The Duo-Grid and Cubed-Sphere Grid Imprinting

Motivation

Addressing the challenge of running localized high-resolution simulations within a global model, the duo-grid imprints a finer mesh over a region of interest, reducing computational cost by an order of magnitude compared to traditional regridding approaches.

The problem: grid imprinting

The gnomonic cubed-sphere grid has excellent accuracy and uniformity, but the coordinates have a kink at the cube edges. In the halo region this kink leaves a visible imprint of the cube in the solution and requires special edge handling throughout the solver.

The Duo-Grid

To reduce grid imprinting, we implemented the novel Duo-Grid within FV3. The Duo-Grid remaps a cube face’s data from the neighboring face, moving it from the kinked locations to natural locations along great circle lines using 1D piecewise linear interpolation. A separate 2D interpolation algorithm fills the correct data at the eight corners of the cubed-sphere, which FV3’s 2D advection scheme requires.

Validation

The Duo-Grid was evaluated across a comprehensive suite of idealized test cases spanning both two-dimensional shallow-water dynamics and three-dimensional hydrostatic and non-hydrostatic flows. These tests were designed to assess the impact of the Duo-Grid on grid imprinting, numerical errors, and the overall behavior of the FV3 dynamical core.

The steady-state geostrophic balance test provides a direct assessment of cubed-sphere grid imprinting. When the flow is oriented perpendicular to the cubed-sphere edges, the conventional kinked grid produces errors aligned with the cube geometry. With the Duo-Grid, these grid-aligned errors are substantially reduced.

The improvement extends to fully three-dimensional dynamics. In the baroclinic wave test, the Duo-Grid suppresses the development of cubed-sphere imprinting and errors in the southern hemisphere while maintaining the evolution of the solution over time.

The Duo-Grid was further evaluated using a broad suite of standard idealized tests, including shallow-water steady-state geostrophic flow, the splash test, Rossby–Haurwitz wave, colliding modons, cosine-bell advection, and the three-dimensional non-hydrostatic baroclinic wave.

Across these tests, the Duo-Grid consistently reduces grid imprinting and numerical errors while preserving the accuracy and numerical characteristics of the original FV3 formulation.

Key results

• Grid imprinting of the cubed sphere is greatly reduced in idealized tests and practically eliminated.
• Duo-Grid decreases the growth rate of error norms in all cases compared to the kinked grid, up to one order of magnitude.
• Order of accuracy of FV3’s horizontal discretization is conserved.
• Dispersion and dissipation properties are identical to those of the original FV3 algorithm.
• Edge handling code is eliminated -> significant performance gain in current/future GPU development
• FV3’s robustness and accuracy have increased.

These results indicate a clear improvement in FV3’s robustness.

Reference

Mouallem, J., Harris, L., and Chen, X.: Implementation of the Novel Duo-Grid in GFDL’s FV3 Dynamical Core, Journal of Advances in Modeling Earth Systems, 15(12), 2023. https://doi.org/10.1029/2023MS003712