A non-Gaussian analysis scheme using rank histograms for ensemble data assimilation

• Published in: Nonlinear Processes in Geophysics
• Main Authors: S. Metref, E. Cosme, C. Snyder, P. Brasseur
• Format: Article in Journal/Newspaper
• Language: English
• Published: Copernicus Publications 2014
• Subjects: Science; Q; Physics; QC1-999; Geophysics. Cosmic physics; QC801-809; North Atlantic
• Online Access: https://doi.org/10.5194/npg-21-869-2014; https://doaj.org/article/e64b69a2e7014f7d82af187b93b4935a

One challenge of geophysical data assimilation is to address the issue of non-Gaussianities in the distributions of the physical variables ensuing, in many cases, from nonlinear dynamical models. Non-Gaussian ensemble analysis methods fall into two categories, those remapping the ensemble particles by approximating the best linear unbiased estimate, for example, the ensemble Kalman filter (EnKF), and those resampling the particles by directly applying Bayes' rule, like particle filters. In this article, it is suggested that the most common remapping methods can only handle weakly non-Gaussian distributions, while the others suffer from sampling issues. In between those two categories, a new remapping method directly applying Bayes' rule, the multivariate rank histogram filter (MRHF), is introduced as an extension of the rank histogram filter (RHF) first introduced by Anderson (2010). Its performance is evaluated and compared with several data assimilation methods, on different levels of non-Gaussianity with the Lorenz 63 model. The method's behavior is then illustrated on a simple density estimation problem using ensemble simulations from a coupled physical–biogeochemical model of the North Atlantic ocean. The MRHF performs well with low-dimensional systems in strongly non-Gaussian regimes.