The Mathematical Modeling of the Atmospheric Diffusion Equation

Khaled Sadek Mohamed Essa; Mohamed Magdy Abd El-Wahab; Hussein Mahmoud ELsman; Adel Shahta Soliman; Samy Mahmoud ELGmmal; Aly Ahamed Wheida

doi:doi:10.11648/j.ijema.20140202.18

The Mathematical Modeling of the Atmospheric Diffusion Equation

Khaled Sadek Mohamed Essa, Mohamed Magdy Abd El-Wahab, Hussein Mahmoud ELsman, Adel Shahta Soliman, Samy Mahmoud ELGmmal, Aly Ahamed Wheida

Published in International Journal of Environmental Monitoring and Analysis (Volume 2, Issue 2)

Received: 12 February 2014 Accepted: 29 April 2014 Published: 30 April 2014

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Abstract

The advection diffusion equation (ADE) is solved in two directions to obtain the crosswind integrated concentration. The solution is solved using separation variables technique and considering the wind speed depends on the vertical height and eddy diffusivity depends on downwind and vertical distances. Comparing between the two predicted concentrations and observed concentration data are taken on the Copenhagen in Denmark.

Published in	International Journal of Environmental Monitoring and Analysis (Volume 2, Issue 2)
DOI	10.11648/j.ijema.20140202.18
Page(s)	112-116
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Advection Diffusion Equation, Predicted Normalized Crosswind Integrated Concentrations, Separation Variables

References

[1]	Demuth, C. "A contribution to the analytical steady solution of the diffusion equation” Atmos. Environ, 1`2, 1255(1978).
[2]	Tirabassi, T., Tagliazucca, M., Zannetti, P., KAPPAG, "A non-Gaussian plume dispersion model" JAPCA 36, 592-596, (1986).
[3]	Lin, J.S. and Hildemann L.M., "generalized mathematical schemes to analytical solve the atmospheric diffusion equation with dry deposition, Atmos. Environ". 31, 59-(1997).
[4]	John M. Stockie, The Mathematics of atmospheric dispersion molding. Society for Industrial and Applied Mathematics. Vol. 53.No.2 pp. 349-372, (2011).
[5]	Van Ulden A.P., Hotslag, A. A. M., and “Estimation of atmospheric boundary layer parameters for diffusion applications Journal of Climate and Applied Meteorology 24, 1196- 1207(1978).
[6]	Pasquill, F., Smith, F.B., "Atmospheric Diffusion 3rd edition". Wiley, New York, USA,(1983).
[7]	Seinfeld, J.H” Atmospheric Chemistry and physics of Air Pollution”. Wiley, New York, (1986).
[8]	Sharan, M., Singh, M.P., Yadav, A.K," Mathematical model for atmospheric dispersion in low winds with eddy diffusivities as linear functions of downwind distance". Atmospheric Environment 30, 1137-1145, (1996).
[9]	Essa K.S.M., and E,A.Found ,"Estimated of crosswind integrated Gaussian and Non-Gaussian concentration by using different dispersion schemes". Australian Journal of Basic and Applied Sciences, 5(11): 1580-1587, (2011).
[10]	Arya, S. P "Modeling and parameterization of near –source diffusion in weak wind" J. Appl .Met. 34, 1112-1122. (1995).
[11]	Essa K. S. M., Maha S. EL-Qtaify" Diffusion from a point source in an urban Atmosphere" Meteol. Atmo, Phys., 92, 95-101, (2006).
[12]	Gryning S. E., and Lyck E “Atmospheric dispersion from elevated sources in an urban area: Comparison between tracer experiments and model calculations”, J. Climate Appl. Meteor.,23, pp. 651-660., (1984).
[13]	Gryning S.E., Holtslag, A.A.M., Irwin, J.S., Sivertsen, B., “Applied dispersion modeling based on meteorological scaling parameters”, Atoms. Environ. 21 (1), 79-89 (1987).
[14]	Hanna S. R., 1989, "confidence limit for air quality models as estimated by bootstrap and Jackknife resembling methods", Atom. Environ. 23, 1385-139

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APA Style

Khaled Sadek Mohamed Essa, Mohamed Magdy Abd El-Wahab, Hussein Mahmoud ELsman, Adel Shahta Soliman, Samy Mahmoud ELGmmal, et al. (2014). The Mathematical Modeling of the Atmospheric Diffusion Equation. International Journal of Environmental Monitoring and Analysis, 2(2), 112-116. https://doi.org/10.11648/j.ijema.20140202.18

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ACS Style

Khaled Sadek Mohamed Essa; Mohamed Magdy Abd El-Wahab; Hussein Mahmoud ELsman; Adel Shahta Soliman; Samy Mahmoud ELGmmal, et al. The Mathematical Modeling of the Atmospheric Diffusion Equation. Int. J. Environ. Monit. Anal. 2014, 2(2), 112-116. doi: 10.11648/j.ijema.20140202.18

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AMA Style

Khaled Sadek Mohamed Essa, Mohamed Magdy Abd El-Wahab, Hussein Mahmoud ELsman, Adel Shahta Soliman, Samy Mahmoud ELGmmal, et al. The Mathematical Modeling of the Atmospheric Diffusion Equation. Int J Environ Monit Anal. 2014;2(2):112-116. doi: 10.11648/j.ijema.20140202.18

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@article{10.11648/j.ijema.20140202.18,
  author = {Khaled Sadek Mohamed Essa and Mohamed Magdy Abd El-Wahab and Hussein Mahmoud ELsman and Adel Shahta Soliman and Samy Mahmoud ELGmmal and Aly Ahamed Wheida},
  title = {The Mathematical Modeling of the Atmospheric Diffusion Equation},
  journal = {International Journal of Environmental Monitoring and Analysis},
  volume = {2},
  number = {2},
  pages = {112-116},
  doi = {10.11648/j.ijema.20140202.18},
  url = {https://doi.org/10.11648/j.ijema.20140202.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijema.20140202.18},
  abstract = {The advection diffusion equation (ADE) is solved in two directions to obtain the crosswind integrated concentration. The solution is solved using separation variables technique and considering the wind speed depends on the vertical height and eddy diffusivity depends on downwind and vertical distances. Comparing between the two predicted concentrations and observed concentration data are taken on the Copenhagen in Denmark.},
 year = {2014}
}

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TY  - JOUR
T1  - The Mathematical Modeling of the Atmospheric Diffusion Equation
AU  - Khaled Sadek Mohamed Essa
AU  - Mohamed Magdy Abd El-Wahab
AU  - Hussein Mahmoud ELsman
AU  - Adel Shahta Soliman
AU  - Samy Mahmoud ELGmmal
AU  - Aly Ahamed Wheida
Y1  - 2014/04/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ijema.20140202.18
DO  - 10.11648/j.ijema.20140202.18
T2  - International Journal of Environmental Monitoring and Analysis
JF  - International Journal of Environmental Monitoring and Analysis
JO  - International Journal of Environmental Monitoring and Analysis
SP  - 112
EP  - 116
PB  - Science Publishing Group
SN  - 2328-7667
UR  - https://doi.org/10.11648/j.ijema.20140202.18
AB  - The advection diffusion equation (ADE) is solved in two directions to obtain the crosswind integrated concentration. The solution is solved using separation variables technique and considering the wind speed depends on the vertical height and eddy diffusivity depends on downwind and vertical distances. Comparing between the two predicted concentrations and observed concentration data are taken on the Copenhagen in Denmark.
VL  - 2
IS  - 2
ER  -

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Author Information

Khaled Sadek Mohamed Essa

Department of Mathematics and Theoretical Physics, Nuclear Research Centre, Cairo, Egypt
Mohamed Magdy Abd El-Wahab

Astronomy Department, Faculty of Science, Cairo University, Cairo, Egypt
Hussein Mahmoud ELsman

Physics Department, Faculty of science, Monofia University, Monofia, Egypt
Adel Shahta Soliman

Theoretical Physics Department, National Research Centre, Cairo, Egypt
Samy Mahmoud ELGmmal

Physics Department, Faculty of science, Monofia University, Monofia, Egypt
Aly Ahamed Wheida

Theoretical Physics Department, National Research Centre, Cairo, Egypt

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Plain Text BibTeX RIS

APA Style

Khaled Sadek Mohamed Essa, Mohamed Magdy Abd El-Wahab, Hussein Mahmoud ELsman, Adel Shahta Soliman, Samy Mahmoud ELGmmal, et al. (2014). The Mathematical Modeling of the Atmospheric Diffusion Equation. International Journal of Environmental Monitoring and Analysis, 2(2), 112-116. https://doi.org/10.11648/j.ijema.20140202.18

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ACS Style

Khaled Sadek Mohamed Essa; Mohamed Magdy Abd El-Wahab; Hussein Mahmoud ELsman; Adel Shahta Soliman; Samy Mahmoud ELGmmal, et al. The Mathematical Modeling of the Atmospheric Diffusion Equation. Int. J. Environ. Monit. Anal. 2014, 2(2), 112-116. doi: 10.11648/j.ijema.20140202.18

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AMA Style

Khaled Sadek Mohamed Essa, Mohamed Magdy Abd El-Wahab, Hussein Mahmoud ELsman, Adel Shahta Soliman, Samy Mahmoud ELGmmal, et al. The Mathematical Modeling of the Atmospheric Diffusion Equation. Int J Environ Monit Anal. 2014;2(2):112-116. doi: 10.11648/j.ijema.20140202.18

Copy | Download

@article{10.11648/j.ijema.20140202.18,
  author = {Khaled Sadek Mohamed Essa and Mohamed Magdy Abd El-Wahab and Hussein Mahmoud ELsman and Adel Shahta Soliman and Samy Mahmoud ELGmmal and Aly Ahamed Wheida},
  title = {The Mathematical Modeling of the Atmospheric Diffusion Equation},
  journal = {International Journal of Environmental Monitoring and Analysis},
  volume = {2},
  number = {2},
  pages = {112-116},
  doi = {10.11648/j.ijema.20140202.18},
  url = {https://doi.org/10.11648/j.ijema.20140202.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijema.20140202.18},
  abstract = {The advection diffusion equation (ADE) is solved in two directions to obtain the crosswind integrated concentration. The solution is solved using separation variables technique and considering the wind speed depends on the vertical height and eddy diffusivity depends on downwind and vertical distances. Comparing between the two predicted concentrations and observed concentration data are taken on the Copenhagen in Denmark.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - The Mathematical Modeling of the Atmospheric Diffusion Equation
AU  - Khaled Sadek Mohamed Essa
AU  - Mohamed Magdy Abd El-Wahab
AU  - Hussein Mahmoud ELsman
AU  - Adel Shahta Soliman
AU  - Samy Mahmoud ELGmmal
AU  - Aly Ahamed Wheida
Y1  - 2014/04/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ijema.20140202.18
DO  - 10.11648/j.ijema.20140202.18
T2  - International Journal of Environmental Monitoring and Analysis
JF  - International Journal of Environmental Monitoring and Analysis
JO  - International Journal of Environmental Monitoring and Analysis
SP  - 112
EP  - 116
PB  - Science Publishing Group
SN  - 2328-7667
UR  - https://doi.org/10.11648/j.ijema.20140202.18
AB  - The advection diffusion equation (ADE) is solved in two directions to obtain the crosswind integrated concentration. The solution is solved using separation variables technique and considering the wind speed depends on the vertical height and eddy diffusivity depends on downwind and vertical distances. Comparing between the two predicted concentrations and observed concentration data are taken on the Copenhagen in Denmark.
VL  - 2
IS  - 2
ER  -

Copy | Download