Discussion
Which accuracy does hydrostatic balance hold to for synoptic scale motion?
Answer: D
Vertical accelerations in large scale flow are around \( 10^{-7} \) metres per second squared against a gravitational acceleration near 10, so the two vertical terms balance to about one part in \( 10^{8} \). That is why pressure can be used as a vertical coordinate with confidence. The horizontal geostrophic balance, by contrast, is good only to about ten per cent. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.
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