Weather and Climate Modeling

For which of the following flows is the shallow-water model a good approximation?

Tsunami propagation in the open ocean?

Airflow over a mountain ridge?

Deep Ocean currents?

River flooding during heavy rainfall?

Tidal bores in estuaries?

Breaking ocean waves on the shore?

Key: 1) Horizontal Scale much larger than vertical. 2) Same horizontal windspeed in the whole depth

So:

Tsunami propagation in the open ocean

Airflow over a mountain ridge

River flooding during heavy rainfall

Tidal bores in estuaries

Which of them best represents a hydraulic jump?

Zurich Lake, Canoe River, Waterfall

Canoe River

Why are staggered grids often used in numerical implementations of the shallow-water equations?

They improve conservation and numerical stability.

Which are the vertical coordinates in z-coordinates, in p-coordinates and in isentropic coordinates?

z-coordinates: (x,y,z), so vertical coordinate is height z

p-coordinates: (x,y,p), so vertical coordinate is pressure p

isentropic coordinates (x,y,θ), so vertical coordinate is potential temperature θ