Homework Questions for Chapter 7 - Precipitation

Follow the Problem solving steps discussed in class

1.

a. How many minutes would it take drizzle with a diameter of 200 micrometers to reach the surface if it falls at its terminal fall velocity from the base of a cloud 1000 meters above the ground? Assume the air is saturated beneath the cloud, the drizzle does not evaporate, and the air is still.

b. Suppose the drizzle evaporates on its way to the ground. If the drop size is 200 micrometers for the first 450 meters of descent, 100 micrometers for the next 450 meters, and 20 micrometers for the final 100 meters, how long will it take the drizzle to reach the ground if it falls in still air?

2. For droplets in warm clouds growing by condensation, the radius of the droplet (R) increases as the square root of time (t) by:

where c is a dimensionless constant, D is a diffusion coefficient, and S is a measure of supersaturation of the air far away from the droplet.

a. Make a plot of R (in units of micrometers) versus time for t = 0 to 3 hours. Assume c=0.0023, D = 2x10-5 m2 s-1, S=1% supersaturation.

b. Based on your plot in (a), would you expect a droplet growing by condensation to fall out of the cloud after 20 minutes? Why or why not?

3. At what relative humidity will pure water droplets of the following sizes grow by condensation:

a. 10 microns

b. 4 microns

c. 1 micron

d. Haze particles can form when the relative humidity is less than 100%. Are these haze particles pure water droplets or solution droplets? Why?

EXTRA CREDIT:

Heavier rain scatters more of the radar's microwave energy back to the radar than lighter rain. The radar reflectivity factor (Z) is expressed as:

where D is the diameter of the raindrops in some volume (V). Note that the units of Z are (mm6 m-3). The radar reflectivity is expressed as decibels dB of Z - or dBZ and is defined as dBZ = 10 log(Z). It is the radar reflectivity in dBZ that you see plotted on radar images.

If you have:

• one drop 5 mm in diameter

• two drops 3 mm in diameter

• one drop 1 mm in diameter

all in 1 m-3 of air, then what is the value of the radar reflectivity in dBZ?