Preprints
https://doi.org/10.5194/gmd-2021-89
https://doi.org/10.5194/gmd-2021-89

Submitted as: model description paper 23 Apr 2021

Submitted as: model description paper | 23 Apr 2021

Review status: this preprint is currently under review for the journal GMD.

SymPKF (v1.0): a symbolic and computational toolbox for the design of parametric Kalman filter dynamics

Olivier Pannekoucke1,2,3 and Philippe Arbogast4 Olivier Pannekoucke and Philippe Arbogast
  • 1INPT-ENM, Toulouse, France
  • 2CNRM, Université de Toulouse, Météo-France, CNRS, Toulouse, France
  • 3CERFACS, Toulouse, France
  • 4Météo-France, Toulouse, France

Abstract. Recent researches in data assimilation lead to the introduction of the parametric Kalman filter (PKF): an implementation of the Kalman filter, where the covariance matrices are approximated by a parameterized covariance model. In the PKF, the dynamics of the covariance during the forecast step relies on the prediction of the covariance parameters. Hence, the design of the parameter dynamics is crucial while it can be tedious to do this by hand. This contribution introduces a python package, SymPKF, able to compute PKF dynamics for univariate statistics and when the covariance model is parameterized from the variance and the local anisotropy of the correlations. The ability of SymPKF to produce the PKF dynamics is shown on a non-linear diffusive advection (Burgers equation) over a 1D domain and the linear advection over a 2D domain. The computation of the PKF dynamics is performed at a symbolic level, but an automatic code generator is also introduced to perform numerical simulations. A final multivariate example illustrates the potential of SymPKF to go beyond the univariate case.

Olivier Pannekoucke and Philippe Arbogast

Status: open (until 18 Jun 2021)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse

Olivier Pannekoucke and Philippe Arbogast

Model code and software

SymPKF: a symbolic and computational toolbox for the design of parametric Kalman filter dynamics O. Pannekoucke https://github.com/opannekoucke/sympkf

Olivier Pannekoucke and Philippe Arbogast

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Short summary
This contributes to the research on uncertainty prediction, important either for determining the weather today or for estimating the risk in prediction. The problem is that uncertainty prediction is numerically very expensive. An alternative has been proposed where the uncertainty is presented in a simplified form where only the dynamics of certain parameters are required. This tool allows to determine the symbolic equations of these parameter dynamics as well as its numerical computation.