Discussion
Which property makes potential vorticity a complete description of balanced flow?
Answer: C
Given a balance condition and suitable boundary values, the distribution of potential vorticity determines the streamfunction, the wind and the temperature everywhere. This invertibility principle is why a single scalar field can carry the whole of balanced dynamics. It requires differentiating observed fields, it is negative in the southern hemisphere, and its vertical variation is part of what is being described rather than a constraint. Checking the units of each quantity catches a wrong formula before the arithmetic begins.
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