Dataset associated with "Detection of non-Gaussian behaviour using machine learning techniques"

An important assumption made in most variational, ensemble and hybrid based data assimilation systems is that all minimised errors are Gaussian random variables. There has been theory developed at the Cooperative Institute for Research in the Atmosphere (CIRA) that enables for the Gaussian assumption for the different types of errors to be relaxed to a lognormally distributed random variable. While this is a first step towards using more consistent distributions to model the errors involved in numerical weather/ocean prediction, we still need to be able to identify when we need to assign a lognormal distribution in a mixed Gaussian-lognormal approach. In this paper, we present some machine learning techniques and experiments with the Lorenz 63 model. Using these machine learning techniques, we show detection of non-Gaussian distributions can be done using two methods; a support vector machine, and a neural network. This is done by training past data to classify 1) differences with the distribution statistics (means and modes) and 2) the skewness of the probability density function.