Improvement of the EDMF Scheme using Kain Fristch approach for Meso-NH and AROME Improvement of the Eddy-Diffusivity Mass Flux scheme using Kain-Fritsch

Improvement of the EDMF Scheme using Kain Fristch approach for Meso-NH and AROMEImprovement of the EDMF Scheme using Kain Fristch approach for Meso-NH and AROME

Improvement of the Eddy-Improvement of the Eddy-Diffusivity Mass Flux scheme Diffusivity Mass Flux scheme

using Kain-Fritsch approach for using Kain-Fritsch approach for Meso-NH and AROMEMeso-NH and AROME

CNRM/GMME/TURBAU

Julien PERGAUD, Sylvie MALARDEL,Valery MASSON

July 2006, 3rd


Introduction : EDMF scheme and purpose of our work

1/ Description of improved EDMF scheme– Equations for the Updraft Model– Definition of Lateral Mass Exchanges

– Closure Assumptions

2/ First Results for different study cases – Eurocs/ARM– Bomex

Conclusion : Work in progress and questions


Introduction

• Updraft starting from the ground– Dry BL – Dry BL and

shallow Cu– Sc BL (not

tested yet)

• Use of conservatives variables

EDMF Scheme

• EDMF scheme Soares et al,2004

TurbulenceConvection schemeSoares et al,2004


IntroductionEDMF Scheme :Results Eurocs/Arm (Malardel,Auguste)

'θw'EDMF L

'rw'EDMF tEDMF Rc

LES Rc

'θw'LES L

LES Rc

'θw'LES L

'rw'LES t


IntroductionEDMF Scheme : Results Bomex (Malardel,Auguste)

EDMF Rc'θw'EDMF L

'rw'EDMF t

LES RcLES Rc

'rw'EDMF t

'θw'LES L 'rw'LES t


IntroductionEDMF Scheme : improvement

Soares et al,2004

Continuity of mass flux

defintion

Better definition of entrainmentdetrainment


• Eq for w

• Eq for conservative

variables

Description of EDMF improved scheme

DEz

M

u

u

DφφEz

Mφ

w²M

EbaB

z

ww

1/ Equations for the updraft model

EDMF

KFB

w and MF equationsthe fractionnal updraft area

• Eq for the Mass flux


• Entrainment and detrainment in clouds are defined as in the KF formulation (Kain & Fritsch,1990):

2/ Definition of Lateral Mass Exchanges

Updraft-Cloud Zone

Limit between Updraft and environmentD

EE

ENVIRONMENT





Limit between Updraft and environment

Updraft-Cloud ZoneMaximum

updraft part detrainable to environment

ENVIRONMENT





Updraft-cloud Zone

Maximum environmental

part entrainable to the updraft


ENVIRONMENT





Updraft-cloud Zone

Updraft-environmental Mixture Zone


ENVIRONMENT





ENVIRONMENT


Mu

Updraft-Cloud Zone

BuoyantAir

HeavyAir

BuoyantAir

HeavyAir

Mt





ENVIRONMENT


EE

MuBuoyant

Air

HeavyAir

Updraft-Cloud Zone

BuoyantAir

HeavyAirD

E



• KF formalism : E and D depends on v between environment and updraft

where with

- f(x) is a gaussian type distribution with f(0)=f(1)=0,

- c is the critical mixed fraction and the environmental mass fraction linked to the buoyancy

- Ro is the cloud Radius


χc

χf(χ)dχΔMtE0

1

1χc

χ)f(χ)dχ(ΔMtD

0/ RcMM etrut 2.0etrc




dnL

MCE

E )1(

upL

MCD

D )1(

• From the ground to the Condensation Level, entrainment and detrainment are defined as in Lappen & Randall ,2001:

Lup and Ldn are the downward and upward BL89 mixing lengths

is the fractionnal updraft area.

In Lappen & Randall (2001) CE =1.0 and CD =1.5

This formulation needs diagnosed

Link with the turbulence



3/ Closure assumptions

e

w'θ'θθ

sLLu

e

w'r'rr

sttu

• Initialisation of the parcel characteristics using Soares et al (2004)

with =0.3

• Moreover the mass flux at the ground is defined as :

sMss eCM3

2

where CMs corresponds to a fractionnal updraft area

defined for each study case



First Results for different study cases1/ Eurocs/ARM

Evolution of Mean rc (kg/kg)

LES 1 D



Profile of Mass flux, Entrainment and Detrainment averaged between 8 and 9 hours

Mass Flux Entrainment Detrainment

LCLLCL

LCL

sMss eCM3

2 09.0MsC



1D Results

Average between8 and 9 hours

Evolutionof flux over 15 hours

LES Results



'θw' L 'θw' L



LES Results



'rw' t

1D Results



'rw' t


First Results for different study cases2/ BOMEX

LES 1 D

Evolution of Mean rc (kg/kg)



Profile of Mass flux, Entrainment and Detrainment averaged between 8 and 9 hours

Mass Flux Entrainment Detrainment

LCL LCLLCL

sMss eCM3

2 05.0MsC



'θw' L

'rw' t

LES Results


1D Results

Average between5 and 6 hours'rw' t

'θw' L



The next stages in our work will be to

• Improve the closure asumption : surface mass flux

•Assess the sensibility of the scheme to different parameters : a and b in the w equation, CE and CD, and Ro

• Test the scheme with others cases : dry Bl or Sc Bl

• Implement the scheme in AROME and test in 3D runs

,...),,'',( CINCAPEwefM vs



Some questions are interesting

• Must we use a prognostic approach to have a better view of the convection?

for example

• Links with deep convection, 3D runs ?

w²M

EbaB

z

ww

t

w

Documents

Improvement of the EDMF Scheme using Kain Fristch approach for Meso-NH and AROME Improvement of the Eddy-Diffusivity Mass Flux scheme using Kain-Fritsch