Cooperative Institute for Research in the Atmosphere

Non-Gaussian Data Assimilation Developments at CIRA

The underlying assumption for variational and Kalman filter based data assimilation algorithms is that the associated errors are Gaussian distributed random variables.  Over the last 18 years at CIRA we have worked on relaxing this assumption to allow for lognormally distributed, and recently reverse-lognormally distributed errors.  The first part of this talk will be an overview of the development of the lognormal and the mixed Gaussian-lognormal variational approaches along with a representer, formulation, as well as the recent development of the mixed Gaussian-lognormal based Kalman filter.

In the second part, we introduce the reverse-lognormal distribution to be able to include negatively skewed errors. All these ideas can then be combined to develop a mixed version of the maximum likelihood ensemble filter. The main question then remains: how do we decide the underlying distribution of the errors? To answer this question we have developed a basic machine learning algorithm that can help us.