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Summer SchoolRio de JaneiroMarch 2009
6. MODELING CONVECTIVE PBL
Amauri Pereira de Oliveira
Group of Micrometeorology
2
Topics
1. Micrometeorology
2. PBL properties
3. PBL modeling
4. Modeling surface-biosphere interaction
5. Modeling Maritime PBL
6. Modeling Convective PBL
3
Modeling Convective PBL
4
Convective PBL
Nieuwstadt, F.T.M. and Duynkerke, P.G., 1996: Turbulence in the boundary layer, Atmospheric Research, 40, 111-142.
5
Similarity Theory - CBL
Monin and Obukhov similarity
Holstlag and Neuiwastadt 1988.
Mixing Layer Similarity
Free Convection Similarity
6
LES MODEL
Investigation of Carbon Monoxide in the city of Sao Paulo using LES
7
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
10
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
13
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
20
LES Model
The motion equation are filtered in order
to describe only motions with a length
scale larger than a given threshold.
21
Reynolds Average
f
)x('f)x(f)x(f
22
LES Filter
)x(f)x(f~
)x(f
f
large eddies
23
Convective Boundary Layer
Updraft
Source: Marques Filho (2004)
Cross section
24
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
32
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
33
Initial Conditions – Vertical profiles
34
Boundary Condition Sensible heat flux
21,29
6,69-t2senBw 0
Bθ = 0.209 K m s-1
t = time in hours
35
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.
36
Boundary condition CO flux at the
surface
BCO = 0.024 ppm ms-1
t1 = 9 hour
t2 = 19 hour
= 3 hourt
37
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
39
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
40
PBL height
41
Potential temperature and sensible heat flux
42
Zonal component and momentum flux
43
Variance of the wind speed components and TKE
44
CO concentration and vertical flux
45
Comparison with observation – Potential temperature at the
surface
46
Comparison with observation – CO
concentration at the surface
47
Entrainment intensity
48
Surface emission, entrainment and hypothetical horizontal
advection
48
i
0
VeicularEmissãoz
wc
t
CO
i
i
ntoEntranhamez
wc
t
CO
i
i
iaDivergênciz
wc
z
wc
t
CO
0
49
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.
50
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.
51
Where advection is important