Discussion
Which relation holds between hydrostatic balance and the thermal wind?
Answer: D
Differentiating the geostrophic relation with respect to pressure and substituting the hydrostatic relation eliminates the geopotential and yields the thermal wind. Both parent relations are therefore required, and the thermal wind fails wherever either fails. The derivation is short and worth performing once, since it makes clear why virtual temperature appears in the result. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.
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