A 4DEnVar‐Based Ensemble Four‐Dimensional Variational (En4DVar) Hybrid Data Assimilation System for Global NWP: System Description and Primary Tests. (26th August 2022) - Zhu, Shujun; Wang, Bin; Zhang, Lin; Liu, Juanjuan; Liu, Yongzhu; Gong, Jiandong; Xu, Shiming; Wang, Yong; Huang, Wenyu; Liu, Li; He, Yujun; Wu, Xiangjun; et al.
Abstract: This study developed an ensemble four‐dimensional variational (En4DVar) hybrid data assimilation system. Different from most of the available En4DVar systems that adopted ensemble Kalman Filter class or ensemble data assimilation 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. Plain Language Summary: Dynamically balanced complete error structure and explicit flow dependence of the background error covariance (BEC) are two key factors which affect the analysis quality of a data assimilation (DA) system. The untruncated and balanced BEC in the four‐dimensional variational (4DVar) DA approach has no explicit flow dependence, while the localized flow‐dependent ensemble BEC usually breaks the balance. The hybrid of the 4DVar approach and an ensemble class DA method can achieve these two important characteristics of BEC. In this study, a hybrid DA system called ensemble 4DVar (En4DVar) system was developed. It has two unique features. First, it uses a four‐dimensional ensemble‐variational (4DEnVar) system to dynamically provide the ensemble covariance, which differs from most of the available En4DVar systems that estimate their dynamic covariances with the ensemble Kalman Filter class approaches or ensemble of 4DVars method. Second, the ensemble covariance is localized in the sample space using a limited number of leading eigenvectors of the correlation function. In the single‐point observation experiments and observing system simulation experiments, the new En4DVar system exhibited obvious flow‐dependent characteristic and higher forecast skill than both the 4DVar and 4DEnVar systems although its analysis error is between those of the latter two. Key Points: An ensemble four‐dimensional variational (En4DVar) data assimilation system with a hybrid background error covariance was developed for global numerical weather prediction The hybrid covariance is realized by linearly combining the climatological covariance of four‐dimensional variational (4DVar) system and the ensemble covariance of four‐dimensional ensemble‐variational (4DEnVar) system The En4DVar‐initialized forecast is improved relative to 4DVar‐ and 4DEnVar‐initialized forecasts