REVIEW Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation

This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical mod-eling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The non-Gaussian fea-tures are stressed rather than the nonlinearity of the dynamical models, although both aspects are entangled. Ideas recently proposed to deal with these non-Gaussian issues, in order to improve the state or parameter estimation, are emphasized. The general Bayesian solution to the estimation problem and the techniques to solve it are first pre-sented, as well as the obstacles that hinder their use in high-dimensional and complex systems. Approx-imations to the Bayesian solution relying on Gaussian, or on second-order moment closure, have been wholly adopted in geophysical data assimilation (e.g., Kalman filters and quadratic variational solutions). Yet, nonlinear and non-Gaussian effects remain. They essentially originate in the nonlinear models and in the non-Gaussian priors. How these effects are handled within algorithms based on Gaussian assumptions is then described. Statistical tools that can diagnose them and measure deviations from Gaussianity are recalled. The following advanced techniques that seek to handle the estimation problem beyond Gaussianity ar