# Tangent linear model

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## tangent linear model

(Abbreviated TLM.) A model, comprising tangent linear equations, that maps a perturbation vector, δ

**x**(*t*_{1}) =*L*δ**x**(*t*_{0}), from initial time*t*_{0}to forecast time*t*_{1}.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.