Two fundamental phenomena that warm cloud microphysics theory must explain:• Formation of cloud

droplets from supersaturated vapor

• Growth of cloud droplets to raindrops in O(10 min)

Growth of warm cloud droplets

• Activated cloud droplets grow by condensation then collection

• Condensational growth leads to nearly monodispersed distribution of small drops

• Growth of condensationally grown droplets to raindrop size achieved by collision & coalescence (collection)

Growth by condensation

• Consider vapor flux from environment with supersaturation S onto droplet of size r

• Given environmental vapor density ρ(∞) and vapor diffusion coefficient D:

• Ungraded exercise: derive! (p. 222)• Growth rate inversely proportional to r

drdt

SDv

rl

Growth by condensation (cont.)• Consider cloud droplets within rising parcel• Parcel adiabatically cools, supersaturates• CCN begin to activate• S maximized once excess vapor from adiabatic cooling

balanced by condensation onto CCN/droplets (typically within 100 m of cloud base)

• Activated droplets then grow at expense of haze particles• Smaller droplets grow faster than larger droplets, yielding

nearly monodispersed distribution of droplets that grow more slowly with time – insufficient to produce raindrops!

Collision-Coalescence: Collision Efficiency

• Those drops that end up larger than average will also fall faster than average, collecting smaller droplets in paths

• Collision efficiency E is fraction of droplets of size r2

in path of collector drop of size r1 that collide with latter:

E y2

r1 r2 2

y2

r1 r2 2

Collision Efficiency (cont.)• Collector drop much bigger

droplets closely follow streamlines around it y small E small

• For smaller collector drops, for r2/r1 ≈ 0.6-0.9, E decreases due to shrinking relative fall speed

• For r2/r1 nearly 1.0, E increases again due to strong drop-droplet interactions

Coalescence Efficiency E’• Not all colliding droplets coalesce!

• At low/high values of r2/r1, collector drop is only mildly deformed during collision (lower impact energy), minimizing air trapped between drop & droplet, thus maximizing likelihood of drop & droplet making contact

• Presence of electric field can increase E’

• Collection efficiency Ec = EE’

Continuous collection model

2

43

41

4

1 1 2 l c

31 l

1 2 l c1

l

1 2

1 l1

l

dM r v v w Edt

M r

v v w Edrdt

Assume v v , E'v w Edr

dt

Since E and v1 increase with r1, so does dr1/dt, allowing growth by collection to quickly dominate growth by condensation beyond a certain droplet size:

M – mass of collector drop

wl – liquid water content of droplets

ρl - liquid water density

Continuous collection model (cont.)

• Can derive equation for height of collector drops as function of radius given steady updraft speed w (eq. 6.30)

• This equation models general behavior of cloud droplets growing by collection

• v1 < w : drop carried upward by updraft

• v1 > w : drop falls through updraft, possible reaching ground as raindrop

• Derive! (ungraded exercise)

Two fundamental phenomena that warm cloud microphysics theory must explain:• Formation of cloud

droplets from supersaturated vapor

• Growth of cloud droplets to raindrops in O(10 min)

BUT…how to bridge the gap?

• Condensational growth leads to nearly monodispersed distribution of drops – collisions unlikely since fall speeds similar

• Plus, condensational growth slows well before ~20 μm radii required for substantial growth by collection

Possible mechanisms

• Giant CCN as embryos for collector drops• Turbulent enhancement of condensational growth

and collision efficiencies• Radiative broadening of DSD • Stochastic collection model – small fraction of

droplets will grow much faster than average

• Lots of interesting discussion in text (but you’ve already read it, right??)