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

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:

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 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:

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??)