Numerical form of the propagator

• Action of the linearized model can be represented as:

• Parameters defining the tangent linear model depend on a reference trajectory obtained from an integration of the nonlinear model.

• Extended Kalman filter: identical to the Kalman filter except that

  • the forecast integration is carried out with the nonlinear model
  • the evolution of the forecast error covariances is made with the tangent linear model.
  • Ref.: Ghil (1989), Gauthier et al., 1993 (Mon. Wea. Rev., p.1803-1820)

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