Filling oceans on a spherical multiple-cell grid

Abstract

Shallow water equations (SWEs) are discretised on a regional spherical multiple-cell (SMC) grid. The SMC grid uses unstructured techniques with rectangular cells and supports multi-resolutions like mesh refinement. The numerical schemes on the 2-D SMC grid are combinations of the conventional finite-difference ones and flux-form finite-volume formulations in 1-D loops. Semi-implicit schemes are used for both Coriolis terms and potential energy gradients. The water height equation is solved with a C-grid mass-conserving advection scheme and a diffusion term to suppress numerical instability. Mixed A- and D-grid schemes are applied on the momentum equation, plus a weighted average to remove short waves. Boundary conditions are incorporated on all cell faces so that any cell could be wet or dry depending on whether its water height is positive. Approximations across refinement interfaces are explained. A filling or flooding experiment on a four-level (3-6-12-25 km) Mediterranean Sea grid is used for demonstration. The test is done by emptying the whole Mediterranean Sea at start and then filling the basins with flood water from selected river mouths and strait channels, until the whole Mediterranean Sea is filled up. This experiment illustrates that the SWEs model on the multi-resolution SMC grid can simulate the filling process as expected and restore a flat sea surface at the end. Another test is carried out to simulate possible tsunami waves when the flat sea surface is disturbed by volcanic eruptions or earthquake movements. Results indicate that vertical shift of sea surface at one site in the Ionian Sea may generate tsunami waves and orientation of the initial disturbance has a profound influence on the subsequent tsunami waves, which could spread out to the whole Mediterranean Sea in a few hours. Further improvements are required to simulate real tsunamis and coastal surges.