Discussion
Assertion (A): Hydrostatic balance holds almost exactly for large-scale atmospheric motion.
Reason (R): Vertical accelerations are many orders of magnitude smaller than the acceleration due to gravity.
Select the correct answer from the options below.
Answer: D
Because the residual vertical acceleration is around \( 10^{-7} \) metres per second squared against a gravitational acceleration near 10, the two vertical terms must balance to about one part in a hundred million. The reason is precisely why the assertion holds. The balance fails only where the horizontal scale of the motion becomes comparable with its depth, as in deep convection, which is exactly the case that non-hydrostatic models were developed to handle.
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