1. Phenomenology, Simulation and Parameterization of Atmospheric Convection
Pier Siebesma
Today: “Dry” Atmospheric Convection
Tomorrow: “Moist” Convection and Clouds

2. 1. Phenomenology

3. The Place of the Convective Boundary Layer

4. Evolution of the Convective Boundary Layer
Cabauw
Atmospheric
Profiling Station
(KNMI)

5. A View of the Convective Boundary Layer
Courtesy: Adriaan Schuitemaker

7. Encroachment

8. Encroachment

9. Encroachment

10. 2. Large Eddy Simulations

11. Large Eddy Simulation (LES) Model (Dx<100m)
High Resolution non-hydrostatic Model (Boussinesq or Anelastic) 10~50m
Large eddies explicitly resolved by NS-equations
inertial range partially resolved
Therefore: subgrid eddies can be realistically parametrised by using Kolmogorov theory
Used for parameterization development of turbulence, convection, clouds
Inertial Range
Resolution LES 5 3
ln(Energy)
DissipationRange
ln(wave number)

12. Dynamics of thermodynamical variables in LES

13. :average over the horizontal domain
Remark:
Richardson law!!

16. LES example: Classic Dry Convection PBL Case
Nx=Ny=128, Nz=150
Lx=Ly=6.4km, Lz=3km
Dx=Dy=50m, Dz=20m
Lapse Rate: G= K m-1
Prescribed Surface Heat Flux : Qs = K ms-1
Siebesma et al JAS 2007

17. Potential Temperature: q
Vertical velocity: w
Courtesy: Chiel van Heerwaarden

18. Quasi-Stationarity <-> Linear Fluxes
Non-dimensionalise:

19. Internal Structure of PBL
Rescale profiles

20. Growth of the PBL
PBL height : Height where potential temperature has the largest gradient

21. Mixed Layer Model of PBL growth
Assume well-mixed profiles of q.
Use simple top-entrainment assumption. q
Boundary layer height grows as:
Encroachment:

22. Courtesy: Harm Jonker

23. Courtesy : Harm Jonker

24. Courtesy : Harm Jonker

25. 3. Parameterized dry convection in Climate Models

26. Horizontal Kinetic Energy
Energy Spectra in the atmosphere (1)
Classic Picture (Frisch 86)
Horizontal Kinetic Energy
1km
2d-turbulence E
3d-turbulence E
Notation:
10000 km
10km
1 mm

27. Spectral Gap

28. Spectral Gap? k-3 k-5/3 5000 km cyclones 500 km 2 km
GASP aircraft data near tropopause
Nastrom and Gage (1985)

29. Grid Averaged Equations of thermodynamic variables
Large scale
advection
Large scale
subsidence
turbulent transport
Net Condensation Rate
DX=DY~100km , DZ~100m

30. Mixed Layer Models?
Mixed Layer models useful for understanding, but…..
Not easily implementable in large scale models
No information on the internal structure
Only applicable under convective conditions
No transition possibe to other regimes (neutral, sheardriven, stable)

31. Classic Parameterization of Turbulent Transport in de CBL
Eddy-diffusivity models, i.e.
Natural Extension of Surface Layer Similarity theory
Diffusion tends to make profiles well mixed
Extension of mixing-length theory for shear-driven turbulence (Prandtl 1932)

32. K-profile: The simplest Practical Eddy Diffusivity Approach (1)
The eddy diffusivity K should forfill three constraints:
K-profile should match surface layer similarity near zero
K-profile should go to zero near the inversion
Maximum value of K should be around:
z/zinv 1
0.1
K w* /zinv
Optional: Prescribe K at the top of the boundary layer as to get the right entrainment rate.
(Operational in ECMWF model)

33. “flux against the gradient”
A critique on the K-profile method (or an any eddy diffusivity method) (1)
Diagnose the K that we would need from LES:
K>0
Forbidden area
“flux against the gradient”
K<0
K>0
Down-gradient diffusion cannot account for upward transport in the upper part of the PBL

34. Physical Reason!
In the convective BL undiluted parcels can rise from the surface layer all the way to the inversion.
Convection is an inherent non-local process.
The local gradientof the profile in the upper half of the convective BL is irrelevant to this process.
Theories based on the local gradient (K-diffusion) fail for the Convective BL.

35. “Standard “ remedy Add the socalled countergradient term:
Long History:
Ertel
Priestley
Deardorff ,1972
Holtslag and Moeng
Holtslag and Boville
B. Stevens
And many more…………….
zinv

36. Single Column Model tests for convective BL
Only Diffusion: ED
Diffusion + Counter-Gradient: ED-CG
and solve
(Analytical quasi-stationary solutions: B. Stevens MWR 2003)
Lapse Rate: G= K m-1
Prescribed Surface Heat Flux : Qs = K ms-1
Dz =20m
Siebesma et al JAS 2007

37. ED-CG ED
LES ED
Mean profile after 10 hrs

38. Breakdown of the flux into an eddy diffusivity and a countergradient contribution
No entrainment flux since the countergradient (CG) term is balancing the ED-term.
LES
ED-CG CG ED
Countergradient approach
Correct internal structure but…..
Underestimation of ventilation to free atmosphere
Cannot be extended to cloudy boundary layer
total