Comparing numerical accuracy and stability for different horizontal discretizations in MPAS-Ocean

This manuscript investigates the effectiveness of two possible horizontal discretizations for the global ocean model MPAS-Ocean, both applied to Spherical Centroidal Voronoi Tessellations (SCVTs). The first discretization is TRiSK, a C-grid, finite-volume method, that possesses many desirable mimetic properties, but has a low order accuracy. The second discretization was introduced for the first time by Peixoto (2016), and consists of modifications to the TRiSK scheme designed to achieve at least first-order accuracy in the L∞ norm, with the loss of some of the mimetic properties. Tests on shallow-water and primitive-equation models show that the scheme due to Peixoto is indeed more accurate, but presents stability issues with respect to TRiSK. TRiSK is indeed found to be often more stable in time and more robust with respect to errors in the geometric properties of the grid. •We compare two discretizations for MPAS-Ocean: TRiSK and the Peixoto scheme.•We test the two methods on a shallow water model and a fully 3D model.•We find that the Peixoto scheme is more accurate than TRiSK but is more unstable.•In the Peixoto scheme energy enters the system and slowly builds up over time.•TRiSK keeps the system energy in balance resulting in a long-timescale stability.