Quasi-geostrophic Theory Questions and Answers

Answer: C

The expansion requires a small Rossby number, which fails near the equator where the Coriolis parameter vanishes, so the theory has essentially nothing to say about tropical dynamics. The mid-latitude free troposphere is exactly where it works best, the stratosphere is well described by it, and the storm tracks are its principal domain of application despite their strong shear. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: D

With horizontal temperature gradients unable to persist in the tropics, the thermodynamic equation reduces to a balance between diabatic heating and adiabatic cooling by ascent. The vertical motion is therefore set directly by the heating rate. This weak temperature gradient balance plays the role in the tropics that geostrophy plays in mid-latitudes and organises tropical reasoning in the same way. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: A

Following the barotropic success on ENIAC, two and three level quasi-geostrophic models were developed through the 1950s and gave the first useful forecasts of cyclone development. They were superseded by primitive equation models in the 1960s once computers allowed. The barotropic forecast came first and was not quasi-geostrophic, and the other options belong to much later eras. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: B

By filtering gravity and sound waves entirely, the quasi-geostrophic system removed the severe time step restriction that had wrecked Richardson's attempt and made forecasting feasible on the computers of the day. That was the decisive practical advantage. They are useless in the tropics, require the same observations, and conservation properties depend on the numerical scheme rather than on the equation set. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: C

Semi-implicit schemes treat the fast waves implicitly and remove them from the time step restriction, so the primitive equations became affordable while retaining their greater accuracy. Semi-Lagrangian advection extended the step further. Quasi-geostrophic theory remains valid in mid-latitudes but is less accurate than the full equations, and satellite data can be assimilated into any system. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: D

Although no operational forecast model uses it, quasi-geostrophic reasoning remains the standard language for explaining why a system is developing, through the omega and height tendency equations and potential vorticity thinking. Forecasters interpret model output in these terms daily. Ocean models do exploit the small Rossby number in idealised studies but operational ocean models use primitive equations too. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: A

The omega equation, particularly in its Q vector form, tells a forecaster where ascent is being forced and therefore where cloud and precipitation should develop. It is the single most used product of the theory. The height tendency equation is conceptually useful but less directly applied, the two-level model is a teaching device, and Eliassen-Palm fluxes belong to research on the general circulation. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: B

The Q vector is simply a rearrangement of the quasi-geostrophic omega equation, so it inherits every one of its assumptions including geostrophic advection and constant static stability. It removes the cancellation between the two classical terms without extending the range of validity. It is computed routinely from model fields, gives a quantitative forcing, and applies in both hemispheres with the appropriate sign. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: C

The standard formulation takes the static stability parameter as a function of pressure only, using a horizontally averaged reference profile. Allowing it to vary horizontally would make the omega equation nonlinear. The assumption is poor near fronts and in convective regions, where the effective stability of saturated ascent is much lower, which is one reason the diagnosed ascent underestimates the observed vertical motion there. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: D

A uniform stability cannot represent the very low effective stability of saturated ascent in the warm conveyor belt, so the diagnosed vertical motion is spread over too wide an area and is too weak at its maximum. Adding a diabatic term and using a moist stability substantially improves the diagnosis. The position of the ascent relative to the front is correctly given.