A new vertical coordinate system for a 3D unstructured-grid model

•A new type of localized vertical grid (LSC2) is implemented in a 3D model.•It significantly reduces pressure gradient error, diapycnic mixing.•It is free of staircases.•Results show improved representation of stratification in lakes and oceans.

We present a new vertical coordinate system for cross-scale applications. Dubbed LSC2 (Localized Sigma Coordinates with Shaved Cell), the new system allows each node of the grid to have its own vertical grid, while still maintaining reasonable smoothness across horizontal and vertical dimensions. Furthermore, the staircase created by the mismatch of vertical levels at adjacent nodes is eliminated with a simple shaved-cell like approach using the concept of degenerate prisms. The new system is demonstrated to have the benefits of both terrain-following and Z-coordinate systems, while minimizing their adverse effects. We implement LSC2 in a 3D unstructured-grid model (SELFE) and demonstrate its superior performance with test cases on lake and ocean stratification.