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Recent researches in data assimilation lead to the introduction of theparametric Kalman filter (PKF): an implementation of the Kalman filter, wherethe covariance matrices are approximated by a parameterized covariance model.In the PKF, the dynamics of the covariance during the forecast step relies onthe prediction of the covariance parameters. Hence, the design of the parameterdynamics is crucial while it can be tedious to do this by hand. Thiscontribution introduces a python package, SymPKF, able to compute PKF dynamicsfor univariate statistics and when the covariance model is parameterized fromthe variance and the local anisotropy of the correlations. The ability ofSymPKF 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 anautomatic code generator is also introduced to perform numerical simulations. Afinal multivariate example illustrates the potential of SymPKF to go beyond theunivariate case.

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