Hierarchical ensemble Kalman filters for stochastic parameters and hyper-parameters inference
Model errors in the ensemble Kalman filter are usually accounted through the use of multiphysics schemes, additive or multiplicative covariance inflation, stochastic parameterizations or a combination of them. Under these approaches, several parameters need to be optimized to properly assess the model uncertainties. Parameters related to the covariance structure of a stochastic additive term can not be inferred using the state augmentation approach. We propose a hierarchical data assimilation scheme based on two nested ensemble Kalman filter to infer offline optimal values for these type of parameters. In a low-order system, it was possible to infer the amplitude and covariance structure of the additive stochastic forcing for different types of covariance formulation. A simplified variant of the proposed scheme can also be applied to infer filter hyper-parameters like covariance localization scale and additive inflation amplitude. These schemes can be used as an a priori offline optimization of the data assimilation system.
Dr. Guillermo Scheffler CIMA-CONICET/UBA, Argentina