Convective Parameterization 24 October 2012. Thematic Outline of Basic Concepts What is a convective...

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

http://www.mmm.ucar.edu/wrf/users/workshops/WS2012/ppts/lecture1.pdf

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 high-impact 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


EL

LFC

dzz

zzgCAPE

LFC

SL

dzz

zzgCIN

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 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.

Budget-Based Insight

Slide 32 of StensrudFor more details on the apparent heat source and moisture sink, see also http://derecho.math.uwm.edu/classes/TropMet/climo.pdf.


Slide 34 of StensrudDeep moist convection (blue): warms and dries at all levels, particularly between 850-400 hPa.


Slide 35 of StensrudStratiform 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 / convective2. “Resolved” / non-convective


• 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.


mesoscale convective system wintertime mid-latitude cyclone

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

Conv

ectiv

e %

of r

ain


• 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

• 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 = observationsEX = explicit

BM = Betts-MillerKF = Kain-Fritsch

GR = GrellAK = Anthes-Kuo

Practical Examples

• 36 km simulations of three warm-season convective systems, now looking at bias scores…

Again, note the differences both as a function of time and as a function of the parameterization!

EX = explicitBM = Betts-MillerKF = Kain-Fritsch

GR = GrellAK = Anthes-Kuo

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

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


• 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:

t

b

p

p

r dpg

qqP

pt is the pressure at the top of the cloudpb is the pressure at the bottom of the cloud

qr is the reference profile specific humidityq 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 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!

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 < 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?


• 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)…

critRH

RHC

1

11

where C = cloud fraction and RHcrit = a specified RH above which cloud is assumed to form

0 ≤ C ≤ 1 for RHcrit ≤ 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 24 October 2012. Thematic Outline of Basic Concepts What is a convective...

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