How it works
An ocean model computes on an array of cells indexed i, j and k, and time. In index space that
array is a box of identical cubes. In the ocean each cell is somewhere else entirely: the
horizontal grid is curvilinear, a bent and stretched net of quadrilaterals on the sphere, and the
vertical grid follows the terrain, so every column has the same N layers whether it is 20 m or
5000 m deep.
Horizontal carries each column from its place in the array to its place on the globe; Vertical
carries each layer from its place in the array to its depth. Halfway, or one without the other,
is where the model's view and the map's view can be compared. The data come along unchanged: a
cell's value belongs to its index, wherever the cell is drawn.
The layers are ROMS's s-coordinate. A stretching function C(s) of the fraction s from -1 at the
floor to 0 at the surface sets where the layers go (theta_s crowds them to the surface, theta_b
to the floor), and the transform blends that with plain sigma, an even split of the column,
down to the critical depth hc. Steep bathymetry is the classic trouble: neighbouring columns'
layers slope steeply, measured by rx0 (the slope of the floor) and rx1 (Haney's number, the
slope of the layers), so models smooth the sea floor first.
The grids and temperature here are synthetic. The two grids are conformal (square cells
everywhere): a Mercator ring round Antarctica that wraps in i, and a log-polar fan off New South
Wales, finest at the coast. The temperature has a seasonal mixed layer, a thermocline and
eddies that drift along i.
- Formulas from the ROMS wiki, Vertical S-coordinate:
Song and Haidvogel (1994), Shchepetkin and McWilliams (2005, 2009).
- Smoothing: the minimal positive rx0 method of Sikiric, Janekovic and Kuzmic (2009).
- In the spirit of an Eonfusion visualization
of the GEMS Southern Ocean model (Meijers and Bindoff).
- Bathymetry: GEBCO Compilation Group (2026) GEBCO 2026 Grid, from
Source Cooperative.