Discussion
The geostrophic wind speed is given by which expression, with \( \Phi \) the geopotential?
Answer: D
On a constant pressure surface the geostrophic wind has magnitude \( |\nabla\Phi|/f \), with the wind directed along the height contours. Density has disappeared because pressure is being used as the vertical coordinate, which is the chief practical advantage of that choice. In height coordinates the equivalent expression is the pressure gradient divided by the product of density and \( f \), so the two forms agree but the pressure coordinate version is simpler and is what upper air charts are built around.
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