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.