Pedro M. M. Soares*Pedro M. A. Miranda*

João Teixeira^

*University of Lisbon, CGUL, IDL, Lisbon, Portugal

^Jet Propulsion Laboratory – California Institute of Technology, Pasadena, CA, USA

A new parameterization for Momentum Transport in the CBL

CFMIP/GCSS BL WG Workshop

OUTLINE1. EDMF parameterization for momentum2. Case studies3. Results4. Conclusions

MotivationTo illustrate the potential, of a poor’s man EDMF,

for momentum transport in the CBL…without any tuning

)(Mz

Kw u

EDMF Parameterization

Turbulent transport for heat and moisture: • for clear BL (Siebesma and Teixeira, 2000; Teixeira and Siebesma, 2000)• for clear and cumulus boundary layers (Soares et al. 2004)• improved updraft model Siebesma et al. 2007• …

Also turbulent transport of Momentum:

• clear BL Soares et al. 2007 (personnal communication)• clear and cumulus BLs (today…)

tl q,

vuqtl ,,,

EDMF formulation (MesoNH – old)

aBwbz

ww u

uu

2

Ascending parcel

lulul

z

Entrainment

Vertical speed

Entrainment& detrainment

)()( 2/1

i

sviv ze

wbz

Initial buoyancy

ih

h eC

LK 2

1

3

2

TKE closure

z

M

Mc

c

1

uuwaM Clear BL/Sub-cloud

CloudMF

ED

+

Soares et al. 2004

EDMF formulation (adding for momentum)

)( uuMz

uKuw u

x

pauMuM

z

uM uuu

u

For deep convection Kershaw and Gregory (1997), the updraft momentum components are given by:

,z

uMc

x

pa u

uu

Gregory et al. (1997) showed dependency of this term with the average shear:

z

M

M

1

z

ucuu

z

uuu

u

for u:

Brown 1999 – LES BomexCarr and Bretherton 2001 – CMT Tropical Pacific: Budget estimates

Entrainment / detrainment formulation

UPDRAFTSAscending parcel with entrainment

uu

z

zzz

ci

11

Determine:

• ;

• BL height, zi;

• if condensation, LCL, and cloud top.

uuuutul vuwq ,,,, ,,

DCBLCuBL

(De Rooy and Siebesma, 2008)

11 1;

1

m

zzzm

zcz

t

ulq ,

z

ucuu

z

uuu

u

guarantee a zero M at cloud top

CASE studies (inspired on):

Nieuwstadt Bomex

1DMeso-NH

LESDALES

0

1

2

3

-4 -2 0 2 4 6 8 10 12

u (ms-1)

heig

ht (

km)

u01 u02 u03Nieuwstadt

Bomex

Nieuwstadt case (without shear)

0

1

2

3

-4 -2 0 2 4 6 8 10 12

u (ms-1)

heig

ht (

km)

u01 u02 u03

0

1

2

2.0 2.5 3.0 3.5 4.0

u(ms-1)

heig

ht (

km)

new - 2h old les new - 5h old les

0.0

0.5

1.0

1.5

2.0

2.5

2.5 3.0 3.5 4.0

u (ms-1)

heig

ht (

km)

2h 5h

without shear term

u01

new - edmf also for momentumold - edmf only in thl, qt

Nieuwstadt case (without shear)

ED and MF cont. to total flux

0

1

2

3

-4 -2 0 2 4 6 8 10 12

u (ms-1)

heig

ht (

km)

u01 u02 u03

0.0

0.5

1.0

1.5

2.0

2.5

-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02

heig

ht (

km)

ED 2h MF ED 5h MF

u'w'

u01

momentum transport made by organized updrafts (MF) contribute significantly to the total turbulent flux

Nieuwstadt case (without shear)

Average and Updraft profiles

0

1

2

3

-4 -2 0 2 4 6 8 10 12

u (ms-1)

heig

ht (

km)

u01 u02 u03

u01

0.0

0.5

1.0

1.5

2.0

2.5

2.5 3.0 3.5 4.0

upd - 2h ave upd - 5h ave

u (ms-1)

heig

ht (

km)

Nieuwstadt case (with shear) u02

0

1

2

3

-4 -2 0 2 4 6 8 10 12

u (ms-1)

heig

ht (km

)

u01 u02 u03

0.0

0.5

1.0

1.5

2.0

2.5

2 3 4 5 6 7 8

u (ms-1)

heig

ht (

km)

new - 2h old ws LES new - 5h old ws LES

0

1

2

0.0 0.1 0.2 0.3

v (ms-1)

heig

ht (

km)

new - 2h old ws LES new - 5h old ws LES

ws – without shear term

Nieuwstadt case (with shear)

zoom in:

u020

1

2

3

-4 -2 0 2 4 6 8 10 12

u (ms-1)

heig

ht (km

)

u01 u02 u03

0.0

0.1

0.2

0.3

0.4

0.5

3.0 3.5 4.0 4.5 5.0 5.5

u (ms-1)

heig

ht (

km)

new - 2h old ws LES new - 5h old ws LES

0.5

1.0

1.5

2.0

4.5 5.0 5.5 6.0

u (ms-1)

heig

ht (

km)

new - 2h old ws LES new - 5h old ws LES

the shear term impact on the momentum seems to be is small

Nieuwstad case (with shear) u03

0

1

2

3

-4 -2 0 2 4 6 8 10 12

u (ms-1)

heig

ht (km

)

u01 u02 u03

0.0

0.5

1.0

1.5

2.0

2.5

-1 0 1 2 3

u (ms-1)

heig

ht (

km)

new - 2h old LES new - 5h old LES

0.0

0.5

1.0

1.5

2.0

2.5

-0.1 0.0 0.1 0.2 0.3 0.4

v (ms-1)

heig

ht (

km)

new - 2h old LES new - 5h old LES

Bomex case (standard)

00

new - edmf also for momentumold - edmf only in thl, qt

0.0

0.5

1.0

1.5

2.0

-9 -8 -7 -6 -5

u (ms-1)

heig

ht(

km)

new - 2h old LES new - 5h old LES

Bomex case (modified 1)

01

0.0

0.5

1.0

1.5

2.0

-10 -9 -8 -7 -6 -5

u (ms-1)

heig

ht (

km)

new - 2h old LES new - 5h old LES

Bomex case (modified 2)

02

0.0

0.5

1.0

1.5

2.0

-8 -6 -4 -2

u (ms-1)

heig

ht (

km)

new - 2h old LES new - 5h old LES

Conclusions

• The extension of the EDMF (simple version) to represent momentum transport in the CBL shows promising results;

• the results show improvements in momentum average profiles both for clear and shallow cumulus BLs;

• for the nieuwstadt cases the shear term seems to have a reduced impact (opposite from Brown 1999 in Bomex);

• need of LES updraft analysis to understand the relative importance of each contribution;

• the mass-flux formulation in the cloudlayer needs improvements, for example through .c