Atmospheric dispersion modeling

# Atmospheric dispersion modeling

Overview

Atmospheric dispersion modeling is the mathematical simulation
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...

of how air pollutants
Air pollution
Air pollution is the introduction of chemicals, particulate matter, or biological materials that cause harm or discomfort to humans or other living organisms, or cause damage to the natural environment or built environment, into the atmosphere....

disperse in the ambient atmosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

. It is performed with computer programs that solve the mathematical equations and algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

s which simulate the pollutant dispersion. The dispersion models
Air pollution dispersion terminology
Air pollution dispersion terminology includes the words and technical terms that have a special meaning to those who work in the field of air pollution dispersion modeling...

are used to estimate or to predict the downwind concentration
Concentration
In chemistry, concentration is defined as the abundance of a constituent divided by the total volume of a mixture. Four types can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration...

of air pollutants or toxins 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.
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Encyclopedia

Atmospheric dispersion modeling is the mathematical simulation
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...

of how air pollutants
Air pollution
Air pollution is the introduction of chemicals, particulate matter, or biological materials that cause harm or discomfort to humans or other living organisms, or cause damage to the natural environment or built environment, into the atmosphere....

disperse in the ambient atmosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

. It is performed with computer programs that solve the mathematical equations and algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

s which simulate the pollutant dispersion. The dispersion models
Air pollution dispersion terminology
Air pollution dispersion terminology includes the words and technical terms that have a special meaning to those who work in the field of air pollution dispersion modeling...

are used to estimate or to predict the downwind concentration
Concentration
In chemistry, concentration is defined as the abundance of a constituent divided by the total volume of a mixture. Four types can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration...

of air pollutants or toxins 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
National Ambient Air Quality Standards
The National Ambient Air Quality Standards are standards established by the United States Environmental Protection Agency under authority of the Clean Air Act that apply for outdoor air throughout the country...

(NAAQS) in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

and other nations. The models also serve to assist in the design of effective control strategies to reduce emissions of harmful air pollutants.

Air dispersion models are also used by public safety responders and emergency management personnel for emergency planning of accidental chemical releases. Models are used to determine the consequences of accidental releases of hazardous or toxic materials, Accidental releases may result fires, spills or explosions that involve hazardous materials, such as chemicals or radionuclides. The results of dispersion modeling, using worst case accidental release source terms
Accidental release source terms
Accidental release source terms are the mathematical equations that quantify the flow rate at which accidental releases of air pollutants into the ambient environment can occur at industrial facilities such as petroleum refineries, petrochemical plants, natural gas processing plants, oil and gas ...

and meteorological conditions, can provide an estimate of location impacted areas, ambient concentrations, and be used to determine protective actions appropriate in the event a release occurs. Appropriate protective actions may include evacuation or shelter-in-place for persons in the downwind direction. At industrial facilities, this type of consequence assessment or emergency planning is required under the Clean Air Act (United States)
Clean Air Act (United States)
The Clean Air Act is a United States federal law enacted by Congress, and signed by President Richard Nixon on December 31, 1970 to control air pollution on a national level. It requires the Environmental Protection Agency to develop and enforce regulations to protect the general public from...

(CAA) codified in part 60 of Title 40 of the Code of Federal Regulations
Code of Federal Regulations
The Code of Federal Regulations is the codification of the general and permanent rules and regulations published in the Federal Register by the executive departments and agencies of the Federal Government of the United States.The CFR is published by the Office of the Federal Register, an agency...

.

The dispersion models vary depending on the mathematics used to develop the model, but all require the input of data that may include:
• Meteorological
Meteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...

conditions such as wind speed and direction, the amount of atmospheric turbulence
Turbulence
In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...

(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.
• Source term (the concentration or quantity of toxins in emission or accidental release source terms
Accidental release source terms
Accidental release source terms are the mathematical equations that quantify the flow rate at which accidental releases of air pollutants into the ambient environment can occur at industrial facilities such as petroleum refineries, petrochemical plants, natural gas processing plants, oil and gas ...

) and temperature of the material
• Emissions or release parameters such as source location and height, type of source (i.e., fire, pool or vent stack)and exit velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

, exit temperature and mass flow rate
Mass flow rate
Mass flow rate is the mass of substance which passes through a given surface per unit time. Its unit is mass divided by time, so kilogram per second in SI units, and slug per second or pound per second in US customary units...

or release rate.
• Terrain elevations at the source location and at the receptor location(s), 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, surface roughness or the use of a more generic parameter “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 may also include isopleths showing areas of minimal to high concentrations that define areas of the highest health risk. The isopleths plots are useful in determining protective actions for the public and 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
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

is needed to understand where airborne pollutants disperse in the atmosphere. The layer closest to the Earth's surface is known as the troposphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

. It extends from sea-level to a height of about 18 km and contains about 80 percent of the mass of the overall atmosphere. The stratosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

is the next layer and extends from 18 km to about 50 km. The third layer is the mesosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

which extends from 50 km 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)
Planetary boundary layer
The planetary boundary layer , also known as the atmospheric boundary layer , is the lowest part of the atmosphere and its behavior is directly influenced by its contact with a planetary surface. On Earth it usually responds to changes in surface forcing in an hour or less...

or the planetary boundary layer (PBL)
Planetary boundary layer
The planetary boundary layer , also known as the atmospheric boundary layer , is the lowest part of the atmosphere and its behavior is directly influenced by its contact with a planetary surface. On Earth it usually responds to changes in surface forcing in an hour or less...

and extends from the Earth's surface 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
Capping inversion
A capping inversion is an elevated inversion layer that caps a convective boundary layer.The boundary layer is the part of the atmosphere which is closest to the ground. Normally, the sun heats the ground, which in turn heats the air just above it. Thermals form when this warm air rises into the...

(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 of the most important 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 extend horizontally up to 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. 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 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
Clean Air Act
A Clean Air Act is one of a number of pieces of legislation relating to the reduction of airborne contaminants, smog and air pollution in general. The use by governments to enforce clean air standards has contributed to an improvement in human health and longer life spans...

, 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
Air pollution dispersion terminology
Air pollution dispersion terminology includes the words and technical terms that have a special meaning to those who work in the field of air pollution dispersion modeling...

shown below:

 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 pointAir pollution dispersion terminologyAir pollution dispersion terminology includes the words and technical terms that have a special meaning to those who work in the field of air pollution dispersion modeling... 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 deviationStandard deviationStandard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average... 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 functionExponential functionIn mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...

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.

The resulting calculations for air pollutant concentrations
Air pollutant concentrations
Air pollutant concentrations, as measured or as calculated by air pollution dispersion modeling, must often be converted or corrected to be expressed as required by the regulations issued by various governmental agencies...

are often expressed as an air pollutant concentration contour map
Contour line
A contour line of a function of two variables is a curve along which the function has a constant value. In cartography, a contour line joins points of equal elevation above a given level, such as mean sea level...

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.

Whereas older models rely on stability classes (see air pollution dispersion terminology
Air pollution dispersion terminology
Air pollution dispersion terminology includes the words and technical terms that have a special meaning to those who work in the field of air pollution dispersion modeling...

) for the determination of and , more recent models increasingly rely on the Monin-Obukhov similarity theory
Monin-Obukhov Length
The is used to describe the effects of buoyancy on turbulent flows, particularly in the lower tenth of the atmospheric boundary layer. It was first defined by Alexander Obukhov in 1946,...

to derive these parameters.

## 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 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. In 1968, at a symposium sponsored by CONCAWE (a Dutch organization), he compared many of the plume rise models then available in the literature. In that same year, Briggs also wrote the section of the publication edited by Slade 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, 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.

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
Flue gas
Flue gas is the gas exiting to the atmosphere via a flue, which is a pipe or channel for conveying exhaust gases from a fireplace, oven, furnace, boiler or steam generator. Quite often, the flue gas refers to the combustion exhaust gas produced at power plants...

from steam-generating boilers burning fossil fuel
Fossil fuel
Fossil fuels are fuels formed by natural processes such as anaerobic decomposition of buried dead organisms. The age of the organisms and their resulting fossil fuels is typically millions of years, and sometimes exceeds 650 million years...

s 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 to obtain the plume rise trajectory of bent-over buoyant plumes is presented below:
 Δh where: = plume rise, in m = buoyancy factor, in m4s−3 = downwind distance from plume source, in m = downwind distance from plume source to point of maximum plume rise, in m = windspeed at actual stack height, in m/s = stability parameter, in s−2

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

### Atmospheric dispersion models

• List of atmospheric dispersion models provides a more comprehensive list of models than listed below. It includes a very brief description of each model.
The ADMS 3 is an advanced atmospheric pollution dispersion model for calculating concentrations of atmospheric pollutants emitted both continuously from point, line, volume and area sources, or intermittently from point sources...

• AERMOD
AERMOD
The AERMOD atmospheric dispersion modeling system is an integrated system that includes three modules: *A steady-state dispersion model designed for short-range dispersion of air pollutant emissions from stationary industrial sources....

• ATSTEP
ATSTEP
ATSTEP is a Gaussian puff model for diagnosis and prognosis of the atmospheric dispersion, deposition, gamma radiation and doses of released radioactivity in case of accidents in nuclear power plants or during transport, and from dirty bombs....

• CALPUFF
CALPUFF
CALPUFF is an advanced, integrated Gaussian puff modeling system for the simulation of atmospheric pollution dispersion distributed by the Atmospheric Studies Group at TRC Solutions...

• DISPERSION21
DISPERSION21
DISPERSION21 is a local scale atmospheric pollution dispersion model developed by the air quality research unit at SMHI, the Swedish Meteorological and Hydrological Institute, located in Norrköping...

• FLACS
• HYSPLIT
• HYPACT
• ISC3
ISC3
ISC3 model is a popular steady-state Gaussian plume model which can be used to assess pollutant concentrations from a wide variety of sources associated with an industrial complex.This model can account for the following:...

• NAME
Name
A name is a word or term used for identification. Names can identify a class or category of things, or a single thing, either uniquely, or within a given context. A personal name identifies a specific unique and identifiable individual person, and may or may not include a middle name...

• MERCURE
MERCURE
MERCURE is an atmospheric dispersion modeling CFD code developed by Électricité de France and distributed by ARIA Technologies, a French company....

• OSPM
Operational Street Pollution Model
The Operational Street Pollution Model is an atmospheric dispersion model for simulating the dispersion of air pollutants in so-called street canyons. It was developed by the National Environmental Research Institute of Denmark, Department of Atmospheric Environment...

• RIMPUFF
RIMPUFF
RIMPUFF is a local-scale puff diffusion model developed by Risø DTU National Laboratory for Sustainable Energy, Denmark. It is an emergency response model to help emergency management organisations deal with chemical, nuclear, biological and radiological releases to the atmosphere.RIMPUFF is in...

• SAFE AIR
SAFE AIR
SAFE AIR is an advanced atmospheric pollution dispersion model for calculating concentrations of atmospheric pollutants emitted both continuously or intermittently from point, line, volume and area sources...

• PUFF-PLUME
PUFF-PLUME
PUFF-PLUME is a model used to help predict how air pollution disperses in the atmosphere. It is a Gaussian atmospheric transport chemical/radionuclide dispersion model that includes wet and dry deposition, real-time input of meteorological observations and forecasts, dose estimates from inhalation...

### Organizations

• Air Quality Modeling Group
Air Quality Modeling Group
The Air Quality Modeling Group is in the U.S. EPA's Office of Air and Radiation and provides leadership and direction on the full range of air quality models, air pollution dispersion models and other mathematical simulation techniques used in assessing pollution control strategies and the...

• Air Resources Laboratory
Air Resources Laboratory
The Air Resources Laboratory is an air quality and climate laboratory in the Office of Oceanic and Atmospheric Research which is an operating unit within the National Oceanic and Atmospheric Administration in the UNited States...

• Finnish Meteorological Institute
Finnish Meteorological Institute
The Finnish Meteorological Institute is the government agency responsible for gathering and reporting weather data and forecasts in Finland. It is a part of the Ministry of Transport and Communications but it operates semi-autonomously....

• KNMI, Royal Dutch Meteorological Institute
• National Environmental Research Institute of Denmark
National Environmental Research Institute of Denmark
NERI, the National Environmental Research Institute of Denmark is an independent research institute under the Aarhus University. NERI undertakes scientific consultancy work and monitoring of nature and the environment as well as applied and strategic research...

• Swedish Meteorological and Hydrological Institute
• TA Luft
TA Luft
Germany has a well known air pollution control regulation titled "Technical Instructions on Air Quality Control" and commonly referred to as the TA Luft. The first version of the TA Luft was established in 1964. It has subsequently been revised in 1974, 1983, 1988 and 2002...

• UK Atmospheric Dispersion Modelling Liaison Committee
UK Atmospheric Dispersion Modelling Liaison Committee
The UK Atmospheric Dispersion Modelling Liaison Committee is composed of representatives from UK governmental departments, agencies and research organizations as well as from non-governmental organizations and groups...

• UK Dispersion Modelling Bureau
UK Dispersion Modelling Bureau
The UK Dispersion Modelling Bureau is part of the Met Office which is the UK's national weather and meteorological service...

• Desert Research Institute
Desert Research Institute
The Desert Research Institute is the nonprofit research campus of the Nevada System of Higher Education , the organization that oversees all publicly-supported higher education in the U.S. state of Nevada...

### Others

• Bibliography of atmospheric dispersion modeling
• Air pollution dispersion terminology
Air pollution dispersion terminology
Air pollution dispersion terminology includes the words and technical terms that have a special meaning to those who work in the field of air pollution dispersion modeling...

• List of atmospheric dispersion models
• Portable Emissions Measurement System (PEMS)