Divergence and Vertical Motion Questions and Answers

Answer: C

Divergence is a small difference between large wind components, so a one per cent error in the wind can produce an error of one hundred per cent in the divergence, and those errors accumulate as the profile is integrated. The usual remedy is to adjust the profile so that omega vanishes at the top of the atmosphere. Vertical resolution is a secondary concern and there is no systematic sign error associated with curvature. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: D

O'Brien's correction distributes the error through the profile so that the physically required upper boundary condition of zero omega is satisfied, weighting the adjustment towards the levels where the divergence is least reliable. Substituting geostrophic winds would give zero divergence on an f-plane and hence no omega at all, which defeats the purpose. Density conversion and smoothing address different issues. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: A

The omega equation diagnoses vertical motion from the vorticity advection and the thermal advection, both of which are far more robustly analysed than divergence. It is derived by combining the quasi-geostrophic vorticity and thermodynamic equations to eliminate the time derivatives. The thermal wind and hypsometric relations are diagnostic relations among other fields, and the vorticity equation is an ingredient rather than the result. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: B

Ascent is forced where cyclonic vorticity advection increases with height and where warm advection is occurring, which is why the region ahead of an upper trough is a region of cloud and rain. Friction and diabatic heating appear as additional terms in extended forms but not in the classical adiabatic version. Learning to read the two classical terms off a chart is among the most useful skills the quasi-geostrophic system provides. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: C

It is the vertical derivative of the vorticity advection that forces vertical motion, so advection increasing with height, typically because the upper trough is stronger than the surface feature, produces ascent. Uniform advection through the depth of the column produces none at all. This is why the term is properly called differential vorticity advection rather than simply vorticity advection. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: D

Warm advection forces ascent and cold advection forces descent, which is why the warm conveyor belt ahead of a surface warm front is the principal cloud and rain producing feature of a mid-latitude cyclone. The physical argument is that warm advection would otherwise destroy thermal wind balance, and the ascent is the ageostrophic response that restores it. Stratification affects the magnitude of the response but not its sign. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: A

The warm conveyor belt ascends ahead of the surface warm front, driven by both warm advection and positive vorticity advection aloft, and it produces the broad shield of layered cloud and steady precipitation. Cold advection behind the cold front forces descent, which is why the sky clears there apart from shallow convection. The dry intrusion is precisely the descending stratospheric air. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: B

The warm conveyor belt is the broad ascending flow of warm moist air that rises over the frontal surface and produces the characteristic comma cloud head. The cold conveyor belt is a separate lower level airstream, the dry intrusion is descending stratospheric air, and the sting jet is a descending feature associated with some explosively deepening cyclones. The conveyor belt model is the standard three-airstream description of a cyclone. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: C

Water vapour imagery responds to the humidity of the upper troposphere, so descending dry stratospheric air appears as a dark zone that wraps around the back of a developing cyclone. Its position relative to the cloud head is a valuable indicator of the stage of development. Bright infrared regions mark high cold cloud tops, which is the opposite of a dry intrusion.

Answer: D

In a typical developing system convergence occupies the lower troposphere and divergence the upper, with the change of sign at a level of non-divergence around 500 to 600 hectopascals. That level is where the barotropic vorticity equation is most nearly valid, which is why 500 hectopascals was chosen for the earliest numerical forecasts. The tropopause lies well above the divergence maximum rather than at the transition. Checking the units of each quantity catches a wrong formula before the arithmetic begins.