  Recent researches in data assimilation lead to the introduction of the
parametric Kalman filter (PKF): an implementation of the Kalman filter, where
the covariance matrices are approximated by a parameterized covariance model.
In the PKF, the dynamics of the covariance during the forecast step relies on
the prediction of the covariance parameters. Hence, the design of the parameter
dynamics is crucial while it can be tedious to do this by hand. This
contribution introduces a python package, SymPKF, able to compute PKF dynamics
for univariate statistics and when the covariance model is parameterized from
the variance and the local anisotropy of the correlations. The ability of
SymPKF 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 an
automatic code generator is also introduced to perform numerical simulations. A
final multivariate example illustrates the potential of SymPKF to go beyond the
univariate case.

Data Analysis, Statistics and Probability;Mathematical Software;Numerical Analysis;Numerical Analysis