# A comparison of two methods of deriving the tangent linear model

## Lawless [A.S.] ; NICHOLS, N.K.

The tangent linear model has become widely used within numerical meteorology, both as an explicit model of perturbation growth and as a means of determining the adjoint model. In this study we look at two ways of finding such a linear model; the usual method of linearizing a discrete nonlinear model is compared with the method used at the UK Meteorological Office, in which a numerical scheme is applied to the continuous linearized equations. The methods are compared using a simple initial value problem. The two methods produce different linear models, which may exhibit quite different behaviour if model instabilities are present. We demonstrate problems which may arise when applying the standard test of a tangent linear model.

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