ATS 620

Fall 2011

Problem Set #4

Due 23 September 2011

1. Using the form derived in class for the saturation ratio above a solution droplet, write a program (using your language of choice) to plot Koehler curves for NaCl (dry mass of 10-18 kg and 10-19 kg) and (NH4)2SO4 (dry mass of 10-18 kg and10-19 kg). From your plot (which should have 4 curves and needs to be turned in) answer the following questions (20 points):

a)The radius of a droplet that will form on a sodium chloride particle of mass 10-18 kg at 0.1 % supersaturation.

b)The relative humidity of the air adjacent to a droplet of radius 0.04 m, which contains 10-19 kg of dissolved ammonium sulfate.

c)The critical supersaturation required for an ammonium sulfate particle of mass 10-19 kg to grow beyond the haze state.

d)For the same dry mass, why are the curves for NaCl and (NH4)2SO4different? Please explain.

2. Consider a spherical drop with radius r. Beginning with the assumption of steady state in the notes, derive the following equation for the diffusion growth of a droplet (state all assumptions and show all work (10 points):

3. Consider a cloud droplet (radius = 10 m) growing by vapor deposition (condensational growth) in an environment with a constant supersaturation of 1.0 %. Calculate the time it takes for the droplet to grow to a precipitation-sized hydrometeor (radius = 1 mm) by vapor deposition alone. Ignore solution, curvature and radiation effects. Discuss your results in relation to the typical lifetimes of clouds (10 points).

You will need the following values:

T = 280 K

K = 2.5x10-2 J m-1 s-1 K-1

D = 2.41x10-5 m2 s-1

Lv = 2.5x106 J kg-1

4. Assuming that cloud condensation nuclei are only removed from the atmosphere by first serving as the centers on which cloud droplets form, and subsequently grow to form precipitation particles, estimate the residence time of the cloud condensation nuclei in a column extending from the surface of the earth up to an altitude of 5 km. Assume that the annual rainfall is 100 cm and the cloud liquid water content is 0.3 g m-3 (10 points).