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An Analytical Simple Formula for the Ground Level Concentration from a Point Source
Institute of Atmospheric Science and Climate (ISAC), National Council of Researches (CNR), Via Gobetti, 101, I-40129 Bologna, Italy
Departamento de Engenharia Mecânica, Universidade Federal do Rio Grande do Sul (UFRGS), Sarmento Leite, 425, 3° andar, Porto Alegre, RS 90046-900, Brazil
Departamento de Matemática e Estatística (IFM/DME), Universidade Federal de Pelotas (UFPel), Pelotas, RS 96010-900, Brazil
* Author to whom correspondence should be addressed.
Received: 30 January 2011; in revised form: 2 March 2011 / Accepted: 8 March 2011 / Published: 24 March 2011
Abstract: The Advection-Diffusion Equation is solved for a constant pollutant emission from a point-like source placed inside an unstable Atmospheric Boundary Layer. The solution is obtained adopting the novel analytical approach: Generalized Integral Laplace Transform Technique. The concentration solution of the equation is expressed through an infinite series expansion. After setting a realistic scenario through the wind and diffusivity parameterizations, the Ground Level Concentration (GLC) is determined, and an explicit approximate expression is provided for it, allowing an analytically simple expression for the position and value of the maximum. Remarks arise regarding the ability to express value and position of the GLC as explicit functions of the parameters defining the Atmospheric Boundary Layer scenario and the source height.
Keywords: air pollution modeling; analytical solutions; advection-diffusion equation; maximum concentration
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Tirabassi, T.; Tiesi, A.; Vilhena, M.T.; Bodmann, B.E.; Buske, D. An Analytical Simple Formula for the Ground Level Concentration from a Point Source. Atmosphere 2011, 2, 21-35.
Tirabassi T, Tiesi A, Vilhena MT, Bodmann BE, Buske D. An Analytical Simple Formula for the Ground Level Concentration from a Point Source. Atmosphere. 2011; 2(2):21-35.
Tirabassi, Tiziano; Tiesi, Alessandro; Vilhena, Marco T.; Bodmann, Bardo E.J.; Buske, Daniela. 2011. "An Analytical Simple Formula for the Ground Level Concentration from a Point Source." Atmosphere 2, no. 2: 21-35.