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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 12, issue 6
Nonlin. Processes Geophys., 12, 775–782, 2005
https://doi.org/10.5194/npg-12-775-2005
© Author(s) 2005. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Special issue: Quantifying predictability

Nonlin. Processes Geophys., 12, 775–782, 2005
https://doi.org/10.5194/npg-12-775-2005
© Author(s) 2005. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  09 Aug 2005

09 Aug 2005

A Kalman filter application to a spectral wave model

J. P. Pinto1, M. C. Bernadino1, and A. Pires Silva2 J. P. Pinto et al.
  • 1Marinha, Instituto Hidrográfico, Portugal
  • 2Instituto Superior Técnico, Lisbon, Portugal

Abstract. A sequential time dependent data assimilation scheme based on the Kalman filter is applied to a spectral wave model. Usually, the first guess covariance matrices used in optimal interpolation schemes are exponential spreading functions, which remain constant. In the present work the first guess correlation errors evolve in time according to the dynamic constraints of the wave model. A system error noise is deduced and used to balance numerical errors. The assimilation procedure is tested in a standard situation of swell propagation, where the Kalman filter is used to assimilate the significant wave height. The evolution of the wave field is described by a linear two-dimensional advection equation and the propagation of the error covariance matrix is derived according to Kalman's linear theory. Model simulations were performed in a 2-dimensional domain with deep-water conditions, a relatively small surface area and without wind forcing or dissipation. A true state simulation and a first guess simulation were used to illustrate the assimilation outcome, showing a reasonable performance of the Kalman filter.

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