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Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.
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Transcript of Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.
![Page 1: Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.](https://reader033.fdocuments.in/reader033/viewer/2022042702/56649cff5503460f949cffb1/html5/thumbnails/1.jpg)
Cloud Microphysics
Dr. Corey Potvin, CIMMS/NSSL
METR 5004 Lecture #1Oct 1, 2013
![Page 2: Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.](https://reader033.fdocuments.in/reader033/viewer/2022042702/56649cff5503460f949cffb1/html5/thumbnails/2.jpg)
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)
![Page 3: Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.](https://reader033.fdocuments.in/reader033/viewer/2022042702/56649cff5503460f949cffb1/html5/thumbnails/3.jpg)
Warm cloud microphysics
![Page 4: Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.](https://reader033.fdocuments.in/reader033/viewer/2022042702/56649cff5503460f949cffb1/html5/thumbnails/4.jpg)
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
![Page 5: Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.](https://reader033.fdocuments.in/reader033/viewer/2022042702/56649cff5503460f949cffb1/html5/thumbnails/5.jpg)
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
![Page 6: Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.](https://reader033.fdocuments.in/reader033/viewer/2022042702/56649cff5503460f949cffb1/html5/thumbnails/6.jpg)
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
![Page 7: Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.](https://reader033.fdocuments.in/reader033/viewer/2022042702/56649cff5503460f949cffb1/html5/thumbnails/7.jpg)
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
![Page 8: Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.](https://reader033.fdocuments.in/reader033/viewer/2022042702/56649cff5503460f949cffb1/html5/thumbnails/8.jpg)
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( ) =4πR2σ −
43πR3nkT ln
ees
Gibbs free energies – roughly, microscopic energy of system
Net change in system energy
Work to create unit area of droplet surface
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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
=8πσR−4πR2nkTlnees
![Page 10: Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.](https://reader033.fdocuments.in/reader033/viewer/2022042702/56649cff5503460f949cffb1/html5/thumbnails/10.jpg)
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
![Page 11: Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.](https://reader033.fdocuments.in/reader033/viewer/2022042702/56649cff5503460f949cffb1/html5/thumbnails/11.jpg)
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
![Page 12: Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.](https://reader033.fdocuments.in/reader033/viewer/2022042702/56649cff5503460f949cffb1/html5/thumbnails/12.jpg)
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 =
4
3πr3ρ' −m
⎛⎝⎜
⎞⎠⎟
/ Mw
![Page 13: Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.](https://reader033.fdocuments.in/reader033/viewer/2022042702/56649cff5503460f949cffb1/html5/thumbnails/13.jpg)
Computing f (cont.)
f =#molespurewater
total #molesinsolution=
43πr3ρ' −m
⎛⎝⎜
⎞⎠⎟
/ Mw
43πr3ρ' −m
⎛⎝⎜
⎞⎠⎟
/ Mw+ im/ Ms
= 1+imMw
Ms43πr3ρ' −m
⎛⎝⎜
⎞⎠⎟
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
−1
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Kohler curves• Combining curvature and solute effects, can model
equilibrium conditions for range of droplet sizes:
S ≡e'es
=e'e
ees
= f exp2σ '
n'kTr
⎛
⎝⎜
⎞
⎠⎟
(r*, S*) – activation radius, critical saturation ratio – spontaneous growth occurs for r > r*
Saturation ratio for solution droplet
Rogers & Yau
![Page 15: Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.](https://reader033.fdocuments.in/reader033/viewer/2022042702/56649cff5503460f949cffb1/html5/thumbnails/15.jpg)
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
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Kohler curves (cont.)
(r*, S*)Left of peak Right of peak
Equilibrium Stable Unstable
Dominant effect Solute Curvature
Droplet type Haze particles Activated CCN
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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”
![Page 18: Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013.](https://reader033.fdocuments.in/reader033/viewer/2022042702/56649cff5503460f949cffb1/html5/thumbnails/18.jpg)
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)