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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Wind angle can be used in determining the directions associated with different sources of CH4.
“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
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Self-citationEstimating Mean Wind Profiles Inside Realistic Urban Canopies
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On the Theory of the Divergence Method for Quantifying Source Emissions From Satellite Observations
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- 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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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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