1. 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)

2. 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)

3. 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

4. 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!

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

6. Collision Efficiency (cont.)
Collector drop much bigger  droplets closely follow streamlines around it  y small  E small
For smaller collector drops, for r2/r1 ≈ , E decreases due to shrinking relative fall speed
For r2/r1 nearly 1.0, E increases again due to strong drop-droplet interactions

7. 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’

8. Continuous collection model
M – mass of collector drop
wl – liquid water content of droplets
ρl - liquid water density
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:

9. 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)

10. 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)

11. 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

12. 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??)