The Yin–Yang grid, while offering advantages such as quasi-uniformity and pole-singularity avoidance, inherently lacks global conservation owing to interpolation at grid boundaries. To address this problem, we proposed a compact flux correcting method to ensure conservation based on a third-order multimoment constrained finite volume scheme. Using the nine point values within each computational cell, a bivariate quadratic polynomial was constructed for high-fidelity boundary interpolation and flux reconstruction. Identical flux across the boundary of overlapped grids was enforced in the Yin and Yang components with the help of the polynomial. A third-order conservative advection scheme was therefore achieved on the Yin–Yang grid, effectively balancing numerical accuracy and computational efficiency. Several standard numerical tests were conducted to confirm the performance of the interpolation algorithm and the conservation calculation scheme. Results revealed that the high accuracy and the stability of the strict conservation scheme are helpful in passive transport situations on Yin–Yang grids.

The definition of a reference state close to the realistic atmosphere in an atmospheric model is essential for deriving prognostic deviations and improving numerical accuracy. In this study, a new dynamical framework allowing easy switching between a one-dimensional (1D) and a three-dimensional (3D) time-independent reference state is developed for the semi-implicit semi-Lagrangian solver in a global non-hydrostatic atmospheric model on Yin–Yang grids. The 3D reference state is introduced with consideration of additional horizontal gradient terms of reference-state terms, which is different from the 1D reference state. It is characterized by reduced magnitude of deviations, more accurate pressure gradient force, as well as alleviated numerical noise. Four idealized benchmark tests and multiple full-physics real-case forecasts are carried out to assess the impact of the 3D and 1D reference states. The 3D reference state shows significant advantages in the simulation of atmospheric transport and wave propagation in the idealized experiments. In the real-case forecasts, batched forecasts from June to August 2021 show a comprehensive improvement in medium-range prediction by using the 3D reference state. The new scheme achieves an enhanced prediction skill for large-scale circulation and extends the effective forecast period by 0.8 days in the Northern Hemisphere.