In this study, the adaption of a novel three-point multi-moment constrained finite-volume transport scheme for uniform points with center constraints (MCV3_UPCC) to cubed sphere geometry is implemented and described. For the MCV3_UPCC scheme, the three equidistant solution points are located within a single cell and a polynomial of 4th degree can be built by imposing the multi-moment center constraints. The resultant scheme has third-order accuracy and guarantees the exact numerical conservation. The Fourier analysis of MCV3_UPCC scheme demonstrates that the novel MCV3_UPCC has better numerical dissipation and dispersion than the original 3rd order Multi-moment Constrained finite Volume (MCV3) scheme. Then it is applied to quasi-uniform cubed-sphere grid, which is designed to avoid the polar problem on the traditional latitude–longitude grid. To suppress the non-physical numerical oscillations, a bound-preserving (BP) algorithm to constrain the conserved advected tracer to within the initial maxi-mum and minimum values is also implemented. The scheme is validated with several widely used benchmarks involving prescribed non-divergent two-dimensional flow on the sphere and different initial tracer distributions. The resulting conservative transport model with high-order accuracy and positive preserving property is comparable to other high-order schemes and has the potential for the numerical simulation of various traces in the atmosphere.

An application study of three kinds of vertical approximate Riemann solvers have been carried out based on a multi-moment nonhydrostatic atmospheric model, which has the characteristics of high accuracy and numerical conservation. The conservative finite difference scheme is used in the vertical direction and the numerical flux in the cell boundary is realized by solving the Riemann problem, which plays a key role in accurately simulating vertical motion in the nonhydrostatic atmosphere. LLF (Local Lax-Friderich), LMARS (Low Mach Approximate Riemann Solver) and HLLC (Harten-Lax-van Leer Contact) are three kinds of approximate Riemann solvers commonly used in the computational fluid dynamics (CFD), and their computational cost and complexity are gradually increasing. One-dimensional standard numerical test show that the cost of LLF solver is the lowest, yet it has strong dissipation. LMARS is assumed to be suitable for atmospheric flow, and its numerical viscosity is not so large and the cost of computation is modest. The inclusion of the third wave in HLLC can avoid excessive numerical dissipation of the intermediate characteristic field. By adjusting the coefficient of the largest eigenvalue of different eigenwaves in LLF solver, the optimized LLF solver can achieve the same performance as that by the relatively complex LMARS and HLLC approximate Riemann solvers, and remain the lowest computational cost. Two-dimensional nonhydrostatic numerical test indicate that the optimized LLF approximate Riemann solver correctly simulates small-scale nonhydrostatic vertical motion and is competitive with the more complex LMARS and HLLC approximate Riemann solvers without increasing the amount of computation. This result provides a good reference for the study of nonhydrostatic atmospheric numerical models.

The exact discrete hydrostatic balance cannot be kept in general when the vertical momentum equation is discretized in atmospheric numerical models. In order to exactly balance the discrete vertical pressure gradient force and gravity force, a well-balanced multi-moment constrained finite volume method for nonhydrostatic atmospheric flow is developed by introducing a well-balanced numerical formulation, in which a numerical reconstruction of the gravity source term is conducted in terms of a thermodynamic reference state that satisfies the hydrostatic balance. One-dimensional benchmarks show that the well-balanced multi-moment constrained finite volume method can maintain the numerical error of the hydrostatic reference state up to machine round off with a coarse grid spacing and can well simulate the propagation of small perturbations even in case of initial small perturbation. Two-dimensional nonhydrostatic thermal bubble test further confirms its ability of simulating nonhydrostatic atmospheric motion accurately. The above numerical experiments have verified the well-balanced property and applicability of the well-balanced multi-moment constrained finite volume method, which provides a good reference for the development of nonhydrostatic atmospheric models.

The CMA-CUACE-Haze atmospheric chemistry model developed in China is an important tool for aerosol process simulation and assessment, yet there is a lack of atmospheric chemistry variable analysis system. In this paper, an assimilation system for regional chemical weather coupling based on the CMA-MESO three-dimensional variational analysis is developed, which takes uncorrelated PM_2.5 and PM_2.5-10 variables as control variables and utilizes the modeled background error covariance to achieve assimilation analysis of aerosol observations of PM_2.5 and PM₁₀. The validity of the design of the coupled assimilation system is verified by aerosol single-station ideal tests, and assimilation experiment of aerosol PM_2.5 and PM₁₀ observations has been conducted for the heavy pollution process in December 2016. The analysis results indicate that the coupled atmospheric chemistry-weather assimilation system can perform simultaneous miniaturization analysis of aerosol observations and weather variable observations, and the analysis fields between atmospheric chemistry variables and weather variables do not affect each other. The assimilation of aerosol observations reasonably corrects the atmospheric chemical background field, and the analytical fields of PM_2.5 and PM₁₀ variables are closer to the observations. Aerosol assimilation has a significant effect on pollutant forecasts and the effect can last up to 72 h. The regional coupled chemistry-weather assimilation system developed in this study can provide more accurate chemical initial fields for the CMA-CUACE-Haze model.

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.