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Encyclopedia > Atmospheric dispersion model

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 and vehicular traffic. 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 facilites are or will be in compliance with national ambient air quality standards. The models also serve to assist in the design of effective control strategies to reduce emissions of harmful air pollutants. A computer simulation or a computer model is a computer program that attempts to simulate an abstract model of a particular system. ... This power plant in New Mexico releases sulfur dioxide and particulate matter into the air. ... Layers of Atmosphere (NOAA) Earths atmosphere is a layer of gases surrounding the planet Earth and retained by the Earths gravity. ... Flowcharts are often used to represent algorithms. ... Atmospheric dispersion models are computer programs that use mathematical algorithms to simulate how pollutants in the ambient atmosphere disperse and, in some cases, how they react in the atmosphere. ... In chemistry, concentration is the measure of how much of a given substance there is mixed with another substance. ... The Air Quality Index (AQI) is a standardized index of the air quality in a given location, given in parts per billion. ... Emission standards limit the amount of pollution that can be released into the atmosphere. ...

The dispersion models require the input of data which includes:

  • 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 and the height to the bottom of any inversion aloft that may be present.
  • Emissions parameters such as source location and height, source vent stack diameter and exit velocity, exit temperature and mass flow rate.
  • Terrain elevations at the source location and at the receptor location.
  • The location, height and width of any obstructions (such as buildings or other structures) in the path of the emitted gaseous plume.

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. Satellite image of Hurricane Hugo with a polar low visible at the top of the image. ... In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. ... Temperature inversion in Bratislava Casual view from old part of city, same Bridge A temperature inversion is a meteorological phenomenon where air temperature increases with height. ... The velocity of an object is simply its speed in a particular direction. ... Mass flow rate is the movement of mass per time. ...

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


Gaussian air pollutant dispersion equation

The technical literature on air pollution dispersion is quite extensive and dates back to the 1930's and earlier. One of the early air pollutant plume dispersion equations was derived by Bosanquet and Pearson[1] in 1936. Their equation did not assume Gaussian distribution nor did it include the effect of ground reflection of the pollutant plume. The normal distribution, also called Gaussian distribution, is an extremely important probability distribution in many fields. ...

Sir Graham Sutton derived an air pollutant plume dispersion equation in 1947[2] 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 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:

It has been suggested that Clean Air Act (1970) and Clean Air Act (1990) be merged into this article or section. ...

C = frac{;Q}{u}cdotfrac{;f}{sigma_ysqrt{2pi}};cdotfrac{;g_1 + g_2 + g_3}{sigma_zsqrt{2pi}}


f =; crosswind;, dispersion;, parameter

f =;exp;[-,y^2/,(2;sigma_y^2;);]

g_2 =;vertical;,dispersion;,for;,reflection;, from;,the;, ground

g_2=;exp;[-,(z + H)^2/,(2;sigma_z^2;);]

g_3 =;vertical;,dispersion;,for;,reflection;, from;,inversion;,aloft

g_3 =;sum_{m=1}^infty;big{exp;[-,(z - H - 2mL)^2/,(2;sigma_z^2;);]

+, exp;[-,(z + H + 2mL)^2/,(2;sigma_z^2;);]
+, exp;[-,(z + H - 2mL)^2/,(2;sigma_z^2;);]
+, exp;[-,(z - H + 2mL)^2/,(2;sigma_z^2;);]big}

C =;concentration;,of;,emissions,;, mbox{g}/mbox{m}^3, ;,at;,any;,receptor;,located:


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 g3 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.

It should be noted that σz and σy 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 resulting calculations for air pollutant concentrations are often expressed as an air pollutant concentration contour map in order to show the spatial variation in contaminant levels over a wide area under study. In this way the contour lines can overlay sensitive receptor locations and reveal the spatial relationship of air pollutants to areas of interest. This power plant in New Mexico releases sulfur dioxide and particulate matter into the air. ... Elevation contour map A contour line (also level set, isopleth, isogram or isarithm) for a function of two variables is a curve connecting points where the function has a same particular value. ...

The 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—and 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).

To determine ΔH, many if not most of the air dispersion models developed and used between the late 1960s and the early 2000s used what are known as "the Brigg's equations". Briggs published his first plume rise model observations and comparisons in 1965.[3] In 1968, at a symposium sponsored by CONCAWE (a Dutch organization), he compared many of the plume rise models then available in the literature.[4] In that same year, Briggs also wrote the section of the publication edited by Slade[5] 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[6], in which he proposed a set of of plume rise equations which have became widely known as "the Briggs equations". Subsequently, Briggs modified his 1969 plume rise equations in 1971 and in 1972.[7][8]

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' 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). Flue gas is gas that exits to the atmosphere via a flue, which is a pipe or channel for conveying exhaust gases from a fireplace, furnace, boiler or generator. ... Coal rail cars in Ashtabula, Ohio Fossil fuels, also known as mineral fuels, are hydrocarbon-containing natural resources such as coal, oil and natural gas. ...

A logic diagram for using the Briggs equations[9] to obtain the plume rise trajectory of bent-over buoyant plumes is presented below:

Further reading

For those who would like to learn more about this topic, it is suggested that either one of the following books be read:

  • Beychok, M.R., Fundamentals of Stack Gas Dispersion Modeling, 4th Edition, published by author, 2005. www.air-dispersion.com
  • Turner, D.B., Workbook of atmospheric dispersion estimates: an introduction to dispersion modeling, 2nd Edition, 1994.  www.crcpress.com


  1. ^ Bosanquet, C.H. and Pearson, J.L., "The spread of smoke and gases from chimneys", Trans. Faraday Soc., 32:1249, 1936
  2. ^ Sutton, O.G., "The problem of diffusion in the lower atmosphere", QJRMS, 73:257, 1947 and "The theoretical distribution of airborne pollution from factory chimneys", QJRMS, 73:426, 1947
  3. ^ Briggs, G.A., "A plume rise model compared with observations", JAPCA, 15:433-438, 1965
  4. ^ Briggs, G.A., "CONCAWE meeting: discussion of the comparative consequences of different plume rise formulas", Atmos. Envir., 2:228-232, 1968
  5. ^ Slade, D.H. (editor), "Meteorology and atomic energy 1968", Air Resources Laboratory, U.S. Dept. of Commerce, 1968
  6. ^ Briggs, G.A., "Plume Rise", USAEC Critical Review Series, 1969
  7. ^ Briggs, G.A., "Some recent analyses of plume rise observation", Proc. Second Internat'l. Clean Air Congress, Academic Press, New York, 1971
  8. ^ Briggs, G.A., "Discussion: chimney plumes in neutral and stable surroundings", Atmos. Envir., 6:507-510, 1972
  9. ^ Beychok, Milton R. (2005). Fundamentals Of Stack Gas Dispersion, 4th Edition, author-published. ISBN 0964458802. www.air-dispersion.com

See also

Atmospheric dispersion models are computer programs that use mathematical algorithms to simulate how pollutants in the ambient atmosphere disperse and, in some cases, how they react in the atmosphere. ... Roadway air dispersion is applied to highway segments Roadway air dispersion modeling is the study of air pollutant transport from a roadway or other linear emitter. ...

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