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Evaluating Data Assimilation Algorithms

Law, K. J. H. and Stuart, A. M. (2012) Evaluating Data Assimilation Algorithms. Monthly Weather Review, 140 . pp. 3757-3782. ISSN 0027-0644. doi:10.1175/MWR-D-11-00257.1. https://resolver.caltech.edu/CaltechAUTHORS:20160728-150615482

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Abstract

Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given all the observations on a time window of interest, plays a central conceptual role. The aim of this paper is to use this Bayesian posterior probability distribution as a gold standard against which to evaluate various commonly used data assimilation algorithms. A key aspect of geophysical data assimilation is the high dimensionality and limited predictability of the computational model. This paper examines the two-dimensional Navier–Stokes equations in a periodic geometry, which has these features and yet is tractable for explicit and accurate computation of the posterior distribution by state-of-the-art statistical sampling techniques. The commonly used algorithms that are evaluated, as quantified by the relative error in reproducing moments of the posterior, are four-dimensional variational data assimilation (4DVAR) and a variety of sequential filtering approximations based on three-dimensional variational data assimilation (3DVAR) and on extended and ensemble Kalman filters. The primary conclusions are that, under the assumption of a well-defined posterior probability distribution, (i) with appropriate parameter choices, approximate filters can perform well in reproducing the mean of the desired probability distribution, (ii) they do not perform as well in reproducing the covariance, and (iii) the error is compounded by the need to modify the covariance, in order to induce stability. Thus, filters can be a useful tool in predicting mean behavior but should be viewed with caution as predictors of uncertainty. These conclusions are intrinsic to the algorithms when assumptions underlying them are not valid and will not change if the model complexity is increased.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1175/MWR-D-11-00257.1DOIArticle
http://journals.ametsoc.org/doi/abs/10.1175/MWR-D-11-00257.1PublisherArticle
https://arxiv.org/abs/1107.4118arXivDiscussion Paper
Additional Information:© 2012 American Meteorological Society. Manuscript received 27 September 2011, in final form 27 March 2011. Both authors are grateful to the referees for numerous suggestions that have improved the presentation of this material. In particular, we thank Chris Snyder. KJHL is grateful to the EPSRC for funding. AMS is grateful to EPSRC, ERC, and ONR for funding.
Funders:
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
European Research Council (ERC)UNSPECIFIED
Office of Naval Research (ONR)UNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ96
DOI:10.1175/MWR-D-11-00257.1
Record Number:CaltechAUTHORS:20160728-150615482
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160728-150615482
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69289
Collection:CaltechAUTHORS
Deposited By: Linda Taddeo
Deposited On:29 Jul 2016 20:41
Last Modified:11 Nov 2021 04:11

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