Entrainment in stratocumulus clouds

Stephan de Roode (KNMI)

Entrainment in stratocumulus clouds

4 6 8 10

total specific humidity [g/kg]

0 0.5

liquid water content [g/kg]

284 288 292 2960

100

200

300

400

500

600

700

800

temperature [K]

cloud top

cloud base

stratocumulus vertical structure

290 295 300

virtual potential temperature [K]

θv =θ 1+0.61q−ql( ) θl ≈θ−Lvcp

ql

liquid water potential temperature [K]

284 288 292 2960

100

200

300

400

500

600

700

800

temperature [K]

cloud top

cloud base

stratocumulus: vertical structure

Key questions

• How well is stratocumulus represented in models?

• Entrainment

- what is it?

- why important?

- how parameterized?

• Boundary-layer mixing and cloud liquid water path

- perfect boundary-conditions, perfect cloud structure?

• FIRE I observations revisited

- a different view on entrainment

ISCCP stratocumulus cloud climatology

ECMWF RE-ANALYSIS shortwave radiation errors

GCSS intercomparison cases

• Stratocumulus case based on observations (FIRE I)

• Prescribe

- initial state

- large-scale horizontal advection

- large-scale subsidence rate

• Simulation of diurnal cycle

- 1D versions of General Circulation Models

- Large-Eddy Simulation Models (LES)

GCSS intercomparison cases

0 5 10 15-10

-5

0

Δθl [ ]K

Δq

t

[ / ]g kg

03 ( )ASTEX RF EUCREM

( )FIRE I EUROCS

01 ( )DYCOMS II RF GCSS

initial jumps for three

GCSS stratocumulus cases• Stratocumulus case based on observations (FIRE I)

• Prescribe

- initial state

- large-scale horizontal advection

- large-scale subsidence rate

• Simulation of diurnal cycle

- 1D versions of General Circulation Models

- Large-Eddy Simulation Models (LES)

GCSS FIRE I intercomparison participants

Fine-scale turbulence models [Large-Eddy Simulation Models (LES)] : Δx=Δy=50m, Δz=10m1. IMAU - Peter G. Duynkerke, Stephan de Roode, M. C. van Zanten and P. Jonker2. MPI - Andreas Chlond, Frank Müller, and Igor Sednev3. WVU - David Lewellen 4. INM - Javier Calvo, Joan Cuxart, Dolores Olmeda, Enrique Sanchez 5. UKMO - Adrian P. Lock 6. NCAR - Chin-Hoh Moeng (NCAR)

1D versions of General Circulation Models [Single-Column Models (SCM)]1. LMD - Sylvain Cheinet 2. MPI - Andreas Chlond, Frank Müller, and Igor Sednev3. Meteo France I - Hervé Grenier4. Meteo France II - Jean-Marcel Piriou5. ECMWF - Martin Köhler6. CSU - Cara-Lyn Lappen7. KNMI - Geert Lenderink8. UKMO - Adrian P. Lock9. INM - Javier Calvo, Joan Cuxart, Dolores Olmeda, Enrique Sanchez

3D results from Large-Eddy Simulation results -The cloud liquid water path

Local time [h] LWP [g/m2] SWnet,sfc [W/m2]

night-time 0100 ≤ t ≤ 0400 156 ± 11

daytime 1100 ≤ t ≤ 1400 69 ± 20 551 ± 104

0

50

100

150

200

250

0 8 16 24 32 40 48

MMobs

obs

IMAU

MPI

UKMO

INM

NCAR

WVU

LWP [ g m

-2 ]

local time [hours]

What is entrainment?Why is entrainment important?

Entrainment- mixing of relatively warm and dry air from above the inversion into the cloud layer- important for cloud evolution

3D results from Large-Eddy Simulation results -Entrainment rates

Local time [h] LWP [g/m2] SWnet,sfc [W/m2] entrainment rate [cm/s]

night-time 0100 ≤ t ≤ 0400 156 ± 11 0.58 ± 0.08

daytime 1100 ≤ t ≤ 1400 69 ± 20 551 ± 104 0.36 ± 0.03

0.2

0.4

0.6

0.8

0 8 16 24 32 40 48

IMAUMPIUKMOINMNCARWVUmean

local time [hours]

Boundary-layer representation

w'ψ' =−Kψ∂ψ∂z

w'ψ' =Mc ψc −ψ( )

1D results from General Circulation Models -The cloud liquid water path (LWP)

0

50

100

150

200

250

0 8 16 24 32 40 48

MMobsobsKNMI RACMOINM MESO-NHINM HIRLAMCSU MassfluxLMD GCMMPI ECHAMARPEGE Clim.UKMOARPEGE NWPECMWF

LWP [ g m

-2 ]

local time [hours]

Single Column Model liquid water path results very sensitive to

• entrainment rate

• drizzle parameterization

• convection scheme (erroneous triggering of cumulus clouds)

Key questions


• Entrainment

- what is it?

- why important?






The clear convective boundary layer (CBL) -Entrainment scaling from observations

Entrainment rate we scales as

• A ≈ 0.2

• H boundary-layer height

• (g/θ0) Δθv buoyancy jump across the inversion

• w* convective velocity scale: vertically integrated buoyancy flux

we=A w*

3

gθ0

H Δθv

Buoyancy flux in stratocumulus

convective velocity scale w* depends on entrainment rate we

w'θv'T =−weΔθv,sat

-0.04 -0.03 -0.02 -0.01 0 0.01 0.020

200

400

600

800

virtual potential temperature flux <w' θv> [ / ] ' Km s

entrainment

longwave radiative cooling

condensation

Solve entrainment rate

we=A w*

3

gθ0

H Δθv we =

2.5AWNE

Δθv +2.5A T2Δθv,dry+T4Δθv,sat( )

solve for entrainment rate

we __________forcing WNE

"jumps"


we=A w*

3

gθ0

H Δθv we =

2.5AWNE



"jumps"

-0.04 -0.02 0 0.02 0.040

0.2

0.4

0.6

0.8

1

<w'θv>'

WE

WNE

<w'θv>'



we=A w*

3

gθ0

H Δθv we =

2.5AWNE



"jumps"

-0.04 -0.02 0 0.02 0.040

0.2

0.4

0.6

0.8

1

<w'θv>'

WE

WNE

<w'θv>'



we=A w*

3

gθ0

H Δθv we =

2.5AWNE



"jumps"

-0.04 -0.02 0 0.02 0.040

0.2

0.4

0.6

0.8

1

<w'θv>'

WE

WNE

<w'θv>'


Stability jumps

Stability jumps

Stability jumps

Entrainment parameterizations for stratocumulus -Results based on LES results

• Nicholls and Turton (1986)

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

• Lock (1998)

• Lilly (2002)

we = 2.5AWNE

Δθv +2.5A T2Δθv,dry +T4Δθv,sat( )

we = 2.5AWNE

Δθv,NT +2.5A T2Δθv,dry+T4Δθv,sat( )

we = AWNE

T2Δθv,dry+T4Δθv,sat

we = 2AAL WNE +αtAwΔFL / ρcp

Δθv

we = ADLWNE,DL

Δθv,DL +ADL L 2Δθv,dry+L4Δθv,sat( )

• Based on observations of clear CBL

Sensitivity of entrainment parameterizations to inversion jumps

observations from ASTEX Flight A209__________________________________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 liquid. water content = 0.5 g/kgLWP = 100 g/m2

Compute entrainment rate from parameterizations as a function of inversion jumps

Entrainment rate [cm/s] sensitivity to inversion jumps

Entrainment rate [cm/s] parameterizationsof observed cases

Parameterization Case Observed

Moeng Lock Lilly Nicholls-Turton

Lewellen

North Sea NT620 0.55 0.50 0.13 0.30 0.30 0.33

North Sea NT624 0.56 0.76 0.28 0.55 0.66 0.61

ASTEX A209 0.9 ± 0.3 1.23 0.42 0.86 1.06 0.97

ASTEX RF06 1.0 ± 0.6 1.24 0.48 1.04 1.31 1.33

DYCOMSII RF01 0.38 ± 0.10 0.72 0.69 0.62 0.60 0.64

FIRE I 0.58 ± 0.08

(mean LES)

0.57 0.16 0.37 0.35 0.50

high low

Entrainment results mirror the LES results where they are based on

• Turbulent flux at the top of the boundary layer due to entrainment:

("flux-jump" relation)

• Top-flux with K-diffusion:

Entrainment parameterizations -

Implementation in K-diffusion schemes

w'ψ'T =−weΔψ

w'ψ'T =−KψΔψΔz

⇒ Kψ =weΔz

Key questions


• Entrainment

- what is it?

- why important?






Compute eddy- diffusivity

coefficients from FIRE I

LES

Kψ =−w'ψ'

∂ψ / ∂z

288 292 296 300 3040

200

400

600

800

1000

Liquid water potential temperature θl [ ]K

0.005 0.008 0.010

200

400

600

800

1000

total water content [g/kg]

-0.04 00

200

400

600

800

1000

<w'θl> [ / ]' mK s

0 100

1.5 10-5

0

200

400

600

800

1000

<w'qt'> [(g/kg) m/s]

K-coefficients from FIRE I LES

Kψ =−w'ψ'

∂ψ / ∂z

0 100 200 300 400 500 6000

100

200

300

400

500

600

K_ θl

_K qt

[Eddy diffusivity coefficient m2 / ]s

Importance of eddy-diffusivity coefficients on internal boundary-layer structure

• Change magnitude K profiles

• Compute vertical profiles θl and qt from integration

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]

∂ψ∂z

=−w'ψ'Kψ

same

change

Total water content profiles for different K-profiles but identical vertical flux

8 8.5 9 9.5 100

100

200

300

400

500

600

Kref

x 0.2

Kref

x 0.5

Kref

Kref

x 2

Kref

x 5

Kref

x inf

total water content [g/kg]

Liquid water content profiles for different K-profiles

K factor LWP [g/m2]

0.2 2

0.5 52

1.0 79

2.0 94

5.0 103

109

Magnitude K-coefficient in interior BL important for liquid water content!

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

100

200

300

400

500

600

Kref

x 0.2

Kref

x 0.5

Kref

Kref

x 2

Kref

x 5

Kref

x inf

liquid water content [g/kg]

Key questions


• Entrainment

- what is it?

- why important?






FIRE I stratocumulus over the Pacific Ocean -

Aircraft lidar observations of cloud-top height

0

200

400

600

800

1000

0 10 20 30 40 50 60 70

horizontal distance [km]

Thermodynamic structure of clear air above cloud top depressions

clear air value

mean in-cloud value

Evaporation of cloud top by turbulent mixing horizontal winds

vertical velocity

liquid water content

liquid water potential temperature

total water content

turbulence turbulence

evaporation

12 km

Observations of moist and cold layers on top of stratocumulus

Entrainment mixing scenario

Conclusions

• Entrainment parameterizations

- extrapolation of Large-Eddy Simulation results

- considerable differences

different heat and moisture budgets

• Cloud liquid water path and K-diffusion turbulence schemes

- different solutions for identical surface and cloud-top fluxes

different albedo

• Entrainment observations

- may induce the formation of moist layers above cloud top

opposes general view on the entrainment process

stability jumps

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Entrainment in stratocumulus clouds

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