Download - Convective Parameterization
Convective Parameterization
Mike Baldwin
NCEP/EMC/GSC
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
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…
sfcvdiffhdiffevapcondconvv
sfcvdiffhdiffevapcondconvrad
PPPPPdt
dq
PPPPPPdt
d
/
/
rwater vapo
etemperatur
• …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
• where c is a convective timescale, typically 30min to 1hr
sfcvdiffhdiffconv PPP)P(fvx
p
dt
du
1
momentum
convc
initialfinal
conv
Pt
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• mass or moisture convergence exceeding a
certain threshold at a grid point• positive destabilization rate• perturbed parcels can reach their level of free
convection• 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 is condensed out)
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 Mass-Flux 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)– Find highest e air in column below ~400mb
level…does CAPE exists?– Is cap too strong? How far does parcel have
to be lifted to reach LFC? Is Psource-PLFC < 150mb?
– 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:
tenvironmenconv dt
)CAPE(d
dt
)CAPE(d
Grell and Grell-Pan Schemes
• Feeding back the effects of convection– Introduce tendency terms in the prognostic
equations for temperature and moisture:
– where represents T or qv
c
initialfinal
convt
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/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
• 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 non-existent)
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
topcld
base cld
topcld
base cld
dTCdqL pvv
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, Tp based on grid point vertical velocity:
• Tp = (wg - wc)1/3 + Tp(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 -> Tp=1.0 K
– wg - wc=10 cm/s -> Tp=2.5 K
• In the Eta Model, an additional perturbation, Tp (RH) (magnitude ~0.5K) is given to account for low RH
• So…In a typical convective environment with some larger-scale forcing,
• Tp ~ 1 - 2 K
Kain-Fritsch convective initiation check
• Is (Tp(LCL) + Tp) > Tg????
– If no, move up one model level and repeat process above
– If yes, compute a vertical velocity perturbation, Wp, based on magnitude of Tp.
– For Tp=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
top
bottom
top
bottomv Tq 00
:precip negative
Shallow convection allowed
•
top
bottom
top
bottomv Tq 00
precip no conv,shallow
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
updraftpath
downdraftpath
updraftsourcelayer
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%
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