An Introduction to solving the least-squares problem in variational data assimilation

Dauzickaite, I., Freitag, M., Gurol, S., Lawless, A. ORCID: https://orcid.org/0000-0002-3016-6568, Ramage, A., Scott, J. ORCID: https://orcid.org/0000-0003-2130-1091 and Tabeart, J. (2026) An Introduction to solving the least-squares problem in variational data assimilation. SIAM Review. ISSN 1095-7200 (In Press)

Abstract/Summary

Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weather and ocean forecasting. The approach involves a large-scale generalized nonlinear least-squares problem. Solving the resulting sequence of sparse linear subproblems requires the use of sophisticated numerical linear algebra methods. In practical applications, the computational demands severely limit the number of iterations of a Krylov subspace solver that can be performed and so high-quality preconditioners are vital. In this paper, we present a numerical linear algebra perspective on variational data assimilation and discuss contemporary solution methods for the challenges posed by large-scale geophysical applications. The principal contribution is a focused treatment of the underlying linear algebraic subproblems, accompanied by a concise and clear introduction to the essential concepts of variational data assimilation and an extensive bibliography.

Item Type	Article
URI	https://centaur.reading.ac.uk/id/eprint/129320
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	SIAM
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