A four-dimensional ensemble-variational (4DEnVar) data assimilation (DA) system was developed for global numerical weather predictions (NWPs). Instead of using the adjoint technique, this system utilizes a dimension-reduced projection (DRP) technique to minimize the cost function of the standard four-dimensional variational (4DVar) DA. It dynamically predicts ensemble background error covariance (BEC) initialized from its previous inflated analyses and realizes the flow-dependence of BEC in the variational configuration during the assimilation cycle. These inflated analyses, linear combinations of the ensemble analyses increment and balanced random perturbations, aim to prevent the predicted BEC from underestimation as well as to implicitly achieve the hybrid of the flow-dependent and static BEC matrices. A limited number of leading eigenvectors of the localization correlation function are selected to filter out the spurious correlations in the BEC matrix (B-matrix). In order to evaluate the new system, single-point observation experiments (SOEs) and observing system simulation experiments (OSSEs) were conducted with sounding and cloud-derived wind data. The flow-dependent characteristic was verified in the SOEs that utilized the localized ensemble covariance and compared with that of 4DVar. In the OSSEs, 4DEnVar reduced the analysis errors compared with 4DVar. The deterministic forecast initialized from the 4DEnVar ensemble mean analysis has better (worse) performance in the medium-range (long-range) forecasts in the Northern Extratropics and opposite performance in the Southern Extratropics, and exhibits slightly worse effects in the Tropics. Moreover, the ensemble mean forecast initialized from the 4DEnVar ensemble analyses has higher forecast skills than 4DVar.

This study developed an ensemble four-dimensional variational (En4DVar) hybrid data assimilation (DA) system. Different from most of the available En4DVar systems that adopted ensemble Kalman Filter class or ensemble DA approaches to produce ensemble covariances for their hybrid background error covariances (BECs), it used a four-dimensional ensemble-variational (4DEnVar) system to obtain the ensemble covariance. The localization scheme for 4DEnVar applied orthogonal functions to decompose the correlation matrix so that it was implemented easily and rapidly. In terms of analysis quality and forecast skill, the En4DVar system was evaluated in the single-point observation experiments and observing system simulation experiments (OSSEs) with sounding and cloud-derived wind observations, using its standalone four-dimensional variational (4DVar) and 4DEnVar components as references. The single-point observation experiments visually verified the explicit flow-dependent characteristic of the BEC due to the introduction of the ensemble covariance from the 4DEnVar system. The OSSE-based sensitivity experiments revealed different contributions of the weight for the ensemble covariance in the En4DVar system to the forecasts in the Northern and Southern Extratropics and Tropics. A much higher weight for the ensemble covariance in a properly inflated hybrid covariance helped En4DVar produce the most reasonable analysis. The forecast initialized by En4DVar is overall better than by 4DVar and 4DEnVar, although the quality of En4DVar analysis is between those of 4DVar and 4DEnVar ensemble mean analyses. It indicates that the flow-dependent ensemble covariance provided by 4DEnVar dominantly contributes to the improvements in the En4DVar-initialized forecast, with certain but necessary constraint from the balanced climatological covariance.