Tangent linear models

From Glossary of Meteorology
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tangent linear model

(Abbreviated TLM.) A model, comprising tangent linear equations, that maps a perturbation vector, δx(t1) = Lδx(t0), from initial time t0 to forecast time t1.

Here, L is the tangent linear operator and x is the model state vector. A TLM provides a first-order approximation to the evolution of perturbations in a nonlinear forecast trajectory.
See tangent linear approximation, small perturbation, adjoint model.