Jian-Wen Bao

NOAA/ESRL/Physical Sciences Division

in collaboration with Christopher. W. Fairall,

Sara. A. Michelson, Laura Bianco

Atmospheric Boundary Layer Modeling for Numerical Weather

Prediction at NOAA/ESRL

Presented inReykjavik, IcelandSeptember 5, 2008

OUTLINE• Parameterization of subgrid, atmospheric

boundary layer (ABL) mixing

• Parameterization of sea-spray modified surface-layer heat and momentum fluxes

• Comparisons of conventional ABL parameterization schemes with three-dimensional subgrid turbulence closure schemes

• Theoretical and practical aspects of the implementation of a Mellor-Yamada level 2.5, two-equation ABL scheme in NWP models

• Physical process in the atmosphere

Specification of heating, moistening and frictional terms in terms of dependent variables of prediction model →Each process is a specialized branch of atmospheric sciences.

* Parameterization

The formulation of physical process in terms of the model variables as parameters (constants or functional relations).

ln,

p

d H dqS

dt c T dt

θ = =

Atmospheric Scales of Motion

Unresolvable scales in NWP models

0,x∆ →

Subgrid scale process Any numerical model of the atmosphere must use a finite resolution in representing continuum certain physical & dynamical phenomena that are smaller than computational grid.

- Subgrid process (Energy perspective)

the energy dissipation takes place by molecular viscosity

real atmosphere

Objective of subgrid scale parameterization

To design the physical formulation of energy sink, withdrawing the equivalent amount of energy comparable to cascading energy down at the grid scale in real atmopshere.

•

3L

Unresolvable amount of E

E

idealize situation

ABL Mixing and Surface Layer

Surface layer : compute surface fluxes and update surface temperature and humidity by solving soil model and surface energy budget

Surface energy budget

ln,

p

d H dqS

dt c T dt

θ = =

ABL

2,( ) : diffusivity, , = ( )c c m t m t

c c Uk k k k l f Ri

t z z z

∂ ∂ ∂ ∂=∂ ∂ ∂ ∂

※

Local Reynolds number

( ( ))c c

c ck

t z zγ∂ ∂ ∂= −

∂ ∂ ∂ 2

0

1*

(1 )

( )

( ( ) )

( ' ')( )

0.1

pzm s

mibcr

v s

vs va T

s

tr

m

s m

zk kw z

h

U hh R

g h

wb

w

hp bk

h

w u

θθ θ

θθ θ θ

φφφ−

= −

=−

= + =

= +

=

- Local vertical diffusion

- Nonlocal ABL

Vertical diffusion (ABL)

TKE (Turbulent Kinetic Energy) Dependent Diffusivity

TKE eqn.:

(Mellor & Yamada, 1982)

1[ ]

( )

i j i jj i j k

j k

i j z ij

u u u uu u u u

t x x

u u k fn e

ρ∂ ∂ ∂+ = − +

∂ ∂ ∂

=

L

→ →

Bulk method

wind shear

0

0

0

0

0

, ( , , )

at surface layer

above sfc

where

p H a

H a a

D a a

D H i

zP

z

H C C V T

E LC V qM

C V V

C C fn R Z

H Tk

T z C z

t Tk

zk

ρ

ρ

τ ρ

θρθ

θρθ

= ∆

= ∆

=

=

∂ ∂= +∂ ∂ ∂∂ ∂= ∂

r

r

rr

L

( , )z ifn R S=

Surface Layer Parameterization

Monin-Obukov similarity

* *

( / ), ( / )z zm t

k kuz L z L

u z u z

θφ φ∂ ∂= =∂ ∂

00

0

ln( ) ( , , )sh

sm m m sz

hdzF dz h z L

z zφ ψ= = −∫

Φ

Integrate,

curving factor:

Surface Layer Parameterization

s

*

zz

ln

uku

Φ+

=

0

Parameterization of sea-spray modified surface-layer heat

and momentum fluxes

Sea Spray and Tropical Cyclones

The effect of the sea spray on the hurricane dynamics is two-fold:

Thermodynamics: The variation of the bulk energy due to the evaporation of droplets in the sea spray and subsequent cooling of the atmosphere (J. Lighthill, 1999)

Mechanics: Significant reduction of turbulent intensity in the flow and consequently a flow acceleration (G. I. Barenblatt et. al, 2005)

Ocean

Atmosphere

Ocean spray

Sandwich model:

Sea Spray

Thermal Evolution of Sea Spray in Air

• Droplets thrown in air: Source – Qn(r ) at h

• Individual drops transfer heat/moisture to air

• Cumulative effect computed by integrating over droplet spectrum:

Ql’=Droplet latent heat flux

Qs’=Drop sensible heat flux F r S r d rv n= ∫4 3 3π / ( )

)(4 aphpaap TTrDcfDropHeat −= ρπ

)(4 apvap qqrDfreDropMoistu −= ρπ

Q c F T Ts w p w v o a' ( )= −ρ

hdepthoverrVrSrn fn )(/)()( =

)(' apaeal qqhFLQ −= ρ

∫= drreDropMoisturnhLQ el *)('

∫∞

=z nn dzzQS )(

∫= drrV

rrSrfDF

F

npva *

)(

)()(4π

Droplet Source Functions

P energy wave breaking σ surface tensionr droplet radiusη Kolmogorov microscale in the ocean f fraction of P going into droplet productionUtop wind speed near breaker topUb group speed of breaking waveΛ Unspecified length scale (or, P/ Λ volume dissipation near surface)

Fairall et al. 1994

Fairall-Banner Physical Model (2008):

Balance of energy produced by wave breaking and lost in production of drops and bubbles. Error function describes probability drop trajectory escapes surface.

2/)]/

(1[*])(4

9exp[)(

3

4 3/43

u

fbtopkn

SlopeVUUerf

r

PfrrS

r

σπηα

σπ −+

+−Λ

=

)()()( 0 rSUWrS nbn =

Spray Production and Dynamics Experiment (SPANDEX)

Thermal Feedback

Defined by distortions of the temperature & humidity profiles in the Droplet evaporation zone: δT δq

Thermal Feedback Parameterization

.)(

)]()1()[( 0

Dmfcc

DmfLTTfTTDmcT

ievpvdpd

ieewaeaiwa δρρ

δδδ++

−−−+−=

step)time (model scaletime mequilibriudtime

dtimemassfluxmi

== *δ

Sea Spray enthalpy balance from Andreas and Emanuel 2001

massfluxL

Qf

e

le

'=

From Andreas and Emanuel 2001, JAS

Sea-Spray Modification of Momentum Flux

,Sgwzu

w'u'θ

w''θ

z

w'e'

te

fσε −−∂∂−−

∂∂

−=∂∂ g

where wf is the terminal velocity of the droplet, S is the additional buoyancy term due to spray loading, and σ indicates the relative excess of the droplet density over the air density.

The TKE equation in the Kepert-Fairall-Bao explicit sea-spray model is revised to include the momentum effect:

Basic consideration: the very turbulence that transports heat across the air-sea interface is also responsible for the momentum transport and the generation of sea spray.

Parameterization of the Sea-Spray Modification of Momentum Flux (e.g., Barenblatt 1996 and Lykossov 2001)

SwzS

Kw'S',0Sgwσεzu

w'u' fsf =∂∂−==++

∂∂

s

*

zz

ln

ku

ψ

u

+

=

0

=

+

≠

−

−

+

=

−−

1ln1ln

111

1ln12

1

ω

ωωω

ω

ψ

ω

forz

z

forz

z

h

h

s

α

α

,,2*

2

* u

Szkg

kurhf σβα ==

wω :fw

:β :hz( ) 310≅−=

a

aw

ρρρσ

Where the mean fall speed of droplets

empirical parameter spray generation height

where S is the spray concentration profile.

Impact on the Exchange Coefficients

HWRF Test with Katrina (2005)

initial time: 0000 UTC 27 August 2005

KATRINA 2005082700 HWRF Maximum Wind Speed (m/s) from track info

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70

Forecast Hour

Win

d S

pee

d (

m/s

)

Best track estimate

Control

Spray ft=1 ss=1.0

Spray ft=1 ss=10.0

Spray ft=1 ss=1.0 w/ momentum zr=10

max. wind speed

KATRINA 2005082700 HWRF Maximum Wind Speed (m/s) from track info

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70

Forecast Hour

Win

d S

pee

d (

m/s

)

Best track estimate

Control

Spray ft=1 ss=1.0

Spray ft=1 ss=10.0

Spray ft=1 ss=1.0 w/ momentum zr=10

KATRINA 2005082700 HWRF Minimum Sea Level Pressure (mb) from track info

840

860

880

900

920

940

960

980

0 10 20 30 40 50 60 70

Forecast Hour

Se

a L

ev

el P

ress

ure

(m

b)

Observations

Control

spray ft=1 ss=1.0

spray ft=1 ss=10.0

spray ft=1 ss=1.0 zr=10

track

min. sea-level pressure

Wind Speed of Hurricane Katrina (2005)

control thermal

thermal + momentum

Valid at 0060 UTC29 Aug 2005

control thermal

thermal + momentum

E-W cross sectionValid at 0060 UTC29 Aug 2005

Wind Speed of Hurricane Katrina (2005)

Summary and Conclusions• The impact of the sea-spray parameterization scheme on the track

forecast is negligible, despite the noticeable impact on the intensity.

• Both the intensity and structure are influenced by the parameterized thermal and kinematic effects of sea spray.

• The response of the storm intensity does not appear to be proportional to the change in the droplet source strength and feedback strength.

• The errors in the HWRF model forecast can only be partially attributed to the errors in the surface fluxes.

• The performance of the sea-spray parameterization scheme in the HWRF model needs to be further evaluated and calibrated.

Comparisons of conventional ABL parameterization schemes with three-

dimensional subgrid turbulence closure schemes

Motivation

A challenge to air-quality modeling, as horizontal grid spacing (∆s) decreases and becomes smaller than the depth of the atmospheric boundary layer, is how to parameterize the turbulence mixing on the subgrid scale. When ∆s is so small that the scale separation between horizontal and vertical mixing becomes less clear, conventional 1-D parameterizations for subgrid mixing used in NWP models becomes theoretically less valid and the use of parameterizations for 3-D subgrid mixing is required. In this study, we compare the results from the use of 1-D parameterized subgrid mixing with those from the use of two different parameterization schemes for 3-D subgrid mixing.

J. C. Wyngaard (2004)

Iterative Interaction of Modeling and ObservationIterative Interaction of Modeling and Observation

1-D Model 3-D Model

Observations

Short-Term Goal: Continue evaluating and improving current parameterizations in research and operational models

Long-Term Goal: Take up the challenge of the BL modeling in the “Terra Incognita”

Configuration of the WRFv2.1.2 Grid and Physics Options

• One-way nested grid: 36, 12, 4, 1, and 0.2 km• Noah Land-Surface Model• Monin-Obukhov surface layer scheme• Chemistry option: RADM2• Emissions: anthropogenic point sources only• Vertical levels: 50• 241 x 201 grid points for the 0.2 km grid• Length of forecast:

- 24h for coarser meshes, initialized at 00 UTC on 25 Aug 2000 - 10h for 0.2km mesh, initialized at 12 UTC on 25 Aug 2000

Options for subgrid turbulence mixing: - the Mellor-Yamada-Janjic (MYJ) boundary layer scheme

- the 3-D Smagorinsky closure- the 3-D turbulent kinetic energy (TKE) closure

WRF coding changes:- Coupling of surface fluxes of heat and momentum with the subgrid-scale

turbulent mixing closures - Removal of the impact of clouds on the radiation and photolysis.- Adjustment to the background chemistry

Ozone concentrations at the lowest model level at 1700 UTC (noon local time) for the simulations using a) MYJ parameterization, b) Smagorinsky closure, and c) TKE closure. The line indicates the position of the cross sections.

a b

c

Ozone concentrations as the previous figure, but 4 hours later, at 2100 UTC (4 pm local time).

a b

c

South-north cross sections of ozone concentrations at 1700 UTC through the lines shown above for the simulations using the a) MYJ parameterization, b) Smagorinsky closure, and c) TKE closure.

a b

c

a b

c

Time-height cross-sections of potential temperature averaged over a 40x40 box in the central urban area, for simulations using the a) MYJ parameterization, b) Smagorinsky closure, c) TKE closure.

a b

c

Conclusion

The results from this case study indicate that the subgrid-scale turbulence mixing is important in the WRF/Chem model for the grid spacing of 200 m. Different options for parameterizing subgrid turbulence mixing results in significant differences in the transient maxima of surface ozone concentrations. However, observations sufficient for diagnostic comparisons would be required to determine which of the three options for subgrid mixing is most appropriate.

Theoretical and practical aspects of the implementation of a Mellor-Yamada

level 2.5, two-equation ABL scheme in NWP models

ε−+=∂∂

∂∂−∂

∂

bsq PPqz

Sqlzt

q

222

2

∂∂−∂

∂−=zVwv

zUwuPs vb wgP θβ−=

lBq

1

3=ε

zUKwu m ∂

∂=−

zVKwv m ∂

∂=−zvKw Hv ∂

Θ∂=− θMm lqSK = HH lqSK =

lblsll PPlqz

qlSz

lqt

ε−+=∂∂

∂∂+∂

∂

22

The k-kl Model of Mellor and Yamada (1974, 1982) and Kantha and Clayson (1994)

ssl PlEP 1=bbl PlEP 2=

lB

qFl

1

3

=ε

( )[ ]3212

1

1

1631

61

2

CBAGA

BA

A

S

H

M

−+−

−

=

( )[ ]

( )

−

−++−−

=

H

HH

H

GAA

GSCAACBA

AS

21

22111

1

1

91

12936

1

Assume quasi-equilibrium (Ps + Pb = ε) in the specification of sM and sH

∂∂+

∂∂

=

22

2

2

z

V

z

U

q

lGM z

gq

lG v

H ∂Θ∂

−= β

2

2

)2.0,0.3,3,75.2(),,,( 21 =lSFEE

=),,,,,,( 12121 βqSCBBAA

(0.65999, 0.65749, 11.879, 7.227, 0.00083, 0.2, 1./270.)

Recommended values of empirical parameters

Possible improvements over the 2.5 level M-Y scheme:

1. Prognostic length scale: l

2. Inclusion of counter-gradient flux by using high levels of the M-Y scheme

Question of Inquiry:

If there is a need to increase the complexity of the PBL scheme in operational models, what is the minimal effective addition?

Motivation of this Study

• The use of the prognostic length scale leads to various two-equation schemes (k-kl, k-ε, k-ω, k-τ, etc.)

• H. Burchard (2002) and L. Kantha (2003) have shown that all the two-equation schemes are fundamentally equivalent; a generic length-scale prognostic equation can be used in the two-equation scheme.

• It is important to find out whether the replacement of the diagnostic length scale with a prognostic one will yield any significant gains in NWP models.

Details to Consider

Issues to Address before Implementation

• How to determine the empirical closure constants in the length-scale equation: physical constraints

• How to ensure physically sensible performance of the scheme: Non-singularity

• Reduce the computational mode in numerical integration

It has been recognized that realizability constraints suitable for the atmospheric PBL need to be established to make the scheme perform reasonably and robustly (e.g., Galperin et al. 1988).

0010.maxGHG =≤Regime I: Ri < 0

Regime III: Ri ≥ Ric = 0.72

Regime II: 0 ≤ Ri < Ric = 0.72

)zvg/(maxGql ∂

Θ∂≤ β

zvgqCl ∂

Θ∂< β4

).C( 5604

=

The eddy diffusion coefficients are specified using the gradient Richardson number–dependent parameterization proposed by Large et al. (1994).

0=l

( ) ( ) ( )

( ) ( )

∂∂

∂∂−

∂∂

∂∂+

−−−−−=∂∂

22

1

32

22

12

//

222

qz

Kz

llqz

Kz

B

qFNKlESKlE

t

lq

mmlm

Hm

σσ

0=∂∂

t

l02 =N 0/* == zuS κ 2

*2/12 2 ucq −= µ

zl κ=

*u

κ

1=lσ

( )12/12

2

1EFc −= −

µκ

the surface friction velocity

the von Karman constant

the surface friction velocity

Applying this equation into a steady neutral surface layer in which

One yields:

Test Cases(1) Convective PBL development:

Air-pollution episode with weak ambient mesoscale forcing during 0000 UTC 30 July- 0000 UTC 1 August, 2000 (MM5 model)

(2) Bore propagation observed during IHOP:

Convective bore propagation with strong ambient mesoscale forcing during 0000- 1200 UTC 4 June, 2002 (MM5 model)

(3) Mountain Wave Breaking:

Downslope windstorm on the leeside of Mnt. Öræfajökull on 16 Sept 2004 (WRF model) by Ólafur Rögnvaldsson, Hálfdán Ágústsson and Haraldur Ólafsson

one-equation model: θvtwo-equation model: θv

one-equation model: 2 x ΤΚΕ two-equation model: 2 x ΤΚΕ

one-equation model: ΚMC one-equation model: lone-equation model: ΚHone-equation model: ΚM

two-equation model: ΚM two-equation model: ΚH two-equation model: l

TKE, θ, and circulation vectors

The Two-Equation Scheme The MYJ Scheme

Downslope windstorm on the leeside of Mnt. Öræfajökull in Southeast Iceland on 16 Sept 2004

Simulated surface wind speed [ms−1] at lowest half-sigma level (approximately 40 m.a.g.) by MM5 (left panels) and WRF (right panels) at 16 September 2004, 0600 UTC. Top panels show results from the ETA and MYJ boundary layer schemes and the bottom panel shows results using the new two equation PBL model.

Downslope windstorm on the leeside of Mnt. Öræfajökull in Southeast Iceland on 16 Sept 2004(Ólafur Rögnvaldsson, Hálfdán Ágústsson and Haraldur Ólafsson)

Cross section along line AB showing potential temperature (red lines) [K], wind along the cross section (blue arrows) [ms−1] and turbulent kinetic energy (TKE) [J/kg] for MM5 (left panels) and WRF (right panels) at 16September 2004, 0600 UTC. Top panels show results from the ETA and MYJ boundary layer schemes and the bottom panel shows results using the new two equation PBL model.

Observed (solid black) and simulated (solid blue – MM5/ETA, blue dash– MM5/2EQ, solid red – WRF/MYJ, red dash – WRF/2EQ) 10 metre wind speed[ms−1] (left) and 2-metre temperature [C] (right) at station SKAFT (WMO#4172) in the lee of Mnt. Öræfajökull.

Conclusions• If the length scale is defined as the characteristic length scale of the largest

energy-containing eddies and is related to the distance that these eddies travel in the vertical direction before losing their initial TKE due to turbulent mixing and buoyancy effects, it is concluded that the closure constants in the length-scale equation should be different than those proposed previously for oceanic applications.

• To ensure physically sensible performance of the scheme, necessary constraints on the length scale and for numerically integrating the scheme.

• The constraints on the length scale are derived by requiring that the TKE equation be nonsingular under different stability regimes in terms of the gradient Richardson number.

• The numerical integration is performed using an innovative splitting algorithm to control the computational modes encountered when using conventional numerical schemes.

• The results from a series of numerical experiments indicate that when properly choosing these constants, the evolution of the ABL structure simulated by the scheme is similar to the original scheme of the MY closure in MM5-V3 where the length scale is diagnosed. However, outside of the ABL the two scheme show noticeable differences, particularly in some down-slope wind cases.

Jian-Wen Bao1, Sara A. Michelson1,2, Evelyn D. Grell1,

Georg A. Grell2,3, Irina V. Djalalova1,2

1NOAA/Earth System Research Lab./Physical Sciences Div., Boulder, CO2NOAA/CIRES, Boulder, CO

3NOAA/Earth System Research Lab./Global Systems Div., Boulder, CO

Investigation of Orographic Venting of Atmospheric Boundary Layer Air Using Observations and the WRF-Chem Model

Presented inReykjavik, IcelandSeptember 5, 2008

Outline

• Problem: Transport of ABL Pollution in Central Valley

- Orographical confinement

- Ventilation of the ABL air and diurnal wind change

• WRF-Chem Model Simulations

- A poor air quality case study

- Tracer modeling

• Summary and Conclusions

Central Valley:600 km long100 km wideN: Sacramento ValleyS: San Joaquin Valley

Central Valley:600 km long100 km wideN: Sacramento ValleyS: San Joaquin Valley

• Daytime prominent flow pattern

marine incoming flow + up-valley flow + up-slope flow

• Nighttime prominent flow pattern

weakened marine incoming flow + down-valley flow in SV + enhanced up-valley flow in the SJV + down-slope flow along the foothills

Sacramento Valley (SV)

San Joaquin Valley (SJV)

Transport of ABL Pollution in Central Valley: Summertime Low-Level Winds

What about the Diurnal Variation of Orographic

Ventilation of the ABL Air???

WRF-Chem Model

The Weather Research and Forecast (WRF) model coupled with Chemistry (WRF-Chem) has been developed by NOAA with contributions from NCAR, PNNL, EPA, and university scientists. It includes:

• Full-blown 3-D NWP model

• Aerosol direct and indirect effects

• Automatic generation of chemical

mechanisms

• Global to local scale:1-and 2-way

nesting capabilities

• A sophisticated fire plume model

Case Study120-h simulation from 1200 UTC July 29 to 1200 UTC August 3, 2000

• a 5-day case of surface ozone exceedances for the

Central Valley of California

• Central California Ozone Study (CCOS) surface and

wind profiler observations available

5-Day Average Wind Comparison

Obs0000UTC

Obs1200UTC

WRF0000UTC

WRF1200UTC

Diurnal Cycle of Low-Level Flows

MM5 WRF

San Joaquin Valley San Joaquin Valley

August 2, 2000300 m MSL

00 UTC Aug 2

00 UTC Aug 3

Transport Modeling

• Lagrangian parcel dispersion model

• Plume dispersion model

• New application option in the WRF-Chem model:

On-line tracer modeling with grid-scale and subgrid turbulence transport

Horizontal Transport

• 299 x 329 4-km horizontal grids

• 50 vertical levels

• uniform initial “blanket” tracer in the valley

Streamline and Pollution Concentration at 200 m AGL

Sunrise : ~ 1300 UTC Sunset: ~ 0300 UTC

The Fresno Eddy

The Catalina Eddy

Horizontal Recirculation

The Schultz Eddy

Location of Cross Sections

SCHULTZ EDDY TRACER INITIALIZED IN THE

LOWEST 250 M IN THE CENTRAL VALLEY

A B

Looking north-west along the valley

Vectors indicate along cross-section circulation.The Coast Range The Sierra Mountains

Sunrise : ~ 1300 UTC Sunset: ~ 0300 UTC

Vectors indicate along cross-section circulation.

FRESNO EDDYTRACER INITIALIZED IN THE

LOWEST 250 M IN THE CENTRAL VALLEY

Looking north-west along the valley

E F

The Coast Range The Sierra Mountains

Sunrise : ~ 1300 UTC Sunset: ~ 0300 UTCAlpine Pumping

Summary and Conclusions

• The horizontal ventilation/recirculation of low-level pollution in the Central Valley is closely associated with the diurnal variation in the intensity of the incoming flow and slope flows.

• Both the Schultz and Fresno eddies result from the interaction of the slope and valley flows, and thus are integral part of the valley-scale ventilation/recirculation.

• Although the mechanism similar to “Alpine Pumping” causes ventilation along the Coast Range and the Sierra Mountains, the ventilation in the SV is enhanced by the down-slope flow associated with large-scale flow intrusion.

• Up-slope and down-slope flows play an important role in the vertical recirculatation of low-level pollution.

• The nocturnal low-level jet keeps the previous-day pollutants “elevated” above the valley floor so as to be mixed downward into the daytime ABL the next day.