Shutyaev, V. and Gejadze, I and Copeland, G.J.M and Le Dimet, F.X. (2012) Optimal solution error covariance in highly nonlinear problems of variational data assimilation. Nonlinear Processes in Geophysics, 19 (2). pp. 177184. ISSN 10235809

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Abstract
The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem (see, e.g.[1]) to find the initial condition, boundary conditions 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 functional of an auxiliary data assimilation problem ([2], [3]). The relationship between the optimal solution error covariance matrix and the Hessian of the auxiliary control problem is discussed for different degrees of validity of the tangent linear hypothesis. For problems with strongly nonlinear dynamics a new statistical method based on 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 quasiNewton BFGS) with preconditioning. The method allows us to get a sensible approximation of the posterior covariance matrix with a small sample size. Numerical examples are presented for the model governed by Burgers equation with a nonlinear viscous term. The first author acknowledges the funding through the project 090100284 of the Russian Foundation for Basic Research, and the FCP program "Kadry".
Item type:  Article 

ID code:  34291 
Keywords:  variational data assimilation, nonlinear evolution model, optimal control problem, optimal solution error, covariances, Engineering (General). Civil engineering (General), Geochemistry and Petrology, Statistical and Nonlinear Physics, Geophysics 
Subjects:  Technology > Engineering (General). Civil engineering (General) 
Department:  Faculty of Engineering > Civil and Environmental Engineering 
Depositing user:  Pure Administrator 
Date Deposited:  12 Oct 2011 13:49 
Last modified:  27 Mar 2015 01:37 
URI:  http://strathprints.strath.ac.uk/id/eprint/34291 
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