Convection mini-workshop, Hamburg, July 14, 2004 Parameterization of convection Andreas Chlond...

Convection mini-workshop, Hamburg, July 14, 2004

Parameterization of convection

Andreas ChlondDepartment Climate Processes

*Thanks to F. Nober, P. Bechthold, A. Tompkins and the ECMWF


Andreas Chlond: Parameterization of convection

Outline

• Introduction Why do we have to parameterize? What is a parameterization?

• How to parameterize? Classical approach Super-parameterization Parameterization of intermediate complexity



Why do we have to parameterize?

• Climate und regional models predict coarse grained, large-scale variables

• Small scales processes are not resolved by large-scale models, because they are sub-grid scale

• The effect of the the sub-grid processes on the large-scale has to be presented statistically

• The procedure of expressing the effect of sub-grid processes is called a parameterization

Turbulence, convection, clouds, radiation etc.



What is a parameterization?•The statistical contribution of sub-grid processes

must, therefore, be expressed in terms of the large-scale parameters themselves. The mathematical procedure involved is generally called a parameterization.

SUBROUTINE vdiff (kidia,kfdia,klon,klp2,ktdia,klev,klev, & & paclcm,paphm1,papm1,pgeom1,pum1,pvm1,pxm1)

! Description:!-- Computation of the exchange coefficientsIMPLICIT NONE! Scalar arguments with intent(In):INTEGER, INTENT (IN) :: kfdia, kidia, klev, klevm1, klevp1,& & klp2, ktdia, ktrac

DO jl = kidia, kfdia zdu2 = MAX(zepdu2,pum1(jl,klev)**2+pvm1(jl,klev)**2) zqmitte = (pqm1(jl,klev)+zqs(jl)*zhsoil(jl))/2.zmult4 = zfux*zmult5 - 1. zcons = zcons12*paphm1(jl,klevp1)/(ptm1(jl,klev)* & & (1.+vtmpc1*pqm1(jl,klev)-pxm1(jl,klev))) END DO

From Nature

To its

Representation



What is convection doing?

•Convection is of crucial importance for the global energy and water balance (Convection transports heat, water vapor, momentum … and chemical constituents upwards …. Water vapor then condenses and falls out -> net convective heating/drying

•Convection generates and/or influences a number of phenomena important to forecasting (thunderstorms, heavy precipitation, hurricanes)

•An important parameter for the strength of convection is CAPE

•Convection affects the atmosphere through condensation / evaporation and eddy transports



Convection parameterization – How?

Conventional approach:

•Start from first principles and write down exact equations for the process under consideration

•Close equations (Closure problem)

Introduce additional (empirical) information

Calibrate constants (observations, PRMs)



Task of convection parametrisation(1) total Q1 and Q2

To calculate the collective effects of an ensemble of convective clouds in a model column as a function of grid-scale variablesRecall: these effects are represented by Q1-QR, Q2 and Q3

Hence: parametrization needs to describe CONVECTIVE CONTRIBUTIONS to Q1/Q2: condensation/evaporation and transport terms and their vertical distribution.

p

secLQQQ RC

)(11



Task of convection parametrisation (2):in practice this means:

Determine vertical distribution of heating, moistening and momentum changes

Cloud model

Determine the overall amount of the energy conversion, convective precipitation=heat release

Closure

Determine occurrence/localisation of convection

Trigger



Types of convection schemes

• Schemes based on moisture budgets–Kuo, 1965, 1974, J. Atmos. Sci.

• Adjustment schemes–moist convective adjustement, Manabe, 1965, Mon. Wea. Rev.

–penetrative adjustment scheme, Betts and Miller, 1986, Quart. J. Roy. Met. Soc., Betts-Miller-Janic

• Mass-flux schemes (bulk+spectral)–entraining plume - spectral model, Arakawa and Schubert, 1974, J. Atmos. Sci.

–Entraining/detraining plume - bulk model, e.g., Bougeault, 1985, Mon. Wea. Rev., Tiedtke, 1989, Mon. Wea. Rev., Gregory and Rowntree, 1990, Mon. Wea . Rev., Kain and Fritsch, 1990, J. Atmos. Sci., Donner , 1993, J. Atmos. Sci., Bechtold et al 2001, Quart. J. Roy. Met. Soc.

–episodic mixing, Emanuel, 1991, J. Atmos. Sci.



The “Kuo” scheme

Closure: Convective activity is linked to large-scale moisture convergence

dzt

qbP

ls

0

)1(

Main problem: here convection is assumed to consume water and not energy



Adjustment schemes

e.g. Betts and Miller, 1986, QJRMS:

When atmosphere is unstable to parcel lifted from PBL and there is a deep moist layer - adjust state back to reference profile over some time-scale, i.e.,

qq

t

q ref

conv

.TT

t

T ref

conv

.

Tref is constructed from moist adiabat from cloud base but no universal reference profiles for q exist. However, scheme is robust and produces “smooth” fields.



The bulk mass-flux approach

p

secLQ C

)(1

Aim: Look for a simple expression of the eddy transport term

Condensation term Eddy transport term

?



The bulk mass-flux approach:Cloud – Environment decomposition

Total Area: A

Cumulus area: a

Fractional coverage with cumulus elements:

A

a

Define area average:

ec 1

ec


Simplifications :

•Neglect subplume correlations

•The small area approximation:

ec ;1)1(1

ecc *Define convective mass-flux:

**

cc

c wg

M

Then: c

cgM

Then:




With the above we can rewrite:

p

ssMgecLQ

cc

C

)(

)(1

p

qqMLgecLQ

cc

)(

)(2

To predict the influence of convection on the large-scale with this approach we now need to describe the convective mass-flux, the values of the thermodynamic (and momentum) variables inside the convective elements and the condensation/evaporation term. This requires, as usual, a cloud model and a closure to determine the absolute (scaled) value of the mass-flux.

A bulk mass flux scheme:What needs to be considered

Entrainment/Detrainment

Downdraughts

Link to cloud parameterization

Cloud base mass flux - Closure

Type of convection shallow/deep

Where does convection occur

Generation and fallout of precipitation



Outline






•Run a 2D CSRM as a “super-parameterization” in a GCM

•This idea was first suggested by W. Grabowski of NCAR

Super-Parameterization:



Grabowski’s approach



What do we get?

•Explicit deep convection

•Explicit fractional cloudiness

•Explicit cloud overlap and possible 3d cloud effects

•Convectively generated gravity waves

But

•A GCM using a super-parameterization is three orders of magnitude more expensive than a GCM that uses conventional parameterizations. On the other hand super-parameterizations provide a way to utilize more processors for a given GCM resolution



Outline





• An ensemble of potentially different clouds has to be described by ONE AVERAGED cloud.

• Dynamical and microphysical details are not represented

• Due to the mass-flux approach the information about cloud cover and vertical velocity is not available.

Problems with mass-flux schemes


Parameterization of intermediate complexity: The ensemble approach



LES vs. SCM: Diurnal variation of cloud cover (ARM case)



Cumulus-Prey-Predator Model (1)

Philosophy (adapted from population dynamics):

• Different possible clouds correspond to different

species. These species are in competition for an external food supply.

• In case of clouds this food is given by CAPE (Convective Available Potential Energy)



1

2

K_22

K_12 K_21

F_1

F_2

K_11



Cumulus-Prey- Predator Model (2)

Mathematical: Search for the cloud ensemble (consistingof the possible clouds) that is most effective in consumingCAPE.

The solution of the Lotka – Volterra – Equation does it!

The interaction between the different cloud types and the clouds and the non-convective processes is determined by the energetic of the system.

Cloud – Field – Model



ECHAM GCMInput data: vertical profiles of temperature and humidity

Cloud – Field - Model

Cloud Model

Calculation of interactioncoefficients

Cloud Spectrum

Output data: heating ratestransport, precipitation



Comparison: Cloud – Field – Model, LES and ECHAM5 (1)



Comparison: Cloud – Field – Model, LES and ECHAM5 (1)



We should discuss and must decide …

•Classical approach

Simple, but to take conventional approach much beyond were we are now, it seems likely that we will have to make the parameterizations very complicated

•Super-Parameterization

More expensive, but SPs can use thousands of processors with good computational efficiency.

•Parameterization of intermediate complexity

Good compromise



Heating Rates ECHAM (zonal mean, DJF) (K/day)Convection Stratiform Clouds

Vertical Diffusion Radiation

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Convection mini-workshop, Hamburg, July 14, 2004 Parameterization of convection Andreas Chlond...

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