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5 Sigma-Coordinate Model     continued...

Finally, processes such as tides and storm surges are quite important aspects of shallow water circulation and to simulate these effects, the rigid lid approximation has to be revoked and free surface dynamics included. Since this results in severe time step limitations due to constraints introduced by fast external surface gravity wave motions, generated at the air--sea interface, it becomes necessary to invoke mode splitting as a solution strategy. Mode splitting consists of splitting the solution into two parts, the barotropic (external mode) part governed by the two-dimensional vertically integrated form of the governing equations and the baroclinic (internal mode) part governed by the full equations, as demonstrated in section 5.5. The baroclinic mode is solved less frequently relative to the barotropic mode, consistent with the slower propagation speed of the internal mode disturbances vis-a-vis the external mode. Considerable savings accrue as a result. However care must be taken to ensure that conservation properties are not violated by mode-splitting.