1. Clouds and cloud microphysics Wojciech W. Grabowski National Center for Atmospheric Research, Boulder, Colorado, USA (on collaborative leave at CNRM, Toulouse, France)

2. Clouds and cloud microphysics cloud microphysics: branch of cloud physics concerned with processes governing formation and growth of cloud droplets and ice crystals in clouds, and formation of precipitation

3. PLAN: 1. Cloud dynamics and microphysics: a small cumulus. 2. Cloud-physics textbook glance at (warm) cloud microphysics: ♠ Why and how clouds form? ♠ Once formed, how cloud droplets grow into raindrops? 3. Growth of cloud droplets in adiabatic cores. or Why do atmospheric scientists (cloud physicists) and physicists/mathematicians need to interact?

4. Clouds form when the air reaches saturation (water saturation for warm clouds). This is typically because of the vertical motion within the atmosphere. small Cumulus humilis clouds only mark tops of boundary-layer eddies… deeper Cumulus (mediocris or congestus) clouds have life (dynamics) of their own…

5. cloud base (activation of cloud droplets) airflow interfacial instabilities calm (low- turbulence) environment turbulent cloud

7. (Austin et al. JAS 1985) droplet spectra vertical and along-track velocity liquid water content

8. (Austin et al. JAS 1985) droplet spectra vertical and along-track velocity liquid water content

10. Gerber et al. (AMS Cloud Physics Conference, Madison, July 2006; published in JMSJ 2008)

11. Turbulent entrainment is a fundamental feature of small convective clouds (and most of other clouds as well)…

12. Blyth et al. (JAS 1988)

13. Turbulent entrainment is a fundamental feature of small convective clouds (and most of other clouds as well)… Where are these structures coming from?

14. Cloud-environment interface instability Klaassen and Clark (JAS 1984) Grabowski (JAS 1989) Grabowski and Clark (JAS 1991, 1993a, 1993b)

15. Turbulent entrainment is a fundamental feature of small convective clouds (and most of other clouds as well)… …but its impact on the spectrum of cloud droplets is still poorly understood.

16. (Jensen et al. JAS 1985) observed, adiabatic fraction AF ≈ 1; σ R =1.3 μm observed, AF ≈ 0.8; σ R =1.8 μm observed, AF ≈ 0.8; σ R =1.3 μm calculated adiabatic spectrum; σ R =0.1 μm observed, AF ≈ 1; bimodal Observed cloud droplet spectra averaged over ~100m:

17. Brenguier and Chaumat JAS 2001 Cloud droplet spectra in near-adiabatic cores using Fast FSSP

18. Brenguier and Chaumat JAS 2001 Cloud droplet spectra in near-adiabatic cores using Fast FSSP Effect of small dilution Instrumental artifacts (coincidences), possibly some collisional growth

19. Glance of textbook cloud physics for warm (ice-free) clouds: - initial formation of cloud droplets (activation); - growth by diffusion of water vapor; - growth by collision-coalescence.

20. What determines the concentration of cloud droplets? To answer this, one needs to understand formation of cloud droplets, that is, the activation of cloud condensation nuclei (CCN). This typically happens near the cloud base, when the rising air parcel approaches saturation.

21. Surface tension (Kelvin) effect Solute (Raoult) effect Saturated water vapor pressure over an aqueous solution droplet with radius r Saturated water vapor pressure over plain water surface Saturation ratio: Koehler (1921) theory

22. m s =10 -17 g m s =10 -16 g m s =10 -15 g 0.11.10..01 Radius (micrometers) Saturation ratio S -1% 1%

23. environmental conditions stable unstable haze particlesactivated droplets

24. CCN, soluble salt particles, have different sizes. Large CCN are nucleated first, activation of smaller ones follow as the supersaturation builds up. Once sufficient number of CCN is activated, supersaturation levels off, and activation is completed. In general, concentration of activated droplets depends on the updraft speed at the activation region and characteristics of CCN (e.g., clean maritime versus polluted continental).

25. Activation of CCN: N - total concentration of activated droplets S – supersaturation (in %) N = a S b a, b – parameters characterizing CCN: a ~ 100 cm -3 – pristine (e.g., maritime) air a ~ 1,000 cm -3 – continental air 0 < b < 1 (typically, b=0.5)

26. Growth of a droplet by diffusion of water vapor (growth by condensation): Once droplets are larger than a few microns, Raoult and Kelvin effect can be neglected… Large droplets grow slower than small ones: if the conditions experienced by the population is the same, the spectrum of cloud droplets will narrow with time (i.e., the height above cloud base)…

27. Grazing trajectory Growth of water droplets by gravitational collision-coalescence: Note: droplet inertia is the key; without it, there will be no collisions… Collision efficiency:

28. Time scales for droplet growth by condensation and by collision-coalescence:

29. Time scale for droplet growth by condensation: For S=0.1%: τ d =10 3 sec for r=10μm; cloud droplet: several minutes τ d =10 5 sec for r=100μm; drizzle drop: hours

30. Time scale for droplet growth by collision-coalescence: Consider: Stokes droplets of mean size r and spectral width Δr (Δr<<r) E c – collision efficiency q c – total liquid water content (kg/m 3 ) Assuming Δr ~ 2 μm, E c ~ 1, q c ~ 3 g/m 3 gives τ c ~ 10 3 sec (tens of minutes) Look at the factors involved….

31. How to model these processes? ♠ Multi-phase approach: following individual droplets; often used in DNS studies, impractical for LES and larger-scales. ♠ Continuous-medium approach: represent condensed water through mixing ratios (total mass of particles per unit of mass of air)

35. Geometry for gravitational collisions

36. Bin model results (maritime conditions, w=5 m/s):

37. Application of the bin-resolving microphysics to the problem of turbulent mixing between cloudy and clear air: cloud chamber mixing versus DNS simulation (Andrejczuk et al. JAS 2006). 30 cm Such an approach can be used at very small scales (DNS with Δx = 2.5 mm)

38. PLAN: 1. Cloud dynamics and microphysics: a small cumulus. 2. Cloud-physics textbook glance at (warm) cloud microphysics: ♠ Why and how clouds form? ♠ Once formed, how cloud droplets grow into raindrops? 3. Growth of cloud droplets in adiabatic cores. or Why do atmospheric scientists (cloud physicists) and physicists/mathematicians need to interact?

39. Droplet inertial response time: τ p = 2ρ w r 2 /9μ ρ w – water density (~10 3 kg m -3 ) μ – air dynamic viscosity (~1.5∙10 -5 kg m -1 s -1 )

40. Parameters describing interaction of cloud droplets with turbulence for the case of no gravity: Stokes number: St = τ p / τ η τ p - droplet response time τ η – Kolmogorov timescale

41. initial conditions solution at a later time Kolmogorov scale Clustering of nonsedimenting particles for St ~ 1 Shaw et al (JAS 1998)

42. initial conditions solution at a later time Kolmogorov scale Clustering of nonsedimenting particles for St ~ 1 Is this how cloud microscale looks like? Shaw et al (JAS 1998)

43. Fast FSSP observations (near-adiabatic samples): remarkable agreement with Poisson (random) statistics: Chaumat and Brenguier (JAS 2001)

44. Parameters describing interaction of cloud droplets with turbulence for the case with gravity: Stokes number: St = τ p / τ η τ p - droplet response time τ η – Kolmogorov timescale Nondimensional sedimentation velocity: Sv = v p / v η v p - droplet sedimentation velocity (gτ p for small droplets) v η – Kolmogorov velocity scale

45. Vaillancourt et al. JAS 2002 DNS simulations with sedimenting droplets for conditions relevant to cloud physics (ε=160 cm 2 s -3 ) Vorticity (contour 15 s -1 ) r=15 micron r=20 micron r=10 micron

46. Vaillancourt and Yau (BAMS 2000) Parameter space for cloud physics is different from the one traditionally looked at in DNS and laboratory experiments with particle- laden flows…

47. The small differences from randomness have a small effect on droplet growth by diffusion of water vapor in adiabatic cores because droplets rearrange themselves rapidly… Vaillancourt et al. (JAS 2002) Lanotte et al. (JAS, in press): increasing Reynolds number does not help much… DNS: = 13 μmpseudo-LES: = 5 μm

48. Concluding comments: Cloud-turbulence problem spans a wide range of spatial scales. For a small cumulus, this range is from a few hundred meters down to 1 mm (a typical mean distance between cloud droplets and, coincidentally, the typical Kolmogorov microscale for cloud turbulence). This is 5 to 6 decades. Since such a range will unlikely be resolved in DNS, multiscale approaches and theory should help us to understand the interactions between turbulence and cloud particles. This is why cloud physicist have to talk to theoretical physicists and mathematicians. Laboratory, theoretical, and modeling studies across the fluid mechanics community have big impact on physicists and mathematicians. Unfortunately, these studies are often irrelevant to cloud physics. This is why physicists and mathematicians need to talk to cloud physicists.

49. Concluding comments, cont: Small-scale turbulence and resulting small preferential concentration has insignificant effect on cloud droplet growth by diffusion of water vapor in homogeneous (on larger scales) regions. This is mostly because of the short decorrelation time of the supersaturation field due to fast rearrangement of droplet positions. But turbulence has most likely a significant impact on droplet collisions. Effects of entrainment and mixing is the key to understand droplet spectral evolution in clouds. This is a challenging problem because of the wide range of spatial and temporal scales, and difficulty in observations, laboratory, and modeling of these multiscale anisotropics processes. Yet effects of entrainmnet and mixing have far reaching consequences, for instance, for the mean albedo of the Earth.

50. Large-eddy turbulence and cloud-base activation: Clark and Hall (JAS 1979) droplet concentration width of the spectrum model setup

51. Brenguier and Grabowski (JAS 1993)