Summer school rio de janeiro march 2009 6 modeling convective pbl
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Summer School Rio de Janeiro March 2009 6. MODELING CONVECTIVE PBL. Amauri Pereira de Oliveira. Group of Micrometeorology. Topics. Micrometeorology PBL properties PBL modeling Modeling surface-biosphere interaction Modeling Maritime PBL Modeling Convective PBL. Modeling Convective PBL.

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Summer school rio de janeiro march 2009 6 modeling convective pbl

Summer SchoolRio de JaneiroMarch 20096. MODELING CONVECTIVE PBL

Amauri Pereira de Oliveira

Group of Micrometeorology


  • Micrometeorology

  • PBL properties

  • PBL modeling

  • Modeling surface-biosphere interaction

  • Modeling Maritime PBL

  • Modeling Convective PBL

Convective PBL

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

Similarity Theory - CBL

Mixing Layer Similarity

Monin and Obukhov similarity

Free Convection Similarity

Holstlag and Neuiwastadt 1988.

Les model

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

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.

Available at

Objective and Rizza, U., 2008:

  • 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.

Metropolitan region of s o paulo mrsp
Metropolitan region of São Paulo (MRSP) and Rizza, U., 2008:

  • Conurbation of 39 cities

  • 20 million habitants

  • 7 millions vehicles

  • 1.48 tons of CO per year

Location during winter

LES domain

CO measurements

Air pollution




8,051 km2

23º33’S, 46º44’W

Altitude 742m

60 km far from Atlantic ocean

Topography during winter



of São Paulo


Les domain
LES domain during winter

LES domain

Relatively flat

Carbon monoxide seasonal evolution 1996 to 2005
Carbon Monoxide – Seasonal Evolution during winter(1996 to 2005)


Carbon monoxide diurnal evolution june 1996 2005
Carbon Monoxide – Diurnal evolution during winterJune (1996 -2005)



Wind – Seasonal evolution during winter(1996 -2005)

Winds in São Paulo are weak.

Wind diurnal evolution june 1996 2005
Wind – Diurnal evolution - June ( during winter1996 -2005)

Morning winds are weaker than

in the afternoon

Stronger SE wind in the afternoon is due to

Sea Breeze

LES Model during winter

Les model1
LES Model during winter

The motion equation are filtered in order to describe only motions with a length scale larger than a given threshold.

Reynolds average
Reynolds Average during winter


Les filter
LES Filter during winter


large eddies

Convective boundary layer
Convective Boundary Layer during winter

Cross section


Source: Marques Filho (2004)

Convective pbl les simulation
Convective PBL – LES Simulation during winter

( zi /L ~ - 800)

Source: Marques Filho (2004)

Spectral properties les simulation
Spectral Properties – LES Simulation during winter

Fonte: Marques Filho (2004)

Tke budget
TKE budget during winter

Caso DA2=

Les model moeng

It was developed by Moeng (1984) and modified by Sullivan during winteret al. (1994):

  • 6 prognostic equations

  • 1 diagnostic

LES Model – Moeng

Filtering all variables by

Set of equations used in the les model
Set of equations used in the LES model during winter








homogeneous during winter


Sullivan et al. (1994) subgrid parametrization

Sub grid
Sub Grid during winter

TKE equation


Turbulent diffisivity coefficients



LES Model- Moeng during winter

Boundary conditions

  • Periodic in the lateral

  • Rigid at surface

  • Radiative at the top

Surfaces Horizontally Homogeneous

  • Sensible heat flux (prescribed)

  • Momentum flux (MOST)

Grid points during winter

(128, 128, 128)


(2ms-1; 0ms-1)

(Lx, Ly, Lz)

(10 km; 10 km; 2 km )


295 K


78.125 m

5 K


15.625 m


5 K km-1

Time step

1 sec


0.16 m

Total time

36000 time steps


2.5 ppm


300 m

2.30 ppm

93.75m(6 levels).


0 ppm km-1

Numeric Model

Boundary condition sensible heat flux
Boundary during winterConditionSensible heat flux

Bθ = 0.209 K m s-1

t = time in hours

Boundary condition co flux at surface
Boundary Condition – CO flux at surface during winter

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.

Boundary condition co flux at the surface
Boundary condition during winterCO flux at the surface

BCO = 0.024 ppm ms-1

t1 = 9 hour

t2 = 19 hour

= 3 hour

Results during winter

  • 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.

Quasi-steady equilibrium after 1000 s during winter

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

E= 0.5 (u´2+v´2+w´2).

Initial jump

Pbl height
PBL height during winter

Conclusion advection

  • 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.

Conclusion advection

  • 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.