The representation of stratocumulus with eddy diffusivity closure models

Stephan de Roode

KNMI

Global stratocumulus presence

Motivation of the problem

ECMWF underestimates stratocumulus

ECMWF underpredicts stratocumulus Liquid Water Path (LWP)

Duynkerke and Teixeira (2001)

RACMO uses ECMWF physics!

Entrainment of relatively warm and dry inversion air into the cloudy boundary layer

Bjorn Stevens

Entrainment: the holy grail in stratocumulus research

"Dogma": solve the stratocumulus problem by getting the entrainment rate right in a model

Topics:

1. Dogma is not true

2. Entrainment rates from a TKE scheme compared to parameterizations

Tendency equation for the mean

Computation of the flux

Turbulent transport in closure models

zK''w

S

z''w

t

Eddy diffusivities diagnosed from LES results - Results from the FIRE I stratocumulus intercomparison case

LES result

0 100 200 300 400 500 6000

100

200

300

400

500

600

Kl

Kqt

Eddy diffusivity K [m 2s-1]

heig

ht [m

]

● LES: Eddy diffusivities for heat and moisture differ

Eddy diffusivities in K-closure models - Results from the FIRE I stratocumulus intercomparison case

LES result 6 single-column models (SCMs)

0 100 200 300 400 500 6000

100

200

300

400

500

600

Kl

Kqt

Eddy diffusivity K [m 2s-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

● SCM: typically much smaller values than LES

Kheat = Kmoisture

Should we care about eddy diffusivity profiles in SCMs?

Simple experiment

1. Prescribe surface latent and sensible heat flux

2. Prescribe entrainment fluxes

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

Use fixed flux profiles from LES results(so we know the entrainment fluxes)

'dz

'zK'z''w z

z'z

0'z

0

Vary eddy diffusivity profiles with a constant factor c

0 200 400 600 800 10000

100

200

300

400

500

600

Kref x 0.2Kref x 0.5KrefKref x 2Kref x 5

Eddy diffusivity K [m 2/s]

heig

ht [m

]

● Kref is identical to Kqt from LES

● Multiply Kref times constant factor c

'dz

'zK'z''w z

z'z

0'z

0

Remember the dogma?

Dogma: solve the stratocumulus problem by getting the entrainment rate right in a model

If we prescribe the entrainment fluxes, do we get the right cloud structure?

Mean state solutions

287.6 287.7 287.80

100

200

300

400

500

600

c=0.35c=0.5c=1c=2adiabatl (LES)

heig

ht [m

]

l [K]

8.6 8.8 9 9.2 9.4 9.6 9.8q

t [g kg-1]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7q

l [g kg-1]

Liquid Water Path and cloud transmissivity

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

]Fdown,surface /F

down,cloud top

eddy diffusivity multiplication factor c

LWP and cloud transmission VERY sensitive to eddy-diffusivity profile

ECMWF low eddy diffusivities explain low specific humidity

0 10 20 30 40 50 60 70 800

100

200

300

400

500

600

heig

ht [m

]

[m2 s-1]

Kq

ECMWF eddy diffusivity from Troen and Mahrt (1986)

p

3*

3*h h

z1hzhkcwuK

0v

0

3* ''w

Tghw

Computation of the flux

Representation of entrainment rate we

ECMWF K-profile K = we z , we from parametrization

RACMO 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

we = fct (H, LE, zb, zi, Fl, qt, l, LWP or ql,max)

Simulation of ASTEX stratocumulus case

ASTEX A209 boundary conditions_________________________________cloud base height = 240 mcloud top height = 755 msensible heat flux = 10 W/m2

latent heat flux = 30 W/m2

longwave flux jump = 70 W/m2

max liq. water content = 0.5 g/kgLWP = 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

1. Note differences2. Buoyancy reversal3. Moisture jump sensitivity

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

1. Note differences2. Buoyancy reversal3. Moisture jump sensitivity

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

1. Note differences2. Buoyancy reversal3. Moisture jump sensitivity

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

1. Note differences2. Buoyancy reversal3. Moisture jump sensitivity

vertical lines

sensitivity to moisture jumps qt

RACMO

How does a TKE model represent entrainment?

● Some model details

● Run ASTEX stratocumulus, and check sensitivity to entrainment jumps

• 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'w

zzV'w'v

zU'w'u''wg

tE

vv

zTKEc''w

du

111

zqB

zA1

zqB

zAEc''w t

dl

dt

wl

wHv

Entrainment sensitivity to inversion jumps from a TKE model

buoyancy reversal criterion

•ASTEX A209

entrainment rates decrease in this regime

many parameterizations predict rates that go to infinity

slightly larger values than Stage-Businger

Entrainment rate depends on moisture jump

Conclusions

Eddy diffusivity experiments

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

entrainment rate

TKE model● appears to be capable to represent realistic entrainment rates

FIRE I stratocumulus observations of the stratocumulus inversion structure

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

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

cL

LEH

K/'q'wK/''w

z/qz/

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 mcloud top height = 755 msensible heat flux = 10 W/m2

latent heat flux = 30 W/m2

longwave flux jump = 70 W/m2

max liq. water content = 0.5 g/kgLWP = 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