Two fundamental phenomena that warm cloud microphysics theory must explain:

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 supersaturationS 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 Eis fraction of droplets of size r2 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 ysmall Esmall • For smaller collector drops, for r2/r1 ≈ 0.6-0.9, Edecreases 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 v1increase 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??)