Data Assimilation with Gaussian Mixture Models using the Dynamically Orthogonal Field Equations. Part II. Applications
Name
Lermusiaux_Data Assimilation II.pdf
Size
8.84 MB
Format
Adobe PDF
Checksum (MD5)
245cd12752ff7c79db75699b41beeb04
Author(s)
Sondergaard, Thomas
Lermusiaux, Pierre F. J.
Date Issued
2012
Journal
Monthly Weather Review
Publisher
American Meteorological Society
Citation
Sondergaard, Thomas, and Pierre F. J. Lermusiaux. Data Assimilation with Gaussian Mixture Models Using the Dynamically Orthogonal Field Equations. Part II: Applications. Monthly Weather Review: 121011101334009, 2012.
Version
Author's final manuscript
Abstract
The properties and capabilities of the GMM-DO filter are assessed and exemplified by applications to two dynamical systems: (1) the Double Well Diffusion and (2) Sudden Expansion flows; both of which admit far-from-Gaussian statistics. The former test case, or twin experiment, validates the use of the EM algorithm and Bayesian Information Criterion with Gaussian Mixture Models in a filtering context; the latter further exemplifies its ability to efficiently handle state vectors of non-trivial dimensionality and dynamics with jets and eddies. For each test case, qualitative and quantitative comparisons are made with contemporary filters. The sensitivity to input parameters is illustrated and discussed. Properties of the filter are examined and its estimates are described, including: the equation-based and adaptive prediction of the probability densities; the evolution of the mean field, stochastic subspace modes and stochastic coefficients; the fitting of Gaussian Mixture Models; and, the efficient and analytical Bayesian updates at assimilation times and the corresponding data impacts. The advantages of respecting nonlinear dynamics and preserving non-Gaussian statistics are brought to light. For realistic test cases admitting complex distributions and with sparse or noisy measurements, the GMM-DO filter is shown to fundamentally improve the filtering skill, outperforming simpler schemes invoking the Gaussian parametric distribution.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1175/MWR-D-11-00296.1
