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