1. If the environmental lapse rate is 10.5 C per kilometer, is the atmosphere said to be absolutely stable, conditionally unstable, or absolutely unstable? Why?
   
   
   • The atmosphere is absolutely unstable, because the environmental lapse rate is less than the dry adiabatic rate. A rising parcel will always be warmer than its environment in this case, so it will be buoyant and continue to rise. Hence it is an unstable environment.
     
   
   
2. If the environmental lapse rate is greater than 4o C per kilometer and less than 9.8o C per kilometer, the atmosphere is said to be conditionally unstable. What condition decides whether a parcel will rise or not in this situation?
   
   
   • The condition that decides whether a parcel rises in this situation is whether or not the parcel is saturated. If it is, it will rise and cool at the moist adiabatic rate. If it is not, it will cool at the dry adiabatic rate. In this situation, a saturated air parcel can become buoyant because of the latent heat released by condensation.
     
   
   
3. [Use Figure 6.1 and Figure 6.3 to answer this question] If you observe cumulus clouds over the Catalina mountains, is the atmosphere stable or unstable? If you observe altostratus clouds over the mountains, is the atmosphere stable or unstable?
   
   
   • Cumulus clouds would indicate an unstable environment in the presence of orograpgic lifting over the mountains. Altostratus clouds would indicate orographic lifting taking place under stable conditions.
     
   
   
4. How does advection of warm air at the surface change the atmosphere's stability?
   
   
   • Remember that warm air is less dense than cold air, so it will want to rise. Colder air, being "heavier", will want to sink. When cold air lies above warm air, we say that this is unstable because the cold air will tend to sink and the warm air will tend to rise. Introducing warmer air at the surface will decrease the atmosphere's stability (i.e. make the atmosphere more unstable), since the warmer surface air will want to rise. See figure 6.18 in the text.
     
   
   
5. Cumulonimbus cloud tops frequently exhibit what characteristic shape? What causes this?
   
   
   • These clouds typically have a flat cirrus cloud extending horizontally outward from their tops; these are called anvil tops. The usually result when rising air in the cloud encounters the tmperature inversion that marks the top of the tropopshere. The parcels cannot rise any farther in this stable environment, so they spread out away from the cloud.
     
   
   
6. Warm, moist air is carried by winds over a cold, frozen surface. The surface temperature is less than the air's dew point temperature. What is likely to form?
   
   
   • Under these conditions, advection fog is likely to form.
     
   
   
7. Explain the difference between hygroscopic and hygrophobic nuclei. Why are hygroscopic nuclei important to cloud formation?
   
   
   • Hygroscopic nuclei attract water vapor molecules. Hydrophobic nuclei repel water vapor molecules. Hygroscopic nuclei are important because they allow drop growth by condensation and deposition to occur at a relative humidity of less than 100 %.
     
   
   
8. Suppose you have air in a container. The air is free of any microscopic solid particles. The air's temperature is -10o C (below freezing!). What form of water will you find in the container?
   
   
   • The temperature is below freezing, so you might think ice would form. But the air is free of microscopic solid particles (i.e. no condensation nuclei), so there are no sites for nucleation to occur. Under these conditions, you would find supercooled water in the container.
     
   
   
9. If you take the same particle-free sample of air from question 7 and cool it down to a temperature of - 40o C, what form of water will you find inside the container? Convert the temperature (- 40o C) into degrees Fahrenheit.[see conversion formula on p. 420]
   
   
   • Even if there are no condensation nuclei present, once the temperature reaches -39 C or below, spontaneous nucleation will occur. In this case, you will find ice crystals in your container. A temperature of -40 C is equal to -40 F.
     
   
   
10. What is the smallest size a raindrop can be? What is the largest size? Why are we not pelted by basketball-sized raindrops?
    
    
    • According to the text, the smallest sized precipitation particles are about 0.2 millimeters in diameter (p. 187) - this is about 200 micrometers. I may have said in class that the minimim size is more like 0.5 millimeters. Either answer is acceptable. The important thing to remember is that it is a fraction of a millimeter, but still 10-20 times larger than a typical cloud droplet. The largest-sized precipitation particles are about 5 millimeters in diameter. Larger drops will be subject to breakup by atmospheric turbulence (p. 189). That is why there is an upper limit on precipitation size.