Discussion
Which parameter determines whether the balance holds?
Answer: B
Scale analysis shows that the ratio of the vertical acceleration to gravity is of order the square of the aspect ratio, so a flat disturbance is hydrostatic and a tall narrow one is not. With a ratio of one in a hundred for synoptic motion the balance is extremely good. The Rossby number governs the horizontal balance instead and has no bearing on the vertical one. Checking the units of each quantity catches a wrong formula before the arithmetic begins.
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