Quasi-geostrophic Theory Questions and Answers

Answer: A

Rossby waves owe their existence entirely to the meridional gradient of planetary vorticity, so they cannot exist where the Coriolis parameter is constant. Baroclinic instability survives on an f-plane, as the Eady model demonstrates, because the required potential vorticity gradient is supplied by the boundaries. Geostrophic balance and ageostrophic vertical motion are both unaffected. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: B

With no vertical structure the quasi-geostrophic system reduces to the barotropic vorticity equation, whose only wave solution is the Rossby wave propagating westward relative to the mean flow. Gravity and acoustic waves have been filtered out by construction. Kelvin waves require either a boundary or the equatorial waveguide, neither of which the mid-latitude barotropic system provides. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: C

The intrinsic westward phase speed is proportional to beta times the square of the wavelength, so long waves may be stationary or retrogressive against a westerly flow while short waves are carried rapidly eastward. This dispersion is what separates the slowly evolving long wave pattern from the fast moving short waves within it, and it underlies the whole distinction between planetary and synoptic scales on a chart. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: D

Because the dispersion relation is nonlinear in wavenumber, the group velocity can be eastward even where the phase velocity is westward, which produces the downstream development observed in Rossby wave trains. A disturbance in one ocean basin can thereby influence weather downstream several days later. This distinction between phase and energy propagation is one of the most practically significant results in the subject. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: A

Rossby wave energy propagating eastward faster than the individual troughs and ridges seeds new development downstream, so a disturbance over the Pacific can trigger cyclogenesis over North America days later. This is a genuine consequence of the group velocity exceeding the phase velocity. Occlusion and steering are quite separate processes belonging to the life cycle of a single system. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Answer: B

Errors in the analysis over a data-sparse region travel downstream at the group velocity, which is faster than the systems themselves, so they contaminate the forecast far from their origin. This is one reason global observation coverage matters for regional forecasting. It constrains rather than extends predictability, and confinement of errors is precisely what does not happen. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: C

The unforced quasi-geostrophic system conserves the domain integrals of energy and of potential enstrophy, which is the mean square potential vorticity. These two constraints together determine the direction of the turbulent energy cascade in two-dimensional and quasi-geostrophic flow. Point values of vorticity and temperature change as parcels move, and omega is diagnosed afresh at each instant. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: D

The simultaneous conservation of energy and enstrophy forces an inverse energy cascade towards larger scales and a forward enstrophy cascade towards smaller ones. This is why atmospheric eddies tend to merge into larger structures rather than fragmenting, and why blocking highs can form. Three dimensional turbulence, lacking the enstrophy constraint, cascades energy downscale instead. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: A

Energy accumulating at large scales can organise into persistent large amplitude structures, and blocking highs that divert the storm track for a week or more are the most striking example. Their persistence is one of the harder forecasting problems. Molecular dissipation belongs to the far end of the forward enstrophy cascade, and convection and frontogenesis are governed by different mechanisms. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Answer: B

Blocks are persistent once established, which helps the forecast, but the transitions into and out of a blocked state remain among the least predictable events in mid-latitude meteorology. Models represent them but often with systematic errors in frequency and duration. They are essentially stationary rather than fast moving and occur in both hemispheres, being particularly common over the North Atlantic and North Pacific. The shared properties explain why these belong to one family, and the differences explain why more than one exists.