Inter-comparison, hybridization and coupling of ensemble-based and variational data assimilation systems

Fuqing Zhang
Penn State University


Inter-comparisons between variational, ensemble-based and hybrid data assimilations are presented on a regional weather research and forecasting model (WRF) over the continental United States during an active summer month of June 2003. Five different data assimilation (DA) methods are considered, including three/four- dimensional variational methods (3D/4DVar) with NMC-based background error covariance, ensemble Kalman filter (EnKF) with flow-dependent forecast error uncertainties and the hybrid approach that couples either 3DVar or 4DVar with EnKF (E3DVAR or E4DVAR). In E3DVAR and E4DVAR, the ensemble-based background error covariance is incorporated into the 3D/4D-Var minimization via the alpha-control transform, while the ensemble perturbations are updated in EnKF but their mean is replaced by the 3DVAR or 4DVar analysis. Among those DA experiments, E4DVAR is more flexible, whose flow-dependent benefits can be addressed both on the explicit background error covariance estimated by EnKF ensembles and its implicit counterpart modeled by 4DVar trajectory, moreover the capability of 4D-Var on dealing with asynchronous and high-volume observations also gives the coupled E4DVAR method more flexibility, especially for those mesoscale weather systems. For the experiments, various conventional observations are assimilated over the North America region during June 2003, and comparisons of DA performances are demonstrated by the forecast error verifications against radiosonde measurements. B ased on the month-long statistical results, E4DVAR significantly outperformed all the other DA methods for a 48-h lead time, whose root mean square errors kept in a lower level than the others during the whole month. The monthly mean results also show that E4DAVR had the lowest forecast errors for both dynamical and thermal variables, followed by E3DVAR, EnKF, 4DVar and 3DVar in sequence.

The second half of the talk we will be presenting a pseudo-ensemble hybrid data assimilation (PEDA) system that has been recently developed and implemented in the Weather Research and Forecast model for tropical cyclone initialization. The PEDA estimates the background error covariance matrix using a pseudo-ensemble with samples selected from a library of idealized tropical cyclone vortices, which is introduced into the hybrid 3DVar minimization algorithm. The library is comprised of a large quantity of previously spun-up tropical cyclone vortices that vary in size, intensity, and structure, which are binned according to maximum wind speed. The PEDA method benefits from the multivariate, anisotropic covariance typically used in ensemble approaches to data assimilation, while maintaining the same computational cost as the standard 3DVar. Preliminary experiments from 30 cases of the 2008-2010 Atlantic storms with airborne Doppler observations give very promising performance.