Large Eddy Simulation of

PBL turbulence and clouds

Chin-Hoh Moeng

National Center for Atmospheric Research

OUTLINE

1. The LES technique

2. PBL turbulence and clouds

3. Role of LES in PBL research

4. Future direction

Numerical methods of studying turbulence

• Reynolds-average modeling (RANS)

model just ensemble statistics

• Direct numerical simulation (DNS)

resolve for all eddies

• Large eddy simulation (LES)

intermediate approach

1. LES

turbulent flow

Energy-containing eddies

Subfilter scale eddies

(not so important)

(important eddies)

Example: An 1-D flow field

)()(~

)( xfxfxf

f

Apply filter

Reynolds average model (RANS)

)(')()( xfxfxf

f

Apply ensemble avg

non-turbulent

LES EQUATIONS

2

2

0

1

j

i

i

i

j

ij

i

x

u

x

p

T

g

x

uu

t

u

dxdydzGuu ii ~

2

2

0

~)~~(~1~~~

~

j

i

j

jiji

i

i

j

ij

i

x

u

x

uuuu

x

p

T

g

x

uu

t

u

~

SFS

Apply filter G

The premise of LES

• Large eddies, most energy and fluxes, explicitly calculated

• Small eddies, little energy and fluxes, parameterized, SFS model

LES solution is supposed to be insensitive to SFS model

Caution

• near walls: eddies small, unresolved

• very stable region: eddies intermittent

• cloud, radiation, chemistry…

introduce more uncertainties

Major differences between geophysical and engineer flows

• inertial (vs. viscous) layer near walls (molecular term is always neglected)• entrainment-into-inversion (vs. rigid top)• buoyancy effect• cloud processes

fL

PBL

~ meters

2. WHAT IS THE PBL?

• turbulent layer– lowest ~km on the Earth surface

• directly affected by surface – heating, moisture, pollution, sfc drag

• diurnal cycle over land– convective and stable PBLs

PBL TURBULENCE

• dispersion

• transport

• ground temperature

• air-sea interaction

• global radiation budget

via marine stratocumulus clouds

ANNUAL STRATUS CLOUD AMOUNT

~ 100%

< 10%

transition

marine stratocumulus off California coast

persistent all NH summer!

from aircraft

capped by a strong inversion

Stratocumulus-topped PBL

~ 50%

< 10%

ocean

PBL

4% increase in area covered by PBL stratocumulus cloud

2-3 K cooling of global temperature

(Randall et al 1984)

Stratocumulus-topped PBL

cold ocean water

PBL

entrainment

radiative cooling

evaporation

drizzlecondensation

Warm and dry aloft

two cloud-top processesradiation evaporation

entrainment

PBL

cold ocean surface

cloud-top mixing process

TBTaT

lball

QQQ )1(

)1(

fluid a

fluid b

saturation point

v

b

a

:1

:

1

ISSUES on marine stratocumulus PBL

• formation and dissipation processes?

• parameterization in climate model?

• cloud albedo?

• cloud amount or if global warming occurs?

Different PBL Regimes

• convective PBL• stable PBL• oceanic boundary layer• shallow cumulus-topped• stratocumulus-topped• PBL over wavy surface• …

3. LES ofDIFFERENT PBL REGIMES

• Domain setup

• Large-scale forcing

• Flow characteristics

Clear convective PBL

gU

z

km5~

Q

Convective updrafts

~ 2

km

The stable PBL

gU

z

Q

km1

STABLE BOUNDARY LAYER

w contours

Wind profile

Heat flux profile

m500

Oceanic boundary layer

z

m300~

Add vortex force for Langmuir flows McWilliam et al 1997

m100

sfc

Shallow cumulus clouds

gU

z

Q

layercloud

Add phase change---condensation/evaporation

~ 6 km

~3 k

m

~ 12 hr

How to include condensation/evaporation in LES?

...

...

......0

TT

ll

v

qVt

q

Vt

T

g

t

w

);( Tlv qF

conserved variables

Stratocumulus-topped PBL

gU

zlayercloud

Add latent heat and longwave radiation

~ 5 km

~1 k

m

erad cooling

cloud layer

thin rad cooling layer

>10K

F F

hei

ght

0

Q_radIR radiative fluxes

O(100K/day)

How to include longwave radiation in LES?

radl

toprad

radprad

Qt

zzFF

z

FcQ

..........

)exp(

LES vs.

observation

mean thermodynamic properties

time evolution of cloud top, bottom w-variance and skewness

heat fluxesmoisture flux

buoyancy flux

radl Fw ;Twq vw

Z (

m) cld top

cld base

How do we studyPBL turbulence and clouds

with LES?

• Study turbulence behavior and processes responsible for transport

(creative thinking; flow vis.)

• Develop or calibrate ensemble-mean models (RAN models)

(large database)

CLASSICAL EXAMPLES

• Deardorff (1972; JAS)- mixed layer scaling

• Lamb (1978; atmos. env)- plume dispersion property

izw ,

Entrainment

Sullivan et al 1998JAS

So far, idealized PBLs:

• Flat surface

• Periodic B.C. in horizontal

• Shallow cloud regimes

Challenge of LESfor PBL Research

Real-world PBLs:– complex terrain

– complex land use

– ocean waves

– severe weather

4. FUTURE RESEARCH

Extending LES applications to real-world PBL problems

Use a state-of-the-art weather model

Why Weather Research and Forecast (WRF) model?

• Available input data:– Terrain, land properties, meteorol conditions

• Higher-order numerical schemes• Terrain-following coordinate• Design for massive parallel computers

– partition in vertical columns

500 km

20 km

nest an LES inside the WRF model

Technical Issues

• Inflow boundary conditions• SFS representation near irregular

surfaces• Proper scaling; how to represent

ensemble statistics

???

How to describe a turbulent inflow?

SUMMARY

• LES in advancing PBL research

• Marine stratocumulus in climate models

• Technical issues in extending LES to real PBLs