Numerical Solution Technique
Horizontal and Vertical Discretization
The ROMS governing equations are discretized over variable topography using a stretched, terrain-following, vertical coordinate. As a result, each grid cell may have different level thickness (Hz) and volume. The model state variables are vertically staggered so that horizontal momentum (u, v), density, and tracers (active and passive) are located at the center of the grid cell. The vertical velocity (ω, w) and vertical mixing variables (Akt, Akv, etc) are located at the bottom and top faces of cell. See diagram below.
The total thickness of the water column is ζ(i,j)+h(i,j) . The bathymetry (h) is usually time invariant whereas the free-surface (ζ) evolves in time. However, in sediment applications h changes with time when SED_MORPH is activated. At input and output, the bathymetry is always a positive quantity. However, the depths z_r(i,j,k) and z_w(i,j,k) of every grid cell are negative quantities in ROMS.
