Two fundamental phenomena that warm cloud microphysics theory must explain:
description
Transcript of Two fundamental phenomena that warm cloud microphysics theory must explain:
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??)