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Inner-Loop Stopping Criteria for Incremental Four-Dimensional Variational Data Assimilation

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  • 1 Department of Mathematics, University of Reading, Reading, United Kingdom
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Abstract

Incremental four-dimensional variational data assimilation is a method that solves the assimilation problem by minimizing a sequence of approximate “inner-loop” functions. In any implementation of such a scheme a decision must be made as to how accurately to solve each of the inner minimization problems. In this paper recently developed theory is applied to derive a new stopping criterion for the inner-loop minimizations, which guarantees convergence of the outer loops. This new criterion is shown to give improved convergence compared with other commonly used inner-loop stopping criteria.

Corresponding author address: Dr. A. S. Lawless, Department of Mathematics, University of Reading, Whiteknights, P.O. Box 220, Reading, Berkshire RG6 6AX, United Kingdom. Email: a.s.lawless@reading.ac.uk

Abstract

Incremental four-dimensional variational data assimilation is a method that solves the assimilation problem by minimizing a sequence of approximate “inner-loop” functions. In any implementation of such a scheme a decision must be made as to how accurately to solve each of the inner minimization problems. In this paper recently developed theory is applied to derive a new stopping criterion for the inner-loop minimizations, which guarantees convergence of the outer loops. This new criterion is shown to give improved convergence compared with other commonly used inner-loop stopping criteria.

Corresponding author address: Dr. A. S. Lawless, Department of Mathematics, University of Reading, Whiteknights, P.O. Box 220, Reading, Berkshire RG6 6AX, United Kingdom. Email: a.s.lawless@reading.ac.uk

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