PBL transports and clouds 3-2007 Martin Köhler 1

An integral approach to modeling PBL transports and cloudsMartin Köhler, ECMWF

• EDMF @ ECMWF now and future– dry PBL– stratocumulus– shallow cumulus

• stratocumulus: evaluation against observations– EPIC marine stratus field experiment– GLAS cloud and cloud top height

• ongoing work– parcel numerics– stratocumulus down-drafts – shallow cumulus

PBL transports and clouds 3-2007 Martin Köhler 2

ARPEGE

EquatorDateline

California

GCSS Pacific Cross-Section Intercomparison Project

pres

sure

[hPa

]

100200300400500600700800900

1000

pres

sure

[hPa

]

100200300400500600700800900

1000

GFLD AM2 NCAR CAM3 NCEP

HadGAM ERA-40

liquid water [g/kg]

0.30.150.080.040.030.020.010

JJA1998Joao Teixeira

EquatorDateline

California

ECMWF

EquatorDateline

California EquatorDateline

California

PBL transports and clouds 3-2007 Martin Köhler 3

Integral appraoch to PBL transports: EDMF

M1M

K

M2

Shallow cumulus Deep cumulusStratocumulusdry BL

zcb

zi

zi

KbotM

Ktop

KbotKbot

operational

PBL transports and clouds 3-2007 Martin Köhler 4

EDMF: two box M/K decomposition(Siebesma and Cuijpers, 1995)

)()1( φφφφφ −+′′−+′′=′′ uu

e

e

u

u wawawaw

M

M-fluxenv. fluxsub-core flux

zK∂∂

−φ

PBL transports and clouds 3-2007 Martin Köhler 5

A statistical mass flux framework for organized eddies

( )' ' φφ φ φ∂= − + −

∂ uw K Mz

dry PBL

PBL transports and clouds 3-2007 Martin Köhler 6

A statistical mass flux framework for organized eddies

( )' ' φφ φ φ∂= − + −

∂ uw K Mz

Stratocumulus UP

PBL transports and clouds 3-2007 Martin Köhler 7

A statistical mass flux framework for organized eddies

( ),' ' φφ φ φ∂= − + −

∂ ∑ i u ii

w K Mz

Stratocumulus UP / DOWN

PBL transports and clouds 3-2007 Martin Köhler 8

A statistical mass flux framework for organized eddies

( ),' ' φφ φ φ∂= − + −

∂ ∑ i u ii

w K Mz

Shallow Convection

Roel Neggers

PBL transports and clouds 3-2007 Martin Köhler 9

Shallow ConvectionRoel Neggers, Martin Köhler, Anton Beljaars

PBL transports and clouds 3-2007 Martin Köhler 10

Shallow ConvectionRoel Neggers , Martin Köhler, Anton Beljaars

moist

dryK

PBL transports and clouds 3-2007 Martin Köhler 11

Stratocumulus UP: EPIC column from 3D forecasts

PBL transports and clouds 3-2007 Martin Köhler 12

ECMWF vs GLAS cloud fraction

ECMWF

GLASres: 76m

Maike AhlgrimmITCZ off ChileARM

SGP

PBL transports and clouds 3-2007 Martin Köhler 13

ECMWF vs GLAS observations: cloud top height

SC top too low!

GLAS cloud top heightGLAS strcu fraction

ECMWF cloud top heightECMWF strcu fraction

cloud top < 2km, cld > 80% Maike Ahlgrimm

PBL transports and clouds 3-2007 Martin Köhler 14

EDMF PBL: analytical updraft(with Peter Janssen)

• Parcel dominates PBL height (wu=0) and updraft properties (θu, qu, uu).• PBL height dominates mixing.• Parcel is dominated by entrainment.• Entrainment rule gives infinite entrainment at surface and PBL top.

1

uwε

τ=

( )2

212

1

uu

u

u

uu

ddz

d gdzw w

w

θ θ

θ

θ

θθ

ε

ε

ετ

= − −

−= − +

=

Updraft equations: ( )2

[m]

[m]

τθθ

τ

θ≡ −

≡ u

ugT

W w

Rescale:

Assume: constθ =

2'' ' 2 ' 1 0+ + + =WW W WThen:

Solution: ln( )β− = − topz zT T

PBL height: 0 0= +top T Wz

PBL transports and clouds 3-2007 Martin Köhler 15

EDMF PBL: analytical updraft(with Peter Janssen)

( )2

[m]

[m]

τθθ

τ

θ≡ −

≡ u

ugT

W w

positive buoyancy branch

1eβ

1β

1e

αβ

−

0z α=

1β

−

T, W

Z0.5

-0.5

0.0

-1.0 -0.5 0.50.0 1.0

PBL transports and clouds 3-2007 Martin Köhler 16

EDMF PBL: analytical updraft(with Peter Janssen)

( )2

[m]

[m]

τθθ

τ

θ≡ −

≡ u

ugT

W w

positive buoyancy branch

1eβ

1β

1e

αβ

−

0z α=

negative buoyancy branch

1β

−

T, W

Z0.5

-0.5

0.0

-1.0 -0.5 0.50.0 1.0

PBL transports and clouds 3-2007 Martin Köhler 17

SiebesmaDryEDMF2006

296 298 300 302 304Potential Temperature [K]

0

500

1000

1500

2000

2500

3000

Hei

ght[m

]

Mod

el L

evel

s

75

80

85

90

EDMF PBL: analytical updraftdry growing PBL case

0

500

1000

1500

2000

297 298 299 300 301

Hei

ght (

m)

Θ (K)

0 hr 1:30 hr 3:30 hr 5:30 hr 7:30 hr 9:30 hr

LES

SiebesmaDryEDMF2006

296 298 300 302 304Potential Temperature [K]

0

500

1000

1500

2000

2500

3000

Hei

ght[m

]

Mod

el L

evel

s

75

80

85

90

analytical 400s

SiebesmaDryEDMF2006

296 298 300 302 304Potential Temperature [K]

0

500

1000

1500

2000

2500

3000

Hei

ght[m

]

Mod

el L

evel

s

75

80

85

90

analytical 500s

numerical 400s

SiebesmaDryEDMF2006

296 298 300 302 304Potential Temperature [K]

0

500

1000

1500

2000

2500

3000

Hei

ght[m

]

Mod

el L

evel

s

75

80

85

90

numerical 500s

ztop(10h) LES=1800m

τ numerical analytical

300 1900m 1800m

400 2200m 1850m

500 2500m 1900m

Siebesma

PBL transports and clouds 3-2007 Martin Köhler 18

stratocumulus organized eddies: DYCOMS-II LES simulation

up-draft

vertical velocity & cloudBjorn Stevens (dx=35m, dz=5m)

down-draft

PBL transports and clouds 3-2007 Martin Köhler 19

stratocumulus down-drafts: scaling arguments

3x zx

up

L L 10 su w

τ ∼ ∼ ∼

IRx

p entr

RT 1Kc z

τρ ∆

∼ ∼IR cooling:

parcel time scale:1/3

top*topv i

v

gw w ' ' z 1m / sθθ⎛ ⎞

= ⎜ ⎟⎝ ⎠

∼

PBL transports and clouds 3-2007 Martin Köhler 20

LES DYCOMS-II: mixing line scatterplot of qt and θl

Steve Krueger, LES, dz=6m

PBL transports and clouds 3-2007 Martin Köhler 21

Steve Krueger, LES, dz=6m

LES DYCOMS-II: mixing line scatterplot of w

PBL transports and clouds 3-2007 Martin Köhler 22

SCM DYCOMS-II: up- and down-drafts

PBL transports and clouds 3-2007 Martin Köhler 23

LES DYCOMS-II: cloud liquid water

Steve Krueger, LES, dz=6m

Cloud Liquid Water

CLW

[g/kg]

PBL transports and clouds 3-2007 Martin Köhler 24

EDMF @ ECMWF

• dry PBL• stratocumulus

– updraft– downdraft

• momentum• plume solution• shallow convection

– dual M– dual cloud

( )' ' φφ φ φ∂= − + −

∂∑ ∑i i uii i

w K Mz