The framework of the 4DVar data assimilation system based on perturbation forecast model：Development and numerical experiment

In order to develop the four-dimensional variational data assimilation (4DVar) system that can be used in regional numerical weather prediction, the framework of the incremental 4DVar is developed in this study on the basis of the recently developed perturbation forecast model GRAPES_PF. At the current stage, this 4DVar framework does not include physical schemes such as short-wave and long-wave radiation, planetary boundary layer, cumulus convection, cloud microphysics, etc. Compared to the operational GRAPES 3DVar system, air temperature is chosen as an extra analysis control variable in the new framework. The linear balance equation, which relates the balanced Exner pressure with stream function, is deduced and solved numerically on the terrain-following vertical coordinate. The adjoint of perturbation Helmholtz equation is solved using the iterative generalized conjugate residual (GCR) approach. To evaluate the validity of this framework, a suite of idealized numerical experiments using pseudo radiosonde data have been carried out to simulate typhoon Mujigae, which occurred over South China Sea in October 2015. The experiments reveal that the 4DVar framework offers results in line with theoretical expectations, i.e., by ingesting more observations in time and through the constraint of perturbation forecast model, the 4DVar leads to more obvious improvements than the 3DVar in both analysis and forecast. This study provides a reasonable framework of four-dimensional variational data assimilation, which can be further implemented with full linear physical package soon.