Toward a multivariate formulation of the parametric Kalman filter assimilation: application to a simplified chemical transport model

This contribution explores a new approach to forecasting multivariate covariances for atmospheric chemistry through the use of the parametric Kalman filter (PKF). In the PKF formalism, the error covariance matrix is modellized by a covariance model relying on parameters, for which the dynamics are then computed. The PKF has been previously formulated in univariate cases, and a multivariate extension for chemical transport models is explored here. This contribution focuses on the situation where the uncertainty is due to the chemistry but not due to the uncertainty of the weather. To do so, a simplified two-species chemical transport model over a 1D domain is introduced, based on the non-linear Lotka-Volterra equations, which allows us to propose a multivariate pseudo covariance model. Then, the multivariate PKF dynamics are formulated and their 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.