User:Milton Beychok/Sandbox: Difference between revisions

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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.


{{TOC|right}}
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>   
This article is about formatting '''embedded inline references''' (also called '''notes''' or '''footnotes''') in an article. Embedded inline references are references that are meant to corroborate  a specific word, statement, paragraph or even sub-section of an article by providing the readers of the article with the details of a book, journal, newspaper report or online website page that substantiates and validates the word, statement, paragraph or sub-section. The location of the word, statement, paragraph or subsection being referenced is marked with a superscript, bracketed number (colored blue) like this for a single reference<font color=blue><sup>[1]</sup></font> or this<font color=blue><sup>[2]</sup></font><font color=blue><sup>[3]</sup></font> for multiple references. All Citizendium article having a status of Developed or Approved should  have a list of references in a "References" or "Footnotes" section at the end of the article.


In Citizendium and many other Wikis, the Wiki markup coding of embedded inline references on the edit page of an article always begins with the tag  <nowiki><ref></nowiki> and ends with the tag  <nowiki></ref></nowiki>. For that reason, the Wiki markup coding of embedded inline references is often referred to as the '''<nowiki><ref> </ref></nowiki>  method'''.
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.


By contrast, some authors use the word "references" to mean listing the details of sources (such as books or journals)  that provided information, corroboration or substantiation  of the article as whole rather than any specific parts of the article. Such lists are placed  at the end of the article with no indication as to what specific part of the article each listed source applies. Within the context of Citizendium, in most cases, such non-specific references are best placed in the "Bibliography" subpage rather than at the end of the article. If such reference lists include hyperlinks to online website pages, then they are best included in the "External Links" subpage. In some few cases, an article may benefit by having a short list of  about 3 books in a section entitled "Further reading" in addition to the "References" or  "Footnotes" section and the "Bibliography" subpage.
The dispersion models vary depending on the mathematics used to develop the model, but all require the input of data that may include:


Some authors also use embedded inline hyperlinks like this [http://www.atsdr.cdc.gov/toxfaqs/index.asp]  or this [http://webbook.nist.gov/cgi/cbook.cgi?Name=Isooctane&Units=SI&cTC=on#Thermo-Condensed] as references. Such references should not be used. When used in an article that is also using the <nowiki><ref> </ref></nowiki>  method, confusion will arise between the numbering of the embedded inline hyperlinks and the embedded inline references.
* 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).


No rules or guidance about references are cast in stone and must absolutely be followed. However, following the methods and guidance in this article will result in consistency from one article to another and, for that reason,  it is strongly recommended they be followed.
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.


==Valid, reliable references==
The atmospheric dispersion models are also known as atmospheric diffusion models, air dispersion models, air quality models, and air pollution dispersion models.


A reference must be accurate, reliable and it must corroborate the statement in the text. To validate or corroborate the statement that  "Mike Brown climbed Mount Everest", referencing a publication about Mount Everest is no good if Mike Brown isn't mentioned.  Similarly, referencing an article about Mike Brown is also no good if it doesn't mention that he climbed Mount Everest. The referenced source must corroborate that Mike's achievement is true.
==Atmospheric layers==


We must use reliable, credible sources such as published books, professional journals, mainstream press report , and reliable web sites. Blogs, MySpace, YouTube, fan sites and extreme minority material are not usually acceptable, nor are your own unpublished essays or research.  Wikipedia articles or other Citizendium articles are not reliable sources.
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.


==Inserting the embedded inline references==
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.


=== ''Single insertion of a reference:'' ===
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.


For the single insertion of a reference, this is placed on the article's edit page at the insertion point of the citation. For example:<br/>
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.


:'''<nowiki><ref>[http://www.eia.doe.gov/bookshelf/brochures/gasoline/index.html Where Does My Gasoline Come from?]  April 2008.</ref></nowiki>'''
==Gaussian air pollutant dispersion equation==


=== ''Multiple insertion of the same reference:'' ===
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.


For the multiple insertion of a reference, the reference tag  <nowiki><ref></nowiki> includes a one-word name for the reference like <nowiki><ref name=xxxxx></nowiki>. For example, this is placed on the article's edit page at the first insertion point of the citation:
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.


:'''<nowiki><ref name=Speight>{{cite book|author=J. G. Speight|title=The Chemistry and Technology of Petroleum|edition=4th Edition|publisher=CRC Press |year=2006|id=ISBN 0-8493-9067-2}}</ref></nowiki>'''
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>


This is placed at the second insertion point of the citation:


:'''<nowiki><ref name=Speight/></nowiki>'''
<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>


And this is placed at the third insertion point of the citation:
{| border="0" cellpadding="2"
 
|-
:'''<nowiki><ref name=Speight/></nowiki>''' ..... and so forth for further insertion points<br/>
|align=right|where:
 
|&nbsp;
=== ''What is produced at the points of insertion:'' ===
|-
 
!align=right|<math>f</math> 
This is an example of what is produced and note that the reference numbers in blue are automatically generated:
|align=left|= crosswind dispersion parameter
 
|-
{|border=0 width=850 align=center
!align=right|&nbsp;
|'''The crude oil distillation unit is the first processing unit in a [[Petroleum refining processes|petroleum crude oil refinery]].<ref name=Speight>{{cite book|author=J. G. Speight|title=The Chemistry and Technology of Petroleum|edition=4th Edition|publisher=CRC Press |year=2006|id=ISBN 0-8493-9067-2}}</ref> It separates the crude oil into [[petroleum naphtha]]<ref name=Speight/> and other intermediate refinery products.<ref name=Speight/> Those intermediate products are subsequently further processed  in other units so as to produce sales products such as [[gasoline]],<ref name=Speight/><ref>[http://www.eia.doe.gov/bookshelf/brochures/gasoline/index.html Where Does My Gasoline Come from?], [[U.S. Department of Energy]], April 2008.</ref> [[diesel oil]], [[fuel oil]]s and [[asphalt]].'''
|align=left|= <math>\exp\;[-\,y^2/\,(2\;\sigma_y^2\;)\;]</math>
|-
!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
|}
|}


Clicking on any one of the above blue reference numbers causes the screen display to scroll down to that reference number listed in the References section at the end of the article.
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.


=== ''Producing the reference or footnote list:'' ===
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.


On the edit page of the article, place either of these at the bottom of an article to produce a references or footnotes section:
<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.


:'''<nowiki>==References==</nowiki>''' &nbsp; &nbsp; &nbsp; &nbsp; '''<nowiki>==Footnotes==</nowiki>'''       
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.
:'''<nowiki>{{reflist}}</nowiki>''' &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; '''<nowiki>{{reflist}}</nowiki>'''
 
This is the list  produced in the references or footnotes section and note that the list numbers are automatically generated:
 
{{reflist}}


<br/>In some cases, when there are a large number of references and many of them are fairly short, space can be conserved by using '''<nowiki>{{reflist|2}}</nowiki>''',  instead of    '''<nowiki>{{reflist}}</nowiki>''', which splits the reference list into two columns.
==Briggs plume rise equations==


== How to use the reference or footnotes list ==
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).


* Clicking on the blue superscript <font color=blue><sup>1.0</sup></font> causes the screen display to scroll back up to the point where the first  reference to Speight's book was inserted. Clicking on the blue superscript <font color=blue><sup>1.1</sup></font> causes the screen display to scroll back up to the point where the the second reference to Speight's book was inserted. Clicking on the blue superscript <font color=blue><sup>1.2</sup></font> causes the screen display to scroll back up to the point where the the third reference to Speight's was inserted ... and so forth.
[[File:Gaussian Plume.png|thumb|right|333px|Visualization of a buoyant Gaussian air pollutant dispersion plume]]


* Clicking on any up arrow (<font color=blue></font>) in the reference list that has no associated superscripts causes the screen display to scroll back up to the point where that single-use references was inserted.
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 models.  That 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>


* Clicking on the superscript bracket reference numbers anywhere in the article's text cause the screen to scroll down far enough to display that reference in the reference list.
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


== How to place the reference insertion points ==
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'''''.


The correct placement of the reference insertions is illustrated by repeating the above example:
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).


{|border=0 width=850 align=center
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:
|'''The crude oil distillation unit is the first processing unit in a [[Petroleum refining processes|petroleum crude oil refinery]].<ref name=Speight>{{cite book|author=J. G. Speight|title=The Chemistry and Technology of Petroleum|edition=4th Edition|publisher=CRC Press |year=2006|id=ISBN 0-8493-9067-2}}</ref> It separates the crude oil into [[petroleum naphtha]]<ref name=Speight/> and other intermediate refinery products.<ref name=Speight/> Those intermediate products are subsequently further processed  in other units so as to produce sales products such as [[gasoline]],<ref name=Speight/><ref>[http://www.eia.doe.gov/bookshelf/brochures/gasoline/index.html Where Does My Gasoline Come from?], [[U.S. Department of Energy]], April 2008.</ref> [[diesel oil]], [[fuel oil]]s and [[asphalt]].'''
[[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/>


Note the placement of the references in the above example. These are the "rules":
==References==
 
{{reflist}}
* A reference for a sentence is inserted immediately after the period at the end of the sentence, with no space between the period and the reference.
* A reference for a single word (that is not followed by a comma) is inserted immediately after the word, with no space between the word and the reference.
* A reference for a single word (that is followed by a comma) is inserted immediately after the comma, with no space between the word and the comma.
* Two or more references at the same point of insertion are placed immediately next to each other with no space between the references.
 
== How to reference books and journals ==
 
A number of templates, such {{tl|cite book}} or {{tl|cite journal}}, are available to format the text between the <nowiki><ref></nowiki> and <nowiki></ref></nowiki> tags in a more structured way. Some of those templates are quite complicated and it is probably best to use the simplest ones.
 
===''Referencing books''===
 
For example, this is a quite simple template that provides the essentials needed to reference a book:
 
:'''<nowiki>{{cite book|author=|title=|edition=|publisher=|year=|pages=|id=ISBN XXXX }}</nowiki>'''


and filled out as per this sample:
== Further reading==


:'''<nowiki>{{cite book|author=John Smith|title=The Age of Reason|edition=2nd Edition|publisher=Johnson Press|year=2007|id=ISBN 0-5678-4325-1}}</nowiki>'''
*{{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}}


which produces this in the reference list:
*{{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}}


:John Smith (2007). ''The Age of Reason'', 2nd Edition. Johnson Press. <font color=blue>ISBN 0-5678-4325-1</font>.
*{{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}}


if the edition is unknown, then simply leave it blank, thus:
*{{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}}


:'''<nowiki>{{cite book|author=John Smith|title=The Age of Reason|edition=|publisher=Johnson Press|year=2007|id=ISBN 0-5678-4325-1}}</nowiki>'''
*{{cite book | author=R. Barrat| title=Atmospheric Dispersion Modelling | edition=1st Edition | publisher=Earthscan Publications | year=2001 | isbn=1-85383-642-7}}


=== ''Referencing journals'' ===
*{{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}}


==How to reference online website pages==
*{{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 }}

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.