Accuracy assessment of the super compact and combined compact schemes for spatial differencing of a two-layer oceanic model: Presentation of linear inertia-gravity and Rossby waves

► Two general discrete dispersion relations on different numerical grids are derived. ► These relations can be used for evaluation of the performance of any numerical scheme. ► The global errors show that the Z grid generates the least error. ► For the Rossby waves, the SCFDM shows improvement over the CCFDM except on C grid.