Discussion
Which terms remain at leading order in the horizontal momentum equation?
Answer: D
Scale analysis shows the pressure gradient and Coriolis terms are each about \( 10^{-3} \) metres per second squared while the acceleration terms are an order of magnitude smaller, so at leading order the two large terms must balance. That balance is geostrophy. Retaining the next order gives the quasi-geostrophic system in which the small imbalance drives the evolution, which is the whole basis of dynamical forecasting. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.
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