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

Pannekoucke, Olivier; Arbogast, Philippe

doi:10.5194/gmd-2021-89

Cited by 4 publications

(2 citation statements)

References 16 publications

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“…To facilitate the design of the PKF dynamics as well as the numerical evaluation, the package SymPKF has been introduced to perform the VLATcov parameter dynamics and to generate a numerical code used for the investigations (Pannekoucke 2021b). The next section introduces and details this tool.…”

Section: Discussion/intermediate Conclusionmentioning

confidence: 99%

SymPKF: a symbolic and computational toolbox for the design of parametric Kalman filter dynamics

Pannekoucke¹,

Arbogast²

2021

Preprint

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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.

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Section: Discussion/intermediate Conclusionmentioning

confidence: 99%

SymPKF: a symbolic and computational toolbox for the design of parametric Kalman filter dynamics

Pannekoucke¹,

Arbogast²

2021

Preprint

Self Cite

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show abstract

“…The computation of dynamical equations (Equations 18a-18c) for the mean, the variance V and the anisotropy g (or s) can be performed using a computed algebra system. To do so, the open source Python toolbox SymPKF has been introduced (Pannekoucke, 2021b;Pannekoucke & Arbogast, 2021), which computes the dynamics of the parameters and renders a numerical code to facilitate the numerical exploration of the PKF approach. Another way to simplify the computation of the parameters dynamics is to identify the contribution of each physical process present in Equation 1 following a splitting strategy (Pannekoucke & Arbogast, 2021;Pannekoucke et al, 2018).…”

Section: Parametric Formulation For the Kalman Filter Forecast Step B...mentioning

confidence: 99%

Boundary Conditions for the Parametric Kalman Filter Forecast

Sabathier,

Pannekoucke,

Maget

et al. 2023

J Adv Model Earth Syst

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This paper is a contribution to the exploration of the parametric Kalman filter (PKF), which is an approximation of the Kalman filter, where the error covariances are approximated by a covariance model. Here we focus on the covariance model parameterized from the variance and the anisotropy of the local correlations, and whose parameters dynamics provides a proxy for the full error‐covariance dynamics. For this covariance model, we aim to provide the boundary condition to specify in the prediction of PKF for bounded domains, focusing on Dirichlet and Neumann conditions when they are prescribed for the physical dynamics. An ensemble validation is proposed for the transport equation and for the heterogeneous diffusion equation over a bounded 1D domain. This ensemble validation requires to specify the auto‐correlation time‐scale needed to populate boundary perturbation that leads to prescribed uncertainty characteristics. The numerical simulations show that the PKF is able to reproduce the uncertainty diagnosed from the ensemble of forecast appropriately perturbed on the boundaries, which show the ability of the PKF to handle boundaries in the prediction of the uncertainties. It results that Dirichlet condition on the physical dynamics implies Dirichlet condition on the variance and on the anisotropy.

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

Pannekoucke

Arbogast

2021

Geosci. Model Dev.

Self Cite

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Abstract. Recent research in data assimilation has led to the introduction of the parametric Kalman filter (PKF): an implementation of the Kalman filter, whereby the covariance matrices are approximated by a parameterized covariance model. In the PKF, the dynamics of the covariance during the forecast step rely 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 nonlinear diffusive advection (the 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.

show abstract

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

Cited by 4 publications

References 16 publications

SymPKF: a symbolic and computational toolbox for the design of parametric Kalman filter dynamics

SymPKF: a symbolic and computational toolbox for the design of parametric Kalman filter dynamics

Boundary Conditions for the Parametric Kalman Filter Forecast

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

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