Hydrostatic Equilibrium Questions and Answers

Answer: C

Latent heat release offsets some of the adiabatic cooling, so the saturated rate is less than 9.8 and varies from about 4 kelvin per kilometre in warm moist air to nearly the dry value in very cold air. It increases with height as the moisture is depleted, which makes the last option partly right, but the essential point is that it is smaller than the dry rate and not constant. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Answer: D

The saturated rate depends on how much water is available to condense, and by Clausius-Clapeyron that is greatest at high temperature, so warm tropical air gives rates near 4 kelvin per kilometre. In very cold air there is almost no water and the rate approaches the dry value. This is why tropical soundings lie so much closer to the moist adiabat than polar ones. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: A

Precipitable water is the vertically integrated water vapour expressed as an equivalent depth of liquid, typically 10 to 25 millimetres in mid-latitudes and up to 60 in the deep tropics. It is an upper bound on what could fall from a column but a poor predictor of actual rainfall, since convergence continually resupplies moisture into a precipitating system. Values well above the seasonal normal are one of the standard indicators used when assessing the potential for extreme rainfall.

Answer: B

Low level convergence continually feeds new moisture into a storm, so a system can produce several times the precipitable water of the column it occupies. Moisture flux convergence rather than the standing moisture content is what determines the total. This is why the quantity is used as an environmental indicator rather than as a quantitative forecast of accumulation.

Answer: C

The wet delay in navigation satellite signals passing through the atmosphere is proportional to the integrated water vapour, so a network of geodetic receivers doubles as a humidity observing system. It provides continuous measurement at a few minute intervals, unlike a radiosonde which gives two profiles a day. The technique was a by-product of geodesy and is now assimilated operationally.

Answer: D

The net upward force on a parcel is the weight of the air it displaces, so a parcel less dense than its surroundings rises and one denser than its surroundings sinks. Buoyancy is exactly the residual left when hydrostatic balance is subtracted from the vertical momentum equation, which is why the two ideas are inseparable. Expressing the result per unit mass gives an acceleration proportional to the fractional density difference, which for the atmosphere is more conveniently written in terms of virtual temperature.

Answer: A

Buoyancy depends on density, and moist air is lighter than dry air at the same temperature, so the comparison must be made using virtual temperature. In the tropics the correction is comparable with the temperature excess of a convective plume, so neglecting it can change the sign of the buoyancy. Potential temperature is the right variable for comparing parcels at different levels but not for evaluating buoyancy at one level.

Answer: B

The buoyant acceleration is gravity times the fractional temperature excess, so one kelvin in 300 gives about 0.033 metres per second squared. Sustained over a few kilometres that is enough to produce updraughts of several metres per second, which is why quite small temperature excesses drive vigorous convection. Working the estimate once makes the magnitude of convective forces intuitive.

Answer: C

Taking the acceleration as constant and using the kinematic result gives a speed of about 18 metres per second after 5 kilometres, which is the parcel theory estimate. Observed updraughts are usually weaker because entrainment of drier environmental air and the weight of condensed water both reduce the buoyancy. The parcel theory value is therefore an upper bound rather than a prediction.

Answer: D

Mixing with cooler drier environmental air dilutes the buoyancy, and the weight of suspended condensate acts as an additional load, so real updraughts fall well short of the undiluted parcel value. Both effects are represented in convective parameterisation schemes through entrainment rates and condensate loading terms. Radiation and Coriolis effects are negligible on convective timescales.