.; Moosavi, A.; Sandu, A. Cluster Sampling Filters for Non-Gaussian Data Assimilation. Atmosphere 2018, 9, 213.http://hdl.handle.net/10919/83719This paper presents a fully non-Gaussian filter for sequential data assimilation. The filter is named the &ldquo;<i>cluster sampling filter</i>&rdquo;, 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.application/pdfenCreative Commons Attribution 4.0 Internationaldata assimilationensemble filtersmarkov chain monte-carlo samplinghamiltonian monte-carlogaussian mixture modelsArticle - Refereed2018-06-25https://doi.org/10.3390/atmos9060213