Convective Parameterization
Jack Kain and Mike Baldwin
OAR/NSSL/CIMMS
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
Eta Grid Points
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
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…
temperatur e
d
 Prad  Pconv  Pcond / evap  Phdiff  Pvdiff  Psfc
dt
water vapo r
dqv
 Pconv  Pcond / evap  Phdiff  Pvdiff  Psfc
dt
momentum
du 1 p

 fv  ( Pconv )  Phdiff  Pvdiff  Psfc
dt  x
• …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
 final  initial


 Pconv
t conv
tc
• where tc is a convective timescale, typically
30min to 1hr
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
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
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)
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
Quasi-equilibrium schemes
• Arakawa-Schubert for example
• Large-scale destabilization rate ~
convective stabilization rate
• Convective stabilization is achieved by
an ensemble of cloud types
Convergence schemes
• Kuo-type schemes
– If:
• 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
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 MassFlux 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
Grell and Grell-Pan Schemes
• Initiation (on/off)
1.) Find highest e 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...
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:
d ( CAPE )
d ( CAPE )

dt
dt
conv
environment
Grell and Grell-Pan Schemes
• Feeding back the effects of convection
– Introduce tendency terms in the prognostic
equations for temperature and moisture:
a final  ainitial
a

t conv
tc
– where a represents T or qv
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
Betts-Miller-Janjic Scheme
• Checks for CAPE, cloud depth, using
highest e 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
Enthalpy conservation
cld top

 L dq
v
cld base
v
cld top

 C dT
p
cld base
• 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 nonexistent) 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
Kain-Fritsch convective
initiation check
• Beginning at the surface, mix in model layers overhead until
a mixture 50-100mb deep is found. This compromises a
potential updraft source layer. Find mean , 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
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 ~ 1 - 2 K
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
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
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
Stabilizing mechanisms of
Kain-Fritsch
• Convective Updraft
– removes high e air from lower
troposphere, transports it aloft
– generates condensation
Stabilizing mechanisms of
Kain-Fritsch
• Convective Downdraft
– draws mass from layer beginning at cloud base
and extending up 150-200mb
– deposits low e 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
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
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
Consider some typical convective
environments
Negative Precipitation
negative precip :
top
 q
v
bottom
0
top
 T  0
bottom
Shallow convection allowed
•
shallow conv, no precip
top
 q
v
bottom
0
top
 T  0
bottom
BMJ Heating/Drying profiles
• heating
K/hr
• drying
%RH/hr
Increase cloud layer RH by
20%
Deep convection allowed
Heating/Drying profiles
Kain-Fritsch Trigger
• Increase
source layer
Td by 1 K
• some
parcels
break cap,
initiate deep
convection
updraft
path
downdraft
path
updraft
source
layer
Kain-Fritsch adjusted profile
Heating/Drying profiles
BMJ 1st guess profiles
After enthalply adjustment
• Deep
convection
allowed
• Strong
cooling from
850-600mb
• rainfall =
0.032 cm/h
Heating/drying profiles
Increase cloud-layer RH by
5%
• Rainfall =
0.211
cm/h
Increase cloud-layer RH by
10%
• Rainfall =
0.388
cm/h
RH increased 10%
Convective Rainfall vs.
Change in cloud-layer RH
1.4
Precip Amount
1.2
1
0.8
BMJ
KF
0.6
0.4
0.2
0
20
10
5
0
-5
-10
-15
Change in cloud-layer RH
-20
BMJ Oklahoma Tornadoes
• Too dry for
deep
convection
• can see
shallow
convection
grow with
time
BMJ Oklahoma Tornadoes
• Still too dry
• 24h fcst
valid 5 Oct
98
BMJ Oklahoma Tornadoes
• Shallow
convection
cloud top now
up to ~650mb
Shallow convection profile
• Transports
moisture
upward