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
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)
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 convectionparameterizing.
Convective Parameterization Tenets
• Activation: what determines the triggering of
• 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
Overarching Principle: Energy
 z    z 
CAPE  g 
 z 
CIN   g
 z    z 
 z 
Overarching Principle: Energy
Convective Parameterization
• 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
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.
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 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
Slide 32 of Stensrud
Budget-Based Insight
Deep moist convection (blue): warms and dries at all levels,
particularly between 850-400 hPa.
Slide 34 of Stensrud
Budget-Based Insight
Stratiform precipitation (yellow): cools and moistens low levels while
warming and drying upper levels.
Slide 35 of Stensrud
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.
Convective vs. Microphysical
• Models with ∆x ≥ 5 km generally employ both.
• Both types of parameterizations can produce
– 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
Convective vs. Microphysical
• 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.
Convective % of rain
Convective vs. Microphysical
mesoscale convective system
wintertime mid-latitude cyclone
Note the widely disparate solutions as a function of time,
convective parameterization, and meteorological event!
Convective vs. Microphysical
• 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
Slide 89 of Stensrud
Practical Examples
(and also associated area of
low pressure near Taiwan)
Slide 92 of Stensrud
Practical Examples
Slide 90 of Stensrud
Practical Examples
Slide 91 of Stensrud
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!
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
Slide 38 of Stensrud
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
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!
Betts-Miller(-Janjic) Scheme
Slide 51 of Stensrud
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.
Betts-Miller(-Janjic) Scheme
(Note: reference profiles are again the darker black lines.)
Slide 53 of Stensrud
Betts-Miller(-Janjic) Scheme
• Precipitation: vertically-integrated measure of
moisture excess (compared to environment)
– As a consequence, very sensitive to moisture content!
– Mathematical formulation:
qr  q
p g dp
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
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
Slide 68 of Stensrud
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!
Slide 70 of Stensrud
Kain-Fritsch Scheme
• Convection is said to be shallow only if the cloud
depth is sufficiently small (< 2000-4000 m,
• 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
Slide 78 of Stensrud
Another Practical Example
Initial sounding
Slide 79 of Stensrud
Another Practical Example
Slide 80 of Stensrud
Another Practical Example
Slide 81 of Stensrud
Another Practical Example
Slide 82 of Stensrud
Another Practical Example
Slide 83 of Stensrud
Another Practical Example
Slide 84 of Stensrud
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.
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.
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?
Cloud-Cover Parameterization
• There exist multiple methods for parameterizing
• Method 1: diagnostic relationships between relative
humidity and sub-grid cloud cover
– Ex: Sundqvist et al. (1989)…
C  1
1  RH
1  RH crit
where C = cloud fraction and RHcrit = a specified RH above which cloud is assumed to form
0 ≤ C ≤ 1 for RHcrit ≤ RH ≤ 100%
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!
Cloud-Cover Parameterization
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