Comparison of ensemble-based and variational-based data assimilation schemes in a quasi-geostrophic model (Formerly Paper 6.11)

Two types of data assimilations methods, variational-based and ensemble-based schemes, are implemented in a quasigeostrophic model on a channel (Rotunno and Bao, 1996). The model variables are potential temperature at the bottom and top levels, and potential vorticity at the interior 5 levels. “Rawinsonde observations” provide velocity components and temperatures at all levels. In this study, we would like to compare how the data assimilation schemes perform when given the same configuration. The variational schemes are 3DVAR (Morss et al, 2001) and 4DVAR (newly developed). The ensemble schemes are the local Ensemble Kalman Filter (LEKF, Ott et al, 2004), and a hybrid system using an ensemble of bred vectors in the regular 3DVAR system (Corazza et al, 2002). For this hybrid system, 20 bred vectors were used to augment the background error covariance in the 3DVAR system. For comparison, the 3DVAR system is optimized for the 12-hour data assimilation cycle by fine tuning the background error covariance. This background error covariance is then used in the 4DVAR and the hybrid systems (3DVAR+BVs). The LEKF converts the model variables (potential vorticity and potential temperature) into u, v and T (observed variables) before performing the assimilation. The volume used around each grid point is a 5x5x7 local column.

Among these 4 schemes, the LEKF scheme converged to the lowest rms error level, and the 4DVAR with 12-hour window time reached the second lowest error level. Our results show that the hybrid system (3DVAR+20 BVs) can greatly improve the performance of the regular 3DVAR system and sometimes is even comparable to the 4DVAR result, at a computational cost much lower than the 4DVAR. Our results also indicate that the ensemble members (in both the LEKF and the 3DVAR+BVs schemes) refreshed with a small amount of random perturbations can be helpful for stabilizing the scheme and reducing the error level.