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The Mathematics of Atmospheric Dispersion Modeling
Abstract
The Gaussian plume model is a standard approach for studying the transport of airborne contaminants due to turbulent diffusion and advection by the wind. This paper reviews the assumptions underlying the model, its derivation from the advection-diffusion equation, and the key properties of the plume solution. The results are then applied to solving an inverse problem in which emission source rates are determined from a given set of ground-level contaminant measurements. This source identification problem can be formulated as an overdetermined linear system of equations that is most easily solved using the method of least squares. Various generalizations of this problem are discussed, and we illustrate our results with an application to the study of zinc emissions from a smelting operation.
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“It is known that wind angle can be used in determining the directions associated with different sources of CH4 (Delkash et al., 2016; Stockie, 2011).”
From Decoding methane concentration in Alberta oil sands: A machine learning exploration (2025) · cites this paper as Stockie, 2011
Citations
Cites
Carslaw, H. S., & Jaeger, J. C. (1947) · International Linear Collider · Cited by 19,877
Crank, J. (1956) · CERN Document Server (European Organization for Nuclear Research) · Cited by 18,978
Atmospheric Chemistry and Physics: From Air Pollution to Climate Change
Seinfeld, J. H., Pandis, S. Ν., & Noone, K. (1998) · Physics Today · doi:10.1063/1.882420 · Cited by 8,843
The Ecology and Evolution of Seed Dispersal: A Theoretical Perspective
Levin, S. A., Muller‐Landau, H. C., Nathan, R., & Chave, J. (2003) · Annual Review of Ecology Evolution and Systematics · doi:10.1146/annurev.ecolsys.34.011802.132428 · Cited by 850
Air Pollution Meteorology and Dispersion
Arya, S. P. (1998) · Cited by 785
Handbook on atmospheric diffusion
Hanna, S. R., Briggs, G. A., & Hosker, R. P. (1982) · doi:10.2172/5591108 · Cited by 784
On the Definition of a Heat Wave
Robinson, P. J. (2001) · Journal of applied meteorology · doi:10.1175/1520-0450(2001)040 · Cited by 766
Boundary value problems of mathematical physics.
Stakgold, I. (1968) · International Linear Collider · Cited by 478
Green's Functions with Applications
Duffy, D. G. (2001) · Chapman & Hall/CRC eBooks · doi:10.1201/9781420034790 · Cited by 420
A theory of eddy diffusion in the atmosphere
Sutton, O. G. (1932) · Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character · doi:10.1098/rspa.1932.0025 · Cited by 288
Emergency response to an anthrax attack
Wein, L. M., Craft, D., & Kaplan, E. H. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0636861100 · Cited by 221
Elementary Applied Partial Differential Equations with Fourier Series and Boundary Value Problems.
Passty, G. B., & Haberman, R. (1985) · American Mathematical Monthly · doi:10.2307/2322469 · Cited by 217
The theoretical scattering of smoke in a turbulent atmosphere
Roberts, O. F. T. (1923) · Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character · doi:10.1098/rspa.1923.0132 · Cited by 197
A first course in partial differential equations, with complex variables and transform methods
Weinberger, H. F. (1995) · CERN Document Server (European Organization for Nuclear Research) · Cited by 190
An analytical model for air pollutant transport and deposition from a point source
Ermak, D. L. (1977) · Atmospheric Environment (1967) · doi:10.1016/0004-6981(77)90140-8 · Cited by 132
藤田, 宏. (1967) · 日本物理學會誌 · Cited by 113
Lushi, E., & Stockie, J. M. (2010) · Atmospheric Environment · doi:10.1016/j.atmosenv.2009.11.039 · Cited by 112
Self-citationA mathematical model for the dispersion of air pollutants in low wind conditions
Sharan, M., Yadav, A. K., Singh, M. P., Agarwal, P., & Nigam, S. (1996) · Atmospheric Environment · doi:10.1016/1352-2310(95)00442-4 · Cited by 108
Mathematical Models in Applied Mechanics
Tayler, A. B., & Keller, J. B. (1988) · Journal of Applied Mechanics · doi:10.1115/1.3173653 · Cited by 79
Spatially explicit modelling of transgenic maize pollen dispersal and cross-pollination
Loos, C., Seppelt, R., Meier-Bethke, S., Schiemann, J., & Richter, O. (2003) · Journal of Theoretical Biology · doi:10.1016/s0022-5193(03)00243-1 · Cited by 77
Lin, J.-S., & Hildemann, L. M. (1996) · Atmospheric Environment · doi:10.1016/1352-2310(95)00287-9 · Cited by 77
Lin, J.-S., & Hildemann, L. M. (1997) · Atmospheric Environment · doi:10.1016/s1352-2310(96)00148-3 · Cited by 74
Line source emission modelling
Nagendra, S. M. S., & Khare, M. (2002) · Atmospheric Environment · doi:10.1016/s1352-2310(02)00177-2 · Cited by 67
FLUID MECHANICS AND HOMELAND SECURITY
Settles, G. S. (2005) · Annual Review of Fluid Mechanics · doi:10.1146/annurev.fluid.38.050304.092111 · Cited by 66
Dispersion of Odours From Ground Level Agricultural Sources
Smith, R. J. (1993) · Journal of Agricultural Engineering Research · doi:10.1006/jaer.1993.1013 · Cited by 59
Mattheij, R. M. M., Rienstra, S. W., & Boonkkamp, J. H. M. T. T. (2005) · Society for Industrial and Applied Mathematics eBooks · Cited by 49
Determination of the source rate released into the environment from a nuclear power plant
Jeong, H., Kim, E.-H., Suh, K.-S., Hwang, W.-T., Han, M. H., & Lee, H.-K. (2005) · Radiation Protection Dosimetry · doi:10.1093/rpd/nch460 · Cited by 43
Llewelyn, R. P. (1983) · Atmospheric Environment (1967) · doi:10.1016/0004-6981(83)90040-9 · Cited by 42
Crosswind shear effects on atmospheric diffusion
Csanady, G. T. (1972) · Atmospheric Environment (1967) · doi:10.1016/s0004-6981(72)80150-1 · Cited by 38
Chrysikopoulos, C. V., Hildemann, L. M., & Roberts, P. V. (1992) · Atmospheric Environment Part A General Topics · doi:10.1016/0960-1686(92)90234-c · Cited by 32
Multiple-source plume models of urban air pollution—their general structure
Calder, K. L. (1977) · Atmospheric Environment (1967) · doi:10.1016/0004-6981(77)90001-4 · Cited by 31
Peterson, T. W., & Seinfeld, J. H. (1977) · Atmospheric Environment (1967) · doi:10.1016/0004-6981(77)90093-2 · Cited by 24
Reaction–diffusion description of biological transport processes in general dimension
Nadler, W., & Stein, D. L. (1996) · The Journal of Chemical Physics · doi:10.1063/1.471810 · Cited by 22
Mathematical modeling in the environment
(1999) · Choice Reviews Online · doi:10.5860/choice.37-0368 · Cited by 17
Diffusion and convection of gaseous and fine particulate from a chimney
MacKay, C., McKee, S., & Mulholland, A. J. (2006) · IMA Journal of Applied Mathematics · doi:10.1093/imamat/hxl016 · Cited by 16
Yang, Y., Wilson, L. T., Makela, M. E., & Marchetti, M. A. (1998) · Ecological Modelling · doi:10.1016/s0304-3800(97)00222-6 · Cited by 16
A Theoretical Model for Particulate Transport from an Elevated Source in the Atmosphere
Fisher, B. E. A., & MACQUEEN, J. F. (1981) · IMA Journal of Applied Mathematics · doi:10.1093/imamat/27.3.359 · Cited by 12
Prediction uncertainty of plume characteristics derived from a small number of measuring points
French, H. K., van der Zee, S. E. A. T. M., & Leijnse, A. (2000) · Hydrogeology Journal · doi:10.1007/s100400050005 · Cited by 9
A model for simulating atmospheric dispersion in low-wind conditions
Okamoto, S., Ohnishi, H., YAMADA, T., Mikami, T., Momose, S., Shinji, H., & Itohiya, T. (2001) · International Journal of Environment and Pollution · doi:10.1504/ijep.2001.000607 · Cited by 6
Boundary-layer diffusion modelling: The Gaussian plume approach versus the spectral solution
Nitsche, H., Wergen, W., & Fraedrich, K. (1977) · Boundary-Layer Meteorology · doi:10.1007/bf00121968 · Cited by 2
Flagged first, then by citations
Research works printed but not linked: 2
- D. M. Cannell, George Green: Mathematician & Physicist, 1793–1841: The Background to His Life and Work , 2nd ed., SIAM, Philadelphia, 2001. · DOI
- 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. · DOI
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Sorted by citations
Dispersion modeling of air pollutants in the atmosphere: a review
Leelőssy, Á., Molnár, F., Izsák, F., Havasi, Á., Lagzi, I., & Mészáros, R. (2014) · Open Geosciences · doi:10.2478/s13533-012-0188-6 · Cited by 251
Real-Time Profiling of Fine-Grained Air Quality Index Distribution Using UAV Sensing
Yang, Y., Zheng, Z., Bian, K., Song, L., & Han, Z. (2017) · IEEE Internet of Things Journal · doi:10.1109/jiot.2017.2777820 · Cited by 170
Optimal WSN Deployment Models for Air Pollution Monitoring
Boubrima, A., Bechkit, W., & Rivano, H. (2017) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2017.2658601 · Cited by 166
Molina, M. A., Gonzalez, F., Fletcher, A. T., & Doshi, A. A. (2015) · Sensors · doi:10.3390/s150819667 · Cited by 156
Mønster, J. G., Samuelsson, J., Kjeldsen, P., Rella, C. W., & Scheutz, C. (2014) · Waste Management · doi:10.1016/j.wasman.2014.03.025 · Cited by 130
Metadata
- Authors
- Stockie, J. M.
- Affiliations
- Simon Fraser University (CA)
- Corresponding author
- Stockie, John M.
- ORCID
- Stockie, John M.
- Venue
- SIAM Review
- Published
- 2011-01
- Volume
- 53
- Issue
- 2
- Pages
- 349-372
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W1992960971
- Cited by
- 386
- References
- 41
- Citations by year
- 2026: 36 · 2025: 53 · 2024: 34 · 2023: 34 · 2022: 39 · 2021: 32 · 2020: 26 · 2019: 21 · 2018: 20 · 2017: 18 · 2016: 22 · 2015: 20 · 2014: 13 · 2013: 8 · 2012: 7
- FWCI
- 8.50
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- SIAM Review (publishedVersion)
- Topics
- Physical Sciences › Environmental Science › Environmental Engineering › Wind and Air Flow Studies
- Physical Sciences › Mathematics › Mathematical Physics › Numerical methods in inverse problems
- Physical Sciences › Earth and Planetary Sciences › Atmospheric Science › Meteorological Phenomena and Simulations
- Keywords
- Gaussian plume model, atmospheric dispersion, advection-diffusion equation, turbulent diffusion, inverse problems, emission source identification, least squares
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