Point Source Identification of a Stationary Atmospheric Pollution Problem

  • Nguyen Cong DieuEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 341)


The adjoint method is effectively applied for identifying a location of the pollutant source in water or air pollution problems. Using the relation between solutions of main (forward) and adjoint (backward) problems, the estimation of pollutant source parameters is defined quite simply. In the paper, we shall utilize the adjoint method for identifying a location source and pollutant power of the stationary atmospheric pollution point source problem. The proposed method is so simple that the pollutant concentration measuring at three points is enough to define unknown parameters. Some numerical examples are presented for illustrating the effectiveness of the method.


Difference Scheme Source Parameter Pollution Problem Adjoint Equation Adjoint Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work is supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant 102.99-2011.24.


  1. 1.
    Chang, W.P., Jia, Y.: Identification of contaminant point source in surface waters based on backward location probability density function method. Adv. Water Resour. 33, 397–410 (2010)CrossRefGoogle Scholar
  2. 2.
    Marchuk A.I.: Adjoint Equations and Analysis of Complex Systems. Kluwer, Dordrecht (1995)Google Scholar
  3. 3.
    Milnes, E., Perrochet, P.: Simultaneous identification of a single pollution point-source location and contaminant time under known flow field. Adv. Water Res. 30, 2439–2446 (2007)CrossRefGoogle Scholar
  4. 4.
    Neupauer, R.M., Wilson, J.L.: Adjoint method for obtaining backward-in-time location and travel time probabilities of a conservative groundwater contaminant. Water Resour. Res. 35, 3389–3398 (1999)CrossRefGoogle Scholar
  5. 5.
    Piasecki, M., Katopodes, K.: Control of contaminant releases in rivers. I: adjoint sensitivityanalysis. J. Hydraul. Engine 123, 486–492 (1997)CrossRefGoogle Scholar
  6. 6.
    Pudykievicz, J.: Application of adjoint tracer transport equation for evaluating source parameters. Atmos. Environ. 32, 3039–3050 (1998)CrossRefGoogle Scholar
  7. 7.
    Quang, A.D., Ehrhard, M., Gia, L.T., Duc, L.: Mathematical modeling and algorithms for simulation of oil pollution. Environ. Model Assess. 17, 275–288 (2012)CrossRefGoogle Scholar
  8. 8.
    Raputa, V.F., Krulova, A.I.: Invert problem for estimating parameters of pollution source in atmospheric boundary layer. Meteorol. Hydrol. 3, 49–58 (1995). (In Russian)Google Scholar
  9. 9.
    Samarskii, A.A.: The Theory of Difference Schemes. Dekker, New York (2001)CrossRefzbMATHGoogle Scholar
  10. 10.
    Skiba, Y.N.: Direct and adjoint estimates in the oil spill problem. Revista Int. de Contaminacion Ambimental. 11, 69–75 (1995)Google Scholar
  11. 11.
    Van Luoc, N., Dang Quang, A., Dieu, N.C.: Analytic and numerical solution of some problems of air pollution. SEA Bull. Math. Spec. Issue 105–117 (1993)Google Scholar
  12. 12.
    Zlatev Z., Dimov I.: Computational and Numerical Challenges in Environmental Modeling. Elsevier, Amsterdam (2006)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Information TechnologyVietnam Academy of Science and TechnologyHanoiVietnam

Personalised recommendations