1. Cloud Microphysics Dr. Corey Potvin, CIMMS/NSSL METR 5004 Lecture #1 Oct 1, 2013

2. 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! corey.potvin@ou.edu; office #4378 (once gov’t reopens)

3. Warm cloud microphysics

4. 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

5. 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 e s BUT can also refer to equilibrium e over cloud particle surface (e.g., e i, e’) Wikipedia

6. Saturation vapor pressure By default, supersaturation refers to e > e s, as when rising parcel cools (e s decreases) e > e s does NOT guarantee net condensation onto cloud particles – not surprising given artificiality of e s ! But, e s useful as reference point when describing (super-) saturation level of air relative to cloud droplet or ice particle Lyndon State College

7. 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

8. 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: Gibbs free energies – roughly, microscopic energy of system Net change in system energy Work to create unit area of droplet surface

9. Critical radius r Subsaturation (e 0  embryonic droplets generally evaporate (all sizes) Supersaturation (e > e s )  dΔE/dR 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

10. Kelvin’s equation & curvature effect Solve d(ΔE)/dR = 0 to relate r, e, e s : 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 > e s required for equilibrium since less energy needed for molecules to escape curved surface Smaller droplet  larger RH (= 100 × e/e s ) needed Critical radius for given ambient vapor pressure Vapor pressure required for droplet of radius r to be in unstable equilibrium

11. 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.

12. Computing f Vapor condenses on CCN of mass m, molecular mass M s, forming droplet of size r Each CCN molecule dissociates into i ions Solution density ρ’, water molecular mass M w Effective # moles of dissolved CCN = im/M s # moles pure water =

13. Computing f (cont.)

14. Kohler curves Combining curvature and solute effects, can model equilibrium conditions for range of droplet sizes: (r*, S*) – activation radius, critical saturation ratio – spontaneous growth occurs for r > r* Saturation ratio for solution droplet Rogers & Yau

15. 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.pdfwww.physics.nmt.edu/~raymond/classes/ph536/notes/microphys.pdf

16. Kohler curves (cont.) (r*, S*) Left of peakRight of peak EquilibriumStableUnstable Dominant effect SoluteCurvature Droplet typeHaze particlesActivated CCN

17. 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”

18. 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)