Stratocumulus – Theory and Model

Martin Köhler(room 108)

• Definition• Phenomenology• Theory• Parameterization• Remaining Challenges• Summary

Stratocumulus - Definition

PBL clouds – visual definition

• Fog: Result of moist air in contact with cold surface. • Stratocumulus: Horizontally variable; near PBL top.• Stratus: Horizontally uniform; near PBL top.• Nimbostratus: Precipitating; deep.

Stratocumulus-Topped Boundary Layer (STBL) physical definition

Mixed layer PBL with cloud near top.

Stratocumulus - Motivation

• Cloud top albedo is 50-80% (in contrast to 7 % at ocean surface).

• A 4% increase in global stratocumulus extend would offset 2-3K global warming from CO2 doubling (Randall et al. 1984).

• Coupled models have large biases in stratocumulus extend and SSTs.

DEMETER CGCM Surface Temperature Bias [K]

-6.0 -5.0 -4.0 -3.0 -2.0 -1.0 1.0 2.0 3.0 4.0 5.0 6.0

Surface Temperature [oC]

Forecast start dates: 05/1987-1996, FC period: months 4-6 (ASO), ens: 0-8

Bias: EXP(ECMWF_assim) regarding ERA-40 reanalysis

-6.0 -5.0 -4.0 -3.0 -2.0 -1.0 1.0 2.0 3.0 4.0 5.0 6.0

Surface Temperature [oC]

Forecast start dates: 05/1987-1995, FC period: months 4-6 (ASO), ens: 0-8

Bias: EXP(UKMO) regarding ERA-40 reanalysis

-6.0 -5.0 -4.0 -3.0 -2.0 -1.0 1.0 2.0 3.0 4.0 5.0 6.0

Surface Temperature [oC]

Forecast start dates: 05/1987-1992, FC period: months 4-6 (ASO), ens: 0-8

Bias: EXP(MPI) regarding ERA-40 reanalysis

-6.0 -5.0 -4.0 -3.0 -2.0 -1.0 1.0 2.0 3.0 4.0 5.0 6.0

Surface Temperature [oC]

Forecast start dates: 05/1987-1994, FC period: months 4-6 (ASO), ens: 0-8

Bias: EXP(CNRM) regarding ERA-40 reanalysis

-6.0 -5.0 -4.0 -3.0 -2.0 -1.0 1.0 2.0 3.0 4.0 5.0 6.0

Surface Temperature [oC]

Forecast start dates: 05/1987-1994, FC period: months 4-6 (ASO), ens: 0-8

Bias: EXP(LODYC) regarding ERA-40 reanalysis

UKMO

MPI

MeteoFrance

LODYC

4-6 month forecasts Aug/Sep/Oct 1987-1996

9 ensemble memberscomparison to ERA-40

www.ecmwf.int/research/demeter

ECMWF

EPIC: Peruvian stratocumulus – model comparison

EPIC obs

NCAR CAM2.0

GFDL AM2.10

ECMWF 23r4

NCEP

Bretherton et al, BAMS 2004

LWC [g/m3] qv [g/kg] [K]

Stratocumulus … from Satellite

MODIStrue color

(1540UTC, 20 Oct. 2001)

EPIC16-21Oct2001

Peru

SST & surface wind

Chile

Stratocumulus …Microphysics

LWP [g/m2] re [m] Nd [cm-3]

true colorMODIS

Stratocumulus … over OceansLos Lagos, Chile

Bernhard Mühr, www.wolkenatlas.deStratocumulus lenticularis

Stratocumulus … over Land

Stratocumulus stratiformis opacus cumulogenitusStratocumulus stratiformis translucidusBernhard Mühr, www.wolkenatlas.de

Yellowstone,USAGermany

Stratocumulus …Macroscales

visibleearth.nasa.gov

closed cellswith diameter:

10-15km

MISR sensoron Terra satellite

Large-eddy Simulation of Stratocumulus

Duynkerke et al. 2003

stratocumulus … LES: DYCOMS II

simulation by Bjorn Stevens (1995)(dx=35m, dz=5m)

vertical velocity

cloud

Annual Stratus Cloud Amount

Klein & Hartmann 1993

Peruvian

Namibian

Californian

North PacificArctic

North Atlantic

China

Circumpolar Ocean

Canarian

Australian

Surface based observations (mean=29%)

Physical processes in marine stratocumulus

Nieuwstadt & Duynkerke 1996

• PBL: turbulent fluxes

• cloud: condensation

• aerosols: drizzle

• radiation: destabilization

• LS dynamics: subsidence

• cloud top entrainment

• decoupling

Mixed layer perspective of stratocumulus

Consider variables that are conserved for moist processes e.g. liquid water potential temperature:

lp

l qTc

stvt

stsvlvt

qqifqq

qqifqqqqq

,

and total water:

Derive virt. potent. temp. flux {

3 ,37.0:15

'' '' ''

''61.0'' ''

21

21

Cat

cloudinqwww

cloudsubqwww

o

tlv

tlv

)61.01( lvv qq }:

Stratocumulus

Deardorff 1976, QJRMS, 102, 563-582.Stevens 2000, Geoph. Res. Letters, 27, 2557-2560.

00

ltqw ''

drizzle

lq

tq

lw ''vw '' tq

lLWR

Radiative cooling

Entrainment

PBL budget considerations: IMET-stratocumulus

m

i

s

iq

sq

mq

0/)()( PqqUCqqw smHmie

0)()( LPdRdRUCcwc SWLWsmHpmiep

-3.0 +3.3 -0.3 [mm/day]

+40 +10 -80 +20 +10 [W/m2]

Moisture budget:

Heat budget:

Stratocumulus parameterization - Ingredients

• Strong mixing– K-diffusion

– mass-flux

– well-mixed assumption

• Cloud scheme– diagnostic

– prognostic

• Cloud top entrainment– Function of cloud top radiative cooling and surface flux

• Radiation interaction

• Transition to trade cumulus– high/low cloud fraction

Old ECMWF Stratocumulus Parameterization – a web

• dry diffusion• variable: dry static energy and WV• PBL top entrainment:

• shallow convection• closure: moist static energy equilibrium in sub-cloud layer• updraft entrainment/detrainment: • cloud creation: detrainment of cloud volume and cloud water

• cloud• supersaturation removal into cloud• cloud top entrainment:

• radiation• resolution: every 3 hours and every 4th point

sfc

v

entr

v swsw 2.0

14103 m

LWp

h

v

entr

v Fcdzswh

sw 5.01

5.00

shallow convection

dry diffusion

Schematic: Old and New PBL

dry top entrainment

cloud top entrainment

cp Flwwe = 0 .5

Sv

cp Flwwe = 0 .2

Sv

qt

l

Current situation "As it should be"

unification – an M/K approach

Combined mass flux/diffusion:

done

next

M1M

K

M2

Shallow cumulus Deep cumulusStratocumulusdry BL

zcb

zi

zi

KbotM

Ktop

KbotKbot

)( ,

iui

iMz

Kw

two box M/K decomposition

u

uuu e

eee

e

e

u

u aa )1(

a

)()1( uu

e

e

u

u wawawaw

M

M-fluxenv. fluxsub-core flux

zK

Siebesma & Cuijpers, 1995

BOMEX LES decomposition

total flux

M-flux

env. flux

sub-core flux

Siebesma & Cuijpers, 1995

M-flux covers 80% of flux

cloud variability

parameterization choices

• updaft model:• entrainment: , τ=500s,

c=0.55

• detrainment: 3·10-4 m-1 in cloud

• parcel determines PBL depth (wup= 0)

• mass flux:

• diffusion:• surface and cloud top driven diffusion

• cloud top entrainment:

LWp

sfc

v

entr

v Fcswsw 2.0

• cloud cover:• total water variance equation

not yet

PBL

qt

z

uqttt

qt

h

w

z

w

z

qqw

t

2'22

2

zc

wu

1

Mz

M)(

Mass-flux K-diffusion

Results: Low cloud cover (new-old)

T511 time=10d

n=1402001 & 2004

old: CY28R4 new PBL

Results: EPIC column extracted from 3D forecasts

Stratocumulus Parameterization Challenges

• cloud top entrainment

• numerics

• drizzle • droplets larger near PBL top critical cloud depth of ~300m• role of aerosols?

• cloud regime (stratocumulus/trade cumulus) • CTEI• open/closed cells• decoupling

(due to solar and terrestrial heating/cooling cloud cut of from moisture supply from below thinning of cloud)

shall. conv.

well mixed

sl

z

Stratus Cloud Amount vs. Stability

Klein & Hartmann 1993

Cloud Top Entrainment Instability (CTEI) - Theory

Randall 1980Deardorff 1980

0 tp qTch

p

sat

p

p

p

T

q

c

L

TL

c

LqgzTch

1

608.11

Randall - Deardorff criteria

Cloud Top Entrainment Instability – Observations

Duynkerke et al. 2003

CTEI criteria

vw ''

LWR

wqw '' lw ''

entrainmentrad. cooling

P

P

N

stratocumulus to trade cumulus transitioncriteria

ChileEPIC, Oct 2001

• cloud thickness:

• static stability: θ700hPa- θsfc < 20K

• cloud top entrainment instability:

• buoyancy flux integral ratio:

N/P > 0.1

03.04.0 tl qLs

mzcld 1000

Stratocumulus & Aerosols

Why?

Summary

• Stratocumulus: important– climate

– land temperature

• Stratocumulus: simple– horizontally uniform

(cloud fraction ~100%)

– vertically uniform

(well-mixed)

• Stratocumulus: difficult to parameterize– multiple processes

– multiple scales