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Advanced Data Assimilation for GeosciencesLecture Notes of the Les Houches School of Physics: Special Issue, June 2012$
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Éric Blayo, Marc Bocquet, Emmanuel Cosme, and Leticia F. Cugliandolo

Print publication date: 2014

Print ISBN-13: 9780198723844

Published to Oxford Scholarship Online: March 2015

DOI: 10.1093/acprof:oso/9780198723844.001.0001

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(p.121) 4 Smoothers
Advanced Data Assimilation for Geosciences

E. Cosme

Oxford University Press

This chapter describes the use of smoothers in data assimilation. The filtering problem in data assimilation consists in estimating the state of a system based on past and present observations. In contrast to filters, amoothers implement Bayesian data assimilation using future observations. Smoothing problems can be posed in different ways. The main formulations in geophysics are fixed-point, fixed-interval, and fixed-lag smoothers. In this chapter, these problems are first introduced in a Bayesian framework, and the most straightforward Bayesian solutions are formulated. Common linear, Gaussian implementations, many of which are based on the classical Kalman filter, are then derived, followed by their ensemble counterparts, based on the usual ensemble Kalman filter techniques. Finally, the pros and cons, as well as the computational complexities, of all the schemes are discussed.

Keywords:   smoother, fixed-point smoother, fixed-interval smoother, fixed-lag smoother, linear Gaussian, Kalman filter, ensemble Kalman filter

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