The ultimate goal is to develop a path towards an operational ensemble Kalman filtering (EnKF) system. Several approaches to EnKF for atmospheric systems have been proposed but not systematically compared. The sensitivity of EnKF to the imperfections of forecast models is unclear. This research explores two questions: 1. What are the relative advantages and disadvantages of two promising EnKF methods? 2. How large are the effects of model errors on data assimilation, and can they be reduced by model bias correction?

Chapter 2 contains a theoretical review, followed by the FORTRAN development and testing of two EnKF methods: a serial ensemble square root filter (serial EnSRF, Whitaker and Hamill 2002) and a local EnKF (LEKF, Ott et al. 2002; 2004). We reproduced the results obtained by Whitaker and Hamill (2002) and Ott et al. (2004) on the Lorenz (1996) model. If we localize the LEKF error covariance, LEKF outperforms serial EnSRF. We also introduce a method to objectively estimate the optimal covariance inflation.

In Chapter 3 we apply the two EnKF methods and the three-dimensional variational method (3DVAR) to the SPEEDY primitive-equation global model (Molteni 2003), a fast but relatively realistic model. Perfect model experiments show that EnKF greatly outperforms 3DVAR. The 2-day forecast "errors of the day" are very similar to the analysis errors, but they are not similar among different methods except in low ensemble dimensional regions. Overall, serial EnSRF outperforms LEKF, but their difference is substantially reduced if we localize the LEKF error covariance or increase the ensemble size. Since LEKF is much more efficient than serial EnSRF when using parallel computers and many observations, LEKF would be the only feasible choice in operations.

In Chapter 4 we remove the perfect model assumption using the NCEP/NCAR reanalysis as the "nature" run. The advantage of EnKF to 3DVAR is reduced. When we apply the model bias estimation proposed by Dee and da Silva (1998), we find that the full dimensional model bias estimation fails. However, if instead we assume that the bias is low dimensional, we obtain a substantial improvement in the EnKF analysis.