Representation errors and retrievals in linear and nonlinear data assimilation

Van Leeuwen, P. J. (2015) Representation errors and retrievals in linear and nonlinear data assimilation. Quarterly Journal of the Royal Meteorological Society, 141 (690). pp. 1612-1623. ISSN 1477-870X doi: 10.1002/qj.2464 (Part A)

Abstract/Summary

This article shows how one can formulate the representation problem starting from Bayes’ theorem. The purpose of this article is to raise awareness of the formal solutions,so that approximations can be placed in a proper context. The representation errors appear in the likelihood, and the different possibilities for the representation of reality in model and observations are discussed, including nonlinear representation probability density functions. Specifically, the assumptions needed in the usual procedure to add a representation error covariance to the error covariance of the observations are discussed,and it is shown that, when several sub-grid observations are present, their mean still has a representation error ; socalled ‘superobbing’ does not resolve the issue. Connection is made to the off-line or on-line retrieval problem, providing a new simple proof of the equivalence of assimilating linear retrievals and original observations. Furthermore, it is shown how nonlinear retrievals can be assimilated without loss of information. Finally we discuss how errors in the observation operator model can be treated consistently in the Bayesian framework, connecting to previous work in this area.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/38470
Identification Number/DOI	10.1002/qj.2464
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Uncontrolled Keywords	data assimilation; representation errors; Bayes' theorem
Publisher	Royal Meteorological Society
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