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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
12 Feb 2018
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Nonlinear Processes in Geophysics (NPG).
Parametric covariance dynamics for the nonlinear diffusive Burgers' equation
Olivier Pannekoucke1, Marc Bocquet2, and Richard Ménard3 1INPT-ENM, CNRM UMR 3589, Météo-France/CNRS, CERFACS, Toulouse, France
2CEREA, joint laboratory École des Ponts ParisTech and EDF R&D, Université Paris-Est, Champs-sur-Marne, France
3ARQI/Air Quality Research Division, Environment and Climate Change Canada, Dorval (Québec), Canada
Abstract. The parametric Kalman filter (PKF) is a computationally efficient alternative method to the ensemble Kalman filter (EnKF). The PKF relies on an approximation of the error covariance matrix by a covariance model with space-time evolving set of parameters. This study extends the PKF to nonlinear dynamics using the diffusive Burgers' equation as an application, focusing on the forecast step of the assimilation cycle. The covariance model considered is based on the diffusion equation, with the diffusion tensor and the error variance as evolving parameter. An analytical derivation of the parameter dynamics highlights a closure issue. Therefore, a closure model is proposed based on the so-called kurtosis of the local correlation functions. Numerical experiments compare the PKF forecast with the statistics obtained from an large ensemble of nonlinear forecasts. These experiments strengthen the closure model and demonstrate the ability of the PKF to reproduce the tangent-linear covariance dynamics, at a low numerical cost.

Citation: Pannekoucke, O., Bocquet, M., and Ménard, R.: Parametric covariance dynamics for the nonlinear diffusive Burgers' equation, Nonlin. Processes Geophys. Discuss.,, in review, 2018.
Olivier Pannekoucke et al.
Olivier Pannekoucke et al.
Olivier Pannekoucke et al.


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