A modified atmospheric non-hydrostatic model on low aspect ratio grids: part II

Sun et al. (2012) proposed a modified non-hydrostatic model (MNH), in which the left-hand side of the continuity equation is multiplied by a parameter δ (4≤δ≤16 in the article) to suppress high-frequency acoustic waves. They showed that the MNH allows a longer time step than the original non-hydrostatic model (NH). The MNH is also more accurate and efficient than the horizontal explicit and vertical implicit scheme (HE–VI) when the aspect ratio (Δx/Δz) is small. In addition to multiplying a parameter δ, here we propose to add a smoothing on the right-hand side of the continuity equation in the MNH to damp shortest sound waves. Linear stability analysis and non-linear model simulations show that the MNH with smoothing (henceforth abbreviated as MNHS) can use twice the time interval of the MNH while maintaining the same accuracy. The MNHS is also more accurate and efficient than HE–VI when the aspect ratio is small.