1. Convective Parameterization
24 October 2012

2. Thematic Outline of Basic Concepts
What is a convective parameterization?
What are the key tenets of convective parameterization?
How are these tenets manifest within selected popular convective parameterizations?
What impact(s) do differences between convective parameterizations have upon model forecasts?
What is a cloud-cover parameterization?

3. “An Overview of Convective Parameterization” – David Stensrud
Additional Reference
“An Overview of Convective Parameterization” – David Stensrud

4. What is Convective Parameterization?
A technique used to predict the effects of sub-grid scale convective clouds upon the model atmosphere in terms of known model variables.
Objective: to define moist convection…
In the right place…
…at the right time…
…with the correct evolution and intensity…
…and with the correct impact upon its environment!

5. General Formulation
Determine whether the model atmosphere at a given grid point supports moist convection.
If so, generate moist convection.
Note that this can occur even if sub-saturated on the grid scale; saturation may be seen between grid points.
Subsequently, mimic the impacts of the moist convection upon its environment.

6. Importance of Moist Convection
Vertical redistribution of heat and moisture.
Produces precipitation, beneficial or devastating in nature.
Associated cloud cover impacts the radiation budget.
Spatial gradients in convective heating impact the Hadley and Walker circulations, monsoons, and ENSO.
Organized convective systems are often associated with high-impact weather and can substantially impact larger-scales.

7. Simplified Perspective
Control on moist convection; feedback to large scale.
In reality, however, smaller-scale processes are also important in triggering moist convection!

8. Types of Moist Convection
Deep, moist convection
Examples: thunderstorms, stratiform precipitation
Large vertical extent
Associated with large-scale low-level convergence and deep conditional instability
Precipitation dries the environment through the removal of water vapor
Precipitation warms the environment through compensating subsidence warming
(Stensrud)

9. Types of Moist Convection
2. Shallow convection
Examples: cumulus clouds
Shallow vertical extent (< 2-4 km)
Non-precipitating in nature
Turbulent mixing within clouds cools and moistens the top of the cloud while warming and drying its bottom
Cloud shading impacts the radiation budget (notably within the planetary boundary layer)
(Stensrud)

10. Why Convective Parameterization?
Think to the typical scales of moist convective activity
Parameterizations typically employed for ∆x ≥ 5 km
Convection crudely resolved for 1 km ≤ ∆x ≤ 5 km
Likely need ∆x ≈ 100 m to truly be able to explicitly resolve moist convection (G. Bryan)

11. Model Nomenclature
A mesoscale model simulation that explicitly resolves moist convection is said to be convection-permitting.
A model simulation that utilizes a convective parameterization is said to be convection-parameterizing.

12. Convective Parameterization Tenets
Activation: what determines the triggering of convection?
Intensity: how strong is the triggered convection?
Vertical Distribution: how are the vertical profiles of temperature, moisture, and momentum modified in response to the convective activity?

13. Overarching Principle: Energy
CAPE: convective available potential energy
Maximum energy available to an ascending parcel as determined via parcel theory (i.e., no explicit consideration of entrainment or detrainment).
CIN: convective inhibition
Energy necessary to lift a parcel pseudoadiabatically from its starting level (SL) to its level of free convection (LFC)
LFC: level above which parcel is positively buoyant

14. Overarching Principle: Energy

15. Overarching Principle: Energy

16. Convective Parameterization Approaches
Deep layer control: ties convective development to the creation of CAPE by large-scale processes
Low level control: ties convective development to the removal of CIN
Many convective parameterizations have properties of both approaches

17. Trigger Functions
The criteria that determine when and where convection is activated within the model.
Based upon what the parameterization developers though was important for convective development.
Differ substantially between individual convective parameterizations!

18. Trigger Functions
deep layer
low level
Slide 88 of Stensrud

19. Selected Considerations
Deep versus shallow convection parameterization
Some schemes parameterize both.
Others, however, only parameterize one or the other.
Why consider them differently? They impact the environment in unique ways! (see again slides 8-9)
What environmental fields are impacted?
Most parameterizations modify heat and moisture fields.
Selected parameterizations also modify momentum fields.

20. Selected Considerations
How are the convective fields modified?
Budget-based studies using field program data give us insight into how convection modifies its environment.
Static schemes: use these data to define reference post-convective profiles, one or more of which the model atmosphere can be modified toward over a period of time.
Dynamic schemes: use these data to define analytical expressions for how convection modifies its environment.

21. Budget-Based Insight
For more details on the apparent heat source and moisture sink, see also
Slide 32 of Stensrud

22. Budget-Based Insight
Deep moist convection (blue): warms and dries at all levels, particularly between hPa.
Slide 34 of Stensrud

23. Budget-Based Insight
Stratiform precipitation (yellow): cools and moistens low levels while warming and drying upper levels.
Slide 35 of Stensrud

24. Selected Considerations
Scale-related considerations…
Convection triggered by large-scale, well-resolved phenomena is relatively easy to parameterize.
Convection triggered by smaller-scale phenomena, namely unresolved phenomena, is difficult to parameterize.
Related idea: geostrophic adjustment between the mass and latent heating fields (see class text for more).
Convection initiation depends upon all scales – thus, parameterizations must be flexible in their design.

25. Convective vs. Microphysical Parameterization
Models with ∆x ≥ 5 km generally employ both.
Both types of parameterizations can produce precipitation…
Convective: does not require grid scale saturation
Microphysical: does require grid scale saturation
As a result, a model often carries two precipitation fields…
Parameterized / convective
“Resolved” / non-convective

26. Convective vs. Microphysical Parameterization
Which type of precipitation dominates is a function of the meteorological phenomenon being studied…
Mesoscale convective system: generally convective along leading edge, non-convective behind
Mid-latitude cyclone: generally convective in warm sector, non-convective elsewhere
It also depends upon the specific formulation of the parameterizations being used by the model.

27. Convective vs. Microphysical Parameterization
mesoscale convective system
wintertime mid-latitude cyclone
Convective % of rain
Note the widely disparate solutions as a function of time, convective parameterization, and meteorological event!

28. Convective vs. Microphysical Parameterization
Most convective and microphysical schemes do not directly interact with one another.
Both act on and modify the same atmospheric state and thus interact indirectly over time.
However, at a given time, they generally do not directly impact each other.

29. Practical Examples
First example: large-scale differences manifest by the choice of convective parameterization
Evolution of a Mei-Yu monsoon-related coastal front between China and Taiwan during 2003
Shaded: 2-m temperature (warmer colors = warmer)
Barbs: 10-m winds (half: 5 kt, full: 10 kt)
Contour: sea-level pressure (hPa; every 2 hPa)

30. Practical Examples
Slide 89 of Stensrud

31. Practical Examples
(and also associated area of low pressure near Taiwan)
Slide 92 of Stensrud

32. Practical Examples
Slide 90 of Stensrud

33. Practical Examples
Slide 91 of Stensrud

34. Practical Examples
Second example: differences in precipitation forecast amounts and skill as a function of parameterization
12 km simulations of a springtime convective system
OBS = observations
EX = explicit
BM = Betts-Miller
KF = Kain-Fritsch
GR = Grell
AK = Anthes-Kuo
Note the differences both as a function of time and as a function of the parameterization!

35. Practical Examples
36 km simulations of three warm-season convective systems, now looking at bias scores…
EX = explicit
BM = Betts-Miller
KF = Kain-Fritsch
GR = Grell
AK = Anthes-Kuo
Again, note the differences both as a function of time and as a function of the parameterization!

36. Practical Examples These examples are of warm-season convection.
The results presented in these examples are sensitive to the type of event considered as well as the model configuration used within the study.
Therefore, care must be taken when generalizing the results of these (or your own!) studies.

37. Parameterization Construction
We now describe the characteristics of three popular convective parameterization schemes.
There exist many more; please refer to the class text or other resources for references to such schemes.
For these three schemes, we focus upon describing their trigger functions, how they modify the environment, and how they compute precipitation.
These general themes apply generally to other schemes!

38. Anthes-Kuo Scheme
Trigger: column-integrated moisture convergence in the presence of conditional instability
Impact: relaxes the temperature profile toward a moist adiabat chosen to provide necessary heating
Slide 38 of Stensrud

39. Anthes-Kuo Scheme
Precipitation: fraction of moisture convergence that is precipitated and used to heat the atmosphere
Problem: moisture convergence does not necessarily result in convective activity!
Thus, this scheme is presently used only to illustrate the basics of convective parameterization.

40. Betts-Miller(-Janjic) Scheme
A large-scale quasi-equilibrium scheme
Deep, moist convection consumes CAPE as quickly as large-scale processes create CAPE.
In this regard, is a deep layer control scheme.
Trigger: CAPE > 0
Includes quantification of cloud depth to determine whether shallow or deep convection is possible
Subsequently determines convective initiation and impacts based upon reference profiles

41. Betts-Miller(-Janjic) Scheme
Reference profiles are based upon similar soundings structures obtained from tropical convection.
Structure: temperature and moisture
Jointly modify profiles in order to conserve total enthalpy.
Is the modified reference moisture profile drier than the observed profile?
If yes, precipitation occurs! Activate convection and nudge the temperature and moisture profiles to the reference profile over a typical convective time scale (~1 h).
If no, rainfall does not occur!

42. Betts-Miller(-Janjic) Scheme
Slide 51 of Stensrud

43. Betts-Miller(-Janjic) Scheme
If precipitation does not occur and/or the cloud depth is sufficiently shallow (< 200 hPa), activate the shallow convection parameterization.
This also acts to relax the temperature and moisture profiles to enthalpy-conserving reference profiles.
As expected, warms and dries the lower half of the cloud while cooling and moistening the upper half.

44. Betts-Miller(-Janjic) Scheme
(Note: reference profiles are again the darker black lines.)
Slide 53 of Stensrud

45. Betts-Miller(-Janjic) Scheme
Precipitation: vertically-integrated measure of moisture excess (compared to environment)
As a consequence, very sensitive to moisture content!
Mathematical formulation:
pt is the pressure at the top of the cloud
pb is the pressure at the bottom of the cloud
qr is the reference profile specific humidity
q is the grid point specific humidity
τ is the time scale of convective adjustment

46. Kain-Fritsch Scheme Trigger: both low-level and deep layer aspects…
Low-level: CIN, sub-cloud mass convergence (equivalent to the vertical mass flux)
Deep layer: presence of CAPE
Is a dynamic scheme, where the impact of convection upon atmospheric fields is handled using mathematical equations (and not reference profiles).
Works in conjunction with microphysical schemes, unlike many other convective parameterizations.

47. Kain-Fritsch Scheme Consider both updrafts and convective downdrafts.
Both phenomena interact with the environment via entrainment and detrainment.
Convection is activated if the parcel is deemed to overcome its CIN and thus be able to reach its LFC.

48. Kain-Fritsch Scheme
Slide 68 of Stensrud

49. Kain-Fritsch Scheme
Activated convection has a given updraft mass flux.
For this updraft mass flux, determine the downdraft mass flux that can be produced via evaporation.
Subsequently, increase the value of the updraft mass flux (controlling convective intensity) until it is able to achieve the desired impact upon the environment.
For this scheme, this is a 90% reduction in CAPE.
Other atmospheric fields are modified to bring this about.

50. Kain-Fritsch Scheme
Note: time scale is a function of the horizontal grid spacing and velocity in the cloud layer. Thus, the Kain-Fritsch scheme is influenced by the horizontal grid spacing it is used with in the model!
Slide 70 of Stensrud

51. Kain-Fritsch Scheme
Convection is said to be shallow only if the cloud depth is sufficiently small (< m, temperature-dependent).
Precipitation: P = ES
E = precipitation efficiency, or the ratio of precipitation to the amount of water that can be precipitated
S = sum of vertical vapor and liquid fluxes 150 hPa above the LCL

52. Another Practical Example
Slide 78 of Stensrud

53. Another Practical Example
Initial sounding
Slide 79 of Stensrud

54. Another Practical Example
Slide 80 of Stensrud

55. Another Practical Example
Slide 81 of Stensrud

56. Another Practical Example
Slide 82 of Stensrud

57. Another Practical Example
Slide 83 of Stensrud

58. Another Practical Example
Slide 84 of Stensrud

59. Open Questions Aerosol effects upon convection (seeding, etc.)
Horizontal grid spacing
Parameterizations are often tuned for grid spacings ≥ 20 km but are needed down to ∆x = 5 km.
Interactivity with other parameterizations
How to best represent the trigger function?

60. Open Questions Issues with convective system propagation
Not always handled well by parameterizations.
Impacts synoptic-scale to climate-scale simulations.
Issues with representing the Madden-Julian Oscillation, a convectively-driven phenomenon
Modification of momentum profiles in addition to temperature and moisture profiles

61. Open Questions Issues with precipitation amounts
Better representation of maximum precipitation amounts
Overprediction of light precipitation amounts
Even as the field moves toward convection-permitting simulations for mesoscale applications, we are a long way away from being able to do so for synoptic- to climate-scale applications!
Thus, we cannot neglect this aspect of the model system moving forward, much as we may want to do so!

62. Cloud-Cover Parameterization
With high-resolution, cloud-resolving models, it is possible to reasonably assume that an entire grid box is either cloudy or cloud-free.
For larger-scale weather and climate models, however, this assumption is not reasonable.
Thus, the cloud geometry within each grid box must be parameterized to aid in properly computing the radiation and surface energy budgets.

63. Cloud-Cover Parameterization
Geometric cloud properties to consider include...
How much of the three-dimensional grid box is covered by cloud, both in the horizontal and in the vertical?
How do clouds overlap in the vertical?
A cloud-cover parameterization operates under the assumption that clouds may exist on the sub-grid scale even if the grid-scale is subsaturated.
Most cloud-cover parameterizations only consider the horizontal cloud fraction.

64. Cloud-Cover Parameterization
Over the grid increment, q < qs.
On the sub-grid scale, however, q ≥ qs at certain locations.
How to properly assess cloud cover and its impacts in such a scenario?

65. Cloud-Cover Parameterization
There exist multiple methods for parameterizing cloud-cover.
Method 1: diagnostic relationships between relative humidity and sub-grid cloud cover
Ex: Sundqvist et al. (1989)…
where C = cloud fraction and RHcrit = a specified RH above which cloud is assumed to form
0 ≤ C ≤ 1 for RHcrit ≤ RH ≤ 100%

66. Cloud-Cover Parameterization
There exist many permutations of this method…
Slingo (1980, 1987): cloud type and altitude variability
Xu and Randall (1996): inclusion of non-RH predictors
Method 2: specify the sub-grid PDF for RH
Distribution can be symmetric or non-symmetric
Can also include temperature influence upon saturation
Solution is only as good as the specified distribution!

67. Cloud-Cover Parameterization