Using Machine learning techniques to switch background error distributions to improve data assimilation

With the development of non-Gaussian based data assimilation in the variational formulation, and the understanding that the underlying distribution can change dynamically, we need techniques that allow us to switch between the distributions to ensure a consistent background error model. To address this question, we have used different machine learning techniques with different criteria to determine if the behavior of the variable has switched between Gaussian and lognormal, but also back to Gaussian. In this presentation, we shall present results using machine learning algorithms to determine when the z component of the Lorenz 1963 model switches between Gaussian, lognormal, and back, through using skewness changing from 0 to determine this change and show that by switching between the distribution, the analysis error is improved compared to just assuming a Gaussian all the time. We carry out a sensitivity study to understand the impact of the size of the training data on their performance using Lorenz 63 model. We also compare their performance using test dataset.