Entrainment rates in stratocumulus computed from a 1D TKE model

Stephan de Roode

KNMI

Computation of the flux

Representation of entrainment rate we

1. K-profile K = we z , we from parametrization

2. TKE model K(z) = TKE(z)1/2 l(z) , we implicit

Question

Does we from a TKE model compare well to we from parametrizations?

Turbulent mixing and entrainment in simple closure models

zK''w

Entrainment parameterizations designed from LES of stratocumulus (Stevens 2002)

• Nicholls and Turton (1986) we 2.5AWNE

v,NT 2.5A T2v,dry T4 v,sat

• Stage and Businger (1981) Lewellen and Lewellen (1998) VanZanten et al. (1999)

we AWNE

T2v,dry T4 v,sat

• Lilly (2002) we ADLWNE,DL

v,DL ADL L2v,dry L4v,sat

• Moeng (2000)

l

pLb

LlMe

c/e3F''wAw

m

• Lock (1998)

v

pLWtNEALe

c/FAWA2w

Stability jumps

v,sat = 2 (the CTEI criterion, Randall 1980, Deardorff 1980)

Solve entrainment rate for a stratocumulus-topped boundary layer

we A w*

3

g

0 H v

we 2.5AWNE

v 2.5A T2v,dry T4v,sat

-0.04 -0.02 0 0.02 0.040

0.2

0.4

0.6

0.8

1

<w'v'>

WE

WNE

<w'v'>

norm

alize

d h

eig

ht

solve for entrainment rate

Solve entrainment rate for a stratocumulus-topped boundary layer

we A w*

3

g

0 H v

we 2.5AWNE

v 2.5A T2v,dry T4v,sat

-0.04 -0.02 0 0.02 0.040

0.2

0.4

0.6

0.8

1

<w'v'>

WE

WNE

<w'v'>

norm

alize

d h

eig

ht

solve for entrainment rate

Solve entrainment rate for a stratocumulus-topped boundary layer

we A w*

3

g

0 H v

we 2.5AWNE

v 2.5A T2v,dry T4v,sat

we __________forcing WNE

"jumps"

-0.04 -0.02 0 0.02 0.040

0.2

0.4

0.6

0.8

1

<w'v'>

WE

WNE

<w'v'>

norm

alize

d h

eig

ht

solve for entrainment rate

Entrainment parameterizations designed from LES of stratocumulus (Stevens 2002)

• Nicholls and Turton (1986) we 2.5AWNE

v,NT 2.5A T2v,dry T4 v,sat

• Stage and Businger (1981) Lewellen and Lewellen (1998) VanZanten et al. (1999)

we AWNE

T2v,dry T4 v,sat

• Lilly (2002) we ADLWNE,DL

v,DL ADL L2v,dry L4v,sat

• Moeng (2000)

l

pLb

LlMe

c/e3F''wAw

m

• Lock (1998)

v

pLWtNEALe

c/FAWA2w

GCSS stratocumulus cases

-10

-5

0

0 5 10 15

q

t [g

/kg

]

l [K]

buoyancy reversal criterion

DYCOMS II RF01

FIRE I (EUROCS)

initial jumps for differentGCSS stratocumulus cases

ASTEX A209 ASTEX RF06 (EUCREM)

DYCOMS II RF02

ASTEX A209 boundary conditions

_________________________________

cloud base height = 240 m

cloud top height = 755 m

sensible heat flux = 10 W/m2

latent heat flux = 30 W/m2

longwave flux jump = 70 W/m2

max liq. water content = 0.5 g/kg

LWP = 100 g/m2

l = 5.5 K

qt = -1.1 g/kg

fill in these values in parameterizations,

but vary the inversion jumps l and qt

Entrainment rate [cm/s] sensitivity to inversion jumps -Boundary conditions as for ASTEX A209

• TKE equation

• Flux

• 'integral' length scale (Lenderink & Holtslag 2004)

• buoyancy flux weighed with cloud fraction

• ASTEX A209 forcing and initialization

• t = 60 s , z = 5 m

• Mass flux scheme turned off, no precipitation

Some details of the TKE model simulation

'p'w

'E'wzz

V'w'v

z

U'w'u''w

g

t

Ev

v

zTKEc''w

du

111

z

qB

zA1

z

qB

zAEc''w t

dl

dt

wl

wHv

Entrainment sensitivity to inversion jumps from a TKE model

• Moisture jump sensitivity

• No buoyancy reversal: entrainment rates slightly larger than parameterizations

• Buoyancy reversal: entrainment rates decrease

buoyancy reversal criterion

•ASTEX A209

Eddy diffusivities in K-closure models - Results from the EUROCS stratocumulus case

LES result results from 6 differents SCMs

0 100 200 300 400 500 6000

100

200

300

400

500

600

Kl

Kqt

Eddy diffusivity K [m2s

-1]

heig

ht

[m]

0 10 20 30 40 50 60 70 800

100

200

300

400

500

600

heig

ht

[m]

[m2 s

-1]

Kq

● LES: Eddy diffusivities for heat and moisture differ (like CBL, Wyngaard and Brost 1980)

● SCM: typically smaller values than LES

Should we care about eddy diffusivity profiles in SCMs?

Simple experiment

1. Prescribe surface latent and sensible heat flux

2. Prescribe entrainment rate

Given jumps of l and qt, fluxes at BL top are fixed

3. Consider quasi-steady state solutions

fluxes linear function of height

Consider mean state solutions from 'dz

'zK

'z''w z

z'z

0'z

0

Vary eddy diffusivity profiles with a constant factor

0 200 400 600 800 10000

100

200

300

400

500

600

Kref

x 0.2

Kref

x 0.5

Kref

Kref

x 2

Kref

x 5

Eddy diffusivity K [m2/s]

heig

ht

[m]

● Kref is identical to Kqt from LES

● 0.2 x Kref is very close to Kql from LES

LWP and shortwave radiation (normalized) solutions as a function of the eddy-diffusivity multiplication factor c

0

20

40

60

80

100

0

0.2

0.4

0.6

0.8

1

0.4 0.8 1.2 1.6 2 2.4 2.8

LWP

Fdown,surface

/Fdown,cloud top

LWP

[g

m-2

]F

dow

n,su

rface /F

dow

n,c

lou

d to

p

eddy diffusivity multiplication factor c

Mean state solutions

287.6 287.7 287.8

0

100

200

300

400

500

600

c=0.35

c=0.5

c=1

c=2

adiabat

l (LES)

heig

ht

[m]

l [K]

8.6 8.8 9 9.2 9.4 9.6 9.8

qt [g kg

-1]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

ql [g kg

-1]

Similar K profiles for heat and moisture -Interpretation

Gradient ratio: (K drops out)

Typical flux values near the surface for marine stratocumulus:

H=10 W/m2 and LE = 100 W/m2

Then a 0.1 K decrease in l corresponds to a change of 0.4 g/kg in qt

The larger the latent heat flux LE, the larger the vertical gradient in qt will be!

p

v

t

l

t

l

c

L

LE

H

K/'q'w

K/''w

z/q

z/

Conclusions

TKE model

● appears to be capable to represent realistic entrainment rates

Eddy diffusivity experiments

● stratocumulus may dissappear by incorrect BL internal structure, even for 'perfect'

entrainment rate

● observations often show adiabatic LWPs (Albrecht et al. 1990, Bretherton et al. 2004),

suggesting large values for Kqt

Recommendation

● pay more attention to K-profiles from LES

http://www.knmi.nl/~roode/publications.html

FIRE I stratocumulus observations of the stratocumulus inversion structure

de Roode and Wang : Do stratocumulus clouds detrain? FIRE I data revisited. BLM, in press