Convective Parameterization

Convective Parameterization

24 October 2012

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?

Additional Reference

“ An Overview of Convective Parameterization ” –

David Stensrud

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!

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.

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 highimpact weather and can substantially impact larger-scales.

Simplified Perspective

• Control on moist convection; feedback to large scale.

• In reality, however, smaller-scale processes are also important in triggering moist convection!

Types of Moist Convection

1. 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)

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)

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)

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.

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?

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


CAPE

 g



EL

LFC

    

   z dz CIN

  g

LFC



SL

    

   z dz


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

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!

Trigger Functions deep layer low level

Slide 88 of Stensrud

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.


• 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 postconvective 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.

Budget-Based Insight

For more details on the apparent heat source and moisture sink, see also http://derecho.math.uwm.edu/classes/TropMet/climo.pdf.



Deep moist convection (blue): warms and dries at all levels, particularly between 850-400 hPa.



Stratiform precipitation (yellow): cools and moistens low levels while warming and drying upper levels.



• 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.

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…

1.

Parameterized / convective

2.

“Resolved” / non-convective


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.


Parameterization mesoscale convective system wintertime mid-latitude cyclone

Note the widely disparate solutions as a function of time, convective parameterization, and meteorological event!


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.

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)

Practical Examples


Practical Examples

(and also associated area of low pressure near Taiwan)


Practical Examples


Practical Examples


Practical Examples

• Second example: differences in precipitation forecast amounts and skill as a function of parameterization

• 12 km simulations of a springtime convective system

Note the differences both as a function of time and as a function of the parameterization!

OBS = observations

EX = explicit

BM = Betts-Miller

KF = Kain-Fritsch

GR = Grell

AK = Anthes-Kuo

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!

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.

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!

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


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.

Betts-Miller(-Janjic) Scheme

• A large-scale quasi-equilibrium scheme

– Deep, moist convection consumes CAPE as quickly as largescale 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


• 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!




• 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.


(Note: reference profiles are again the darker black lines.)



• Precipitation: vertically-integrated measure of moisture excess (compared to environment)

– As a consequence, very sensitive to moisture content!

– Mathematical formulation:

P

 p t  p b q r



 g q dp p b p t is the pressure at the top of the cloud is the pressure at the bottom of the cloud q r is the reference profile specific humidity q is the grid point specific humidity

τ is the time scale of convective adjustment

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.

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.

Kain-Fritsch Scheme


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.

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!


Kain-Fritsch Scheme

• Convection is said to be shallow only if the cloud depth is sufficiently small (< 2000-4000 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

Another Practical Example



Initial sounding












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?

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

Open Questions

• Issues with precipitation amounts

– Better representation of maximum precipitation amounts

– Overprediction of light precipitation amounts

• Even as the field moves toward convectionpermitting 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!

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.


• 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.


Over the grid increment, q < q s

.

On the sub-grid scale, however, q ≥ q s at certain locations.

How to properly assess cloud cover and its impacts in such a scenario?


• 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)…

C



1



1



1



RH

RH crit where C = cloud fraction and RH crit

= a specified RH above which cloud is assumed to form

0 ≤ C ≤ 1 for RH crit

≤ RH ≤ 100%


• 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!


Convective Parameterization

Convective Parameterization

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