1

Precipitation Processes

METR 2011

Introduction In order to grow things on earth, they need water. The way that the earth naturally irrigates is through snowfall and rainfall. Therefore, it is important to understand how we get clouds and subsequent rain or snow to fall from them. This lab will introduce you to the concepts and a few equations related to the growth of cloud droplets and raindrops. Growth of Cloud Drops Cloud drops form on cloud condensation nuclei (CCN), which are small particles suspended in the atmosphere that are mainly hydroscopic. There are many different things that can serve as CCN in the atmosphere including dust, aerosols, smoke, sea salt, etc. If we didn’t have CCN, then we would need a relative humidity (RH) on the order of 300–400% to be able to get cloud droplets to form. Since we typically only see maximum RH on the order of 102%, therefore we must, MUST have CCN in the atmosphere in order to have clouds and subsequently precipitation. The water vapor surrounding a CCN particle or a cloud droplet wants to be in equilibrium, meaning that the vapor pressure of the drop/substance wants to be the same as the environment. There are two main effects that determine what that equilibrium level is for different CCN particles, curvature and solution. These two effects can be written as an equation for the equilibrium saturation ratio (S),

31

r

b

r

aS !+=

where

TRa

vl!

"2=

!

b =3im

sM

v

4"#lM

s

where a is the curvature term and b is the solution term. The terms in a and b are the following: σ is the surface tension, ρl is the water density, Rv is the Gas constant for water vapor, T is the air temperature, i is van’t hoff factor, ms is the mass of the solute, Mv is the molar mass of water (H2O), and Ms is the Molar mass of solute. The supersaturation can also be define from vapor pressure as,

2

!

S =e

es

"1#

$ %

&

' ( *100

where e is the vapor pressure and es is the saturation vapor pressure. Different solutes will have different effects and plotting them on a log plot is called a Kohler curve (Fig. 1). This is a graphical way to be able to determine when and how a cloud droplet will grow by condensation. Often it takes some time for droplets to grow until it reaches a critical saturation level or radius, at which point it will continuously grow by condensation. The critical radius and super-saturation levels for a given particle are,

abr 3*

= and b

aS27

413

*+=

where r* is the critical radius and S* is the critical saturation ratio and a and b are as before. In general, over land there are more CCN particles and thus there are more cloud droplets on average than over the ocean where there are fewer CCN particles. Once cloud droplets grow big enough, then we will begin to see them and then we have clouds!

Figure 1. Kohler curve for Ammonium Sulfate (NH4)2SO2.

3

Collision and Coalescence When “warm” cloud droplets become large enough, they will begin to fall as the motions on the cloud are no longer enough to overcome the effects of gravity. As these cloud drops fall through the cloud, they interact with other cloud drops in their downward falls, colliding and collecting with some drops that are in their paths. After sufficient time, the falling drops will fall at their terminal velocities where the air resistance equals the force of gravity, where larger drops fall faster than smaller drops (Table 1).

Radius (µm) Rate of Fall (m s-1) Type of Drop 2500 (2.5 mm) 8.9 Large Raindrop

500 4.0 Small Raindrop 250 2.8 Fine Rain or Large Drizzle 100 1.5 Drizzle 50 0.3 Large Cloud Droplet 25 0.076 Ordinary Cloud Droplet 5 0.003 Small Cloud Droplet

0.5 0.000004 Large Condensation Nucleus Table 1. Relationship between droplet size and terminal fall velocity.

As drops fall through a column of air, they will collide with many cloud drops and will do one of three things: (1) collide and coalesce, (2) collide and bounce off of each other, or (3) collide and break apart into many smaller pieces. As you move further in your meteorological education you will learn more about how and why falling cloud drops and rain drops fall and grow, but for now, just know these basic concepts of falling cloud and rain drops. As a drop continues to fall through the cloud, and if it grows big enough, it will emerge at the bottom of the cloud as a raindrop and will likely encounter changing environmental conditions. Beneath the cloud, RH drops below 100% and in order to reach equilibrium the raindrops will begin to evaporate. Therefore, only drops large enough to survive any evaporation will make it to the ground (Table 2). If all of the rain evaporates before reaching the ground this is called virga.

Drop Radius (µm)

Maximum fall distance before evaporation (m)

2500 280,000 1000 42,000 500 1,000 200 500 100 150 50 0.1 10 0.033 2 0.00002 1 0.0000033

Table 2. Maximum fall distance for varying drop sizes

4

Bergeron Process Ice crystals typically form on ice nuclei as opposed to liquid cloud drops forming on CCN. The only difference between the two is that ice nuclei have a crystalline structure, which freezing water molecules will easily adhere to. Actually, the saturation vapor pressure over ice is lower than over water and thus if there is ice in the clouds, ice crystals will form preferably over water cloud drops. When clouds are composed of ice crystals (think winter), the process is slightly different from the collision-coalescence processes described above. So, the growth of ice crystals are preferred over water droplets, as the ice particles will attract the water molecules away from cloud drops. Again, once ice crystals become large enough, they too will begin to fall. As they fall they will tend to aggregate as bigger ice particles fall and hit smaller ice particles. There are at least three things that could happen to falling ice particles as they collide with one another: (1) stick together, (2) hit each other and bounce off, or (3) hit each other and break into many smaller ice particles. The ability for two ice particles to stick together is closely related to the temperature of the surrounding air. The closer the air temperature to 0°C, the more “sticky” the ice particles become as a layer of liquid water begins to form on the ice particles making them more likely to stick together. Precipitation Type Typically, both the Bergeron process and the collision-coalescence process are going on in a cloud producing precipitation. At higher altitudes the ice processes dominate, then as the ice crystals fall, they encounter temperatures greater than 0°C and they melt into raindrops or liquid cloud drops. So the vertical profile of the temperature will be the main factor determining the precipitation type at the surface (Fig. 2). If temperatures at the surface are above freezing, then the precipitation type will be rain. If the temperature is always below freezing throughout the entire column where precipitation is falling, the precipitation type will be snow. If falling snow encounters a warm layer aloft, but surface temperatures are below freezing then the snow will melt into rain in the warm layer and depending on how deep the sub-freezing layer is will determine whether the precipitation type will be sleet or freezing rain. A deeper freezing layer will tend to produce more sleet events and a shallower freezing layer will tend to produce mainly freezing rain events.

Figure 2. Vertical profile of temperature and its role in determining precipitation type.

5

Questions: Answer the following questions on a separate sheet of paper. Print out your graphs and include them with the answers on separate paper. Assume σ = 7.5 x 10-2 N/m, i = 2, Rv = 461.5 J kg-1K-1, and ρl = 1000 kg m-3. Assume CCN is composed of sodium chloride (NaCl). Where MNa = 22.99 g mol-1, MCl = 35.45 g mol-1, MH = 1.01 g mol-1, and MO= 16 g mol-1. 1. Plot the Kohler curve for a solute mass of 10-16 g at a temperature of 5 °C. Your radius range should be between 0.01 µm, and 10 µm and your saturation ratio range should be between 0.995 and 1.005. The radius should be on the x-axis and should be a logarithmic axis. Please answer the following questions. (a) Locate and indicate the critical radius and saturation ratio. Draw a vertical line from the bottom of your graph to the critical radius and a horizontal line from the y-axis to the critical saturation ratio. Mark the area bounded by lines you just drew and the bottom and left edge of your graph as A. (b) Show on the graph what would happen to a droplet in area A if it had a radius and saturation ratio that put it to the left of the curve? What if the droplet had a radius and saturation ratio that was to the right of the curve? (c) What if a droplet was at the critical radius and saturation ratio and the humidity were to slightly increase? (d) Calculate the critical radius and the critical saturation values from the equations given in this lab. 2. On a new graph plot the Kohler curve for a solute mass of 10-17 g, 10-16 g, and 10-15 g and a temperature of 5 °C to create a plot with a family of Kohler curves. Your x-axis should have a radius range of 0.01-10µm and your y-axis should have a saturation ratio range of 0.995-1.005. How does the critical radius and critical saturation ratio change with increasing solute mass? Why? 3. In a cloud composed of water droplets and ice crystals, is the saturation vapor pressure greater over the droplets or over the ice? 4. Describe how the process of collision and coalescence produces precipitation.

6

5. How many times faster does a large raindrop (diameter 2500 µm) fall than a cloud droplet (diameter 25 µm), if both are falling at their terminal velocity in still air? 6. a) How many minutes would it take drizzle with a diameter of 250 µm to reach the surface if it falls at its terminal velocity from the base of a cloud 1000 m above the ground? (Assume the air is saturated beneath the cloud, so that the drizzle does not evaporate, and the air is still.) b) Suppose the drizzle in problem 6a starts evaporating on its way to the ground. If the drop size is 250 µm for the first 450 m of descent, 100 µm for the next 450 m, and 20 µm for the final 100 m, how long will it take the drizzle to reach the ground it if falls in still air? 7. Based on the information in Table 2 and your knowledge about the height of cloud bases, approximately what radius marks the distinction between a cloud droplet and a raindrop that reaches the ground? Explain. 8. Using the following soundings, determine the precipitation type for each sounding and explain why. (Color images of the soundings can be found at http://weather.ou.edu/~metr2011H/lab10.html)

7

SOUNDING A

8

SOUNDING B

9

SOUNDING C

10

SOUNDING D