Water Droplet Growth byCondensation & 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

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Courtesy: Steve Platnick, NASA

Homogeneous Nucleation of Droplets;Kelvin’s Equation

Cloud Condensation Nuclei.

Growth of Drops by Condensation

Atmospheric Aerosols

Heterogeneous Nucleation of Droplets;Köhler Curves

Warm CloudsGrowth 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

b. if the particle terminal velocity is -6 ms-1, its fall speed is 2 m/s (up)

-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

PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

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).

Water Droplet Growth - Condensation

How to have difference size of droplet in water cloud?

Water Droplet Growth - Condensation

Evolution of droplet size spectra w/time (w/T∞ dependence for G understood):

PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

large droplets : r(t) ro2 2G senv t

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

With senv in % (note this is the value after nucleation, << smax):

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!

FYI

Water Droplet Growth - Condensation

Growth slows down with increasing droplet size:

PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

R&Y, p. 111

large droplets : dr

dt~

G senv r

Since large droplets grow slower, there is a narrowing of the size distribution with time.

FYI

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?

Reflectance r2 N z

• 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 622 - Clouds, spring ‘04, lect.4, Platnick

Reflectance LWC2

3 N1

3 z

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.

PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

• 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. 

Water Droplet Growth - Collisions

PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

• 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.

Water Droplet Growth - Collisions

concept

PHYS 622 - Clouds, spring ‘04, lect.4, PlatnickPHYS 622 - Clouds, spring ‘04, lect.4, Platnick

Water Droplet Growth - Collisional Growth

VT(R)

R

VT(r)

"capture"distance VT R VT r t

d(sweepout volume)

dt R r 2

VT R VT r R2 VT R

collected mass : dm

dt R2 VT R LWC

also : dm

dt

d

dt

4

3r3

l 4r2 dr

dtl

substitution :dR

dt

VT R LWC

4l

(increases w/R,

vs. condensation wheredR/dt ~ 1/R)

Continuum collection:

PHYS 622 - Clouds, spring ‘04, lect.4, PlatnickPHYS 622 - Clouds, spring ‘04, lect.4, Platnick

Water Droplet Growth - Collisional Growth

dR

dt

3l

R r

R

2

VT R VT r r3 n(r) dr

Integrating over size distribution of small droplets, r, and keeping R+r terms :

PHYS 622 - Clouds, spring ‘04, lect.4, PlatnickPHYS 622 - Clouds, spring ‘04, lect.4, Platnick

Water Droplet Growth - Collisional Growth

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.

dR

dt

3l

R r

R

2

VT R VT r E(R,r) r3 n(r) dr

FYI