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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

  • 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)
  • Conurbation of 39 cities
  • 20 million habitants
  • 7 millions vehicles
  • 1.48 tons of CO per year

LES domain

CO measurements

Air pollution




8,051 km2

23º33’S, 46º44’W

Altitude 742m

60 km far from Atlantic ocean





of São Paulo


les domain
LES domain

LES domain

Relatively flat


Wind – Seasonal evolution (1996 -2005)

Winds in São Paulo are weak.

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

Morning winds are weaker than

in the afternoon

Stronger SE wind in the afternoon is due to

Sea Breeze

les model1
LES Model

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

les filter
LES Filter


large eddies

convective boundary layer
Convective Boundary Layer

Cross section


Source: Marques Filho (2004)

convective pbl les simulation
Convective PBL – LES Simulation

( zi /L ~ - 800)

Source: Marques Filho (2004)

spectral properties les simulation
Spectral Properties – LES Simulation

Fonte: Marques Filho (2004)

tke budget
TKE budget

Caso DA2=

les model moeng

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

  • 6 prognostic equations
  • 1 diagnostic
LES Model – Moeng

Filtering all variables by




Sullivan et al. (1994) subgrid parametrization

sub grid
Sub Grid

TKE equation


Turbulent diffisivity coefficients




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)

Grid points

(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 ConditionSensible 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

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 CO flux at the surface

BCO = 0.024 ppm ms-1

t1 = 9 hour

t2 = 19 hour

= 3 hour

  • 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

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



  • 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.


  • 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.