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This paper is a contribution to the exploration of the parametric Kalmanfilter (PKF), which is an approximation of the Kalman filter, where the errorcovariances are approximated by a covariance model. Here we focus on thecovariance model parameterized from the variance and the anisotropy of thelocal correlations, and whose parameters dynamics provides a proxy for the fullerror-covariance dynamics. For this covariance model, we aim to provide theboundary condition to specify in the prediction of PKF for bounded domains,focusing on Dirichlet and Neumann conditions when they are prescribed for thephysical dynamics. An ensemble validation is proposed for the transportequation and for the heterogeneous diffusion equation over a bounded 1D domain.This ensemble validation requires to specify the auto-correlation time-scaleneeded to populate boundary perturbation that leads to prescribed uncertaintycharacteristics. The numerical simulations show that the PKF is able toreproduce the uncertainty diagnosed from the ensemble of forecast appropriatelyperturbed on the boundaries, which show the ability of the PKF to handleboundaries in the prediction of the uncertainties. It results that Dirichletcondition on the physical dynamics implies Dirichlet condition on the varianceand on the anisotropy. Codes are available athttps://github.com/opannekoucke/pkf-boundary

Boundary Conditions for the Parametric Kalman Filter forecast submited