Introduction to Ocean Numerical Modeling 2 Discretization Global

Introduction to Ocean Numerical Modeling #2 - Discretization Global model SSH Gildas Cambon, IRD/LOPS, France regional model SST gildas. cambon@ird. fr

Ocean modeling principle If we know: • The ocean state at time t : u, v, w, T, S, … • Boundary conditions : surface, bottom, lateral sides We can compute the ocean state at time t+dt by resolving numerically the primitive equations : numerical modeling 2

Ocean modeling principle The ocean is divided into boxes : Discretization

Discretization Structured grids The grid cells have the same number of sides. ROMS Unstructured grids The domain is tiled using more general geometrical shapes (triangles, …) pieced together to optimally fit details of the geometry. üGood for tidal modeling, engineering applications. üProblems: geostrophic balance accuracy, wave scattering by non-uniform grids, conservation and positivity properties, … 4

Horizontal discretization Linear shallow water equation: A staggered difference is 4 times more accurate than non-staggered and improves the dispersion relation because of reduced use of averaging operators n 5

Horizontal discretization §B grid is prefered at coarse resolution, when Coriolis is important: §Superior for poorly resolved inertia-gravity waves. §Good for Rossby waves: collocation of velocity points. §Bad for gravity waves: computational checkboard mode. §C grid is prefered at fine resolution, when Coriolis is less important: §Superior for gravity waves. §Good for well resolved inertia-gravity waves. §Bad for poorly resolved waves: Rossby waves (computational checkboard mode) and inertia-gravity waves due to averaging the Coriolis force. ROMS §Combinations can also be used (A + C) 6

Horizontal discretization ROMS: Arakawa C-grid 7

Horizontal curvilinear grid • Discretized in coastline-and terrain-following curvilinear coordinate • Arakawa C-grid m, n: scale factors relating the differential distances to the physical arc lengths 8

Horizontal curvilinear grid Z coordinate : NEMO sigma ( & stretched) coordinate : ROMS 9

Land Sea Mask

Vertical discretization