# 19.1: Dispersion Factors

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The stream of polluted air downwind of a smoke stack is called a smoke plume. If the plume is buoyant, or if there is a large effluent velocity out of the top of the smoke stack, the center of the plume can rise above the initial emission height. This is called plume rise.

The word “plume” in air pollution work means a long, slender, nearly-horizontal region of polluted air. However, the word “plume” in atmospheric boundary-layer (ABL) studies refers to the relatively wide, nearly vertical updraft portion of buoyant air that is convectively overturning. Because smoke plumes emitted into the boundary layer can be dispersed by convective plumes, one must take great care to not confuse the two usages of the word “plume”.

Dispersion is the name given to the spread and movement of pollutants. Pollution dispersion depends on

• wind speed and direction,
• plume rise, and
• atmospheric turbulence.

Pollutants disperse with time by mixing with the surrounding cleaner air, resulting in an increasingly dilute mixture within a spreading smoke plume.

Wind and turbulence are characteristics of the ambient atmosphere, as were described in earlier chapters. While emissions out of the top of the stack often have strong internal turbulence, this quickly decays, leaving the ambient atmosphere to do the majority of the dispersing.

The direction that the effluent travels is controlled by the local, synoptic, and global-scale winds. Pollutant destinations from known emission sources can be found using a forward trajectory along the mean wind, while source locations of polluted air that reach receptors can be found from a backward trajectory.

The goal of calculating dispersion is to predict or diagnose the pollutant concentration at some point distant from the source. Concentration c is often measured as a mass per unit volume, such as µg m–3. It can also be measured as volume ratio of pollutant gas to clean air, such as parts per million (ppm). See the INFO box for details about units.

A source - receptor framework is used to relate emission factors to predicted downwind concentration values. We can examine pollutants emitted at a known rate from a point source such as a smoke stack. We then follow the pollutants as they are blown downwind and mix with the surrounding air. Eventually, the mixture reaches a receptor such as a sensor, person, plant, animal or structure, where we can determine the expected concentration.

In this chapter, we will assume that the mean wind is known, based on either weather observations, or on forecasts. We will focus on the plume rise and dispersion of the pollutants, which allows us to determine the concentration of pollutants downwind of a known source.

INFO • Pollutant Concentration Units

The amount of a pollutant in the air can be given as a fraction or ratio, q. This is the amount (moles) of pollution divided by the total amount (moles) of all constituents in the air. For air quality, the ratios are typically reported in parts per million (ppm). For example, 10 ppm means 10 parts of pollutant are contained within 106 parts of air. For smaller amounts, parts per billion (ppb) are used.

Although sometimes the ratio of masses is used (e.g., ppmm = parts per million by mass), usually the ratio of volumes is used instead (ppmv = parts per million by volume).

Alternately, the amount can be given as a concentration, c, which is the mass of pollutant in a cubic meter of air. For air pollution, units are often micrograms per cubic meter (µg m–3). Higher concentrations are reported in milligrams per cubic meter, (mg m–3), while lower concentrations can be in nanograms per cubic meter (ng m–3).

The conversion between fractions and concentrations is

$$\ q(\mathrm{ppmv})=\frac{a \cdot T}{P \cdot M_{s}} \cdot c\left(\mu \mathrm{g} / \mathrm{m}^{3}\right)$$

where T is absolute temperature (Kelvin), P is total atmospheric pressure (kPa), Ms is the molecular weight of the pollutant, and a = 0.008314 kPa·K–1·(ppmv)·(µg m–3)–1.

For a standard atmosphere at sea level, where temperature is 15°C and pressure is 101.325 kPa, the equation above reduces to

$$\ q(\mathrm{ppmv})=\frac{b}{M_{s}} \cdot c\left(\mu \mathrm{g} / \mathrm{m}^{3}\right)$$

where b = 0.02363 (ppmv) / (µg m–3).

For example, nitrogen dioxide (NO2) has a molecular weight of Ms = 46.01 g/mole (see Table 1-2 in Chapter 1). If concentration c = 100 µg m–3 for this pollutant, then the equation above gives a volume fraction of q = (0.02363/46.01) · (100) = 0.051 ppmv.

Science Graffito

“The solution to pollution is dilution.”

– Anonymous.

This aphorism was accepted as common sense during the 1800s and 1900s. By building taller smoke stacks, more pollutants could be emitted, because the pollutants would mix with the surrounding clean air and become dilute before reaching the surface.

However, by 2000, society started recognizing the global implications of emitting more pollutants. Issues included greenhouse gases, climate change, and stratospheric ozone destruction. Thus, government regulations changed to include total emission limits.

This page titled 19.1: Dispersion Factors is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Roland Stull via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.