Discussion
Which balance must hold for the thermal wind relation to be valid?
Answer: D
The relation is derived by combining geostrophic and hydrostatic balance, so it fails wherever either does, which means near the equator, in strongly curved flow and in convective systems. A gradient wind version exists but is much more complicated and rarely used. Cyclostrophic and Ekman balances are quite different regimes in which no simple thermal relation applies at all.
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