1. METR125: Cloud Microphysics – Nucleation of water vapor condensation
Wallace and Hobbs, Sections 6.1 and 6.4
Menglin Jin

2. Prof. Jin and Prof. Wallace, AGU

3. Courtesy: Steve Platnick, NASA
Cold Cloud Processes
Courtesy ?
Warm Cloud Processes
Courtesy: Steve Platnick, NASA

4. Rain Drops, Cloud Droplets, and CCN

5. relative sizes of rain drops, cloud drops, and CCN:
raindrops μm = 2 mm
fall at a speed of 4-5 ms-1
cloud drops - 20 μm = 0.02 mm
remain suspended in the air
CCN μm = mm
To get a droplet (20 μm) to grow to raindrop size (2000μm) it must increase in size by a factor of 100 (two orders of magnitude):
2000μm/20μm = 100
this occurs in about 30 minutes in a thunderstorm!!!
this is like a 150 lb person growing in size to 15,000 lbs in half an hour!!!
Q: How does this happen??

6. Video: cloud formation in Tucson
Timelapse of Tucson cloud formations

7. Q: How and why do clouds form on some
regions and not on others????

8. Q: How and why do clouds form on some
regions and not on others????
Q: Why does the atmosphere sometimes produce
stratus clouds (thin layered) while other times we get cumulus,
or cumulonimbus clouds to form??

9. Q: How and why do clouds form on some
regions and not on others????
Q: Why does the atmosphere sometimes produce
stratus clouds (thin layered) while other times we get cumulus,
or cumulonimbus clouds to form??
The answer is largely related to the concept of
atmospheric stability.....

10. Cloud Development - stable environment
Consider this simple situation of a marble in the bottom of a bowl:
if you push the marble up the side of the bowl, it will fall back down
to the bottom, to it's original position
Stable air (parcel) - vertical motion is inhibited
if clouds form, they will be shallow, layered clouds like stratus

11. Cloud Development - unstable environment
If the marble is on the top of the bowl
and you give it a little push, it rolls off the bowl....
does NOT come back to its original position
This is an unstable situation
Unstable air (parcel) - vertical motion occurs
commonly produces cumulus, cumulonimbus clouds
So, the question becomes, how does one determine the stability of the atmosphere?

12. Assessing Atmospheric Stability
To determine whether or not a parcel will rise or sink in the atmosphere, one must compare the parcels temperature (Tp) with that of the environment (Te) at some altitude:
if Tp > Te what will the parcel do?
It will rise since it is less dense than the air
if Tp = Te what will the parcel do?
It will remain at that location
if Tp < Te what will the parcel do?
IT WILL SINK SINCE DENSER THAN THE AIR

13. Assessing Atmospheric Stability
to assess stability, what two pieces
of information do we need ?
We need to know
the vertical temperature profile and
temperature of the parcel of the air

14. consider a rising parcel of air -->>
Determining Air Parcel Temperature: Rising air parcels and adiabatic cooling
consider a rising parcel of air -->>
As the parcel rises,
it will adiabatically expand and cool
adiabatic - a process where the parcel temperature
changes due to an expansion or compression,
no heat is added or taken away from the parcel
the parcel expands since the lower pressure outside allows the air molecules to push out on the parcel walls
since it takes energy for the parcel molecules to "push out" on the parcel walls, they use up some of their
internal energy in the process.
therefore, the parcel also cools since temperature is proportional to molecular internal energy

15. Determining Air Parcel Temperature: Rising air parcels and adiabatic cooling
consider a sinking parcel of air -->>
As the parcel sinks, it will adiabatically compress and warm
the parcel compresses since it is moving into a region of higher pressure
due to the parcel compression, the air molecules gain internal energy
hence, the mean temperature of the parcel increases

16. Dry adiabatic lapse rate
As a parcel of air rises, it cools, but at what rate???
rate of temperature change with height is
called the lapse rate
units of lapse rate are °C km-1
First case: an unsaturated parcel of air
unsaturated parcels cool at a rate of 10°C km-1
- this is called the dry-adiabatic lapse rate
What will be the parcel's temperature be at 1 km?
Answer: 30 degrees Celsius

17. Dry adiabatic lapse rate, cont
What will be the parcel's temperature be at 2 km?
Answer: 20C

18. Moist Adiabatic Lapse Rate
For a saturated parcel of air, i.e.,
when its T=Td, then it cools at
the moist adiabatic lapse rate = 6°C km-1
What will be the parcel's temperature be at 3 km?
ANSWER: 14C

19. Moist Adiabatic Lapse Rate
What will be the parcel's temperature be at 4 km?
Answer: 8C

20. Moist Adiabatic Lapse Rate
Why does the parcel cool at a
slower rate (6 °C km-1) when it is saturated
than at 10°C km-1 when it is unsaturated??
Because latent heat is released into the air parcel as vapor condenses into water. The latent heat counteract the adiabatic cooling.
Answer: Because latent heat is released into the air parcel as vapor condenses into water.
The latent heat counteract the adiabatic cooling.

21. Dry versus Moist-Adiabatic Process
the moist adiabatic lapse rate is less than the dry adiabatic lapse rate because as vapor condenses into water (or water freezes into ice) for a saturated parcel, latent heat is released into the parcel, mitigating the adiabatic cooling -->

22. Absolute Stability

23. Absolute Stability consider the diagram to the right, notice that:
Tup < Tsp < Te
where Tup is the temperature of an unsaturated parcel = 0°C
Tsp = temperature of a saturated parcel = 10°C
Te = environmental temperature = 20°C.
generally, notice that Te is always larger than Tsp and Tup at any level
Hence, an unsaturated or saturated parcel will always be cooler than the environment and will sink back down to the ground
This is an example of absolute stability
The condition for absolute stability is:
Gd>Gm>Ge
Gd is the dry adiabatic lapse rate (10°C km-1)
Gm is the moist adiabatic lapse rate (6°C km-1)
Ge is the environmental lapse rate (variable - 0°C km-1 in this case)
Q: How would you characterize the stability of an inversion layer?

24. Stability of Inversion Layers
How would you characterize the stability of an inversion layer? They are absolutely stable see diagram to the right -->> note that the absolute stability criteria: Ge<Gm<Gd

25. Atmospheric Instability and Cloud Development
What determines the base (bottom) of a cloud??
Q: What determines the height to which the cloud
will grow??
let's use the previous example of a rising air parcel -->>
Q: On this diagram, where is cloud base?
Q: On this diagram, where is cloud top?
LFC – level of free convection where in atmosphere
The environment temperature decreases faster
Than the moist adiabatic lapse rate
LCL –Listed Convection Level

26. Atmospheric Instability and Cloud Development
Q: On this diagram, where is cloud base?
A: Where the parcel reaches saturation - 2 km
Q: On this diagram, where is cloud top?
A: Where the parcel will no longer be able to rise - 9 km
Here, Tp = Te - this is often referred to as the equilibrium level (EL)

27. Example Microphysical Measurements in
Marine Sc Clouds (ASTEX field campaign, near Azores, 1992)
Data from U. Washington C-131 aircraft
PHYS Clouds, spring ‘04, lect.2, Platnick 27

28. Cloud Droplet Formation
S. Platnick notes

29. PHYS 622 - Clouds, spring ‘04, lect. 2, Platnick
Water Cloud Formation
Water clouds form when RH slightly greater than 100% (e.g., 0.3% supersaturation). This is a result of a subset of the atmospheric aerosol serving as nucleation sites (to be discussed later).
Common ways for exceed saturation:
1. Mixing of air masses (warm moist with cool air)
2. Cooling via parcel expansion (adiabatic)
3. Radiative cooling (e.g. ground fog, can lead to process 2)
PHYS Clouds, spring ‘04, lect. 2, Platnick 29

30. PHYS 622 - Clouds, spring ‘04, lect. 2, Platnick
Concepts T e
es(T)
(T1,e1)
(T2,e2)
unsaturated
saturated
Mixing
Radiative
Cooling
Adiabatic expansion
PHYS Clouds, spring ‘04, lect. 2, Platnick 30

31. q, w, e, T of the mixed air See textbook and notes q= M1 M2 q2 q1 +

33. Saturation Vapor Pressure (Clausius-Clapeyron equation)
Water
Air and water vapor T
At equilibrium, evaporation and condensation have the same rate, and the air above the liquid is saturated with water vapor; the partial pressure of water vapor, or the Saturation Vapor Pressure (es) is:
Where Ts=triple point temperature (273.16K), L is the latent heat of vaporization (2.5106 J/kg), es(Ttr) = 611Pa (or 6.11 mb). Rv is the specific gas constant for water vapor (461.5 J-kg1-K1).
Platnick 33

34. Saturation Vapor Pressure
An approximation for the saturation vapor pressure (Rogers & Yau):
Over liquid water:
L = latent heat of vaporization/condensation,
A=2.53 x 108 kPa, B = 5.42 x 103 K.
Over ice:
L = latent heat of sublimation, A=3.41 x 109 kPa, B = 6.13 x 103 K.
Need a sketch of solid-liquid-vapor phase regions.
Platnick 34

35. Rain Drops, Cloud Droplets, and CCN

36. Processes for Cloud Droplet Growth
How does this happen??
By:
condensation
collision/coalescence
ice-crystal process
today

37. Condensation & Collision
Water Droplet Growth
Condensation & Collision
Condensational growth: diffusion of vapor to droplet
Collisional growth: collision and coalescence (accretion, coagulation) between droplets
PHYS Clouds, spring ‘04, lect.4, Platnick

38. Water Droplet Growth - Condensation
Flux of vapor to droplet (schematic shows “net flux” of vapor towards droplet, i.e., droplet grows)
Need to consider:
Vapor flux due to gradient between saturation vapor pressure at droplet surface and environment (at ∞).
Effect of Latent heat effecting droplet saturation vapor pressure (equilibrium temperature accounting for heat flux away from droplet).
From Bill Olsen
PHYS Clouds, spring ‘04, lect.4, Platnick

39. Cloud Droplet Growth by Condensation
Consider pure water in equilibrium with air above it
C-C equation to calculate es

40. Growth by Condensation Cloud Droplet
Consider pure water in equilibrium with air above it:
then the RH = 100%
evaporation = condensation
vapor pressure (e) = saturation vapor pressure (es)
if evaporation > condensation, water is _________
if evaporation < condensation, water is ________
Now, a droplet surface is not flat, instead, it has curvature.....
Q: how does curvature affect the evaporation/condensation process??
Answer 1: Being added to
Answer2: Being removed from

41. Flat versus Curved Water Surfaces

42. Flat versus Curved Water Surfaces: curvature effect
more energy is required to maintain the "curvature" of the drop
therefore, the water molecules on the surface of the drop have more energy
therefore, they evaporate more readily that from the flat water surface (compare the length of the red arrows)
therefore: evaporation rate off curved surface > evaporation rate off of flat surface
since air above both surfaces is saturated, then
evaporation rate = condensation rate
therefore, condensation rate onto droplet > condensation rate onto flat water surface
therefore, esdrop > esflat
therefore:
if RHflat = 100%, then RHdrop > 100%
the air surrounding the drop must be supersaturated!!
This is called the curvature effect

43. Kelvin’s Equastion

44. Curvature Effect Curvature effect -->
notice that for the droplet to be in equilibrium
(evaporation off drop = condensation onto drop),
the environment must be supersaturated
also notice that the curvature effect
is larger for smaller drops
this makes sense since smaller drops
have more curvature that larger drops

45. Discuss: see text book

46. Class activity-Curvature Effect
Q: what will happen to a drop 1.9 μm in size that is in a cloud where the RH is %?
Q: what will happen to a drop 1.9 μm in size that is in a cloud where the RH is %?   

47. Class activity-Curvature Effect
Q: what will happen to a drop 1.9 μm in size that is in a cloud where the RH is %?
Q: what will happen to a drop 1.9 μm in size that is in a cloud where the RH is %?   

48. QUESTIONS FOR THOUGHT:
1. At what relative humidity will pure water droplets of the following sizes grow by condensation:
a. 10 microns
b. 4 microns
c. 1 micron
2.  Explain why very small cloud droplets of pure water evaporate even when the relative humidity is 100%.

49. Solution Droplets
Note that the previous discussion is valid for a pure water drop
if a droplet is comprised of a solution - it can be in equilibrium with the environment at a much lower RH -->
this explains the formation of haze
This process of condensation will grow drops , but not to precipitation sizes (~ 2 mm)
Q: So, if a droplet grows to some size by condensation, how can it continue to grow to precipitation size???

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

51. Köhler Curve How is amount of solution change water droplet formation?
Give example.
How different solution change
water droplet formation?

52. Droplet activated
Find it in text book P214

54. Cloud Droplet Grow by condensation in warm clouds
Section Wallace and Hobbs