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\begin{document}

\title{A Four-Dimensional Ensemble-Variational (4DEnVar) Data Assimilation
System for Global NWPs: System Description and Primary Tests}



\author[1,1]{Shujun Zhu}%
\author[2,2]{Bin Wang}%
\author[3,3]{Lin Zhang}%
\author[2,2]{J. J. Liu}%
\author[4,4]{Yongzhu Liu}%
\author[5,5]{Jiandong Gong}%
\author[1,1]{Shiming Xu}%
\author[1,1]{Yong Wang}%
\author[6,6]{Wenyu Huang}%
\author[7,7]{Li Liu}%
\author[8,8]{Yujun He}%
\author[3,3]{Xiangjun Wu}%
\affil[1]{Department of Earth System Science, Tsinghua University}%
\affil[2]{LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences}%
\affil[3]{Research and Development Division, Numerical Weather Prediction Center of China Meteorological Administration}%
\affil[4]{Numerical Weather Prediction Center of China Meteorological Administration}%
\affil[5]{China Meteorological Administration}%
\affil[6]{Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing, China}%
\affil[7]{Tsinghua University}%
\affil[8]{Chinese Academy of Sciences}%


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  \date{May 28, 2024}


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\begin{abstract}
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.%
\end{abstract}%



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