1. Water Droplet Growth by 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

2. Warm Clouds Cold Cloud Processes Warm Cloud Processes
Homogeneous Nucleation of Droplets;
Kelvin’s Equation
Cloud Condensation Nuclei.
Growth of Drops by Condensation
Atmospheric Aerosols
Heterogeneous Nucleation of Droplets;
Köhler Curves
Warm Clouds
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. The Collision-Coalescence Process
A droplet may continue to grow by diffusion beyond 20 micrometers in diameter, however, once a droplet attains this size, growth is slow and inefficient. Droplets this large begin to collide and coalesce with other droplets as they fall through the cloud, meaning they will bump into and bond to one another and form larger drops. Updrafts in a cloud can transport a droplet upward repeatedly allowing it many opportunities to fall back down through the cloud and collide and coalesce with other droplets.
Initially by diffusion, and subsequently by collision and coalescence, tiny aerosol nuclei grow into large water droplets more than 10,000 times their initial size.

4. Collision/Coalescence
Collision/Coalescence - cloud droplet growth by collision is a dominant process for precipitation formation in warm clouds (tops warmer than about 0°C)
some cloud droplets will grow large enough and will start to fall in the cloud -->> since the bigger drops fall faster than the smaller drops, they will "collect" the smaller drops - the bigger drop grows
droplet fall speed is called its terminal velocity
Usually, air resistance that comes in contact with the water molecules as they fall causes the drag. The combination of these two forces causes a raindrop to reach a terminal velocity when the drag force is approximately equal to the weight of the raindrop. At this point, a raindrop experiences no further acceleration and therefore falls at a constant velocity.
Q: what determines the droplets fall speed relative to the ground??

5. Droplet Fall Speeds and Droplet Growth
Q: what determines the droplets fall speed relative to the ground??
A: droplet size and updraft strength -->
Cumulus (cu)
Class Participation: given a growing cu with an updraft strength of 4 ms-1:
if the particle terminal velocity is -2 ms-1, its fall speed is
b. if the particle terminal velocity is -6 ms-1, its fall speed is
2 m/s (up)
-2 m/s (down)

6. Life cycle of a droplet Growth by collision
the drop initially forms in the updraft of the cloud near cloud base
it grows in size by collisions
since Vg = w + Vt
Vg = ground relative fall speed of the drop
w = updraft velocity
Vt = drop's terminal velocity
then the drop will begin to fall when Vt > w

7. Factors promoting growth by collision/coalescence
Different drop sizes
thicker clouds
stronger updrafts

8. Droplet Growth in a Shallow Stratus Deck
Often, drops will evaporate from shallow stratus before reaching the ground (why?)
or you may get drizzle if they are large enough
QUESTION FOR THOUGHT:
1.  Why is a warm, tropical cumulus cloud more likely to produce
precipitation than a cold, stratus cloud?

9. Warm versus Cold Clouds
Our previous discussion regarding droplet growth by condensation and collisions is valid for warm clouds:
warm clouds - have tops warmer than about 0°C
comprised entirely of water

10. Cold Clouds Q: So how does frozen precipitation form in cold clouds?
Cold clouds are defined as those clouds with tops colder than 0°C
can be comprised of:
water
super-cooled water - liquid droplets observed at temps less than 0°C
ice
Notice that super cooled water is found at altitudes where:
-40°C < Temp < 0°C
only ice is found at altitudes above -40°C
Q: So how does frozen precipitation form in cold clouds?
Next lecture

11. 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).
How to have difference size of droplet in water cloud?
PHYS Clouds, spring ‘04, lect.4, Platnick

12. Water Droplet Growth - Condensation
FYI
Evolution of droplet size spectra w/time (w/T∞ dependence for G understood):
With senv in % (note this is the value after nucleation, << smax):
T (C)
G (cm2/s)*
G (µm2/s)
-10
3.5 x 10-9
0.35
6.0 x 10-9
0.60 10
9.0 x 10-9
0.90 20
12.3 x 10-9
12.3
From Bill Olsen & sep.; G’s from Twomey text. Note: for comparison with R&Y, p With s in absolute, at 10C, G=90 µm2/sec (reasonably close to Fig. 7.1).
* From Twomey, p
T=10C, s=0.05% => for small r0:
r ~ 18 µm after 1 hour (3600 s)
r ~ 62 µm after 12 hours
Diffusional growth can’t explain production of precipitation sizes!
PHYS Clouds, spring ‘04, lect.4, Platnick

13. 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

14. Water Droplet Growth - microphysics approx.
REVIEW
How can we approximate N for such clouds, and what does this tell us about the effect of aerosol (CCN) on cloud microphysics?
Approximation (analytic) for smax, N in developing cloud, no entrainment (from Twomey):
Need relationship between N and s => CCN(s) relationship is needed (i.e., equation for concentration of total nucleated haze particles vs. s, referred to as the CCN spectrum).
Determine smax. r
1.0
Dry particle - CCN
wet haze droplet
activated CCN
PHYS Clouds, spring ‘04, lect.4, Platnick

15. Water Droplet Growth - microphysics approx.
REVIEW
Very important result!
NCCN controls cloud microphysics for clouds with relatively small updraft velocities (e.g., stratiform clouds).
Increase NCCN (e.g., by pollution), then N will also increase (by about the same fractional amount if pollution doesn’t modify k).
Similar to R&Y Fig 7.4 for Smax vs. different updraft velocities.
clean air (e.g., maritime)
“dirty” air (e.g., continental) t
Note: 
=>
PHYS Clouds, spring ‘04, lect.4, Platnick

16. Cloud-aerosol interactions ex. : ship tracks (27 Jan. 2003, N
Cloud-aerosol interactions ex.: ship tracks (27 Jan. 2003, N. Atlantic)
MODIS (MODerate resolution Imaging Spectroradiometer)
PHYS Clouds, spring ‘04, lect.4, Platnick

17. Water Droplet Growth - microphysics approx.
Ship Tracks - example of increase in CCN modifying cloud microphysics
• Cloud reflectance proportional to total cloud droplet cross-sectional area per unit area (in VIS/NIR part of solar spectrum) or the cloud optical thickness:
So what happens when CCN increase?
• Constraint: Assume LWC(z) of cloud remains the same as CCN increases (i.e., no coalescence/precipitation). Then an increase in N implies droplet sizes must be reduced => larger droplet cross-sectional area and R increases. Cloud is more reflective in satellite imagery!
PHYS Clouds, spring ‘04, lect.4, Platnick

18. Water Droplet Growth - Collisions
Droplets collide and coalesce (accrete, merge, coagulate) with other droplets. Collisions require different fall velocities between small and large droplets (ignoring turbulence and other non-gravitational forcing).
Diffusional growth gives narrow size distribution. Turns out that it’s a highly non-linear process, only need 1 in 105 drops with r ~ 20 µm to get process rolling.
How to get size differences? One possibility - mixing.
Homogeneous Mixing: time scale of drop evaporation/equilibrium much longer relative to mixing process. All drops quickly exposed to “entrained” dry air, and evaporate and reach a new equilibrium together Dilution broadens small droplet spectrum, but can’t create large droplets.
Inhomogeneous Mixing: time scale of drop evaporation/equilibrium much shorter than relative to turbulent mixing process. Small sub-volumes of cloud air have different levels of dilution Reduction of droplet sizes in some sub-volumes, little change in others.
Fig. from Bill Olsen
PHYS Clouds, spring ‘04, lect.4, Platnick

19. Water Droplet Growth - Collisions
Droplets collide and coalesce (accrete, merge, coagulate) with other droplets.
Collisions governed primarily by different fall velocities between small and large droplets (ignoring turbulence and other non-gravitational forcing).
Collisions enhanced as droplets grow and differential fall velocities increase.
Not necessarily a very efficient process (requires relatively long times for large precipitation size drops to form).
Rain drops are those large enough to fall out and survive trip to the ground without evaporating in lower/dryer layers of the atmosphere.
concept
Fig. from Bill Olsen
PHYS Clouds, spring ‘04, lect.4, Platnick

20. Water Droplet Growth - Collisional Growth
Continuum collection:
VT(R) R
VT(r)
(increases w/R,
vs. condensation where
dR/dt ~ 1/R)
PHYS Clouds, spring ‘04, lect.4, Platnick
PHYS Clouds, spring ‘04, lect.4, Platnick

21. Water Droplet Growth - Collisional Growth
Integrating over size distribution of small droplets, r, and keeping R+r terms :
PHYS Clouds, spring ‘04, lect.4, Platnick
PHYS Clouds, spring ‘04, lect.4, Platnick

22. Water Droplet Growth - Collisional Growth
FYI
Accounting for collection efficiency, E(R,r):
If small droplet too small or too far center of collector drop, then capture won’t occur.
• E is small for very small r/R, independent of R.
• E increases with r/R up to r/R ~ 0.6
• For r/R > 0.6, difference is drop terminal velocities is very small.
–drop interaction takes a long time, flow fields interact strongly and
droplet can be deflected.
–droplet falling behind collector drop can get drawn into the wake
of the collector; “wake capture” can lead to E > 1 for r/R ≈ 1.
PHYS Clouds, spring ‘04, lect.4, Platnick
PHYS Clouds, spring ‘04, lect.4, Platnick