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The Mathematical Modeling of the Atmospheric Diffusion Equation

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
Cite This Article
  • 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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    T1  - The Mathematical Modeling of the Atmospheric Diffusion Equation
    AU  - Khaled Sadek Mohamed Essa
    AU  - Mohamed Magdy Abd El-Wahab
    AU  - Hussein Mahmoud ELsman
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    AU  - Aly Ahamed Wheida
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    N1  - https://doi.org/10.11648/j.ijema.20140202.18
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    T2  - International Journal of Environmental Monitoring and Analysis
    JF  - International Journal of Environmental Monitoring and Analysis
    JO  - International Journal of Environmental Monitoring and Analysis
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    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
  • Department of Mathematics and Theoretical Physics, Nuclear Research Centre, Cairo, Egypt

  • Astronomy Department, Faculty of Science, Cairo University, Cairo, Egypt

  • Physics Department, Faculty of science, Monofia University, Monofia, Egypt

  • Theoretical Physics Department, National Research Centre, Cairo, Egypt

  • Physics Department, Faculty of science, Monofia University, Monofia, Egypt

  • Theoretical Physics Department, National Research Centre, Cairo, Egypt

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