1. Shallow Cumulus Growth, (an idealized view)
Bjorn Stevens accepted for JAS
“Non-precipating cumulus”
Extension from the dry PBL growth, but now…..
Adding Moisture
dry
cloudy

2. Temporal Evolution

3. Temporal Evolution
cloud top height
dry pbl growth
cloud base height

4. Cloud top height growth
evaporation
condensation
See B. Stevens for analysis explaining the t-scaling

5. Stabilisation of Cloud Base (1)
Mass flux
Growth through dry top-entrainment
Negative in the presense of subsidence
Mass leaking out of PBL through clouds

6. Stabilisation of Cloud Base height (2)
Neggers et al. Theoretical and Computational Fluid Dynamics 2006

7. Bjorn Stevens (accepted JAS)
cloud top height
Pbl-height

8. Shallow Moist Convection (3)
Stratocumulus: properties and parameterizations
Mass Flux Parameterizations for shallow cumulus
Combining Mass Flux and Eddy Diffusivity
Open Problems

9. Stratocumulus

10. The Place of Stratocumulus

11. Characteristics of nocturnal stratocumulus
Courtesy : Bjorn Stevens
DycomsII
Well mixed profiles for moist conserved variables.
Many parameters enter the problem.
Turbulence mainly driven from above (radiative cooling)

12. Mixed Layer Perspective Of Scu
Lilly 1968
Main problem:
How to find the entrainment velocity E
Forcing
Flux at the srf
Flux at the top

13. Entrainment Velocity Remember the dry PBL:
In Scu many more parameters enter into the energetics:
Surface moisture flux.
Surface sensible heat flux.
Condensation/evaporation processes.
Long-wave radiative cooling.
Temperature and humidity jumps at inversion.

14. No lack of entrainment parameterizations!
• Nicholls and Turton (1986)
• Lilly (2002)
• Stage and Businger (1981)
Lewellen and Lewellen (1998)
VanZanten et al. (1999)
• Lock (1998)
• Moeng (2000)
Roode 2007

15. Stratocumulus : Top-entrainment Observations vs Parameterizations
-10 -5 5 10 15 D q t
[g/kg]
D q l
[K]
buoyancy
reversal criterion
DYCOMS II RF01
FIRE I (EUROCS)
initial jumps for different
GCSS stratocumulus cases
ASTEX A209
ASTEX RF06 (EUCREM)
DYCOMS II RF02
Entrainment results (cm/s) of 4 GCSS Cases

16. Stratocumulus : Top-entrainment Observations vs Parameterizations
Entrainment results (cm/s) of 4 GCSS Cases

17. Entrainment rates for ASTEX by varying jumps at the top of Scu
(De Roode, Lenderink and Koehler, to be submitted)

18. Stratocumulus : Parameterizations
Computation of the flux
Representation of top entrainment
Explicit top-entrainment

19. Mechanisms of Breakup of Stratocumulus
Cloud-top entrainment instability
Randall 1980
Deardorf 1980

20. Due to: Buoyancy Reversal
Randall 1980, Deardorff 1980
Mix a fraction of the air 2 with a fraction of air 1
Dryer and warmer
What is the buoyancy of such a mixture?
Moist conserved variables mix linear:
But non-conserved variables, such as not!!
Mixtures can attain densities that are larger than those of its individual components!!!
Break-up

21. Due to: Buoyancy Reversal
Randall 1980, Deardorff 1980
Mix a fraction of the air 2 with a fraction of air 1
Dryer and warmer
What is the buoyancy of such a mixture?
Moist conserved variables mix linear:
But non-conserved variables, such as not!!
Mixtures can attain densities that are larger than those of its individual components!!!
No break-up

22. Cloud Top Entrainment Instability Criterium
If there exists any c for which there is negative buoyancy there will be Scu Breakup.
Does this happen in Nature?
Break-up is a more complex phenomenum!!

23. Courtesy: Steve Krueger University of Utah

24. Courtesy: Steve Krueger University of Utah

25. Decoupling of Scu Quasi-steady state:
Cloud top
Can we rewrite the problem into terms of buoyancy flux, i.e.
Cloud base

26. YES, we can!
unsaturated air
saturated air

27. YES, we can!
unsaturated air
saturated air
Decoupling if buoyancy flux near cloud base becomes sufficiently negatively.

28. Bretherton and Wyant, JAS 1997
Stevens GRL 2000
Bretherton and Wyant, JAS 1997

29. Turbulent mixing parametrizations
Computation of the flux in moist conserved variables
Representation of entrainment rate we
K-profile K = we Dz , we from parametrization
TKE model K(z) = TKE(z)1/2 l(z) , we implicit
Question
Does we from a TKE model compare well to we from parametrizations?

30. Conclusions (Stratocumulus)
Mixing in Scu should be done in moist conserved variables
Key problem is (still) the correct parameterization of the top-entrainment
Recent Field experiments (i.e. DYCOMS) do impose strong(er) constraints on top-entrainment and form critical tests for parameterizations LES data
For higher(vertical) resolution (dz~100m), TKE-schemes without explicit top-entrainment seem to be an acceptable alternative for parameterizations with explicit top-entrainment parameterizations.
OPEN PROBLEMS:
Break up of Scu, Transition to Shallow Cu
Diurnal cycle
Role of drizzle
Mesoscale structures

31. Mass Flux Parameterization for Shallow Cu:

32. What is the mass flux concept?
Estimating (co)variances through smart conditional sampling of joint pdf’s a a a wc

33. two box M/K decompositiona M
sub-core flux
env. flux
M-flux
Siebesma & Cuijpers, 1995
Courtesy : Martin Kohler (ECMWF)

34. Cumulus: Typically 80~90% repesented for moist conserved variables by mass flux appr.

35. Mass Flux Framework e d M
Active cloudy updrafts form a small fraction of the gridbox.
Top-hat approximation
Cloud ensemble is in steady state. M e d

36. How to estimate updraft fields and mass flux?
The old working horse:
Entraining plume model: M e d
Plus boundary conditions
at cloud base.

37. Implementation simple bulk model:
Updraft Calculation in conserved variables:
continue
Stop (= cloud top height)
B>0
3. Check on Buoyancy:
2. Reconstruct non-conserved variables:

38. What is simplest entraining plume based parameterization?
Simply use diagnosed typical values for e and d based on LES and observations and suitable boundary conditions at cloud base (closure)

39. Mass Flux d = e + 0.5 10-3 Diagnose d using M and e
Works “reasonably” well for shallow cumulus:
BOMEX: Siebesma et al JAS 2003
ARM: Brown et al QJRMS 2002
SCMS: Neggers et al QJRMS 2003
ATEX: Stevens et al JAS 2001
More general detrainment formulation; De Rooy and Siebesma: accepted for MWR

40. Schematic transport of a shallow cumulus cloud ensemble
Mass flux closure at cloud base!
Schematic transport of a shallow cumulus cloud ensemble
(Siebesma and Cuypers JAS 1995)

41. Shallow Cumulus: Cloudbase Mass Flux (Closure) Neggers et al 2004 MWR
Coupling of Mb to
sub-cloud layer
moisture
TKE
OR:
Grant 2001 QRMS
CAPE
Coupling of Mb to
cloud layer
Detailed comparisons of SCM with LES indicate that shallow cu is driven by the subcloud layer and that a TKE-type of closure is a superior closure.

42. Standard (schizophrenic) parameterization approach:
This unwanted situation has led to:
Double counting of processes
Problems with transitions between different regimes:
dry pbl  shallow cu
scu  shallow cu
shallow cu deep cu

43. Eddy-Diffusivity/Mass Flux approach : a way out?
Nonlocal (Skewed) transport through strong updrafts in clear and cloudy boundary layer by advective Mass Flux (MF) approach.
Remaining (Gaussian) transport done by an Eddy Diffusivity (ED) approach.
Advantages :
One updraft model for : dry convective BL, subcloud layer, cloud layer.
No trigger function for moist convection needed
No switching required between moist and dry convection needed
zinv

44. Cumulus clouds are the condensed, visible parts of updrafts
LeMone & Pennell (1976, MWR)
Cumulus clouds are the condensed, visible parts of updrafts
that are deeply rooted in the subcloud mixed layer (ML)

45. The (simplest) Mathematical Framework :
zinv

46. 2. Dry Convective Boundary Layer
Further reading: Siebesma, Soares and Teixeira (JAS 2007)

47. Steady State Updraft Equations
Entrainment
wu, qu
Entraining updraft parcel:
e: Fractional entrainment rate:
Vertical velocity eq. of updraft parcel:
Initialisation of updraft eq.:
Updraft transport
K diffusion
aup aK
mixed layer
advection
entrainment
buoyancy
pressure wu

48. Single Column Model tests for convective BL
Only Diffusion: ED
Diffusion + Mass Flux: ED-MF
Diffusion + Counter-Gradient: ED-CG
Solve
with implicit solver

49. Comparison with other approaches
EDMF ED ED
EDMF
ED-CG
ED-CG
PBL height growth
Mean profile after 10 hrs
ED : Unstable Profiles : Too aggressive top-entrainment : too fast pbl -growth
Counter-gradient: Hardly any top-entrainment : too slow pbl-growth Howcome??

50. Remark: mass flux contribution is changing sign in inversion
Breakdown of the flux into an eddy diffusivity and a mass flux contribution
Remark: mass flux contribution is changing sign in inversion

51. Breakdown of the flux into an eddy diffusivity and a countergradient contribution
LES
total
No entrainment flux since the countergradient (CG) term is balancing the ED-term!! CG ED

52. Conclusions ED MF provides good frame work for turbulent mixing:
Correct internal structure
Little sensitivity to initiation height
Correct ventilation (top-entrainment) for free atmosphere
Opens the way to couple to the cumulus topped BL
Countergradient approach
Correct internal structure but…..
Underestimation of ventilation to free atmosphere
Cannot be extended to cloudy boundary layer

53. (Plus other modifications)
Cumulus Topped Boundary Layer
Further reading: Soares, Siebesma and Teixeira QJRMS 2004
Neggers, Koehler nd Beljaars (ECMWF report)
Figure courtesy of Martin Koehler
Moist updraft
Dry updraft
(Plus other modifications)
K diffusion
Flexible moist area fraction
Top 10 % of updrafts that is explicitly modelled

54. more SW radiative cloud forcing in StCu/transition areas,
Implementation in IFS
more SW radiative cloud forcing in StCu/transition areas,
less in Tradewind cumulus areas
Old
Observed
New

55. SW cloud forcing Reduced biases Obs - Model Old New
Neggers, R. A. J., M. Köhler
and A. C. M. Beljaars, 2007:
A dual mass flux scheme for boundary layer convection.
Part I: Transport; ECMWF-ARM report:

56. Stratocumulus -> shallow cumulus transition “bridges” better pronounced
Old
Observed
New

57. A slow, but rewarding Working Strategy Versions of Climate Models
See
Large Eddy Simulation (LES) Models
Cloud Resolving Models (CRM)
Single Column Model
Versions of Climate Models
3d-Climate Models
NWP’s
Global observational
Data sets
Observations from
Field Campaigns
Development
Testing
Evaluation

58. Conceptually on process basis
But… Many open problems remain
Conceptually on process basis
Convective Momentum Transport
Influence of Aerosols/Precipitation on the (thermo)dynamics of Scu and Cu
Mesoscale structures in Scu and Shallow Cu
Transition from shallow to deep convection (deep convective diurnal cycle in tropics)
Parameterization
Vertical velocity in convection.
Detrainment (especially for deep convection)
Convection on the 1km~10km scale. (stochastic convection)
Microphysicis (precip)
Transition regimes.
Climate
Determine and understand the processes that are responsable for the uncertainty in cloud-climate feedback.