Cloud Microphysics

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 eover planar water surface within sealed container at T at equilibrium (evaporation = condensation); denoted es • BUT can also refer to equilibrium eover cloud particle surface (e.g., ei, e’) Wikipedia

6. Saturation vapor pressure • By default, supersaturation refers to e >es, as when rising parcel cools (esdecreases) • e >es does NOT guarantee net condensation onto cloud particles – not surprising given artificiality of es! • But, esuseful 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 nmolecules per unit volume of liquid • Consider surface energy of droplet and energy spent for condensation: Work to create unit area of droplet surface Net change in system energy Gibbs free energies – roughly, microscopic energy of system

9. 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

10. 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 > esrequired 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 rto 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 pressuree’ < 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 fis mole faction of pure water.

12. Computing f • Vapor condenses on CCN of mass m, molecular mass Ms, forming droplet of size r • Each CCN molecule dissociates into iions • Solution density ρ’, water molecular mass Mw • Effective # moles of dissolved CCN = im/Ms • # moles pure water =

13. Computing f(cont.)

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

15. Stable vs. unstable equilibrium • A: rincrease  RH > equilibrium RH rincreases further; similarly for rdecrease (unstable equilibrium) • B: rincrease  RH < equilibrium RH rdecreases; similarly for rincrease (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

16. Kohler curves (cont.) (r*, S*)

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)