Foundations for Universal Non-Gaussian Data Assimilation

In almost all applications of data assimilation, a substantial assumption is made: all variables are well-described by Gaussian error statistics. This assumption has the advantage of making calculations considerably simpler, but it is often not valid, leading to biases in forecasts or, even worse, unphysical predictions. We propose a simple, but effective, way of replacing this assumption, by making use of transforming functions, while remaining consistent with Bayes' theorem. This method allows the errors to have any value of the skewness and kurtosis. We apply this framework to a 3D variational data assimilation method, and find improved performance in a simple atmospheric toy model, compared to an all-Gaussian technique.