A dynamical Gaussian, lognormal, and reverse lognormal Kalman filter

Abstract

We derive a generalization of the Kalman filter that allows for non-Gaussian background and observation errors. The Gaussian assumption is replaced by considering that the errors come from a mixed distribution of Gaussian, lognormal, and reverse lognormal random variables. We detail the derivation for reverse lognormal errors and extend the results to mixed distributions, where the number of Gaussian, lognormal, and reverse lognormal state variables can change dynamically every analysis time. We test the dynamical mixed Kalman filter robustly on two different systems based on the Lorenz 1963 model, and demonstrate that non-Gaussian techniques generally improve the analysis skill if the observations are sparse and uncertain, compared with the Gaussian Kalman filter.