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Four-dimensional variational assimilation in the unstable subspace and the optimal subspace dimension

TitleFour-dimensional variational assimilation in the unstable subspace and the optimal subspace dimension
Publication TypeArticolo su Rivista peer-reviewed
Year of Publication2010
AuthorsTrevisan, A., D'Isidoro Massimo, and Talagrand O.
JournalQuarterly Journal of the Royal Meteorological Society
Volume136
Pagination487-496
ISSN00359009
KeywordsAdjoints, algorithm, Apriori, Control variable, data assimilation, Differential equations, Dynamical instabilities, Evolution equations, four-dimensional modeling, instability, Non-linear model, Nonlinear analysis, nonlinearity, Numerical experiments, numerical method, observational method, Optimal subspace, Quality control, RMS analysis, Theoretical arguments, Value engineering, Variational assimilation, Weather forecasting
Abstract

Key a priori information used in 4D-Var is the knowledge of the system's evolution equations. In this article we propose a method for taking full advantage of the knowledge of the system's dynamical instabilities in order to improve the quality of the analysis. We present an algorithm for four-dimensional variational assimilation in the unstable subspace (4D-Var - AUS), which consists of confining in this subspace the increment of the control variable. The existence of an optimal subspace dimension for this confinement is hypothesized. Theoretical arguments in favour of the present approach are supported by numerical experiments in a simple perfect nonlinear model scenario. It is found that the RMS analysis error is a function of the dimension N of the subspace where the analysis is confined and is a minimum for N approximately equal to the dimension of the unstable and neutral manifold. For all assimilation windows, from 1 to 5 d, 4D-Var - AUS performs better than standard 4D-Var. In the presence of observational noise, the 4D-Var solution, while being closer to the observations, is farther away from the truth. The implementation of 4D-Var - AUS does not require the adjoint integration. Copyright © 2010 Royal Meteorological Society.

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URLhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-77949384336&doi=10.1002%2fqj.571&partnerID=40&md5=84290ec7368a3ab6f0f116657579f943
DOI10.1002/qj.571
Citation KeyTrevisan2010487