Divergence and Vertical Motion Questions and Answers

Answer: A

Integrating convergence upward gives ascent that increases with height until the level of non-divergence, then decreases as divergence takes over, giving a single maximum near the middle. The vertical velocity must vanish at both the ground and the top. A double maximum can occur in systems with two distinct forcing layers but is not the typical structure of a simple developing cyclone.

Answer: B

The kinematic condition requires the flow to be parallel to the surface, which gives a vertical velocity equal to the wind dotted with the terrain slope, so omega is small over flat ground and appreciable over mountains. It also includes a contribution from the local pressure tendency and from the horizontal advection of surface pressure. Treating it as exactly zero is an approximation valid only over flat terrain. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: C

No mass can cross the top of the atmosphere, so omega must vanish there, and this condition is what allows the kinematic profile to be corrected. In a model with a finite lid the same condition is applied at the lid, which is why a poorly placed lid reflects vertically propagating waves back into the domain. Continuity is automatic and the tropopause carries no special boundary condition. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: D

The lower boundary condition gives a vertical velocity equal to the horizontal wind dotted with the gradient of the terrain height, so a 10 metre per second wind crossing a slope of 1 in 100 produces 10 centimetres per second of forced ascent. That is an order of magnitude larger than typical synoptic vertical motion, which is why orographic enhancement of rainfall is so pronounced. Thermal upslope winds are a separate diurnal effect. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: A

A wind of 10 metres per second crossing a modest slope produces around 10 centimetres per second of ascent against a synoptic value near 1 centimetre per second. This is why rainfall totals on windward slopes are so much greater than on adjacent lowlands and why orography must be represented carefully in any model used for hydrological forecasting in mountainous terrain.

Answer: B

Forced ascent increases with the steepness of the slope and with the depth of moist air lifted, so rainfall commonly doubles or triples between the foot and the upper slopes of a range. The maximum often lies slightly upwind of the crest rather than at it, because hydrometeors take time to grow and fall. A decrease with elevation occurs only in the rain shadow beyond the crest.

Answer: C

Descent on the lee slope warms the air adiabatically and evaporates cloud, giving the rain shadow characteristic of the downwind side of every major range. Trapped lee waves do produce alternating vertical motion downstream, which makes the last option partly true, but their wavelength is set by the stability and wind profile rather than by the mountain width, and the immediate lee slope effect is simple descent. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: D

Air descending the lee slope warms at the dry adiabatic rate, and having lost moisture on the windward side it arrives much warmer and drier than it began, which is the foehn or chinook. Temperature rises of ten to twenty kelvin in an hour are recorded. The other options are all local thermally driven circulations that owe nothing to forced descent over a barrier.

Answer: A

Convergence in the frictional layer beneath a cyclonic circulation forces air upward out of the boundary layer, with a vertical velocity proportional to the relative vorticity above. This is the mechanism by which friction spins a vortex down over a few days. Orographic lifting, entrainment and isentropic upglide are all genuine sources of vertical motion but arise from quite different causes. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: B

With a relative vorticity of \( 10^{-5} \) per second and an Ekman depth of about a kilometre, the pumping velocity works out at a few millimetres per second. That is smaller than the synoptic vertical motion aloft but acts persistently, which is why it spins the vortex down over about four days. Recognising that a small persistent effect can matter as much as a larger transient one is a useful habit. The shared properties explain why these belong to one family, and the differences explain why more than one exists.