1. METR125: Cloud Microphysics – grow by condensation
Menglin Jin
For advance knowledge: see Wallace and Hobbs, Sections and 6.4.1

2. Courtesy: Steve Platnick, NASA
Homogeneous Nucleation of Droplets;
Kelvin’s Equation
Cloud Condensation Nuclei.
Warm Clouds.
Growth of Drops by Condensation
Atmospheric Aerosols
Heterogeneous Nucleation of Droplets;
Köhler Curves
Growth of Drops by Collisions.
Ice Nuclei and Ice Crystal in Clouds
Growth of Ice Particles in Clouds
Cold Cloud Processes
Courtesy ?
Warm Cloud Processes
Courtesy: Steve Platnick, NASA

3. Rain Drops, Cloud Droplets, and CCN
Need to remember the typical size of CCN, cloud droplet, and raindrop

4. 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
Or: Volume of rain drop = 106 volume of cloud droplet
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??

5. Processes for Cloud Droplet Growth
Natural Condensation -- Condensation commences at RH=100% when air is cooled. (Would take 24 hours for a droplet to grow to the size of a small raindrop)
Condensation on condensation Nuclei -- Condensation commences with the presence of Cloud Condensation Nuclei at RH=80%, but droplets only grow rapidly at RH=100%. (Still takes over 10 hours for droplets to grow to the size of a small raindrop.)
Collision and Coalescence -- Droplets grow by accretion when they strike other small droplets. Chief process in the clouds vertical development, but also with altocumulus and cirrocumulus. Droplet growth is rapid - the greater the volume of the cloud the more turbulent the flow in that cloud. Best developed in cumulonimbus clouds.
Ice Crystal (Three Phase) Process -- When RH<100% and water droplets occur simultaneously with ice crystals (between 0 and -20C) water droplets evaporate, but ice crystals can continue to grow. Ice crystals resist evaporation (actually sublimation). Ice crystals can continue to grow as random collisions between water vapor molecules leaving the evaporating water droplets collide with the ice crystals. Eventually the water droplets disappear, but the ice crystals grow to such a size that they fall out through the freezing level and arrive at the ground as small to moderate sized rain drops.

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

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

8. Cloud Droplet Formation
REVIEW
Cloud Droplet Formation

9. Clouds Formation Clouds are formed when air containing water vapor
REVIEW
Clouds Formation
Clouds are formed when air containing water vapor
is cooled below a critical temperature called
the dew point and the resulting moisture condenses
into droplets on microscopic dust particles
(condensation nuclei) in the atmosphere.
CLOUDS: A visible mass of liquid/solid water droplets suspended
in the atmosphere above Earth's surface.

10. 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 Ttr=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).
Another form: 10

11. Saturation Vapor Pressure (Clausius-Clapeyron equation)
Another form:
where es is in units of Pa and T is in units of C
to show that as the temperature
increases, es_________
nearly exponentially.
This implies that the atmosphere
is able to hold _____ water
at a higher temperature.
Figure 7 � Saturated Vapor Pressure as function of Temperature
(source: Chow et al., 1988)
Chow et al., 1988) 11

12. 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).
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 12

13. e es(T) (T1,e1) saturated (T2,e2) unsaturated T Concepts
Mixing
Radiative
Cooling
Adiabatic expansion 13

14. q, w, e, T of the mixed air See handout q= M1 M2 q1 + q2 M1+M2 M1+M2
Class Participation: Air parcel A: 20g, 10C, 10g/kg
Air Parcel B: 40g, 30C, 20g/kg, What is mixed parcel’s
temperature?

15. Important Properties:
The saturation vapor pressure above
ice crystals < than above
supercooled
Important Properties:
The saturation vapor pressure above ice crystals < than above supercooled water
wate

16. When both Ice Crystal and water droplet present, which one will grow?
When the air becomes saturated with respect
to water it is supersaturated with respect to ice.
The saturation vapor pressure above
The saturation vapor pressure above
The saturation vapor pressure above
When both Ice Crystal and water droplet present, which one will grow? •
When the air becomes saturated with respect to water,
evaporation = condensation
When the air becomes saturated with respect
to water it is supersaturated with respect to ice.
Thus, the ice collects more water molecules
than its loses by sublimation.
ice crystals < than above
ice crystals < than above
ice crystals < than above
supercooled
supercooled
supercooled
Class participation
wate
wate
wate •
When the air becomes saturated with respect
evaporation = condensation
to water,
to water,
evaporation = condensation •
When the air becomes saturated with respect •
When the air becomes saturated with respect
to water it is supersaturated with respect to ice.
Thus, the ice collects more water molecules
Thus, the ice collects more water molecules
than its loses
by sublimation
than its loses
by sublimation.

17. 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

18. 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

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

20. 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

21. Flat versus Curved Water Surfaces

22. 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

23. Theory Homogeneous (spontaneous) nucleation (cont.)
Recall: a system (droplet + environment) approaches an equilibrium state by reducing its energy (DE<0) in time

24. Theory Subsaturated conditions (e < es)
If droplet grows (R increases), then DE>0, this won’t happen spontaneously.

25. Theory Subsaturated conditions (e < es)
Formation of droplets is not favored
Random collisions of water molecules do occur, forming very small embryonic droplets (that evaporate)
These droplets never grow large enough to become visible

26. Theory Supersaturated conditions (e > es)
If droplet grows (R increases), then DE can be positive or negative

27. Theory Supersaturated conditions (e > es)
- DE initially increases with increasing R
DE is a maximum where R = r
DE decreases with increasing R beyond R = r

28. Theory Supersaturated conditions (e > es)
Embryonic droplets with R < r tend to evaporate
Droplets which grow by chance (collisions) with R > r will continue to grow spontaneously by condensation
They will cause a decrease in the energy (total energy) of the system

29. Theory Kelvin’s formula can be used to
calculate the radius r of a droplet which will be in (unstable) equilibrium with air with a given water vapor pressure e
determine the saturation vapor pressure e over a droplet of specified radius r

30. Theory Kelvin’s formula can be used to
calculate the radius r of a droplet which will be in (unstable) equilibrium with air with a given water vapor pressure e
determine the saturation vapor pressure e over a droplet of specified radius r
r = 0.01 micrometers requires a RH of 112.5%
r = 1.0 micrometer requires a RH of %

31. Discuss: see text book

32. Diffusion Process
Handout:

33. Two phenomena which influence the growth that occurs by diffusion are the _________ effect and the _______ effect.
curvature
solution
Two phenomena which influence the growth that occurs by diffusion are the curvature effect and the solution effect.

34. Droplets, by nature, are _______.
The curvature of a droplet
tends to _______ the concentration of vapor
at the surface of the droplet.
Small droplets have ______ curvature than larger droplets.
In general, given identical atmospheric conditions,
a smaller droplet will have a ________ concentration
of water vapor at its surface than a larger droplet.
Since diffusion is the movement from ______ concentrations
to _____ concentrations,
the curvature effect tends to _______ droplet
growth by diffusion.
As a droplet grows, its curvature ______ and becomes
more like a plane surface and the influence of
the curvature effect ________ as well.

35. Droplets, by nature, are round.
The curvature of a droplet
tends to increase the concentration of vapor
at the surface of the droplet.
Small droplets have more curvature than larger droplets.
In general, given identical atmospheric conditions,
a smaller droplet will have a greater concentration
of water vapor at its surface than a larger droplet.
Since diffusion is the movement from higher concentrations
to lower concentrations,
the curvature effect tends to retard droplet
growth by diffusion.
As a droplet grows, its curvature decreases and becomes
more like a plane surface and the influence of
the curvature effect decreases as well.

36. 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
If the relative humidity decreases,
the droplet will evaporate until it reaches equilibrium.
A droplet that manages to grow to a diameter
of about 20 micrometers will start to grow by
collision and coalescence.

37. 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 %?   

38. 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 %?   

39. 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%.

40. 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???

41. 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?

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

43. See Lecture AEROSOLS

44. Droplet activated
Find it in text book P214

47. Water Droplet Growth - Condensation
FYI
Growth slows down with increasing droplet size:
Since large droplets grow slower, there is a narrowing of the size distribution with time.
R&Y, p. 111
From Bill Olsen & sep.
PHYS Clouds, spring ‘04, lect.4, Platnick

49. rdry= mm
Assumes supersaturation=0.05%, p=900 hPa, T=273K

51. Water Droplet Growth - Condensation
Diffusional growth summary:
Accounted for vapor and thermal fluxes to/away from droplet.
Growth slows down as droplets get larger, size distribution narrows.
Initial nucleated droplet size distribution depends on CCN spectrum & ds/dt seen by air parcel.
Inefficient mechanism for generating large precipitation sized cloud drops (requires hours). Condensation does not account for precipitation (collision/coalescence is the needed for “warm” clouds - to be discussed).

52. 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 52