Summer SchoolRio de JaneiroMarch 2009

6. MODELING CONVECTIVE PBL

Amauri Pereira de Oliveira

Group of Micrometeorology

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Topics

1. Micrometeorology

2. PBL properties

3. PBL modeling

4. Modeling surface-biosphere interaction

5. Modeling Maritime PBL

6. Modeling Convective PBL

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Modeling Convective PBL

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Convective PBL

Nieuwstadt, F.T.M. and Duynkerke, P.G., 1996: Turbulence in the boundary layer, Atmospheric Research, 40, 111-142.

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Similarity Theory - CBL

Monin and Obukhov similarity

Holstlag and Neuiwastadt 1988.

Mixing Layer Similarity

Free Convection Similarity

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LES MODEL

Investigation of Carbon Monoxide in the city of Sao Paulo using LES

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Codato, G., Oliveira, A.P., Soares, J., Marques Filho, E.P., and Rizza, U., 2008: Investigation of carbon monoxide in the city of São Paulo using large eddy simulation. Proceedings of 15th Joint Conference on the Applications of Air Pollution Meteorology with the A&WMA, 88th Annual Meeting, 20-24 January 2008, New Orleans, LA (CDROM).

Codato. G., 2008: Simulação numérica da evolução diurna do monóxido de carbono na camada limite planetária sobre a RMSP com modelo LES. Dissertação de Mestrado. Departamento de Ciências Atmosféricas, Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, São Paulo, SP, Brasil, 94 pp.

http://www.iag.usp.br/meteo/labmicro/index_arquivos/Page1519.htm

Available at

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Objective

To investigate the statistical properties of the convective planetary boundary layer (PBL) over a homogeneous urban surface using LES.

Emphasis in the characterization of the turbulent transport of carbon monoxide at the top of the PBL during daytime.

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Metropolitan region of São Paulo (MRSP)

• Conurbation of 39 cities

• 20 million habitants

• 7 millions vehicles

• 1.48 tons of CO per year

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Air pollution problem in São Paulo is particularly dramatic during

winter

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Location LES domain

CO measurements Air pollutionmonitoringNetworkStations

8,051 km2

23º33’S, 46º44’WAltitude 742m60 km far from Atlantic ocean

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Topography

Metropolitan Regionof São Paulo

Valley

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LES domain

LES domain

Relatively flat

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Carbon Monoxide – Seasonal Evolution

(1996 to 2005)

Winter Maximum

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Carbon Monoxide – Diurnal evolution

June (1996 -2005)

First maximum Second maximum

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Wind – Seasonal evolution (1996 -2005)

Winds in São Paulo are weak.

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Wind – Diurnal evolution - June (1996 -2005)

Morning winds are weaker thanin the afternoon

Stronger SE wind in the afternoon is due toSea Breeze

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Time rate of change of CO in June

i1i

i1i

2

1i

tt

COCO

t

CO

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LES Model

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LES Model

The motion equation are filtered in order

to describe only motions with a length

scale larger than a given threshold.

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Reynolds Average

f

)x('f)x(f)x(f

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LES Filter

)x(f)x(f~

)x(f

f

large eddies

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Convective Boundary Layer

Updraft

Source: Marques Filho (2004)

Cross section

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Convective PBL – LES Simulation

Source: Marques Filho (2004)

( zi /L ~ - 800)

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Spectral Properties – LES Simulation

Fonte: Marques Filho (2004)

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Caso DA2=

iz L 434

TKE budget

iz L 80

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LES Model – MoengIt was developed by Moeng (1984) and modified by Sullivan et al. (1994):

6 prognostic equations

1 diagnostic

Filtering all variables by

i i i i i i i

volume

u (x ) u (x ) G x x dx

ckf

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xyxx xzz y c

pu Pv w f v

t x x x y z

xy yy yzx z c

pv Pw u f u

t y y x y z

0

yzxz zzy x

w P wu v g

t z x y z t

(1)

(2)

(3)

Set of equations used in the LES model

2 PH

x

H

y

H

zx y z

0u v w

x y z

yx zu v wt x y z x y z

0

cu cv cwc c c c

u v w Ft x y z x y z

(4)

(5)

(6)

(7)

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ij M ij ijM2K S 2K S

homogeneous non-homogeneous

Sullivan et al. (1994) subgrid parametrization

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Sub Grid

ij i j i 0

j j 0 i

e e u gu u u w u e p

t x x x

TKE equation

Turbulent diffisivity coefficients

M M H M C HK c e K 1 2 s K K K

1

3onde = s= x y z

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i 0 M i

E

u e p 2K e x

c e

where

1/ 21/ 2

0

0.76

ge

z

Convective

Stable

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LES Model- Moeng

Boundary conditions Periodic in the lateral Rigid at surface Radiative at the top

Surfaces Horizontally Homogeneous Sensible heat flux (prescribed) Momentum flux (MOST)

0

0 0

w

u v, e const.

z z z

1

22 2

* mu v u

z k z

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Grid points (128, 128, 128) ug,vg(2ms-1; 0ms-1)

(Lx, Ly, Lz) (10 km; 10 km; 2 km ) θini 295 K

Δx=Δy 78.125 m 5 K

Δz 15.625 m Γθ 5 K km-1

Time step 1 sec z0 0.16 m

Total time 36000 time steps cini 2.5 ppm

zini 300 m 2.30 ppm

93.75 m (6 levels). Γc 0 ppm km-1

inic

ini

Numeric Model

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Initial Conditions – Vertical profiles

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Boundary Condition Sensible heat flux

21,29

6,69-t2senBw 0

Bθ = 0.209 K m s-1

t = time in hours

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Boundary Condition – CO flux at surface

The amplitude of CO flux at the surface is based on the total emission of CO in the MRSP (1.48 million of tons per year) divided by number of days in one year and by the area representative of traffic in São Paulo (8,051 km2).

In reality the value of Bco was set equal to 1/6 of the value above. This was obtained by trial and error and there is no apparent reason.

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Boundary condition CO flux at the

surface

BCO = 0.024 ppm ms-1

t1 = 9 hour

t2 = 19 hour

= 3 hourt

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Results

• The results are based on the three-dimensional fields generated after turbulence has reached quasi-steady equilibrium;

• The statistics were obtained ensemble averaging 15 outputs, separated by 1200 time steps each, corresponding to 20 minutes. Important to emphasize that the time step is 1 second;

• Statistical properties are estimated at 8:30, 9:30, 10:30, 11:30 and 12:30 LT.

38Initial jump

Time evolution of turbulent kinetic energy per unit of mass volume-averaged in the PBL.

E= 0.5 (u´2+v´2+w´2).

Quasi-steady equilibrium after 1000 s

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Time

(hour)L (m) zi (m)

(m s-1)

(s)

(K)1 -6.7 316 47.56 1.04 305.3 0.102 -4.8 344 72.18 1.20 331.6 0.133 -4.1 389 95.92 1.33 375.2 0.14

4 -4.1 465114.1

31.46 448.8 0.14

5 -4.4 615140.6

71.60 593.4 0.13

6 -5.5 820148.1

31.70 791.0 0.11

7 -6.7 992148.8

61.70 957.1 0.09

8 -8.0 1110138.5

81.56

1070.8

0.07

9 -12.5 1165 93.33 1.241124.

40.04

10 -229.8 1126 5.12 0.331086.

70.00

Lzi *w*t *

PBL characteristic scales

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PBL height

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Potential temperature and sensible heat flux

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Zonal component and momentum flux

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Variance of the wind speed components and TKE

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CO concentration and vertical flux

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Comparison with observation – Potential temperature at the

surface

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Comparison with observation – CO

concentration at the surface

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Entrainment intensity

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Surface emission, entrainment and hypothetical horizontal

advection

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i

0

VeicularEmissãoz

wc

t

CO

i

i

ntoEntranhamez

wc

t

CO

i

i

iaDivergênciz

wc

z

wc

t

CO

0

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Conclusion

• Simulation of daytime evolution PBL over the MRSP carried out using LES model indicated several characteristics consistent with a convective PBL.

• The simulated diurnal evolution of CO concentration indicates that entrainment of clean air at the top of the PBL is one of the dominant mechanism reducing the concentration of CO at the surface as observed in São Paulo during the winter.

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Conclusion

• Comparison between entrainment, surface emission and hypothetical horizontal advection indicates that this late mechanism could be responsible by considerable reducing in the CO diurnal evolution in the city of Sao Paulo.

• Next step would be evaluated the role of horizontal advection.

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Where advection is important