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{{Image|New York smog.jpg|right|350px|Smog over New York skyline in 1988}}
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[[File:Crude oil-fired power plant.jpg|thumb|right|225px|Industrial air pollution source]]
Atmospheric dispersion modeling is the mathematical simulation of how air pollutants disperse in the ambient atmosphere. It is performed with computer programs that solve the mathematical equations and algorithms which simulate the pollutant dispersion. The dispersion models are used to estimate or to predict the downwind concentration of air pollutants emitted from sources such as industrial plants, vehicular traffic or accidental chemical releases.


'''Smog''' is a type of [[air pollution]] and the word "smog" is a combination  of  the words "smoke" and "fog". Modern smog is derived primarily from precursor pollutants,  emitted to the [[atmosphere]] from vehicular [[internal combustion engine]]s and industrial plants, that react in the atmosphere with sunlight to produce secondary pollutants that also combine with the precursor emissions to form the components of [[photochemical smog]].  
Such models are important to governmental agencies tasked with protecting and managing the ambient air quality. The models are typically employed to determine whether existing or proposed new industrial facilities are or will be in compliance with the National Ambient Air Quality Standards (NAAQS) in the United States or similar regulations in other nations. The models also serve to assist in the design of effective control strategies to reduce emissions of harmful air pollutants. During the late 1960's, the Air Pollution Control Office of the U.S. Environmental Protection Agency (U.S. EPA) initiated research projects to develop models for use by urban and transportation planners.<ref>J.C. Fensterstock et al, "Reduction of air pollution potential through environmental planning", ''JAPCA'', Vol. 21, No. 7, 1971.</ref> 


== Origin of the term "smog" ==
Air dispersion models are also used by emergency management personnel to develop emergency plans for accidental chemical releases. The results of dispersion modeling, using worst case accidental releases and meteorological conditions, can provide estimated locations of impacted areas and be used to determine appropriate protective actions. At industrial facilities in the United States, this type of consequence assessment or emergency planning is required under the Clean Air Act (CAA) codified in Part 68 of Title 40 of the Code of Federal Regulations.


Coinage of the term ''smog'' is generally attributed to [[Henry Antoine des Voeux|Dr. Henry Antoine des Voeux]] in his 1905 paper, "Fog and Smoke" for a meeting of the [[Public Health Congress]] in [[London]]. The July 26, 1905 edition of the ''Daily Graphic'', a London newspaper, quoted des Voeux: <i>"... he said it required no science to see that there was something produced in great cities which was not found in the country, and that was smoky fog, or what was known as 'smog'."</i>&thinsp;<ref name=Trum>{{cite book|author=Beatrice Trum Hunter|title=Air and Your Health|edition=|publisher=Basic Health Publications|year=2004|pages=page 82|id=ISBN 1-59120-057-1}}</ref> The next day, the Globe newspaper remarked that "''Dr. des Voeux did a public service in coining a new word for the London fog.''"<ref name=Trum/>
The dispersion models vary depending on the mathematics used to develop the model, but all require the input of data that may include:


== Photochemical smog ==
* Meteorological conditions such as wind speed and direction, the amount of atmospheric turbulence (as characterized by what is called the "stability class"), the ambient air temperature, the height to the bottom of any inversion aloft that may be present, cloud cover and solar radiation.
* The emission parameters such the type of source (i.e., point, line or area), the mass flow rate, the source location and height, the source exit velocity, and the source exit temperature.
* Terrain elevations at the source location and at receptor locations, such as nearby homes, schools, businesses and hospitals.
* The location, height and width of any obstructions (such as buildings or other structures) in the path of the emitted gaseous plume as well as the terrain surface roughness (which may be characterized by the more generic parameters "rural" or "city" terrain).


[[Image:Smog formation.png|right|thumb|425px|Atmospheric chemistry involved in smog formation<ref name=Manahan/><ref name=Sodhi/><ref name=ausetute/><ref name=MTSU/>]]
Many of the modern, advanced dispersion modeling programs include a pre-processor module for the input of meteorological and other data, and many also include a post-processor module for graphing the output data and/or plotting the area impacted by the air pollutants on maps. The plots of areas impacted usually include isopleths showing areas of pollutant concentrations that define areas of the highest health risk. The isopleths plots are useful in determining protective actions for the public and first responders.


Originally, Dr. des Voeux's term ''smog'' referred to a mixture of [[smoke]], [[sulfur dioxide]] (SO<sub>2</sub>) and [[fog]] which was once prevalent in London when [[coal]] with a high [[sulfur]] content was widely used throughout the city as heating fuel. The dark, sulfurous London smog caused reduced visibility, respiratory problems and had a noticeable affect on human health. The so-called [[Great Smog of 1952]] darkened the streets of London and killed approximately 4,000 people in a 4 day period (another 8,000 died from its effects in the following months).<ref>{{cite journal | author = Michelle L. Bell, Devra L. Davis and Tony Fletcher | year = 2004 | month = January | title = A Retrospective Assessment of Mortality from the London Smog Episode of 1959: The Role of Influenza and Pollution | journal = Environmental Health Perspectives| volume = 112 | issue = 1 | pages = 6–8 |url=http://www.ehponline.org/members/2003/6539/6539.html}}</ref> The type of smog experienced in London many decades ago is no longer encountered since other fuels have largely replaced the wide-spread use of high-sulfur coal for heating.
The atmospheric dispersion models are also known as atmospheric diffusion models, air dispersion models, air quality models, and air pollution dispersion models.


Photochemical smog is chemically quite different than the old London-type smog and has a long history. In 1542, when exploring what is now [[California|Southern California]], Juan Rodriguez Cabrillo named San Pedro Bay the "Bay of Smokes" because of the thick haze that covered the area. Complaints of eye irritation from the polluted air in [[Los Angeles]] date back to the late 1860s. In the 1940s, photochemical smog first became apparent in Los Angeles and other large cities on sunny days, although none of those cities had any significant use of coal for heating fuel or for industrial activities.<ref name=Manahan>{{cite book|author=Stanley E. Manahan|title=Environmental Science and Technology: A Sustainable Approach to Green Science and Technology|edition=2nd Edition|publisher=CRC Press|year=2006|id=ISBN 0-8493-9512-7}}</ref><ref name=Sodhi>{{cite book|author=G.S. Sodhi|title=Fundamental Concepts of Environmental Chemistry|edition=2nd Edition|publisher=Alpha Science International|year=2005|id=ISBN 1-84265-218-8}}</ref><ref name=ausetute> [http://www.ausetute.com.au/photsmog.html The Chemistry of Photochemical Smog] From the website of AUS-e-TUTE, an [[Australia|Australian]] interactive learning resource.</ref><ref name=Issues>[http://www.pollutionissues.com/Re-Sy/Smog.html Smog] From the website of Pollution Issues</ref>
==Atmospheric layers==
Photochemical smog  is a daytime phenomenon characterized by a brown haze that reduces visibility and contains [[oxidant]]s, such as [[ozone]] (O<sub>3</sub>), that cause respiratory problems, eye irritation and plants to be damaged. It is a mixture of ozone, [[reactive hydrocarbon]]s, [[nitrogen oxide]] (NO), [[nitrogen dioxide]] (NO<sub>2</sub>), [[aldehyde]]s, [[peroxyacetyl nitrate]] (PAN), [[particulate matter]] and other components.. 


The chemistry involved in the formation of smog is highly complex and involves many different reactions (see the adjacent diagram). The three major ingredients required to form photochemical smog are solar energy (i.e., sunlight), reactive hydrocarbons and nitrogen oxide, the latter two being referred to as the ''precursor pollutants''. As shown in the adjacent diagram, the two precursors enter the atmosphere as [[gas]]es emitted for the most part from vehicular internal combustion engines fuelled by [[gasoline]] and [[diesel oil]]. To a much lesser extent, nitrogen oxide is also emitted from industrial [[combustion]] sources, and reactive hydrocarbons are emitted by [[evaporation]] from the handling and storage of volatile [[hydrocarbons]]<ref>Also referred to as [[volatile organic compounds]] (VOC)</ref> such as gasoline, [[solvent]]s, some [[pesticide]]s and some [[paint]]s. [[Biogenic]] sources such as pine trees and certain other trees are also a relatively minor source of reactive hydrocarbon emissions such as [[isoprene]] and [[α-pinene]].
Discussion of the layers in the Earth's atmosphere is needed to understand where airborne pollutants disperse in the atmosphere. The layer closest to the Earth's surface is known as the ''troposphere''. It extends from sea-level up to a height of about 18 km and contains about 80 percent of the mass of the overall atmosphere. The ''stratosphere'' is the next layer and extends from 18 km up to about 50 km. The third layer is the ''mesosphere'' which extends from 50 km up to about 80 km. There are other layers above 80 km, but they are insignificant with respect to atmospheric dispersion modeling.


Briefly, as depicted in the adjacent diagram,  this a very simplified listing of the [[chemical reaction]]s that take place to form photochemical smog:<ref name=Manahan/><ref name=Sodhi/><ref name=ausetute/><ref name=MTSU>[http://mtsu32.mtsu.edu:11233/Smog-Atm1.htm Photochemical Smog] From the website of [[Middle Tennessee State University]] (MTSU)</ref><ref>[http://www.epa.sa.gov.au/xstd_files/Air/Information%20sheet/info_photosmog.pdf Photochemical smog - what it means for us] The Environmental Protection Authority of [[South Australia]]</ref>
The lowest part of the troposphere is called the ''atmospheric boundary layer (ABL)'' or the ''planetary boundary layer (PBL)'' and extends from the Earth's surface up to about 1.5 to 2.0 km in height. The air temperature of the atmospheric boundary layer decreases with increasing altitude until it reaches what is called the ''inversion layer'' (where the temperature increases with increasing altitude) that caps the atmospheric boundary layer. The upper part of the troposphere (i.e., above the inversion layer) is called the ''free troposphere'' and it extends up to the 18 km height of the troposphere.


* The gaseous precursor nitrogen oxide, emitted primarily from vehicular internal combustion engines, is oxidized to produce gaseous nitrogen dioxide.
The ABL is the most important layer with respect to the emission, transport and dispersion of airborne pollutants. The part of the ABL between the Earth's surface and the bottom of the inversion layer is known as the ''mixing layer''. Almost all of the airborne pollutants emitted into the ambient atmosphere are transported and dispersed within the mixing layer. Some of the emissions penetrate the inversion layer and enter the free troposphere above the ABL.
::'''nitrogen oxide + oxygen <math>\rightarrow</math> nitrogen dioxide'''
::::'''2NO(g) + O<sub>2</sub>(g) <math>\mathrm{\rightarrow}</math> 2NO<sub>2</sub>(g)'''


* The gaseous nitrogen dioxide is broken down by solar energy from sunlight to produce gaseous nitrogen oxide and atomic oxygen (O, an oxygen radical). This process is referred to as ''photolysis'' and hence the term "photochemical smog".
In summary, the layers of the Earth's atmosphere from the surface of the ground upwards are: the ABL made up of the mixing layer capped by the inversion layer; the free troposphere; the stratosphere; the mesosphere and others. Many atmospheric dispersion models are referred to as ''boundary layer models'' because they mainly model air pollutant dispersion within the ABL. To avoid confusion, models referred to as ''mesoscale models'' have dispersion modeling capabilities that can extend horizontally as much as  a few hundred kilometres. It does not mean that they model dispersion in the mesosphere.
::'''nitrogen dioxide +solar energy <math>\rightarrow</math> nitrogen oxide + atomic oxygen
::::'''NO<sub>2</sub>(g) + solar energy <math>\rightarrow</math> NO (g) + O'''


* The atomic oxygen reacts with gaseous atmospheric oxygen (O<sub>2</sub>) to form gaseous ozone (O<sub>3</sub>).
==Gaussian air pollutant dispersion equation==
::'''atomic oxygen + atmospheric oxygen <math>\rightarrow</math> ozone'''
::::'''O + O<sub>2</sub>(g) <math>\rightarrow</math> O<sub>3</sub>(g)'''


* The gaseous ozone also oxidizes gaseous nitrogen oxide to form gaseous nitrogen dioxide and gaseous oxygen.
The technical literature on air pollution dispersion is quite extensive and dates back to the 1930s and earlier. One of the early air pollutant plume dispersion equations was derived by Bosanquet and Pearson.<ref>C.H. Bosanquet and J.L. Pearson, "The spread of smoke and gases from chimneys", ''Trans. Faraday Soc.'', 32:1249, 1936.</ref> Their equation did not assume Gaussian distribution nor did it include the effect of ground reflection of the pollutant plume.
::'''ozone + nitrogen oxide <math>\rightarrow</math> nitrogen dioxide + oxygen'''
::::'''O<sub>3</sub>(g) + NO(g) <math>\rightarrow</math> NO<sub>2</sub>(g) + O<sub>2</sub>(g)


* The gaseous precursor reactive hydrocarbons (RH), emitted primarily from vehicular internal combustion engines, reacts with atomic oxygen, atmospheric oxygen and ozone to produce various  highly reactive hydrocarbon free radicals (RO<sup>•</sup><sub>2</sub>).
Sir Graham Sutton derived an air pollutant plume dispersion equation in 1947<ref>O.G. Sutton, "The problem of diffusion in the lower atmosphere", ''QJRMS'', 73:257, 1947.</ref><ref>O.G. Sutton, "The theoretical distribution of airborne pollution from factory chimneys", ''QJRMS'', 73:426, 1947.</ref> which did include the assumption of Gaussian distribution for the vertical and crosswind dispersion of the plume and also included the effect of ground reflection of the plume.


* The hydrocarbon free radicals then react with other species such as nitrogen dioxide to form peroxyacetyl nitrate (PAN),<ref>Formula of peroxyacetyl nitrate: C<sub>2</sub>H<sub>3</sub>NO<sub>5</sub></ref> aldehydes and other smog components.  
Under the stimulus provided by the advent of stringent environmental control regulations, there was an immense growth in the use of air pollutant plume dispersion calculations between the late 1960s and today. A great many computer programs for calculating the dispersion of air pollutant emissions were developed during that period of time and they were commonly called "air dispersion models". The basis for most of those models was the '''Complete Equation For Gaussian Dispersion Modeling Of Continuous, Buoyant Air Pollution Plumes''' shown below:<ref name=Beychok>{{cite book|author=M.R. Beychok|title=Fundamentals Of Stack Gas Dispersion|edition=4th Edition| publisher=author-published|year=2005|isbn=0-9644588-0-2}}.</ref><ref>{{cite book|author=D. B. Turner| title=Workbook of atmospheric dispersion estimates: an introduction to dispersion modeling| edition=2nd Edition |publisher=CRC Press|year=1994|isbn=1-56670-023-X}}.</ref>
::'''Nitrogen dioxide + oxygen + hydrocarbon free radicals <math>\rightarrow</math> peroxyacetyl nitrate'''
::::'''2NO<sub>2</sub>(g) + O<sub>2</sub>(g) + 2RO<sup>•</sup><sub>2</sub> <math>\rightarrow</math> 2CH<sub>3</sub>CO–OO–NO<sub>2</sub>(g)'''


The various products produced or formed from the precursor pollutants are referred to as ''secondary pollutants''.  All of the above chemical reactions (as well as others) occur more or less simultaneously during sunny, summertime days in most large cities with a great number of automobiles and other vehicles.


== Health effects ==
<math>C = \frac{\;Q}{u}\cdot\frac{\;f}{\sigma_y\sqrt{2\pi}}\;\cdot\frac{\;g_1 + g_2 + g_3}{\sigma_z\sqrt{2\pi}}</math>
{{main|Air Quality Index}}
{{Image|Sao Paulo smog.jpg|left|250px|Smog in São Paulo, Brazil in 2006.}}


{| border="0" width="260" align="right" cellpadding="0" cellspacing="0" |width=100%
{| border="0" cellpadding="2"  
|
{| class=wikitable cellpadding="5" align="right"
|+ United States' AQI<ref>[http://airnow.gov/index.cfm?action=aqibasics.aqi Air Quality Index (AQI) - A Guide to Air Quality and Your Health] From the AIRNow web site jointly maintained by the [[U.S. EPA]], [[National Oceanic and Atmospheric Administration]], [[National Park Service]], tribal, state, and local agencies</ref>
! Air Quality<br/>Index<br/>(AQI)|| Air Quality<br/>Category|| Color<br/>Code
|-
| 0 – 50|| Good|| bgcolor="#00E400"|&nbsp;
|-
|-
| 51 – 100|| Moderate||  bgcolor="#FFFF00"|&nbsp;
|align=right|where:
|-  
|&nbsp;
| 101 – 150|| Unhealthy for<br/>Sensitive Groups|| bgcolor="#FF7E00"|&nbsp;
|-
|-  
!align=right|<math>f</math>  
| 151 – 200|| Unhealthy||bgcolor="#FF0000"|&nbsp;
|align=left|= crosswind dispersion parameter
|-  
|-
| 201 – 300|| Very Unhealthy|| bgcolor="#99004C"|&nbsp;  
!align=right|&nbsp;
|-  
|align=left|= <math>\exp\;[-\,y^2/\,(2\;\sigma_y^2\;)\;]</math>
| 301 – 500|| Hazardous||bgcolor="#7E0023"|&nbsp;
|-
|}
!align=right|<math>g</math>
|align=left|= vertical dispersion parameter = <math>\,g_1 + g_2 + g_3</math>
|-
!align=right|<math>g_1</math>
|align=left|= vertical dispersion with no reflections
|-
!align=right|&nbsp;
|align=left|= <math>\; \exp\;[-\,(z - H)^2/\,(2\;\sigma_z^2\;)\;]</math>
|-
!align=right|<math>g_2</math>
|align=left|= vertical dispersion for reflection from the ground
|-
!align=right|&nbsp;
|align=left|= <math>\;\exp\;[-\,(z + H)^2/\,(2\;\sigma_z^2\;)\;]</math>
|-
!align=right|<math>g_3</math>
|align=left|= vertical dispersion for reflection from an inversion aloft
|-
!align=right|&nbsp;
|align=left|= <math>\sum_{m=1}^\infty\;\big\{\exp\;[-\,(z - H - 2mL)^2/\,(2\;\sigma_z^2\;)\;]</math>
|-
!align=right|&nbsp;
|align=left|&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math>+\, \exp\;[-\,(z + H + 2mL)^2/\,(2\;\sigma_z^2\;)\;]</math>
|-
!align=right|&nbsp;
|align=left|&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math>+\, \exp\;[-\,(z + H - 2mL)^2/\,(2\;\sigma_z^2\;)\;]</math>
|-
!align=right|&nbsp;
|align=left|&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math>+\, \exp\;[-\,(z - H + 2mL)^2/\,(2\;\sigma_z^2\;)\;]\big\}</math>
|-
!align=right|<math>C</math>
|align=left|= concentration of emissions, in g/m³, at any receptor located:
|-
!align=right|&nbsp;
|align=left|&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; x meters downwind from the emission source point
|-
!align=right|&nbsp;
|align=left|&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; y meters crosswind from the emission plume centerline
|-
!align=right|&nbsp;
|align=left|&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; z meters above ground level
|-
!align=right|<math>Q</math>
|align=left|= source pollutant emission rate, in g/s
|-
!align=right|<math>u</math>
|align=left|= horizontal wind velocity along the plume centerline, m/s
|-
!align=right|<math>H</math>
|align=left|= height of emission plume centerline above ground level, in m
|-
!align=right|<math>\sigma_z</math>
|align=left|= vertical standard deviation of the emission distribution, in m
|-
!align=right|<math>\sigma_y</math>
|align=left|= horizontal standard deviation of the emission distribution, in m
|-
!align=right|<math>L</math>
|align=left|= height from ground level to bottom of the inversion aloft, in m
|-
!align=right|<math>\exp</math>
|align=left|= the exponential function
|}
|}


Photochemical smog constitutes a serious health problem in most large cities. It is especially harmful for senior citizens, children, and people with heart and lung conditions such as [[emphysema]], [[bronchitis]], and [[asthma]]. It can inflame breathing passages, decrease the lungs' working capacity, cause shortness of breath, pain when inhaling deeply, wheezing, and coughing. It can cause eye and nose irritation and it dries out the protective membranes of the nose and throat. In general, it interferes with the body's ability to fight infection, increasing susceptibility to illness.<ref>[http://www.airnow.gov/index.cfm?action=smog.page1#4 Smog - Who does it hurt?] From the AIRNow web site jointly maintained by the U.S. EPA, National Oceanic and Atmospheric Administration, National Park Service, tribal, state, and local agencies.</ref><ref name=SCAQMD>[http://www.aqmd.gov/smog/historical/smog_and_health.htm Smog and Health] From the website of the [[South Coast Air Quality Management District]] (SCAQMD).</ref>
The above equation not only includes upward reflection from the ground, it also includes downward reflection from the bottom of any inversion lid present in the atmosphere.


The adjacent table explains the Air Quality Index (AQI) ranges used by the U.S. Environmental Protection Agency (U.S. EPA) and their  corresponding health effect categories and color codes. The U.S. EPA's AQI is also known as the Pollution Standards Index (PSI). A national map of the [[United States]] containing daily AQI forecasts across the nation, using that same color-coding, is published online jointly by the U.S. EPA and [[National Oceanic and Atmospheric Administration]] (NOAA).<ref>[http://www.airnow.gov/index.cfm?action=airnow.national Today's National Air Quality Forecast]</ref>  
The sum of the four exponential terms in <math>g_3</math> converges to a final value quite rapidly. For most cases, the summation of the series with '''''m''''' = 1, '''''m''''' = 2 and '''''m''''' = 3 will provide an adequate solution.
 
If multiple pollutants are measured at a monitoring site, then the largest or "dominant" AQI value is reported for the location.


The U.S. EPA has developed conversion calculators, available online,<ref>[http://airnow.gov/index.cfm?action=resources.aqi_conc_calc AQI Calculator: AQI to Concentration]</ref><ref>[http://airnow.gov/index.cfm?action=resources.conc_aqi_calc  AQI Calculator: Concentration to AQI]</ref> for the conversion of AQI values to [[concentration]] values and for the reverse conversion of concentrations to AQI values.
<math>\sigma_z</math> and <math>\sigma_y</math> are functions of the atmospheric stability class (i.e., a measure of the turbulence in the ambient atmosphere) and of the downwind distance to the receptor. The two most important variables affecting the degree of pollutant emission dispersion obtained are the height of the emission source point and the degree of atmospheric turbulence. The more turbulence, the better the degree of dispersion.


The [[South Coast Air Quality Management District]] (SCAQMD) of [[Southern California]] has published an excellent, comprehensive discussion of the undesirable health effects caused by air pollution. It also includes an extensive listing and discussion of the many medical health effect studies of pollution performed during the past decades starting in about 1950.<ref name=SCAQMD/>
Whereas older models rely on stability classes for the determination of <math>\sigma_y</math> and <math>\sigma_z</math>, more recent models increasingly rely on Monin-Obukhov similarity theory to derive these parameters.


As noted at the top of this section, see [[Air Quality Index]] for information about similar air quality indices in countries other than the United States.
==Briggs plume rise equations==


{{Image|Beijing smog.jpg|right|175px|Smog over the Forbidden City in Beijing, China in 2005.}}
The Gaussian air pollutant dispersion equation (discussed above) requires the input of ''H'' which is the pollutant plume's centerline height above ground level. ''H'' is the sum of ''H''<sub>s</sub> (the actual physical height of the pollutant plume's emission source point) plus Δ''H'' (the plume rise due the plume's buoyancy).


== Areas affected ==
[[File:Gaussian Plume.png|thumb|right|333px|Visualization of a buoyant Gaussian air pollutant dispersion plume]]


Smog can form in almost any location where the level of air pollutants is high, and ii is more likely to occur during periods of warm, sunny weather when the upper air is warm enough to inhibit vertical circulation. It often persists for extended time periods over densely populated cities, such as [[London]], [[New York]][[Cairo]], [[Los Angeles]], [[São Paulo]], [[Mexico City]], [[Beijing]], [[Shanghai]], [[Hong Kong]], [[Kuala Lumpur]] and [[Seoul]]. Smog is especially prevalent in geologic basins encircled by hills or mountains.  
To determine Δ''H'', many if not most of the air dispersion models developed between the late 1960s and the early 2000s used what are known as "the Briggs equations." G.A. Briggs first published his plume rise observations and comparisons in 1965.<ref>G.A. Briggs, "A plume rise model compared with observations", ''JAPCA'', 15:433–438, 1965.</ref> In 1968, at a symposium sponsored by CONCAWE (a Dutch organization), he compared many of the plume rise models then available in the literature.<ref>G.A. Briggs, "CONCAWE meeting: discussion of the comparative consequences of different plume rise formulas", ''Atmos. Envir.'', 2:228–232, 1968.</ref> In that same year, Briggs also wrote the section of the publication edited by Slade<ref>D.H. Slade (editor), "Meteorology and atomic energy 1968", Air Resources Laboratory, U.S. Dept. of Commerce, 1968.</ref> dealing with the comparative analyses of plume rise modelsThat was followed in 1969 by his classical critical review of the entire plume rise literature,<ref>G.A. Briggs, "Plume Rise", ''USAEC Critical Review Series'', 1969.</ref> in which he proposed a set of plume rise equations which have become widely known as "the Briggs equations". Subsequently, Briggs modified his 1969 plume rise equations in 1971 and in 1972.<ref>G.A. Briggs, "Some recent analyses of plume rise observation", ''Proc. Second Internat'l. Clean Air Congress'', Academic Press, New York, 1971.</ref><ref>G.A. Briggs, "Discussion: chimney plumes in neutral and stable surroundings", ''Atmos. Envir.'', 6:507–510, 1972.</ref>


=== London ===
Briggs divided air pollution plumes into these four general categories:
* Cold jet plumes in calm ambient air conditions
* Cold jet plumes in windy ambient air conditions
* Hot, buoyant plumes in calm ambient air conditions
* Hot, buoyant plumes in windy ambient air conditions


In 1306, concerns over air pollution were sufficient for [[Edward I of England|Edward I]] to briefly ban coal fires in London.<ref>{{cite book|author=Barbara Freese|title=Coal: A Human History|edition=Ist Edition|publishrt=Perseus Publishing|year=2003|pages= p.1|id= ISBN 0-7382-0400-5}}</ref> In 1661, [[John Evelyn]], the noted English diarist of his day, published ''[[Fumifugium]]'' in which he suggested the widespread planting of  fragrant trees, shrubs and flowers around London so as to counteract the foul effects the smoke from coal-burning.<ref>{{cite book|author=John Evelyn|title=Fumifugium; or the Inconvenience of the Air and Smoke of London Dissipated|edition=Ist Edition|publisher=Gabriel Bedel and Thomas Collins, London|year=1661|id=}} The full text is available online at [http://ia301538.us.archive.org/2/items/fumifugium00eveluoft/fumifugium00eveluoft.pdf  The Internet Archive]</ref> Two years later, in 1663, a satirical poem known as the ''Ballad of Gresham College'' commemorates Evelyn's book by this verse:<ref>[http://www.meteogroup.co.uk/uk/home/weather/weather_news/news_archive/archive/2007/january/ch/d53dfdd52a/article/fog_and_filthy_air.html Fog and Filthy Air] From the website of the Meteo Group in the United Kingdom]].</ref>
Briggs considered the trajectory of cold jet plumes to be dominated by their initial velocity momentum, and the trajectory of hot, buoyant plumes to be dominated by their buoyant momentum to the extent that their initial velocity momentum was relatively unimportant. Although Briggs proposed plume rise equations for each of the above plume categories, '''''it is important to emphasize that "the Briggs equations" which become widely used are those that he proposed for bent-over, hot buoyant plumes'''''.
::"He shewes that 't is the seacoale smoake,<br/>
:: That allways London doth Inviron,<br/>
:: Which doth our Lungs and Spiritts choake,<br/>
::Our hanging spoyle, and rust our Iron."


{{Image|London smog.jpg|left|250px|Smog over London in 2007}}
In general, Briggs's equations for bent-over, hot buoyant plumes are based on observations and data involving plumes from typical combustion sources such as the flue gas stacks from steam-generating boilers burning fossil fuels in large power plants. Therefore the stack exit velocities were probably in the range of 20 to 100 ft/s (6 to 30 m/s) with exit temperatures ranging from 250 to 500 °F (120 to 260 °C).


In the 1800s, more than a million London residents were burning coal, and winter "fogs" became more than a nuisance. An 1873 coal-smoke saturated fog, thicker and more persistent than natural fog, hovered over the city of days. As now known from subsequent epidemiological findings, the fog caused 268 deaths from bronchitis. Another fog in 1879 lasted from November to March, four long months darkened skies and gloom. Severe episodes of smog continued even into the 20th centuries and were nicknamed "pea-soupers".<ref>[http://www.epa.gov/history/topics/perspect/london.htm London's Historic "Pea-Soupers"]] by David Urbinato.1994, (from the website of the U.S. EPA).</ref>
A logic diagram for using the Briggs equations<ref name=Beychok/> to obtain the plume rise trajectory of bent-over buoyant plumes is presented below:
[[Image:BriggsLogic.png|none]]
:{| border="0" cellpadding="2"
|-
|align=right|where:
|&nbsp;
|-
!align=right| Δh
|align=left|= plume rise, in m
|-
!align=right| F<sup>&nbsp;</sup> <!-- The HTML is needed to line up characters. Do not remove.-->
|align=left|= buoyancy factor, in m<sup>4</sup>s<sup>−3</sup>
|-
!align=right| x
|align=left|= downwind distance from plume source, in m
|-
!align=right| x<sub>f</sub>
|align=left|= downwind distance from plume source to point of maximum plume rise, in m
|-
!align=right| u
|align=left|= windspeed at actual stack height, in m/s
|-
!align=right| s<sup>&nbsp;</sup> <!-- The HTML is needed to line up characters. Do not remove.-->
|align=left|= stability parameter, in s<sup>−2</sup>
|}
The above parameters used in the Briggs' equations are discussed in Beychok's book.<ref name=Beychok/>


As discussed earlier above, the ''Great Smog of 1952'' killed approximately 4,000 people in the short time of 4 days and a further 8,000 died from its effects in the following months. That finally prompted real legislative reform. In 1956, the [[Clean Air Act 1956]], sponsored by the [[Ministry of Housing and Local Government]] in [[England]] and the [[Department of Health]] in [[Scotland]], was enacted by the [[Parliament of the United Kingdom]] and  introduced [[smokeless zone]]s in London. It was in effect until 1964 and  consequently reduced the [[sulfur dioxide]] levels in London's air to the point that made the intense and persistent London smog a thing of the past. It was after this that the great clean-up of London began and buildings recovered their original clean stone façades which, during two centuries, had gradually blackened.
==References==
 
{{reflist}}
However, as clearly shown in the adjacent photograph,  photochemical smog still does occur in modern London.
 
=== Mexico City ===
 
[[Mexico City]] is located in the tropical latitudes on a high plain at an altitude of 2,200 meters, and is surrounded on three sides by mountains that reach elevations of 5,000 meters. The major sources of air pollutants within Mexico City's urban area include exhaust from 3.5 million vehicles, thousands of industries, and mineral dust. The ancient lakebed valley in which the city is situated became a major source of dust when it was drained in the 16th century.<ref name=NASA>[http://earthobservatory.nasa.gov/IOTD/view.php?id=2622 A Hazy Day in Mexico City] From the website of NASA.</ref > The area is known as the  ''Valley of Mexico'', sometimes called the ''Bowl of Mexico''.
 
Due to its location in a highland bowl, cold air sinks down onto the urban area of Mexico City, trapping industrial and vehicle pollution underneath and, as a result, the city has one of the world's worst air pollution problems. Within one generation, the city has changed from being known for some of the cleanest air of the world into one with some of the worst pollution, with pollutants like [[nitrogen dioxide]] being double or even triple international standards.<ref>[http://www.sbg.ac.at/ipk/avstudio/pierofun/mexico/air.htm  Air pollution in Mexico City]] by  Maricela Yip and Pierre Madl, December 14, 2000, [[University of Salzburg]], [[Austria]]</ref> Since solar radiation does not vary significantly with season at tropical latitudes, photochemical smog is present over the city much of the year.<ref name=NASA/>
 
===Southeast Asia ===
{{Image|Kuala Lumpur smog.jpg|right|250px|Haze and smoke in Kuala Lumpur, Malaysia in 2006}}  


[[Southeast Asia]] consists of a ''mainland'' section and a ''maritime'' section. The mainland section includes [[Burma]], [[Cambodia]], [[Laos]], [[Thailand]], [[Vietnam]] and [[Peninsular Malaysia]] and the maritime section includes [[Brunei]], [[East Malaysia]], [[East Timor]], [[Indonesia]],  [[Philippines]], and [[Singapore]].<ref>[http://www.un.org/depts/dhl/maplib/worldregions.htm World Macro Regions and Components]] From the [[United Nations]] website.</ref> The large cities in [[Southeast Asia]] have been plagued by smoky haze and photochemical smog ever since the late 1990s. The  primary cause of the smoky haze have been the extensive forest fires occurring in Indonesia.<ref>{{cite journal| author=Mark E. Harrison,  Susan E. Page and Suwido H. Limin |title =The global impact of Indonesian forest fires|journal=Biologist |volume=56|issue=3|pages=156-163|date=August 2009 |url=http://www.primateshelpingprimates.nl/site/data/document/338.pdf }}</ref>  Farmers and plantation owners are said to be responsible for the fires, which they use to clear tracts of land for further plantings. Other contributing factor are that El Niño conditions have created some very dry seasons with very little rainfall and the peat swamps that underlie the Indonesian forests and add fuel to the fires.
== Further reading==


One of the recent major occurrences of smoky haze in Malaysia, Singapore  and other parts of Southeast Asia occurred in October 2006 and was caused by smoke from forest fires in Indonesia being blown across the Straits of Malacca by south-westerly winds.
*{{cite book | author=M.R. Beychok| title=Fundamentals Of Stack Gas Dispersion | edition=4th Edition | publisher=author-published | year=2005 | isbn=0-9644588-0-2}}


Since December 1997, member countries of the [[Association of Southeast Asia Nations]] (ASEAN) have been undertaking joint efforts in monitoring, preventing and mitigating transboundary haze pollution resulting from land and forest fires, guided by the [[Regional Haze Action Plan]] (RHAP) that was endorsed by the ASEAN Environment Ministers. In addition, the [[ASEAN Agreement on Transboundary Haze Pollution]] (or ASEAN Haze Agreement) was adopted in June2002 and comprehensively addresses all aspects of fire and haze including prevention, emphasizing the underlying causes, monitoring, and mitigation.<ref>[http://haze.asean.org/info/faq-combatinghaze Combating Haze in ASEAN: Frequently Asked Questions] From the website of the  ASEAN.</ref>
*{{cite book | author=K.B. Schnelle and P.R. Dey| title=Atmospheric Dispersion Modeling Compliance Guide  | edition=1st Edition| publisher=McGraw-Hill Professional | year=1999 | isbn=0-07-058059-6}}


In addition to the smoky haze caused by the forest fires, they have resulted in large amounts of the photochemical smog precursor, nitrogen oxide, entering the atmosphere. That, coupled with the great numbers of automobiles and other vehicles used in the large cities of Southeast Asia, has resulted in those cities being subjected to photochemical smog as well as hazy smoke.
*{{cite book | author=D.B. Turner| title=Workbook of Atmospheric Dispersion Estimates: An Introduction to Dispersion Modeling | edition=2nd Edition | publisher=CRC Press | year=1994 | isbn=1-56670-023-X}}


=== Tehran ===
*{{cite book | author= S.P. Arya| title=Air Pollution Meteorology and Dispersion | edition=1st Edition | publisher=Oxford University Press | year=1998 | isbn=0-19-507398-3}}


In December 2005, schools and public offices had to close in [[Tehran]], [[Iran]] and 1600 people were taken to hospital, in a severe smog blamed largely on automobile exhausts..<ref>{{cite news |url=http://news.bbc.co.uk/1/hi/world/middle_east/4516430.stm |title=Hundreds treated over Tehran smog |publisher=[[BBC]] News |date=December 10, 2005}}</ref>
*{{cite book | author=R. Barrat| title=Atmospheric Dispersion Modelling | edition=1st Edition | publisher=Earthscan Publications | year=2001 | isbn=1-85383-642-7}}


=== United States ===
*{{cite book | author=S.R. Hanna and R.E. Britter| title=Wind Flow and Vapor Cloud Dispersion at Industrial and Urban Sites  | edition=1st Edition | publisher=Wiley-American Institute of Chemical Engineers | year=2002 | isbn=0-8169-0863-X}}


The U.S. EPA  has designated over 300 U.S. counties in the United States to be "non-attainment areas" for one or more air pollutants, meaning that they have failed to attain and maintain the [[National Ambient Air Quality Standards]] as required by the [[Clean Air Act (U.S.)|Clean Air Act]] enacted by the [[U.S. Congress]] . The non-attainment areas are largely clustered around large metropolitan areas, with the largest contiguous non-attainment zones being in [[California]] and the [[Northeast]], as can be seen in the map below.<ref>[http://www.epa.gov/air/oaqps/greenbk/mapnmpoll.html EPA Green Book, Counties Designated Non-attainment and Maintenance]</ref> Various U.S. and Canadian government agencies collaborate to produce real-time air quality maps and forecasts.<ref>[http://www.airnow.gov Airnow.gov]</ref>
*{{cite book | author=P. Zannetti| title=Air pollution modeling : theories, computational methods, and available software | edition= | publisher= Van Nostrand Reinhold | year=1990 | isbn=0-442-30805-1 }}
 
{{Image|Nonattainment Areas Map.png|center|475px|}}
 
====Los Angeles and the San Joaquin Valley ====
{{Image|Los Angeles Smog.JPG|right|210px|Los Angeles smog.}}
 
Located in low basins surrounded by mountains, [[Los Angeles]] and the [[San Joaquin Valley]] are known for their photochemical smog. The millions of vehicles in these basins,  plus the added effects of the port complex in [[Los Angeles]], result in the accumulation of photochemical smog precursors and subsequently to the formation of photochemical smog. Strict regulations by the [[California Air Resources Board]] and other  [[California]] government agencies overseeing this problem have reduced the number of smog alerts from several hundred annually to just a few. However, these geographically  predisposed smog areas still have air  pollution levels that are a pressing issue for the more than 25 million people who live there.
 
==== Major incidents in the United States ====
 
* 1948, October, [[Donora]], [[Pennsylvania]]: 20 killed by smog, 600 hospitalized, thousands more stricken.<ref name=Radford>[http://www.radford.edu/~wkovarik/envhist/7forties.html Environmental History Timeline: 1940-1960] From the website of [[Radford University]] in [[Virginia]].</ref>
* 1953, November, New York: Smog kills between 170 and 260 people.<ref name=Radford/>
* 1954, October, Los Angeles: Heavy smog shuts down schools and industry for most of the month.<ref name=Radford/>
* 1963, New York: Smog caused 200 deaths<ref name=Reitze>{{cite book|author=Arnold W. Reitze Jr.|title=Air Pollution Control Law: Compliance and Enforcement|edition=!st Edition|publisher-Environmental Law Institute|year=2001|pages= pp. 14-15|id=ISBN 1-58576-027-7}}</ref>
* 1966, New York: Smog caused 168 deaths<ref name=Reitze/>
 
==References==
{{Reflist|2}}

Latest revision as of 04:25, 22 November 2023


The account of this former contributor was not re-activated after the server upgrade of March 2022.


Industrial air pollution source

Atmospheric dispersion modeling is the mathematical simulation of how air pollutants disperse in the ambient atmosphere. It is performed with computer programs that solve the mathematical equations and algorithms which simulate the pollutant dispersion. The dispersion models are used to estimate or to predict the downwind concentration of air pollutants emitted from sources such as industrial plants, vehicular traffic or accidental chemical releases.

Such models are important to governmental agencies tasked with protecting and managing the ambient air quality. The models are typically employed to determine whether existing or proposed new industrial facilities are or will be in compliance with the National Ambient Air Quality Standards (NAAQS) in the United States or similar regulations in other nations. The models also serve to assist in the design of effective control strategies to reduce emissions of harmful air pollutants. During the late 1960's, the Air Pollution Control Office of the U.S. Environmental Protection Agency (U.S. EPA) initiated research projects to develop models for use by urban and transportation planners.[1]

Air dispersion models are also used by emergency management personnel to develop emergency plans for accidental chemical releases. The results of dispersion modeling, using worst case accidental releases and meteorological conditions, can provide estimated locations of impacted areas and be used to determine appropriate protective actions. At industrial facilities in the United States, this type of consequence assessment or emergency planning is required under the Clean Air Act (CAA) codified in Part 68 of Title 40 of the Code of Federal Regulations.

The dispersion models vary depending on the mathematics used to develop the model, but all require the input of data that may include:

  • Meteorological conditions such as wind speed and direction, the amount of atmospheric turbulence (as characterized by what is called the "stability class"), the ambient air temperature, the height to the bottom of any inversion aloft that may be present, cloud cover and solar radiation.
  • The emission parameters such the type of source (i.e., point, line or area), the mass flow rate, the source location and height, the source exit velocity, and the source exit temperature.
  • Terrain elevations at the source location and at receptor locations, such as nearby homes, schools, businesses and hospitals.
  • The location, height and width of any obstructions (such as buildings or other structures) in the path of the emitted gaseous plume as well as the terrain surface roughness (which may be characterized by the more generic parameters "rural" or "city" terrain).

Many of the modern, advanced dispersion modeling programs include a pre-processor module for the input of meteorological and other data, and many also include a post-processor module for graphing the output data and/or plotting the area impacted by the air pollutants on maps. The plots of areas impacted usually include isopleths showing areas of pollutant concentrations that define areas of the highest health risk. The isopleths plots are useful in determining protective actions for the public and first responders.

The atmospheric dispersion models are also known as atmospheric diffusion models, air dispersion models, air quality models, and air pollution dispersion models.

Atmospheric layers

Discussion of the layers in the Earth's atmosphere is needed to understand where airborne pollutants disperse in the atmosphere. The layer closest to the Earth's surface is known as the troposphere. It extends from sea-level up to a height of about 18 km and contains about 80 percent of the mass of the overall atmosphere. The stratosphere is the next layer and extends from 18 km up to about 50 km. The third layer is the mesosphere which extends from 50 km up to about 80 km. There are other layers above 80 km, but they are insignificant with respect to atmospheric dispersion modeling.

The lowest part of the troposphere is called the atmospheric boundary layer (ABL) or the planetary boundary layer (PBL) and extends from the Earth's surface up to about 1.5 to 2.0 km in height. The air temperature of the atmospheric boundary layer decreases with increasing altitude until it reaches what is called the inversion layer (where the temperature increases with increasing altitude) that caps the atmospheric boundary layer. The upper part of the troposphere (i.e., above the inversion layer) is called the free troposphere and it extends up to the 18 km height of the troposphere.

The ABL is the most important layer with respect to the emission, transport and dispersion of airborne pollutants. The part of the ABL between the Earth's surface and the bottom of the inversion layer is known as the mixing layer. Almost all of the airborne pollutants emitted into the ambient atmosphere are transported and dispersed within the mixing layer. Some of the emissions penetrate the inversion layer and enter the free troposphere above the ABL.

In summary, the layers of the Earth's atmosphere from the surface of the ground upwards are: the ABL made up of the mixing layer capped by the inversion layer; the free troposphere; the stratosphere; the mesosphere and others. Many atmospheric dispersion models are referred to as boundary layer models because they mainly model air pollutant dispersion within the ABL. To avoid confusion, models referred to as mesoscale models have dispersion modeling capabilities that can extend horizontally as much as a few hundred kilometres. It does not mean that they model dispersion in the mesosphere.

Gaussian air pollutant dispersion equation

The technical literature on air pollution dispersion is quite extensive and dates back to the 1930s and earlier. One of the early air pollutant plume dispersion equations was derived by Bosanquet and Pearson.[2] Their equation did not assume Gaussian distribution nor did it include the effect of ground reflection of the pollutant plume.

Sir Graham Sutton derived an air pollutant plume dispersion equation in 1947[3][4] which did include the assumption of Gaussian distribution for the vertical and crosswind dispersion of the plume and also included the effect of ground reflection of the plume.

Under the stimulus provided by the advent of stringent environmental control regulations, there was an immense growth in the use of air pollutant plume dispersion calculations between the late 1960s and today. A great many computer programs for calculating the dispersion of air pollutant emissions were developed during that period of time and they were commonly called "air dispersion models". The basis for most of those models was the Complete Equation For Gaussian Dispersion Modeling Of Continuous, Buoyant Air Pollution Plumes shown below:[5][6]


where:  
= crosswind dispersion parameter
  =
= vertical dispersion parameter =
= vertical dispersion with no reflections
  =
= vertical dispersion for reflection from the ground
  =
= vertical dispersion for reflection from an inversion aloft
  =
           
           
           
= concentration of emissions, in g/m³, at any receptor located:
            x meters downwind from the emission source point
            y meters crosswind from the emission plume centerline
            z meters above ground level
= source pollutant emission rate, in g/s
= horizontal wind velocity along the plume centerline, m/s
= height of emission plume centerline above ground level, in m
= vertical standard deviation of the emission distribution, in m
= horizontal standard deviation of the emission distribution, in m
= height from ground level to bottom of the inversion aloft, in m
= the exponential function

The above equation not only includes upward reflection from the ground, it also includes downward reflection from the bottom of any inversion lid present in the atmosphere.

The sum of the four exponential terms in converges to a final value quite rapidly. For most cases, the summation of the series with m = 1, m = 2 and m = 3 will provide an adequate solution.

and are functions of the atmospheric stability class (i.e., a measure of the turbulence in the ambient atmosphere) and of the downwind distance to the receptor. The two most important variables affecting the degree of pollutant emission dispersion obtained are the height of the emission source point and the degree of atmospheric turbulence. The more turbulence, the better the degree of dispersion.

Whereas older models rely on stability classes for the determination of and , more recent models increasingly rely on Monin-Obukhov similarity theory to derive these parameters.

Briggs plume rise equations

The Gaussian air pollutant dispersion equation (discussed above) requires the input of H which is the pollutant plume's centerline height above ground level. H is the sum of Hs (the actual physical height of the pollutant plume's emission source point) plus ΔH (the plume rise due the plume's buoyancy).

Visualization of a buoyant Gaussian air pollutant dispersion plume

To determine ΔH, many if not most of the air dispersion models developed between the late 1960s and the early 2000s used what are known as "the Briggs equations." G.A. Briggs first published his plume rise observations and comparisons in 1965.[7] In 1968, at a symposium sponsored by CONCAWE (a Dutch organization), he compared many of the plume rise models then available in the literature.[8] In that same year, Briggs also wrote the section of the publication edited by Slade[9] dealing with the comparative analyses of plume rise models. That was followed in 1969 by his classical critical review of the entire plume rise literature,[10] in which he proposed a set of plume rise equations which have become widely known as "the Briggs equations". Subsequently, Briggs modified his 1969 plume rise equations in 1971 and in 1972.[11][12]

Briggs divided air pollution plumes into these four general categories:

  • Cold jet plumes in calm ambient air conditions
  • Cold jet plumes in windy ambient air conditions
  • Hot, buoyant plumes in calm ambient air conditions
  • Hot, buoyant plumes in windy ambient air conditions

Briggs considered the trajectory of cold jet plumes to be dominated by their initial velocity momentum, and the trajectory of hot, buoyant plumes to be dominated by their buoyant momentum to the extent that their initial velocity momentum was relatively unimportant. Although Briggs proposed plume rise equations for each of the above plume categories, it is important to emphasize that "the Briggs equations" which become widely used are those that he proposed for bent-over, hot buoyant plumes.

In general, Briggs's equations for bent-over, hot buoyant plumes are based on observations and data involving plumes from typical combustion sources such as the flue gas stacks from steam-generating boilers burning fossil fuels in large power plants. Therefore the stack exit velocities were probably in the range of 20 to 100 ft/s (6 to 30 m/s) with exit temperatures ranging from 250 to 500 °F (120 to 260 °C).

A logic diagram for using the Briggs equations[5] to obtain the plume rise trajectory of bent-over buoyant plumes is presented below:

BriggsLogic.png
where:  
Δh = plume rise, in m
F  = buoyancy factor, in m4s−3
x = downwind distance from plume source, in m
xf = downwind distance from plume source to point of maximum plume rise, in m
u = windspeed at actual stack height, in m/s
s  = stability parameter, in s−2

The above parameters used in the Briggs' equations are discussed in Beychok's book.[5]

References

  1. J.C. Fensterstock et al, "Reduction of air pollution potential through environmental planning", JAPCA, Vol. 21, No. 7, 1971.
  2. C.H. Bosanquet and J.L. Pearson, "The spread of smoke and gases from chimneys", Trans. Faraday Soc., 32:1249, 1936.
  3. O.G. Sutton, "The problem of diffusion in the lower atmosphere", QJRMS, 73:257, 1947.
  4. O.G. Sutton, "The theoretical distribution of airborne pollution from factory chimneys", QJRMS, 73:426, 1947.
  5. 5.0 5.1 5.2 M.R. Beychok (2005). Fundamentals Of Stack Gas Dispersion, 4th Edition. author-published. ISBN 0-9644588-0-2. .
  6. D. B. Turner (1994). Workbook of atmospheric dispersion estimates: an introduction to dispersion modeling, 2nd Edition. CRC Press. ISBN 1-56670-023-X. .
  7. G.A. Briggs, "A plume rise model compared with observations", JAPCA, 15:433–438, 1965.
  8. G.A. Briggs, "CONCAWE meeting: discussion of the comparative consequences of different plume rise formulas", Atmos. Envir., 2:228–232, 1968.
  9. D.H. Slade (editor), "Meteorology and atomic energy 1968", Air Resources Laboratory, U.S. Dept. of Commerce, 1968.
  10. G.A. Briggs, "Plume Rise", USAEC Critical Review Series, 1969.
  11. G.A. Briggs, "Some recent analyses of plume rise observation", Proc. Second Internat'l. Clean Air Congress, Academic Press, New York, 1971.
  12. G.A. Briggs, "Discussion: chimney plumes in neutral and stable surroundings", Atmos. Envir., 6:507–510, 1972.

Further reading

  • M.R. Beychok (2005). Fundamentals Of Stack Gas Dispersion, 4th Edition. author-published. ISBN 0-9644588-0-2. 
  • K.B. Schnelle and P.R. Dey (1999). Atmospheric Dispersion Modeling Compliance Guide, 1st Edition. McGraw-Hill Professional. ISBN 0-07-058059-6. 
  • D.B. Turner (1994). Workbook of Atmospheric Dispersion Estimates: An Introduction to Dispersion Modeling, 2nd Edition. CRC Press. ISBN 1-56670-023-X. 
  • S.P. Arya (1998). Air Pollution Meteorology and Dispersion, 1st Edition. Oxford University Press. ISBN 0-19-507398-3. 
  • R. Barrat (2001). Atmospheric Dispersion Modelling, 1st Edition. Earthscan Publications. ISBN 1-85383-642-7. 
  • S.R. Hanna and R.E. Britter (2002). Wind Flow and Vapor Cloud Dispersion at Industrial and Urban Sites, 1st Edition. Wiley-American Institute of Chemical Engineers. ISBN 0-8169-0863-X. 
  • P. Zannetti (1990). Air pollution modeling : theories, computational methods, and available software. Van Nostrand Reinhold. ISBN 0-442-30805-1.