Toward Sequential Data Assimilation for NWP Models Using Kalman Filter Tools

Abstract: The aim of the meteorological data assimilation is to provide an initial field for Numerical Weather Prediction (NWP) and to sequentially update the knowledge about it using available observations. Kalman filtering is a robust technique for the sequential estimation of the unobservable model state based on the linear regression concept. In the iterative use together with Kalman smoothing, it can easily be extended to work powerfully in the non-Gaussian and/or  non-linear framework. The huge dimensionality of the model state variable for high resolution NWP models (magnitude 108) makes it impossible with any explicit manipulations of the forecast error covariance matrix required for Kalman filter and Kalman smoother recursions. For NWP models the technical implementation of a Kalman filtering becomes the main challenge which provokes developments of novel data assimilation algorithms.This thesis is concerned with extensions of the Kalman filtering when the assumptions on linearity and Gaussianity of the state space model are violated. The research includes both theoretical studies of the properties of such extensions, within the framework of idealized small-dimensional models, and the development of the data assimilation algorithms for a full scale limited area high resolution NWP forecasting system.This thesis shows that non-Gaussian state space models can efficiently be approximated by a Gaussian state space model with an adaptively estimated variance of the stochastic forcing. That results in a type of local smoothing, in contrast to the global smoothing provided by Gaussian state space models. With regards to NWP models, the thesis shows that the sequential update of the uncertainty about the model state estimate is essential for efficient extraction of information from observations. The Ensemble Kalman filters can be used to represent both flow- and observation-network-dependent structures of the forecast error covariance matrix, in spite of a severe rank-deficiency of the Ensemble Kalman filters. As a culmination of this research the hybrid variational data assimilation has been developed on top of the HIRLAM variational data assimilation system. It provides the possibility of utilizing, during the data assimilation process, the error-of-the-day structure of the forecast error covariance, estimated from the ensemble of perturbations, at the same time as the full rank of the variational data assimilation is preserved.