e c o l o g i c a l m o d e l l i n g 2 0 4 ( 2 0 0 7 ) 516–522 a v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e c o l m o d e l Vertical, lateral and longitudinal eddy diffusivities for a decaying turbulence in the convective boundary layer Antonio G. Goulart a,∗ , Marco T. Vilhena b , Gerv ´ asio A. Degrazia c , Denise T. Flores b a Universidade Federal do Pampa-UNIPAMPA/UFSM, Centro de Tecnologia de Alegrete, Alegrete, RS, Brazil b Universidade Federal do Rio Grande do Sul, Instituto de Matem ´ atica, Porto Alegre, RS, Brazil c Universidade Federal de Santa Maria, Departamento de F ´ ısica, Santa Maria, RS, Brazil a r t i c l e i n f o Article history: Received 14 January 2006 Received in revised form 6 January 2007 Accepted 1 February 2007 Published on line 6 April 2007 Keywords: Eddy diffusivity Convective decaying turbulence Convective boundary layer Energy density spectrum Dispersion model a b s t r a c t A general method to derive eddy diffusivities in a convective decaying turbulence in the convective boundary layer (CBL) is proposed in this paper. The method is based in a model for the budget equation describing the 3D energy density spectrum and the Taylor statis- tical diffusion theory. Firstly, on the basis of a dimensional analysis, the unknown inertial transport term present in dynamical equation for the 3D spectrum is parameterized. The 3D energy density spectrum equation is resolved. To calculate the longitudinal and lateral com- ponents of the eddy diffusivity the turbulent field is considered isotropic in the horizontal direction. The 1D vertical spectrum is derived from the 3D spectrum decaying, employing a weight function that allows to select the magnitude of the vertical spectral component for the construction of the decaying 3D energy density spectrum. Finally, it is reported that an numerical comparison of the proposed 1D eddy diffusivities decaying with the results for convective boundary layer decaying by LES calculations. This eddy diffusivity can be used in the diffusion-advection equation to calculate the field of concentration of pollutants in the low atmosphere. © 2007 Elsevier B.V. All rights reserved. 1. Introduction The investigation and the employment of mathematical oper- ational models for the analysis of environmental impact conditions has revealed itself to be of fundamental impor- tance in the assessment of ecosystems far from equilibrium, in a large range of distinct scales (Abdul-Wahab, 2006). Thusly, air quality models are important instruments to evaluate the impact of air contaminants on human health and on urban and agricultural environments (Gokhale and Khare, 2004). Par- ticularly, such air quality models can be used to predict air pollution indices in an atmospheric boundary layer that favors high concentrations of air contaminants. ∗ Corresponding author at: Universidade Federal do Pampa/UFSM, Centro de Tecnologia de Alegrete-Campus Universit ´ ario, Rua Vasco Alves, 125 Centro, 97541-300 Alegrete, RS, Brazil. Tel.: +55 34261052; fax: +55 32208032. E-mail address: agoulart@pq.cnpq.br (A.G. Goulart). In the atmospheric diffusion models the choice of a cor- rect turbulent parameterization plays a key role to calculate the contaminants concentration in the planetary bound- ary layer (PBL). Therefore, the accuracy of each model to simulate correctly the contaminants concentration field is a direct function on the way turbulent parameters are related to dynamical and thermodynamical evolutive prop- erties of the PBL. As a consequence, eddy diffusivities, which are used in Eulerian operational atmospheric diffu- sion models are properties of the turbulent flow and are described in terms of the physical characteristics and the magnitude of the diffusion in a PBL (Venkatram et al., 2001). 0304-3800/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2007.02.004