2.1 Introduction: Deconstructing the Atmospheric Path of Pollutants

To predict where a pollutant will go and what its concentration will be, we must deconstruct its atmospheric journey into three sequential physical processes. First is plume rise, which determines the initial height a pollutant reaches. Second is atmospheric transport, the process by which the wind carries the pollutant downstream. Finally, there is atmospheric dispersion, the turbulent mixing that spreads the pollutant out, reducing its concentration. A thorough understanding of these three mechanisms is fundamental to the entire field of air pollution meteorology.

2.2 Plume Rise and the Concept of “Effective” Emission Height

The final height achieved by an effluent plume is determined by a combination of its own properties (like exit velocity and buoyancy) and the state of the surrounding atmosphere. Stable atmospheric layers, particularly temperature inversions, act as a ceiling, limiting the plume’s upward rise and forcing it to spread out horizontally. Conversely, in unstable, convective air, a buoyant plume will theoretically continue to rise until it eventually reaches a stable layer. Wind also plays a crucial role; higher wind speeds reduce the final plume rise. In some cases of low efflux velocity and high wind, a negative rise, or “downwash,” can occur, pulling the plume down in the wake of the stack.

Over the years, numerous formulae have been developed to predict plume rise. Early equations were often purely empirical, derived by fitting curves to a limited set of observations. A more physically grounded approach, developed by Briggs and others, uses dimensional analysis to create more robust and universally applicable formulae. These newer equations have gained wide acceptance since the 1970s, in part because they are supported by observational evidence. For example, in neutrally stable air, the theory predicts that the rise should be proportional to horizontal distance to the 2/3 power, which is in good agreement with observations.

The final calculated height of the plume is of paramount importance because it allows us to define a single, critical variable for all subsequent modeling:

• Effective Source Height (H): This is the sum of the physical stack height and the calculated plume rise.

This concept is a cornerstone of pollution modeling. It establishes the starting altitude from which we can then calculate the pollutant’s subsequent journey. Once this effective height is established, the next stage of that journey is determined by atmospheric transport.

2.3 Atmospheric Transport: Following the Wind

The core principle of atmospheric transport is simple: pollutants travel with the wind. The practical application of this principle, however, is complex. Wind data, especially at the level of detail required for pollution studies, is often scarce. While hourly ground-level wind observations are available at airports, these stations can be hundreds of kilometers apart. Furthermore, data on winds above the surface layer, where many pollutants actually travel, is even more limited.

This data gap has led to the development of mesometeorology, the study of weather systems on a scale of several kilometers to about 100 kilometers. On this scale, wind patterns are strongly influenced by local surface features. Hills, valleys, large lakes, and even entire cities create their own complex and time-varying wind patterns, such as daytime sea breezes or nighttime mountain-valley flows. A major task for the air pollution meteorologist is to infer these intricate local wind fields from the sparse data provided by standard weather stations.

In some areas, specialized tools like the tetroon—a tetrahedral balloon that drifts with the wind and is tracked by radar—have been used to conduct detailed local wind studies. As a result, the complex mesoscale wind features of major cities like New York and Chicago are now well understood. While transport determines the path a plume will follow, it is the process of dispersion that determines the plume’s size, shape, and concentration along that path.

2.4 Atmospheric Dispersion: The Role of Turbulence

Atmospheric dispersion is controlled by two key factors. The first is the mean wind speed, which provides a simple diluting effect: for a continuous source, a faster wind will spread the emitted puffs of pollution farther apart, resulting in a lower concentration. The second, and more complex, factor is atmospheric turbulence. Turbulence consists of a chaotic mix of horizontal and vertical eddies that mix the polluted air with the surrounding clean air, causing the plume to spread out and its peak concentration to decrease.

The Twin Engines of Turbulence: Convection and Wind Shear

Atmospheric eddies, the agents of turbulent mixing, are created by two primary mechanisms:

1. Convective Turbulence: This is thermal turbulence, driven by heating from below. When the sun warms the ground, the air near the surface becomes buoyant and rises, creating vertical eddies. This process is strongest when the atmospheric temperature decreases rapidly with height (a steep lapse rate) and is the dominant mixing mechanism on clear, sunny days with light winds.
2. Mechanical Turbulence: This is turbulence generated by wind shear, which is simply a change in wind speed with height. Because wind speed is zero at the ground and increases with altitude, some degree of mechanical turbulence is almost always present. It increases with overall wind speed and is significantly enhanced by surface roughness. This roughness is characterized by a parameter called the “roughness length” (z₀). This value is small over smooth surfaces like sand (around 0.1 cm) but can be several meters over the complex terrain of a city.

The Richardson Number (Ri): A Unified Measure of Stability

The relative dominance of convective versus mechanical turbulence is quantified by a critical dimensionless parameter called the Richardson number (Ri). It represents the ratio of convective energy to mechanical energy. By measuring or estimating the Richardson number, we can classify the atmosphere’s stability and predict its capacity for dispersion.

As visualized in meteorological diagrams, a plume’s behavior changes dramatically with stability. Under convection-dominant conditions (large negative Ri), the plume is caught in strong updrafts and downdrafts, causing it to loop and spread rapidly in all directions. In a neutral atmosphere dominated by mechanical turbulence (Ri ≈ 0), the plume spreads in a relatively uniform, cone-like shape. Finally, in very stable conditions (Ri > 0.25), vertical turbulence is effectively eliminated. The plume is unable to spread vertically and instead fans out horizontally in a thin, flat layer.

In summary, dispersion is strongest on clear days with light winds when convection is dominant. It is weakest during clear nights with light winds when a stable inversion forms. In between these extremes, during periods of strong winds, mechanical turbulence creates intermediate levels of dispersion. These physical principles provide the foundation for the mathematical models we use to estimate pollutant concentrations.