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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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Second-order methods for error propagation in variational data assimilation

Second-order methods for error propagation in variational data assimilation

(p.319) 14 Second-order methods for error propagation in variational data assimilation
Advanced Data Assimilation for Geosciences

F.-X. Le Dimet

I. Gejadze

V. Shutyaev

Oxford University Press

This chapter discusses the use of second-order methods for estimating error propagation in variational data assimilation. The basic variational approach to data assimilation exhibits the optimality system: it can be considered as a generalized model containing all the available information. To estimate the impact of errors due to the parameters of the model and/or to the observations, it is necessary to consider second-order properties. The variational approach can be used to estimate the propagation of uncertainties in the analysis. Two basic cases are considered. In the deterministic framework, the uncertainty is a virtual and deterministic perturbation on the model parameters, whose impact on some criterion is to be found. In the stochastic framework, the uncertainty is a random variable transported by the model as such. The output is a stochastic perturbation on the outputs of the analysis, for which it is necessary to determine its probabilistic characteristics.

Keywords:   data assimilation, variational approach, optimality system, error propagation, second order, deterministic framework, stochastic framework

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