Assignment:
Let us examine how deep convection scavenges water (and along with it water-soluble species) from the atmosphere. Consider a sea-level air parcel at relative humidity of 50% and temperature of 20°C lifted in a convective updraft without exchanging any material with its surroundings. Use the Magnus approximation formula below (approximation of the Clausius-Clapeyron equation) for the saturation vapor pressure of water PH20,SAT (in units of hPa) over liquid as a function of temperature Tc (in units of °C):
PH20, SAT = 6.11e (17.63Tc/ Tc + 243.04)
a. Show that the air parcel will form a cloud at about 1.1 km altitude. (you can ignore the relatively insignificant change in atmospheric pressure between the surface and the cloud base)
b. This saturated (and cloudy) air parcel keeps rising until it reaches the tropopause at 11 km altitude. Assuming a mean wet adiabatic lapse rate Γw= 6.5 K km-1, show that the temperature in the cloud outflow at 11 km is -56°C.
c. The cloud outflow is saturated with respect to ice (cirrus clouds). The saturation water vapor pressure over ice at -56°C is 0.07 hPa. Show that about 97% of the water in the initial air parcel has been scavenged by precipitation (i.e., precipitated) by the time the air parcel exits the cloud at 11 km altitude. (in this case you must account for the decrease in atmospheric pressure with altitude. Use a scale height H= 7.4 km). It is worth noting that scavenging is even more efficient for water-soluble species such as aerosol particles.