Convergent least-squares optimisation methods for variational data assimilation

Cartis, C., Kaouri, M. H., Lawless, A. S. ORCID: https://orcid.org/0000-0002-3016-6568 and Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220 (2024) Convergent least-squares optimisation methods for variational data assimilation. Optimization, 73 (11). pp. 3451-3485. ISSN 1029-4945 doi: 10.1080/02331934.2024.2390119

Abstract/Summary

Data assimilation combines prior (or background) information with observations to estimate the initial state of a dynamical system over a given time-window. A common application is in numerical weather prediction where a previous forecast and atmospheric observations are used to obtain the initial conditions for a numerical weather forecast. In four-dimensional variational data assimilation (4D-Var), the problem is formulated as a nonlinear least-squares problem, usually solved using a variant of the classical Gauss-Newton (GN) method. However, we show that GN may not converge if poorly initialised. In particular, we show that this may occur when there is greater uncertainty in the background information compared to the observations, or when a long time-window is used in 4D-Var allowing more observations. The difficulties GN encounters may lead to inaccurate initial state conditions for subsequent forecasts. To overcome this, we apply two convergent GN variants (line search and regularisation) to the long time-window 4D-Var problem and investigate the cases where they locate a more accurate estimate compared to GN within a given budget of computational time and cost. We show that these methods are able to improve the estimate of the initial state, which may lead to a more accurate forecast.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/117515
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO) Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	Taylor and Francis
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