Cloud microphysics modeling: the state of the art

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 problem: parameterized microphysics in (under)resolved clouds parameterization2 problem: parameterized microphysics in parameterized clouds microphysics at its native scale Cloud microphysics across scales

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

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

16. T, qv

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

18. Vaillancourt et al. JAS 2001

19. Δr~1μm, Δt~10-8s Vaillancourt et al. JAS 2001

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%... Vaillancourt et al. JAS 2001

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

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… … by solving these equations. Take a parcel from the surface and move it up…

30. qv qc 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, cpT + gz + Lqv…

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. 1. 1. maritime a=100 cm-3 continental a=1000 cm-3 N = a Sb b=0.5 0. 0. 600. 600. 0. 0. 20. 20. 0. 0. 0. 500. 0. 500.

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

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

45. Growth of water droplets by gravitational collision-coalescence: Collision efficiency: Grazing trajectory 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.

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

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 mid – mass of the super-particle Mid – concentration of super-particles ΔV – volume of the gridbox Andrejczuk et al. 2008, 2010

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