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Optimal Solution Error Covariance in Highly Nonlinear Problems of Variational Data Assimilation : Volume 19, Issue 2 (16/03/2012)

By Shutyaev, V.

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Book Id: WPLBN0003982446
Format Type: PDF Article :
File Size: Pages 8
Reproduction Date: 2015

Title: Optimal Solution Error Covariance in Highly Nonlinear Problems of Variational Data Assimilation : Volume 19, Issue 2 (16/03/2012)  
Author: Shutyaev, V.
Volume: Vol. 19, Issue 2
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Gejadze, I., M. Copelan, G. J., Dimet, F. L., & Shutyaev, V. (2012). Optimal Solution Error Covariance in Highly Nonlinear Problems of Variational Data Assimilation : Volume 19, Issue 2 (16/03/2012). Retrieved from

Description: Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Gubkina 8, Moscow, Russia. The problem of variational data assimilation (DA) for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition, boundary conditions and/or model parameters. The input data contain observation and background errors, hence there is an error in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can be approximated by the inverse Hessian of the cost function. For problems with strongly nonlinear dynamics, a new statistical method based on the computation of a sample of inverse Hessians is suggested. This method relies on the efficient computation of the inverse Hessian by means of iterative methods (Lanczos and quasi-Newton BFGS) with preconditioning. Numerical examples are presented for the model governed by the Burgers equation with a nonlinear viscous term.

Optimal solution error covariance in highly nonlinear problems of variational data assimilation

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