A comparison of two methods for developing the linearization of a shallow-water model

Lawless, A.S. ORCID: https://orcid.org/0000-0002-3016-6568, Nichols, N.K. ORCID: https://orcid.org/0000-0003-1133-5220 and Ballard, S.P. (2003) A comparison of two methods for developing the linearization of a shallow-water model. Quarterly Journal of the Royal Meteorological Society, 129 (589). pp. 1237-1254. ISSN 1477-870X doi: 10.1256/qj.02.75

Abstract/Summary

We develop the linearization of a semi-implicit semi-Lagrangian model of the one-dimensional shallow-water equations using two different methods. The usual tangent linear model, formed by linearizing the discrete nonlinear model, is compared with a model formed by first linearizing the continuous nonlinear equations and then discretizing. Both models are shown to perform equally well for finite perturbations. However, the asymptotic behaviour of the two models differs as the perturbation size is reduced. This leads to difficulties in showing that the models are correctly coded using the standard tests. To overcome this difficulty we propose a new method for testing linear models, which we demonstrate both theoretically and numerically. © Crown copyright, 2003. Royal Meteorological Society

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/5240
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	Semi-Lagrangian;Tangent linear;Variational data assimilation
Publisher	Royal Meteorological Society
Download/View statistics	View download statistics for this item