Discussion
Arrange the following steps in the derivation of the thermal wind relation in order.
1. Substitute the hydrostatic relation
2. Write geostrophic balance in pressure coordinates
3. Differentiate with respect to pressure
4. Integrate across the layer
Select the correct sequence.
Answer: D
The derivation begins with geostrophic balance in pressure coordinates, differentiates it with respect to pressure, substitutes the hydrostatic relation to introduce temperature, and finally integrates across the layer to obtain the accumulated wind change, giving 2, 3, 1, 4. Following the sequence once makes clear why the result contains a logarithm of the pressure ratio and why virtual temperature appears rather than actual temperature. The shared properties explain why these belong to one family, and the differences explain why more than one exists.
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