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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

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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
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
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
growth by condensation cont
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
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:
collision efficiency cont
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
coalescence efficiency e
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
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:

continuous collection model cont
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 explain1
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
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
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??)