Quasi-geostrophic Theory Questions and Answers

Answer: A

Bomb cyclones over the western Atlantic and Pacific are compact and deepen at rates well beyond the dry Eady prediction, which is exactly what including latent heat release produces. Their preference for the western oceans in winter reflects both the strong baroclinicity there and the abundant moisture supplied by warm ocean currents. Land regions lack the moisture and produce far fewer such events. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: B

No operational model integrates the quasi-geostrophic equations, yet forecasters and researchers routinely interpret model output through the omega equation, the height tendency equation and potential vorticity thinking. The theory supplies the vocabulary in which synoptic development is explained. That a framework can be superseded computationally while remaining indispensable conceptually is a point worth appreciating in its own right.

Answer: C

Because the Coriolis parameter vanishes at the equator, the Rossby number becomes large and the entire expansion on which the system rests loses its justification. The reason therefore explains the assertion exactly. Tropical dynamics is instead organised around the weak temperature gradient balance between diabatic heating and adiabatic cooling, which plays the role geostrophy plays in mid-latitudes.

Answer: D

Both statements follow from the elliptic character of the omega equation, whose operator acts on the unknown with the forcing on the right hand side. The consequence in each case is that the solution at any point depends on the forcing everywhere, so local forcing produces compensating motion or tendency elsewhere. Both therefore require boundary conditions on the whole domain rather than being integrable point by point.

Answer: A

The first two statements are correct. The vertical velocity does not appear in the definition of quasi-geostrophic potential vorticity at all: it enters the vorticity and thermodynamic equations separately and cancels when they are combined. That cancellation is precisely what makes the potential vorticity a conserved quantity following the geostrophic flow.

Answer: B

Charney and Stern gives a necessary rather than a sufficient condition: the potential vorticity gradient must change sign somewhere, but a flow satisfying that may still be stable. The other three descriptions are accurate. Distinguishing necessary from sufficient conditions is worth particular care, since examination questions frequently turn on exactly that word.

Answer: C

The vertical velocity is diagnosed afresh at every instant from the omega equation and is not a conserved quantity in any sense. Total energy and potential enstrophy are conserved as domain integrals, and potential vorticity is conserved following individual parcels. The three genuine conservation laws between them determine much of the qualitative behaviour of the system.