1. Convective Parameterization in NWP Models
Jack Kain
And
Mike Baldwin

2. What is convective parameterization?
A technique used in NWP to predict the collective effects of (many) convective clouds that may exist within a single grid element…As a function of larger-scale processes and/or conditions.

3. Why do NWP models need to worry about it?
Direct Concern: To Predict convective precipitation
Feedback to larger Scales: Deep convection “overturns” the atmosphere, strongly affecting mesoscale dynamics
- Changes vertical stability
- generates and redistributes heat
- removes and redistributes moisture
- makes clouds, strongly affecting surface heating and atmospheric radiation

4. A convective parameterization must decide 3 things:
Activation?  Trigger function
Intensity?  Closure Assumptions
Vertical Distribution?  Cloud model or specified profile

5.  Trigger Functions Moist. Conv. Sub-cloud Mass conv. Cloud-layer
CAPE
Cloud
Depth C I N
Moist.
Conv.
Sub-cloud
Mass conv.
Cloud-layer
Moisture
∂(CAPE)/∂t
BMJ
(Eta) 
Grell
(RUC, AVN) KF
(Research)
Bougeault
(Meteo FR)
Tiedtke
(ECMWF)
Bechtold
Emanuel

6. Closure Assumptions (Intensity)
CAPE
Cloud-layer
moisture
Moisture
Converg.
∂(CAPE)/∂t
Subcloud
Quasi-equil.
BMJ
(Eta) 
Grell
(RUC, AVN) KF
(Research)
Bougeault
(Meteo FR)
Tiedtke
(ECMWF)
Bechtold
Emanuel

7. Vertical Distribution of Heat, Moisture Entraining/Detraining
Entraining/Detraining
Plume
Convective
Adjustment
Buoyancy Sorting
Cloud Model
BMJ
(Eta) 
Grell
(RUC, AVN) KF
(Research)
Bougeault
(Meteo FR)
Tiedtke
(ECMWF)
Bechtold
Emanuel

8. How is the parameterized information fed back to the model?
Consider the Temperature-Tendency Equation in a model:
Where the convective term is simply

9. Consider two very different approaches:
BMJ Scheme (convective adjustment)
KF scheme (mass flux scheme)

10. Procedure followed by BMJ scheme…
1) Find the most unstable air in lowest ~ 200 mb
2) Draw a moist adiabat for this air
3) Compute a first-guess temperature-adjustment profile (Tref)
4) Compute a first-guess dewpoint-adjustment profile (qref)

11. The Next Step is an Enthalpy Adjustment
First Law of Thermodynamics:
With Parameterized Convection, each grid-point column is treated in isolation. Total column latent heating must be directly proportional to total column drying, or dH = 0.

12. Enthalpy is not conserved for first-guess profiles for this sounding!
Must shift Tref and qvref to the left…

13. Imposing Enthalpy Adjustment:

14. Adjusted Enthalpy Profiles:

15. Suppose the cloud layer was drier…reduce RH by 15%:

16. Enthalpy is conserved, but the net temperature change is negative, and the net moisture change is positive: Negative Precipitation!

17. If we systematically change cloud-layer RH in this sounding, it can be shown that precipitation rate generated by the scheme is very sensitive to deep-layer moisture:

18. If the environment is too dry or CAPE layer is less than ~ 200 mb deep, the scheme attempts to initiate shallow (non-precipitating) convection
1) Set cloud-top height as the level within 200 mb of LCL where RH falls off most rapidly with height.
2) Find LCL of cloud-top air; line connecting LCLs of subcloud and cloud-top air is a “mixing line”.
3) Assume Tref has same slope as mixing line; first-guess Tref is anchored on ambient temperature curve.

19. With Shallow Convection, there is no net temperature or moisture change:
and

20. Consider the impact of parameterized BMJ shallow convection in a “normal” diurnal cycle…
Model Initial Condition
Raob
BMX 12 Z 11 May 2000

21. Convective Adjustment Profiles…
Initial time
1 h forecast

22. Convective Adjustment Profiles…
6 h forecast: BMJ convection inactive because “convective entropy change” would be negative. Sounding characteristics that lead to negative entropy change are not easily identified.
3 h forecast

23. Other constraints that cause BMJ shallow convection to “abort”:
- Net entropy change in cloud layer would be negative
- Tref is super-adiabatic
- Tref is isothermal
- qref gives a negative q at some level
- qref gives an increase in q with height
- qref gives super-saturated q at some level

24. Back to the convective adjustment profiles…
9 h forecast – 2100 UTC

25. Compare with raob at 00 Z: 12 h forecast
Model forecast
Raob
BMX 00Z 12 May 2000

26. Consider a transition from shallow to deep convection…
FWD 00Z 20 April 2001
Model Initial Condition
Raob

27. Convective Adjustment Profiles…
1h Forecast

28. Compare with raob at 12 Z: 12 h forecast
Model forecast
Raob
FWD 12Z 20 April 2001

29. More Convective Adjustment Profiles…
16 h forecast
17 h forecast

30. Continuing to work on the sounding…
18 h forecast
21 h forecast

31. Compare with raob at 00 Z: 24 h forecast
Model Forecast
FWD 12Z 20 April 2001

32. BMJ Deep convection activated only briefly at FWD, but 100 miles to the north (ADM), BMJ deep convection was more persistent and strongly modified soundings:
EtaKF Model Forecast
Model Forecast
ADM 22 Z 20 April 2001

33. OK, consider the KF scheme, a “Mass-flux” parameterization

34. Basic procedures…
1) Starting at the surface, mix ~ 50 mb deep layers, lift to LCL
2) Give parcel a boost based on low-level convergence. Can it reach the LFC?
3) If parcel makes it to LFC, allow it to rise and overshoot equilibrium level.
4) Form downdraft from air within ~ 200 mb of cloud base
5) Overturn mass in updraft, downdraft, and surrounding environment until stabilization is achieved.
If cloud depth  3 km, parameterize shallow convection
Updraft Source Layer

35. KF adjustment profiles

36. Focus on deep convection…what is the Updraft Mass Flux (UMF*)?
The mass of air that goes through cloud base divided by the initial mass in the ~ 50 mb updraft source layer:
UMF* = Mu/Musl

37. How is UMF determined?

40. What is UMF* sensitive to?
qe of downdraft air
Lapse rates in cloud layer

41. Increasing humidity in the 900 – 550 mb layer increases downdraft qe
Increasing humidity in the 900 – 550 mb layer increases downdraft qe. This makes stabilization of the boundary layer less efficient and UMF* increases.

44. Summary
Parameterized shallow convection can distort sounding structures, significantly affecting CIN and CAPE; more problematic with BMJ than with KF
BMJ deep convection very sensitive to cloud-layer RH
KF mass flux particularly sensitive to lapse rates in lower half of cloud layer.