1. Cloud microphysics modeling: the state of the art Wojciech W. Grabowski Mesoscale and Microscale Meteorology Laboratory NCAR, Boulder, Colorado, USA

2. An introduction to cloud microphysics modeling Wojciech W. Grabowski Mesoscale and Microscale Meteorology Laboratory NCAR, Boulder, Colorado, USA

4. parameterization 2 problem: parameterized microphysics in parameterized clouds parameterization problem: parameterized microphysics in (under)resolved clouds microphysics at its native scale Cloud microphysics across scales

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

6. Bjorn Stevens, RICO

8. Eulerian versus Lagrangian methodology (continuous medium versus particle-based) Explicit treatment of aerosol effects versus mimicking impacts of aerosols Warm (no-ice) versus ice-bearing clouds Precise and complex versus approximate and easy to apply Understanding the physics versus numerical implementation

9. Eulerian versus Lagrangian methodology (continuous medium versus particle-based) Explicit treatment of aerosol effects versus mimicking impacts of aerosols Warm (no-ice) versus ice-bearing clouds Precise and complex versus approximate and easy to apply Understanding the physics versus numerical implementation

10. Explicit treatment of aerosol effects (particle-based) versus mimicking impacts of aerosols (continuous medium)

11. Eulerian versus Lagrangian methodology (continuous medium versus particle-based) Explicit treatment of aerosol effects versus mimicking impacts of aerosols Warm (no-ice) versus ice-bearing clouds Precise and complex versus approximate and easy to apply Understanding the physics versus numerical implementation

12. Water vapor is a minor constituent: mass loading is typically smaller than 1%; thermodynamic properties (e.g., specific heats etc.) only slightly modified; Suspended small particles (cloud droplets, cloud ice): mass loading is typically smaller than a few tenths of 1%, particles are much smaller than the smallest scale of the flow; multiphase approach is not required, but sometimes used with simplifications (e.g., DNS with suspended droplets, Lagrangian Cloud Model); Precipitation (raindrops, snowflakes, graupel, hail): mass loading can reach a few %, particles are larger than the smallest scale the flow; simplified multiphase approach needed only for very-small-scale modeling.

13. Eulerian versus Lagrangian methodology (continuous medium versus particle-based) Explicit treatment of aerosol effects versus mimicking impacts of aerosols Warm (no-ice) versus ice-bearing clouds Precise and complex versus approximate and easy to apply Understanding the physics versus numerical implementation

14. Droplet size exaggerated compared to the mean distance!

15. water vapor temperature gradients of the temperature and water vapor near the droplet (established on a time scale of ~millisecond) go to ~10 droplet radii…

16. T, q v

17. Vaillancourt et al. JAS 2001 M for macroscopic…

18. Vaillancourt et al. JAS 2001

19. Δr~1μm, Δt~10 -8 s

20. Vaillancourt et al. JAS 2001

21. …perhaps expected considering that the volume affected by the gradients is small compared to the entire volume, about 0.1%...

22. Lagrangian: Eulerian: compressible anelastic Ψ(x,y,z,t) Ψ(x+uΔt, y+vΔt, z+wΔt, t+Δt) Ψ(x, y, z, t+Δt) Lagrangian versus Eulerian governing equations

23. EULERIAN MODELING OF THE CONDENSED PHASE

24. Continuous medium approach: apply density as the main field variable (density of water vapor, density of cloud water, density of rainwater, etc…) In practice, mixing ratios are typically used. Mixing ratio is the ratio between the density (of water vapor, cloud water…) and the dry air density.

25. Mixing ratio versus specific humidity…

26. And we also need equation for the temperature. If only phase changes are included, then potential temperature equation is:

27. Modeling of cloud microphysics: solving a system of PDEs (advection/diffusion type) coupled through source terms…

29. A very simple (but useful) model: rising adiabatic parcel… Take a parcel from the surface and move it up… … by solving these equations.

30. qvqcqvqc Look not only on the patterns (i.e., processes), but also on specific numbers (e.g., temperature change, mixing ratios, etc).

31. Invariant variables: total water, liquid water potential temperature, equivalent potential temperature. Note: equivalent potential temperature is closely related to moist static energy, c p T + gz + Lq v …

32. Adding rain or drizzle:

33. 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.

37. Computational example: Nucleation and growth of cloud droplets in a parcel of air rising with vertical velocity of 1 m/s; 60 bins used; 1D flux-form advection applied in the radius space; Difference between continental/polluted and maritime/pristine aerosols f=f(r,z) or f=f(r,t)

38. maritime a=100 cm -3 continental a=1000 cm -3 N = a S b b=0.5 0. 0.0. 1.1. 1.1. 0.0. 600. 20. 0.500. 0.

39. maritime continental 0. 150. 0. 2. 500. 0.

40. maritime continental 0. 150. 0. 2. !

45. Grazing trajectory Growth of water droplets by gravitational collision-coalescence: Droplet inertia is the key; without it, there will be no collisions. This is why collision efficiency for droplets smaller than 10 μm is very small. Collision efficiency:

46. - cloud water: q c, N c drizzle/rain water: q r, N r Nucleation of cloud droplets: link to CCN characteristics Drizzle/rain development: link to mean droplet size e.g., Morrison and Grabowski JAS 2007, 2008 Double-moment warm-rain microphysics: a compromise between bulk and bin microphysics

47. LAGRANGIAN MODELING OF THE CONDENSED PHASE

48. Lagrangian treatment of the condensed phase:

49. Eulerian dynamics, energy and water vapor transport: Lagrangian physics of “super-particles” a single “super-particle” represents a number of the same airborne particles (aerosol, droplet, ice crystal, etc.) with given attributes Coupling m id – mass of the super-particle M id – concentration of super- particles ΔV – volume of the gridbox Andrejczuk et al. 2008, 2010

50. Andrejczuk et al. 2010 CCN of 190 cm -3 CCN of 1295 cm -3 9 hr 3 hr

51. Andrejczuk et al. 2010 CCN of 190 cm -3 CCN of 1295 cm -3 9 hr 3 hr

52. Summary: A wide range of modeling approaches exists that one can use in modeling various aspects of cloud microphysics. Most of them are within the framework of Eulerian modeling, but use of Lagrangian microphysics is rapidly expanding. The approach selected needs to be tailored to the specific problem at hand. If multiscale dynamics (e.g., convectively coupled waves in the tropics) is the focus, application of as simple microphysics as possible makes sense to use computer time to widen the range of spatial scales. If small-scale dynamics-microphysics interaction is the focus (e.g., entrainment), more emphasis on microphysics is needed. The multiscale nature of clouds (the range of spatial scales), difficulties of cloud observations (in-situ and remote sensing), and increasing appreciation of the role of clouds in weather and climate make the cloud physics an appealing area of research.