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Journal of Atmosphere

June 2015, Volume 1, 1, pp 8-16

Time Dependent Advection Diffusion Equation in Two Dimensions

Khaled S. M. Essa

,

Sawsan E. M. Elsaid

,

Fawzia Mubarak

Khaled S. M. Essa 1 Sawsan E. M. Elsaid 1 Fawzia Mubarak 3


  1. Mathematics and Theoretical Physics, NRC, Atomic Energy Authority, Cairo- Egypt 1

  2. Rad. Protection Dept. NRC, AEA, Cairo, Egypt 3

Pages: 8-16

DOI: 10.18488/journal.94/2015.1.1/94.1.8.16

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Abstract:

In this work, the advection diffusion equation is solved in two dimensional space (x, z) which depends on time using Laplace transform technique to evaluate crosswind integrated of pollutant concentration per emission rate. Two schemes of the eddy diffusivities to get two models (1&2) were applied to evaluate crosswind integrated concentration per emission rate according to boundary layer parameterization. Terabassi et al model was taken as a reference model.  Comparison between these two models, reference model and observed data were carried out. The observed Copenhagen data set is composed of SF6 tracer due to dispersion experiments carried out in Northern Copenhagen, 20 minutes averaged measured concentrations were used.One finds all models were inside a factor of two. Model 2 and reference model were better when compared with the observed data than model 1 with respect to NMSE. The two models are better with respect to FB than reference model. All models were good with respect to the correlation coefficient except model 1.Finally, we can conclude that predicted (Cp) crosswind-integrated concentration normalized with the emission source rate for all models were inside a factor of two with observed data (Co).  Crosswind- integrated concentration normalized with the emission source rate for all models were good when compared with observed data via downwind distances.
Contribution/ Originality
This study contributes in the existing literature with solving the advection diffusion equation in two dimensional spaces (x, z) which depends on time using Laplace transform technique to evaluate crosswind integrated of pollutant concentration per emission rate. Two schemes of the eddy diffusivities to get two models (1&2) were applied to evaluate crosswind integrated concentration per emission rate according to boundary layer parameterization. Terabassi et al model was taken as a reference model.  Comparison between these two models, reference model and observed data were carried out. This study uses new modeling proposal for estimation of crosswind-integrated concentration normalized with the emission source rate.

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Reference:

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