Conditioning of hybrid variational data assimilation

Shataer, S., Lawless, A. S. ORCID: https://orcid.org/0000-0002-3016-6568 and Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220 (2023) Conditioning of hybrid variational data assimilation. Numerical Linear Algebra with Applications. e2534. ISSN 1099-1506 doi: 10.1002/nla.2534

Abstract/Summary

Gaussian assumptions for the prior and likelihood can be found by solving a leastsquares minimization problem . In recent years,we have seen the popularity of hybrid variational data assimilation methods for Numerical Weather Prediction. In these methods, the prior error covariance matrix is a weighted sum of a climatological part and a flow-dependent ensemble part, the latter being rank deficient. The nonlinear least squares problem of variational data assimilation is solved using iterative numerical methods, and the condition number of the Hessian is a good proxy for the convergence behavior of such methods. In this paper, we study the conditioning of the least squares problem in a hybrid four-dimensional variational data assimilation (Hybrid 4D-Var) scheme by establishing bounds on the condition number of the Hessian. In particular, we consider the effect of the ensemble component of the prior covariance on the conditioning of the system. Numerical experiments show that the bounds obtained can be useful in predicting the behavior of the true condition number and the convergence speed of an iterative algorithm.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/113341
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
Publisher	Wiley
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