A classical two-time level semi-implicit semi-Lagrange scheme (SISL) is used in CMA-GFS. Lagrange advection velocity and nonlinear terms are calculated by temporal extrapolation, which can cause computational instability and even integration interruption in large gradient areas such as the areas of jet. A SISL/P-C (predictor-corrector) algorithm is developed in CMA-GFS to reduce the impact of temporal extrapolation and construct a quasi-second order precision time discretization scheme by reducing the semi-implicit coefficients from 0.72 to 0.55. Results of idealized and real-data experiments show that this new scheme can effectively improve forecast accuracy, stability and conservation. The integration time step can be increased from 300 s to 450 s at 0.25° horizontal resolution, and the model calculation efficiency can be increased by 20%.

The atmospheric motion is inherently nonlinear. The high-impact weather events that people concern are generally determined by small- and medium-scale systems overlaid on the large-scale circulation. The accumulation of seemingly minor computational errors can significantly impact the model’s predictive capabilities. When solving these equations, the flow field is commonly separated into basic flow and perturbation flow through the introduction of a reference state. This approach solves the problem of “small differences between large numbers” in terms such as the pressure gradient force (PGF) and improves the spatial discretization accuracy of the model. This paper first reviews the development of zero-dimensional (0D), one-dimensional (1D), two-dimensional (2D), three-dimensional (3D), and four-dimensional (4D) reference state deduction methods. Then, it details the implementation of these different dimensional reference state deduction methods within the context of the Global Regional Assimilation and Prediction System Global Forecast System (GRAPES_GFS) model of China Meteorological Administration (CMA). Furthermore, the accuracy of the different dimensional reference states is tested through multiple benchmark tests. The results demonstrate that the high-dimensional reference state provides a closer approximation to the real atmosphere across various altitudes and latitudes, resulting in a more comprehensive and effective improvement in discretization accuracy. Finally, the paper offers suggestions on issues related to reference state deduction.