The mathematics of atmospheric dispersion modeling

SIAM Review

Volumn 53, Issue 2, 2011, Pages 349-372

  Stockie, John M ^a  

^a SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Advection diffusion equation; Atmospheric dispersion; Contaminant transport; Gaussian plume solution; Inverse problem; Linear least squares

Indexed keywords

ADVECTION DIFFUSION EQUATION; ATMOSPHERIC DISPERSION; CONTAMINANT TRANSPORT; GAUSSIAN PLUMES; LINEAR LEAST SQUARES;

ADVECTION; ATMOSPHERIC TURBULENCE; DIFFUSION; DISPERSIONS; IMPURITIES; LEAST SQUARES APPROXIMATIONS; LINEAR SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; ZINC SMELTING;

INVERSE PROBLEMS;

EID: 80052760865     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/10080991X     Document Type: Article

References (47)

1. S. P. ARYA, Air Pollution Meteorology and Dispersion, Oxford University Press, New York, 1999.
2. J. BLUETT, N. GIMSON, G. FISHER, C. HEYDENRYCH, T. FREEMAN, AND J. GODFREY, Good Practice Guide for Atmospheric Dispersion Modelling, Ref. ME522, Ministry of the Environment, Wellington, New Zealand, 2004. Available online from http://www.mfe.govt.nz/publications/air/atmospheric-dispersion-modelling- jun04/index.html.
3. K. L. CALDER, Multiple-source plume models of urban air pollution: Their general structure, Atmos. Environ., 11(1977), pp. 403-414. (Pubitemid 8126355)
4. D. M. CANNELL, George Green: Mathematician & Physicist, 1793-1841: The Background to His Life and Work, 2nd ed., SIAM, Philadelphia, 2001.
5. H. S. CARSLAW AND J. C. JAEGER, Conduction of Heat in Solids, Clarendon Press, Oxford, 1959.
6. C. V. CHRYSIKOPOULOS, L. M. HILDEMANN, AND P. V. ROBERTS, A three-dimensional steadystate atmospheric dispersion-deposition model for emissions from a ground-level area source, Atmos. Environ., 26 A (1992), pp. 747-757.
7. J. CRANK, The Mathematics of Diffusion, 2nd ed., Oxford University Press, Oxford, 1975.
8. G. T. CSANADY, Crosswind shear effects on atmospheric diffusion, Atmos. Environ., 6(1972), pp. 221-232.
9. D. G. DUFFY, Green's Functions with Applications, Chapman & Hall/CRC, Boca Raton, FL, 2001.
10. D. L. ERMAK, An analytical model for air pollutant transport and deposition from a point source, Atmos. Environ., 11(1977), pp. 231-237. (Pubitemid 8091380)
11. B. E. A. FISHER AND J. F. MACQUEEN, A theoretical model for particulate transport from an elevated source in the atmosphere, IMA J. Appl. Math., 27(1981), pp. 359-371.
12. R. A. FREEZE AND J. A. CHERRY, Groundwater, Prentice-Hall, Englewood Cliffs, NJ, 1979.
13. H. K. FRENCH, S. E. A. T. M. VAN der ZEE, AND A. LEIJNSE, Prediction uncertainty of plume characteristics derived from a small number of measuring points, Hydrogeol. J., 8(2000), pp. 188-199.
14. R. HABERMAN, Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, Pearson Prentice-Hall, Upper Saddle River, NJ, 2004.
15. C. R. HADLOCK, Mathematical Modeling in the Environment, Mathematical Association of America, Washington, DC, 1998.
16. S. R. HANNA, G. A. BRIGGS, AND R. P. HOSKER JR., Handbook on Atmospheric Diffusion, Technical Report DOE/TIC-11223, Technical Information Center, U. S. Department of Energy, 1982.
17. W. R. HOGAN, G. F. COOPER, M. M. WAGNER, AND G. L. WALLSTROM, An Inverted Gaussian Plume Model for Estimating the Location and Amount of Release of Airborne Agents from Downwind Atmospheric Concentrations, Technical Report, Realtime Outbreak and Disease Surveillance Laboratory, University of Pittsburgh, Pittsburgh, PA, 2005.
18. H.-J. JEONG, E.-H. KIM, K.-S. SUH, W.-T. HWANG, M.-H. HAN, AND H.-K. LEE, Determination of the source rate released into the environment from a nuclear power plant, Rad. Prot. Dos., 113(2005), pp. 308-313. (Pubitemid 40724178)
19. S. A. LEVIN, H. C. MULLER-LANDAU, R. NATHAN, AND J. CHAVE, The ecology and evolution of seed dispersal: A theoretical perspective, Ann. Rev. Ecology Evolution Systematics, 34(2003), pp. 575-604. (Pubitemid 38171431)
20. J.-S. LIN AND L. M. HILDEMANN, Analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities, Atmos. Environ., 30(1996), pp. 239-254. (Pubitemid 26444645)
21. J.-S. LIN AND L. M. HILDEMANN, A generalized mathematical scheme to analytically solve the atmospheric diffusion equation with dry deposition, Atmos. Environ., 31(1997), pp. 59-71.
22. R. P. LLEWELYN, An analytical model for the transport, dispersion and elimination of air pollutants emitted from a point source, Atmos. Environ., 17(1983), pp. 249-256.
23. C. LOOS, R. SEPPELT, S. MEIER-BETHKE, J. SCHIEMANN, AND O. RICHTER, Spatially explicit modelling of transgenic maize pollen dispersal and cross-pollination, J. Theoret. Biol., 225(2003), pp. 241-255. (Pubitemid 37324087)
24. E. LUSHI AND J. M. STOCKIE, An inverse Gaussian plume approach for estimating contaminant emissions from multiple point sources, Atmos. Environ., 44(2010), pp. 1097-1107.
25. C. MACKAY, S. MCKEE, AND A. J. MULHOLLAND, Diffusion and convection of gaseous and fine particulate from a chimney, IMA J. Appl. Math., 71(2006), pp. 670-691. (Pubitemid 44542180)
26. R. M. M. MATTHEIJ, S. W. RIENSTRA, AND J. H. M. TEN THIJE BOONKKAMP, Partial Differential Equations: Modeling, Analysis, Computation, SIAM Monogr. Math. Model. Comput. 10, SIAM, Philadelphia, 2005.
27. W. NADLER AND D. L. STEIN, Reaction-diffusion description of biological transport processes in general dimension, J. Chem. Phys., 104(1996), pp. 1918-1936. (Pubitemid 126747299)
28. S. M. S. NAGENDRA AND M. KHARE, Line source emission modelling, Atmos. Environ., 36(2002), pp. 2083-2098. (Pubitemid 34632588)
29. H. NITSCHE, W. WERGEN, AND K. FRAEDRICH, Boundary-layer diffusion modelling: The Gaussian plume approach versus the spectral solution, Bound. Layer Meteorol., 12(1977), pp. 127-139.
30. S. OKAMOTO, H. OHNISHI, T. YAMADA, T. MIKAMI, S. MOMOSE, H. SHINJI, AND T. ITOHIYA, A model for simulating atmospheric dispersion in low wind conditions, Int. J. Environ. Poll., 16(2001), pp. 69-79. (Pubitemid 34554405)
31. T. W. PETERSON AND J. H. SEINFELD, Mathematical model for transport, interconversion, and removal of gaseous and particulate air pollutants: Application to the urban plume, Atmos. Environ., 11(1977), pp. 1171-1184. (Pubitemid 8244354)
32. O. F. T. ROBERTS, The theoretical scattering of smoke in a turbulent atmosphere, Philos. Trans. Roy. Soc. Lond. Ser. A, 104(1924), pp. 640-654.
33. J. H. SEINFELD AND S. N. PANDIS, Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, John Wiley & Sons, New York, 1998.
34. G. S. SETTLES, Fluid mechanics and homeland security, Annu. Rev. Fluid Mech., 38(2006), pp. 87-110. (Pubitemid 43240171)
35. M. SHARAN, A. K. YADAV, M. P. SINGH, P. AGARWAL, AND S. NIGAM, A mathematical model for the dispersion of air pollutants in low wind conditions, Atmos. Environ., 30(1996), pp. 1209-1220.
36. F. B. SMITH, The problem of deposition in atmospheric diffusion of particulate matter, J. Atmospheric Sci., 19(1962), pp. 429-435.
37. R. J. SMITH, Dispersion of odours from ground level agricultural sources, J. Agric. Eng. Res., 54(1993), pp. 187-200.
38. I. STAKGOLD, Boundary Value Problems of Mathematical Physics, Vol. II, Macmillan, New York, 1968.
39. O. G. SUTTON, A theory of eddy diffusion in the atmosphere, Proc. Roy. Soc. Lond. Ser. A, 135(1932), pp. 143-165.
40. A. B. TAYLER, Mathematical Models in Applied Mechanics, Oxford Appl. Math. Comput. Sci. Ser., Clarendon Press, Oxford, 1986.
41. R. TURNER AND T. HURST, Factors influencing volcanic ash dispersal from the 1995 and 1996 eruptions of Mount Ruapehu, New Zealand, J. Appl. Meteorol., 40(2001), pp. 56-69. (Pubitemid 32203435)
42. U. S. Environmental Protection Agency, Guideline on Air Quality Models, Appendix W to Part 51, Title 40: Protection of the Environment, Code of Federal Regulations, 2010, http://ecfr.gpoaccess.gov.
43. L. M. WEIN, D. L. CRAFT, AND E. H. KAPLAN, Emergency response to an anthrax attack, Proc. Natl. Acad. Sci. USA, 100(2003), pp. 4346-4351. (Pubitemid 36418205)
44. H. F. WEINBERGER, A First Course in Partial Differential Equations with Complex Variables and Transform Methods, Blaisdell, New York, 1965.
45. Wikipedia, Atmospheric dispersion modeling, http://en. wikipedia.org/wiki/Atmospheric-dispersion-modeling, 2010.
46. Wikipedia, Inversion (meteorology), http://en. wikipedia.org/wiki/ Inversion-(meteorology), 2010.
47. Y. YANG, L. T. WILSON, M. E. MAKELA, AND M. A. MARCHETTI, Accuracy of numerical methods for solving the advection-diffusion equation as applied to spore and insect dispersal, Ecol. Model., 109(1998), pp. 1-24. (Pubitemid 28278511)