1. Convective Parameterization
Jack Kain and Mike Baldwin
OAR/NSSL/CIMMS

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. Eta Grid Points

4. 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 and larger scale dynamics
Changes vertical stability
Redistributes and generates heat
Redistributes and removes moisture
Makes clouds, strongly affecting surface heating and atmospheric radiation

5. How Does the Feedback Occur in a Model?
At every grid point, predictive variables change at each time step as a function of a number of processes, including convection…

6. …when activated, a convective parameterization computes the changes in temperature and moisture (and possibly cloud water, momentum, etc.) that would occur at each vertical level if convection developed in the given grid-point environment
for example
where tc is a convective timescale, typically 30min to 1hr

7. How to Parameterize...
Relate unresolved effects (convection) to grid-scale properties using statistical or empirical techniques
What properties of convection do we need to predict?
convective triggering (yes/no)
convective intensity (how much rain?)
vertical distribution of heating
vertical distribution of drying

8. When, where, and how much...
Triggering (always requires positive area on a thermodynamic [e.g., Skew-T Log-P] diagram)
- Different approaches
1.) mass or moisture convergence exceeding a certain threshold at a grid point, or
2.) positive destabilization rate, or
3.) perturbed parcels can reach their level of free convection, or
4.) sufficient cloud layer moisture

9. When, where, and how much... Convective intensity (net heating)
proportional to mass or moisture convergence
sufficient to offset large-scale destabilization rate
sufficient to eliminate CAPE (constrained by available moisture)

10. When, where, and how much...
Vertical distribution of heating and drying
determined by nudging to empirical reference profiles
estimated using a simple 1-D cloud model to satisfy the constraints on intensity

11. Quasi-equilibrium schemes
Arakawa-Schubert for example
Large-scale destabilization rate ~ convective stabilization rate
Convective stabilization is achieved by an ensemble of cloud types

12. Convergence schemes Kuo-type schemes If: Then:
atmosphere is conditionally unstable
horizontal moisture (or maybe mass) convergence is positive
Then:
converged moisture is assumed to go up in deep convective clouds (rather than broadscale ascent)
convective heating is distributed vertically according to the distribution of T’-T where T’ is the moist adiabatic profile of most unstable air
moisture is all condensed out (or a specified fraction is condensed out)

13. Current EMC models use different approaches
RUC II: Grell scheme
Eta: Betts-Miller-Janjic (Kain-Fritsch used experimentally)
MRF/AVN: Grell-Pan scheme
Grell, Grell-Pan, and Kain-Fritsch schemes are Mass-Flux schemes*, meaning they use simple cloud models to simulate rearrangements of mass in a vertical column
Betts-Miller-Janjic adjusts to “mean post-convective profiles” based on observational studies

15. Grell and Grell-Pan Schemes
Initiation (on/off)
1.) Find highest qe air in column below ~400mb level…does CAPE exist? 2.) Evaluate CAP strength:
Does lifted parcel reach LFC (level of free convection) within 150 mb of its source level?
3.) Is large-scale destabilization rate > 0?
(i.e. is d(CAPE)/dt > 0?)
If yes to all 3, initiate convection...

16. Grell and Grell-Pan Schemes
Characteristics of convection
use simple models of an updraft and downdraft to simulate mass rearrangements by convection
make updraft and downdraft mass fluxes strong enough that their stabilizing effect approximately balances rate of large-scale destabilization:

17. Grell and Grell-Pan Schemes
Feeding back the effects of convection
Introduce tendency terms in the prognostic equations for temperature and moisture:
where a represents T or qv

18. Kain-Fritsch Scheme
Basic operating procedures are similar to Grell-type schemes except…
Convective inhibition evaluated in terms of negative area, not pressure depth
Large-scale destabilization not required, only CAPE
Updraft and downdraft formulations more sophisticated
Convective intensity based on instantaneous CAPE value rather than d(CAPE)/dt

19. Betts-Miller-Janjic Scheme
Checks for CAPE, cloud depth, using highest qe air in lowest 130mb above surface
makes a “first-guess” at a reference temperature profile based on a moist adiabat
makes a corresponding first guess reference profile for moisture based on an imposed sub-saturation (~relative humidity)
imposes enthalpy conservation

22. Enthalpy conservation
This usually requires an adjustment to the “first-guess” profiles (“sliding over” on a skew-T) of both T and q
Implications of this adjustment:
BMJ convection will be weak (or non-existent) when cloud column RH is low even if CAPE exists, increase with intensity as column moistens
Nudges grid-scale T, q to convectively adjusted profiles over a ~1h time scale

23. Kain-Fritsch convective initiation check
Beginning at the surface, mix in model layers overhead until a mixture mb deep is found. This compromises a potential updraft source layer. Find mean q, qv of this layer.
Lift a parcel with these characteristics to its LCL. At the LCL, compute a temperature perturbation, DTp based on grid point vertical velocity:
DTp = (wg - wc)1/3 + DTp(RH)
where wg is the grid point vertical velocity (cm/s),
wc is a correction factor wc=2*Z(LCL)/2km

24. Kain-Fritsch convective initiation check
For example:
wg - wc=1 cm/s -> DTp=1.0 K
wg - wc=10 cm/s -> DTp=2.5 K
In the Eta Model, an additional perturbation, DTp (RH) (magnitude ~0.5K) is given to account for low RH
So…In a typical convective environment with some larger-scale forcing,
DTp ~ K

25. Kain-Fritsch convective initiation check
Is (DTp(LCL) + DTp) > Tg????
If no, move up one model level and repeat process above
If yes, compute a vertical velocity perturbation, Wp, based on magnitude of DTp.
For DTp=1.5K, Wp ~ 4-5 m/s

26. Kain-Fritsch convective initiation check
Release a parcel at the LCL with T given by Tp(LCL) and vertical velocity Wp, begin solving “parcel buoyancy equation” at model levels overhead
Determine cloud top as highest model level where Wp > 0

27. Kain-Fritsch convective initiation check
Is Z(top) - Z(LCL) > 3km?
If yes, initiate deep convection from this source layer
If no, remember this layer as a possible source for shallow convection, move up to next potential source layer and repeat all above steps
If no potential source layer in the lowest 300mb can generate a convective cloud, move on to next grid point

28. Stabilizing mechanisms of Kain-Fritsch
Convective Updraft
removes high qe air from lower troposphere, transports it aloft
generates condensation

29. Stabilizing mechanisms of Kain-Fritsch
Convective Downdraft
draws mass from layer beginning at cloud base and extending up mb
deposits low qe air in sub-cloud layers
assumed to be saturated above cloud base, RH decreasing at ~10%/km below
continues until it either 1) reaches the surfaces or 2) becomes warmer than the environment
mass flux = updraft mass flux at cloud base

30. Stabilizing mechanisms of Kain-Fritsch
Return flow, i.e., “compensating subsidence”
compensates for any mass surplus or deficit created by updraft and downdraft
typically the updraft creates a mass surplus aloft and deficit below so that return flow is downward

31. Kain-Fritsch precipitation amounts
It depends…
Updraft generates condensation
Updraft dumps condensate into environment
Downdraft evaporates condensate at a rate that depends on
RH of downdraft source air
depth of downdraft
Any leftover condensate accumulates at the ground as precipitation

32. Consider some typical convective environments

33. Negative Precipitation

34. Shallow convection allowed

35. BMJ Heating/Drying profiles
heating K/hr
drying %RH/hr

36. Increase cloud layer RH by 20%

37. Deep convection allowed

38. Heating/Drying profiles

39. Kain-Fritsch Trigger Increase source layer Td by 1 K
some parcels break cap, initiate deep convection
updraft
path
updraft
source
layer
downdraft
path

40. Kain-Fritsch adjusted profile

41. Heating/Drying profiles

42. BMJ 1st guess profiles

43. After enthalply adjustment
Deep convection allowed
Strong cooling from mb
rainfall = cm/h

44. Heating/drying profiles

45. Increase cloud-layer RH by 5%
Rainfall = cm/h

46. Increase cloud-layer RH by 10%
Rainfall = cm/h

47. RH increased 10%

48. Convective Rainfall vs. Change in cloud-layer RH
Precip Amount
Change in cloud-layer RH

49. BMJ Oklahoma Tornadoes
Too dry for deep convection
can see shallow convection grow with time

50. BMJ Oklahoma Tornadoes
Still too dry
24h fcst valid 5 Oct 98

51. BMJ Oklahoma Tornadoes
Shallow convection cloud top now up to ~650mb

52. Shallow convection profile
Transports moisture upward