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.
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