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A comparison of two methods for developing the linearization of a shallow‐water model
Author(s) -
Lawless A. S.,
Nichols N. K.,
Ballard S. P.
Publication year - 2003
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1256/qj.02.75
Subject(s) - linearization , discretization , tangent , nonlinear system , shallow water equations , mathematics , lagrangian , perturbation (astronomy) , waves and shallow water , nonlinear model , linear model , mathematical analysis , geometry , geology , physics , oceanography , statistics , quantum mechanics
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