Gaussian approximations in filters and smoothers for data assimilation
AffiliationUniv Arizona, Dept Math
ensemble Kalman filter
variational data assimilation
MetadataShow full item record
PublisherTAYLOR & FRANCIS LTD
CitationMorzfeld, M., & Hodyss, D. (2019). Gaussian approximations in filters and smoothers for data assimilation. Tellus A: Dynamic Meteorology and Oceanography, 71(1), 1-27.
Rights© 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
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AbstractWe present mathematical arguments and experimental evidence that suggest that Gaussian approximations of posterior distributions are appropriate even if the physical system under consideration is nonlinear. The reason for this is a regularizing effect of the observations that can turn multi-modal prior distributions into nearly Gaussian posterior distributions. This has important ramifications on data assimilation (DA) algorithms in numerical weather prediction because the various algorithms (ensemble Kalman filters/smoothers, variational methods, particle filters (PF)/smoothers (PS)) apply Gaussian approximations to different distributions, which leads to different approximate posterior distributions, and, subsequently, different degrees of error in their representation of the true posterior distribution. In particular, we explain that, in problems with medium' nonlinearity, (i) smoothers and variational methods tend to outperform ensemble Kalman filters; (ii) smoothers can be as accurate as PF, but may require fewer ensemble members; (iii) localization of PFs can introduce errors that are more severe than errors due to Gaussian approximations. In problems with strong' nonlinearity, posterior distributions are not amenable to Gaussian approximation. This happens, e.g. when posterior distributions are multi-modal. PFs can be used on these problems, but the required ensemble size is expected to be large (hundreds to thousands), even if the PFs are localized. Moreover, the usual indicators of performance (small root mean square error and comparable spread) may not be useful in strongly nonlinear problems. We arrive at these conclusions using a combination of theoretical considerations and a suite of numerical DA experiments with low- and high-dimensional nonlinear models in which we can control the nonlinearity.
NoteOpen access journal
VersionFinal published version
SponsorsOffice of Naval Research [N00173-17-2-C003, PE-0601153N]; Alfred P. Sloan Research Fellowship; National Science Foundation [DMS-1619630]