22 Sep 2022
22 Sep 2022
Status: this preprint is open for discussion.

Toward a multivariate formulation of the PKF assimilation: application to a simplified chemical transport model

Antoine Perrot1, Olivier Pannekoucke1,2,3, and Vincent Guidard1 Antoine Perrot et al.
  • 1CNRM, Université de Toulouse, Météo-France, CNRS, Toulouse, France
  • 2CERFACS, Toulouse, France
  • 3INPT-ENM, Toulouse, France

Abstract. This contribution explores a new approach to forecast multivariate covariances for atmospheric chemistry through the use of the parametric Kalman filter (PKF). In the PKF formalism, the error covariance matrix is modelized by a covariance model relying on parameters, for which the dynamics is then computed. The PKF has been formulated in univariate cases, and a multivariate extension for chemical transport models is explored here. To do so, a simplified two-species chemical transport model over a 1D domain is introduced, based on the nonlinear Lotka-Volterra equations, which allows to propose a multivariate pseudo covariance model. Then, the multivariate PKF dynamics is formulated and its results are compared with a large ensemble Kalman filter (EnKF) in several numerical experiments. In these experiments, the PKF accurately reproduces the EnKF. Eventually, the PKF is formulated for a more complex chemical model composed of six chemical species (Generic Reaction Set). Again, the PKF succeeds at reproducing the multivariate covariances diagnosed on the large ensemble.

Antoine Perrot et al.

Status: open (until 17 Nov 2022)

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Antoine Perrot et al.

Antoine Perrot et al.


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Short summary
This work is a theoretical contribution that provides equations for understanding uncertainty prediction applied in air quality where multiple chemical species can interact. A simplified minimal test-bed is introduced that shows the ability our equations to reproduce the statistics estimated from an ensemble of forecast. While the latter estimation is the state of the art, solving equations is numerically less costly, depending on the number of chemical species, and motivates this research.