Discussion
Which problem does the Q vector formulation solve?
Answer: A
Differential vorticity advection and thermal advection frequently have opposite signs and similar magnitudes, so their sum is a small residual that is hard to estimate reliably from charts. Combining them into a single vector removes the cancellation. The Q vector form makes the same quasi-geostrophic assumptions as the classical form, so it does not extend the range of validity, and computational cost was never the issue. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.
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