Homework Questions for Chapter 8 - Precipitation

Questions 1 and 2 will be turned in for a grade. Questions 3-11 will be discussed by the discussion groups in class so please look them over before the discussion session.

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?

c. If an updraft (w=0.1 ms-1) were present in (b), would the drizzle reach the ground? Why or why not?

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 only to eventually fall out of the cloud? Why or why not?

HINT: typical cloud life time is 45-60 minutes.

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?

4. Why is a warm, tropical cumulus cloud more likely to produce precipitation than a cold, stratus cloud?

5. Explain why very small cloud droplets of pure water evaporate even when the relative humidity is 100%.

6. Suppose that a thick nimbostratus cloud contains ice crystals and cloud droplets all about the same size. Which precipitation process will be most important in producing rain from this cloud? Why?

7. Clouds that form over water are usually more efficient in producing precipitation than clouds that form over land. Why?

8. During a recent snowstorm, Denver, CO received 7 cm of snow. 60 km east of Denver, a city received no measurable snowfall, while 150 km east of Denver another city received 10 cm of snow. Since Denver is located to the east of the Rockies, and the upper-level winds were westerly during the snowstorm, give an explanation as to what could account for this snowfall pattern.

9. When cirrus clouds are above a deck of altocumulus clouds, occasionally a clear area, or "hole," will appear in the altocumulus cloud layer. What do you suppose could cause this to happen?

10. It is -12°C in Albany, NY, and freezing rain is falling. Can you explain why?

11. When falling snowflakes become mixed with sleet, why is this condition often followed by the snowflakes changing into rain?

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?