cloud microphysics
DESCRIPTION
Cloud Microphysics. Dr. Corey Potvin , CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013. Preliminaries. Primarily following Wallace & Hobbs Chap. 6 Rogers & Yau useful as parallel text (deeper explanations) Google is your friend! Will make these slides available - PowerPoint PPT PresentationTRANSCRIPT
Preliminaries• Primarily following Wallace & Hobbs Chap. 6
• Rogers & Yau useful as parallel text (deeper explanations)
• Google is your friend!
• Will make these slides available
• Figures from W & H unless otherwise noted
• Leaving out some important details – read book!
• [email protected]; office #4378 (once gov’t reopens)
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)
Lyndon State College
Saturation vapor pressure
• Increases with temperature T (Clausius-Clapeyron)
• By default, refers to vapor pressure e over planar water surface within sealed container at T at equilibrium (evaporation = condensation); denoted es
• BUT can also refer to equilibrium e over cloud particle surface (e.g., ei, e’)
Wikipedia
Saturation vapor pressure
• By default, supersaturation refers to e > es, as when rising parcel cools (es decreases)
• e > es does NOT guarantee net condensation onto cloud particles – not surprising given artificiality of es!
• But, es useful as reference point when describing (super-) saturation level of air relative to cloud droplet or ice particle Lyndon State College
Homogeneous nucleation
• Consider supersaturated air with no aerosols• Are chance collisions of vapor molecules likely
to produce droplets large enough to survive?– Consider change in energy of system ΔE due to
formation of droplet with radius R– Compute R for which ΔE ≤ 0 (lazy universe always
seeks equilibrium) – growth favored– Determine whether such R occur often enough
How big must embryonic droplets be for growth to be favored?
• Take droplet with volume V, surface area A, and n molecules per unit volume of liquid
• Consider surface energy of droplet and energy spent for condensation:
ΔE =Aσ −nV μv−μl( )=4π R2σ −
43π R3nkT ln
eeσ
Gibbs free energies – roughly, microscopic energy of system
Net change in system energy
Work to create unit area of droplet surface
Critical radius r
• Subsaturation (e < es) dΔE/dR > 0 embryonic droplets generally evaporate (all sizes)
• Supersaturation (e > es) dΔE/dR < 0 for r > R sufficiently large droplets tend to grow (energy loss from condensation > energy gain from droplet surface)
• R = r: droplet in unstable equilibrium with environment – small change in size will perpetuate
dΔEdR
=8πσ R −4π R2nkTlneeσ
Kelvin’s equation & curvature effect• Solve d(ΔE)/dR = 0 to relate r, e, es:
• In latter equation and hereafter, e = droplet saturation vapor pressure! Otherwise, net evaporation or condensation of droplet would occur (disequilibrium).
• “Kelvin” or “curvature” effect: e > es required for equilibrium since less energy needed for molecules to escape curved surface
• Smaller droplet larger RH (= 100 × e/es) needed
Critical radius for given ambient vapor pressure
Vapor pressure required for droplet of radius r to be in unstable equilibrium
Heterogeneous nucleation• Some aerosols dissolve when water condenses on them - cloud
condensation nuclei (CCN)
• Due to relatively low water vapor pressure of solute molecules in droplet surface, solution droplet saturation vapor pressure e’ < e
• Raoult’s law for ideal solution containing single solute: saturation vapor pressure of solution = saturation vapor pressure of pure solvent, reduced by mole fraction of solvent. Thus,
where f is mole faction of pure water. e' = fe
Computing f
• Vapor condenses on CCN of mass m, molecular mass Ms, forming droplet of size r
• Each CCN molecule dissociates into i ions• Solution density ρ’, water molecular mass Mw
• Effective # moles of dissolved CCN = im/Ms
• # moles pure water =
43πr3r'−μ
⎛⎝⎜
⎞⎠⎟ / Mw
Computing f (cont.)
f =#μoleσπurewater
total#μoleσinσolution=
43πr3r'−μ
⎛⎝⎜
⎞⎠⎟ / Mw
43πr3r'−μ
⎛⎝⎜
⎞⎠⎟ / Mw + iμ / Mσ
= 1+iμMw
Mσ43πr3r'−μ
⎛⎝⎜
⎞⎠⎟
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
−1
Kohler curves• Combining curvature and solute effects, can model
equilibrium conditions for range of droplet sizes:
S ≡
e'eσ=e'eeeσ= fexπ
2σ '
n'kTr
⎛⎝⎜
⎞⎠⎟
(r*, S*) – activation radius, critical saturation ratio – spontaneous growth occurs for r > r*
Saturation ratio for solution droplet
Rogers & Yau
Stable vs. unstable equilibrium• A: r increase RH >
equilibrium RH r increases further; similarly for r decrease (unstable equilibrium)
• B: r increase RH < equilibrium RH r decreases; similarly for r increase (stable equilibrium)
• C: as in A, but droplet activated (grows spontaneously, i.e., without further RH increases) Adapted from www.physics.nmt.edu/~raymond/classes/ph536/notes/microphys.pdf
Kohler curves (cont.)
(r*, S*)Left of peak Right of peak
Equilibrium Stable Unstable
Dominant effect Solute Curvature
Droplet type Haze particles Activated CCN
Kohler curves (cont.)• Slightly different
perspective – assume solution droplet inserted into air with ambient S
• Red curve – solution droplet grows indefinitely since droplet S < ambient S
• Green curve – droplet grows until stable equilibrium point “A”