A parametric Kalman filter is a Kalman filter where one would not need to forecast the error covariance matrices. They are parametrised, typically, by a variance field and a local diffusion tensor. Instead of forecasting the error covariance matrix or an ensemble as in the ensemble Kalman filter, one would only need to forecast the variance field and the local diffusion tensor. This would potentially yield a numerically very efficient Kalman filter.

In this newly accepted paper, my colleagues Olivier Pannekoucke, Richard Ménard and I have analytically computed the forecast of the local diffusion tensor for the Burgers diffusive equation, inspired by earlier work from Stephen E. Cohn. The Burgers model is simple but has key features of larger geophysical models: nonlinear convection and diffusion. We have checked numerically that this forecast yields a very good approximation of the true forecast obtained independently through a large Monte Carlo simulation.

This study has been published in the Nonlinear Processes in Geophysics special edition dedicated to the legacy of Anna Trevisan. It is entitled Parametric covariance dynamics for the nonlinear diffusive Burgers equation.