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

Lawless, A.S., Nichols, N.K. 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

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To link to this article 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
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Meteorology
Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:5240
Uncontrolled Keywords:Semi-Lagrangian;Tangent linear;Variational data assimilation
Publisher:Royal Meteorological Society

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