Transcript Document

Water Droplet Growth by
Condensation & Collision
•
Condensational growth: diffusion of vapor to droplet
•
Collisional growth: collision and coalescence (accretion, coagulation)
between droplets
PHYS 622 - Clouds, spring ‘04, lect.4, Platnick
Cold 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 Cloud
Processes
Warm Clouds
Courtesy: Steve Platnick, NASA
Growth of Drops by Collisions.
Ice Nuclei and Ice Crystal in Clouds
Growth of Ice Particles in Clouds
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.
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
Q: what determines the droplets fall speed relative to the ground??
Droplet Fall Speeds and Droplet Growth
• Q: what determines
the droplets fall speed
relative to the
ground??
• A: droplet size and
updraft strength -->
•
Class Participation: given a growing cu with an updraft strength of 4 ms-1:
a. if the particle terminal velocity is -2 ms-1, its fall speed is
2 m/s (up)
b. if the particle terminal velocity is -6 ms-1, its fall speed is
-2 m/s (down)
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
Factors promoting growth by
collision/coalescence
• Different drop sizes
• thicker clouds
• stronger updrafts
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?
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
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
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 622 - Clouds, spring ‘04, lect.4, Platnick
Water Droplet Growth - Condensation
FYI
Evolution of droplet size spectra w/time (w/T∞ dependence for G understood):
large droplets: r(t) 
ro2  2G senv  t
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
0
6.0 x 10-9
0.60
10
9.0 x 10-9
0.90
20
12.3 x 10-9
12.3
*
T=10C, s=0.05% => for small r0:
r ~ 18 µm after 1 hour (3600 s)
r ~ 62 µm after 12 hours
From Twomey, p. 103.
Diffusional growth can’t
explain production of
precipitation sizes!
PHYS 622 - Clouds, spring ‘04, lect.4, Platnick
Water Droplet Growth - Condensation
FYI
Growth slows down with increasing droplet size:
large droplets :
G s 
dr
~ env
dt
r
Since large droplets grow slower, there is a narrowing of the size distribution
with time.
R&Y, p. 111
PHYS 622 - Clouds, spring ‘04, lect.4, Platnick
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:
Reflectance   r 2 N z
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!
Reflectance  LWC
2
3
N
1
3
z

PHYS 622 - Clouds, spring ‘04, lect.4, Platnick
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 nonlinear 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 subvolumes, little change in others.
PHYS 622 - Clouds, spring ‘04, lect.4, Platnick
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.
concept
• 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.
PHYS 622 - Clouds, spring ‘04, lect.4, Platnick
Water Droplet Growth - Collisional Growth
Continuum collection:
"capture"distance  VT R  VT rt
R
d(sweepoutvolume)
2
  R r VT R  VT r   R2 VT R
dt

dm
collected mass:
  R2 VT R LWC
dt
also :



VT(R)
VT(r)
dm
d 4 3 
2 dr

l
 r l  4r

dt
dt 3
dt
V R LWC
dR
substitution:
 T
dt
4 l
(increases w/R,
vs. condensation where
dR/dt ~ 1/R)
PHYS 622 - Clouds, spring ‘04, lect.4, Platnick
Water Droplet Growth - Collisional Growth
Integrating over size distribution of small droplets, r, and keeping R+r terms :
dR


dt
3l
R  r 2
  R  VT R VT r r 3 n(r) dr

PHYS 622 - Clouds, spring ‘04, lect.4, Platnick
Water Droplet Growth - Collisional Growth
FYI
Accounting for collection efficiency, E(R,r):
dR


dt
3l
R  r 2
  R  VT R VT r E(R,r) r 3 n(r) dr
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 622 - Clouds, spring ‘04, lect.4, Platnick