Hydrostatic Equilibrium Questions and Answers

Answer: A

The mixing ratio is conserved during dry ascent but the pressure falls, so the vapour pressure falls and with it the dew point, at about 1.8 kelvin per kilometre. The temperature falls much faster at 9.8, which is why the two curves converge and saturation is eventually reached. Their rate of convergence is what gives the 125 metre rule.

Answer: B

No heat is exchanged so potential temperature is conserved, and no water is exchanged so the mixing ratio is conserved. Relative humidity rises towards saturation because the saturation value falls faster than the actual vapour pressure. The vapour pressure itself falls in proportion to the total pressure, since the mixing ratio rather than the vapour pressure is the conserved quantity. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: C

Potential temperature is conserved during adiabatic vertical motion, so it identifies an air mass regardless of the level at which it is found. Temperature, pressure and density all change as a parcel moves vertically and therefore cannot serve the purpose. This is why isentropic analysis follows surfaces of constant potential temperature.

Answer: D

Constant entropy means constant potential temperature, so an adiabatic parcel is confined to its isentropic surface and its vertical motion is entirely determined by the slope of that surface. This is what makes isentropic analysis such a natural way to visualise three dimensional flow. Pressure, temperature and density all change as the parcel moves along the surface. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: A

Since potential temperature increases upward and also increases towards the equator, surfaces of constant potential temperature slope upward towards the pole, that is towards the colder air. Air flowing poleward along such a surface therefore rises. This is the isentropic view of warm advection producing ascent.

Answer: B

Isentropic surfaces slope upward towards the cold pole, so a parcel moving poleward along one must rise, which is precisely the ascent that warm advection produces. Equatorward flow correspondingly descends. This is the same result the omega equation gives, arrived at by a much more direct route that also shows the trajectory.

Answer: C

Confining the trajectory to a two dimensional surface reduces the calculation enormously and automatically captures the vertical motion through the slope of the surface. Isentropic trajectory models were widely used before full three dimensional models became affordable. Diabatic heating breaks the assumption, which is the method's principal limitation.

Answer: D

Condensational heating raises the potential temperature of a parcel, moving it to a higher isentropic surface, so trajectories in cloud cannot be computed by this method. Radiative heating and turbulent mixing have the same effect more slowly. Adiabatic ascent along the surface is exactly what the method represents correctly, and horizontal advection keeps the parcel on the surface. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: A

Once condensation begins, latent heat release raises the potential temperature, but equivalent potential temperature, which accounts for that heat, is conserved. The mixing ratio falls as water is removed by precipitation in the pseudo-adiabatic case. Relative humidity does remain at saturation, which makes that a true statement but not a conserved thermodynamic variable in the required sense. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: B

In the reversible process the condensed water stays with the parcel and can be re-evaporated on descent, while in the pseudo-adiabatic process it falls out immediately. Real ascent lies between the two. The difference in the resulting lapse rate is small, typically a few tenths of a kelvin per kilometre, but the pseudo-adiabatic case is irreversible while the other is not. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.