Non-Gaussian Hybrid Variational Data Assimilation

With the advancement of non-Gaussian based variational techniques the need to extend this to hybrid ensemble-variational techniques is the next step towards operational viability. However, the problem lies in the Gaussian assumptions that are made in the derivation of the Kalman filter. In this presentation we shall show a lognormal, and Gaussian-lognormal based Kalman filter and show its performance against the extended Kalman filter for the Lorenz 63 model. We shall extend this theory to the Maximum Likelihood Ensemble Filter (MLEF) approach to form the LMLEF and the MXMLEF respectively and test as well with the Lorenz 63 model. To form the hybrid data assimilation system the MXMLEF will be combine the MX 3DVAR cost function using alpha control variables. Finally we shall present the complete MX form of the buddy check, gross error check, and equivalent Huber norm quality control measures and test the new gross error check with the Lorenz 63 model.