Rethinking A-Grid for next-generation dynamical cores: High-order numerical analysis challenges conventional wisdom

The choice of grid staggering has been a fundamental design decision in atmospheric dynamical core development for decades. Conventional wisdom, largely derived from low-order Von Neumann analysis, holds that the unstaggered A-Grid exhibits poor dispersion properties near the grid scale, making it unsuitable for geophysical fluid dynamics. This perception has steered the community toward staggered grid formulations (B-, C-, or D-Grid) despite the algorithmic complexity they introduce.

We present a numerical approach to Von Neumann analysis that enables rigorous evaluation of high-order schemes with complex time-stepping methods, including implicit and semi-implicit formulations such as the forward-backward scheme. By numerically solving the Fourier-transformed equations across the two-dimensional space of Courant numbers and numerical phase, this method circumvents the algebraic intractability that has limited traditional analysis to simplified low-order cases.

Our analysis reveals a critical finding: the dispersion and dissipation differences attributable to grid staggering choices diminish substantially with high-order spatial discretization. When combined with the Low Mach number Approximate Riemann Solver (LMARS), which provides implicit scale-selective diffusion matched to the dispersion characteristics, the A-Grid formulation effectively controls numerical noise while maintaining accuracy for well-resolved modes. Idealized tests with discontinuous wave packets validate these theoretical predictions and demonstrate that high-order LMARS produces significantly less numerical noise than inviscid schemes on both staggered and unstaggered grids.

These findings carry significant implications for next-generation dynamical core design. The A-Grid formulation offers compelling advantages: algorithmic simplicity facilitating GPU implementation, straightforward conservation properties, collocated variables simplifying physics-dynamics coupling, and natural compatibility with data-driven approaches in hybrid modeling. Continued adherence to conventional wisdom rooted in low-order analysis risks misguiding the development of dynamical cores optimized for modern computing architectures and emerging AI-integrated Earth system models.