A four-dimensional variational data assimilation approach with analysis at the end of assimilation window. part I: Methodology and preliminary tests

In this paper, we propose a new approach to four-dimensional variational data assimilation (4DVar) with analysis of the initial condition (IC) at the end of assimilation window. The new approach is referred to as "backward 4DVar (B-4DVar)." The minimization of its cost function is fulfilled through an ensemble of historical prediction samples. B-4DVar is computationally efficient because it does not use tangent linear or adjoint models. To prepare it for numerical weather prediction, a B-4DVar assimilation system is developed based on an operational regional prediction model, the Advanced Regional Eta Model (AREM). Two single observation experiments (SOEs) and an observing system simulation experiment (OSSE) are conducted to evaluate the system. The SOEs reveal a characteristic of flow dependence in B-4DVar, which is consistent with statistical estimation of the background error covariance matrix (simply B-matrix) using a group of IC-reliant historical prediction samples. The OSSE suggests that the B-4DVar approach improves the analytic quality of IC by effectively incorporating conventional observations, thereby outperforming the 3DVar. The time-saving feature, flow dependence in B-matrix, and good performance in assimilating conventional observations indicate the potential and feasibility of B-4DVar in operational use.