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 dynamically change every analysis time. We robustly test the dynamical mixed Kalman filter 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 to the Gaussian Kalman filter. This article is protected by copyright. All rights reserved.