Challenges in Developing Finite-Volume Global Weather and Climate Models with Focus on Numerical Accuracy

High-resolution global non-hydrostatic gridded dynamic models have drawn significant attention in recent years in conjunction with the rising demand for improving weather forecasting and climate predictions. By far it is still challenging to build a high-resolution gridded global model, which is required to meet numerical accuracy, dispersion relation, conservation, and computation requirements. Among these requirements, this review focuses on one significant challenge, the numerical accuracy over the entire non-uniform spherical grids. It discusses all these challenges by comparing the schemes adopted in well-known finite-volume-based operational or research dynamical cores. It helps the readers have an overview of how they meet these challenges in a summary table. The analysis and validation in this review are based on the shallow-water equation system. The conclusions can be applied to more complicated models. These challenges should be critical research topics in the future development of finite-volume global models.