Research on reference state deduction methods of different dimensions

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 GRAPES_GFS (Global Regional Assimilation and PrEdiction System Global Forecast System) model of CMA (China Meteorological Administration). 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.