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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 10, issue 3
Nonlin. Processes Geophys., 10, 253–259, 2003
https://doi.org/10.5194/npg-10-253-2003
© Author(s) 2003. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Special issue: Quantifying Predictability

Nonlin. Processes Geophys., 10, 253–259, 2003
https://doi.org/10.5194/npg-10-253-2003
© Author(s) 2003. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  30 Jun 2003

30 Jun 2003

Sequential parameter estimation for stochastic systems

G. A. Kivman G. A. Kivman
  • Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany

Abstract. The quality of the prediction of dynamical system evolution is determined by the accuracy to which initial conditions and forcing are known. Availability of future observations permits reducing the effects of errors in assessment the external model parameters by means of a filtering algorithm. Usually, uncertainties in specifying internal model parameters describing the inner system dynamics are neglected. Since they are characterized by strongly non-Gaussian distributions (parameters are positive, as a rule), traditional Kalman filtering schemes are badly suited to reducing the contribution of this type of uncertainties to the forecast errors. An extension of the Sequential Importance Resampling filter (SIR) is proposed to this aim. The filter is verified against the Ensemble Kalman filter (EnKF) in application to the stochastic Lorenz system. It is shown that the SIR is capable of estimating the system parameters and to predict the evolution of the system with a remarkably better accuracy than the EnKF. This highlights a severe drawback of any Kalman filtering scheme: due to utilizing only first two statistical moments in the analysis step it is unable to deal with probability density functions badly approximated by the normal distribution.

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