Air Dispersion

Error Propagation in Air Dispersion Modeling

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Courtesy of Air Dispersion

Air dispersion modeling has been evolving since before the 1930s.  Over the last 15-25 years, strict environmental regulations and the availability of personal computers have fueled an immense growth in the use of mathematical models to predict the dispersion of air pollution plumes.  Beychok's recently published book, 'Fundamentals Of Stack Gas Dispersion', details the evolution of the widely used Gaussian air dispersion models and their inherent assumptions and constraints.

Unfortunately, many users of such models are completely unaware of those assumptions and constraints and mistakenly believe that the precision achievable with computers equates to accuracy.  This article discusses how the propagation of seemingly small errors in the Gaussian model parameters can cause very large variations in the model's predictions.

In most dispersion models, determining the pollutant concentrations at ground-level receptors beneath an elevated, buoyant plume of dispersing pollutant-containing gas involves two major steps:

First, the height to which the plume rises at a given downwind distance from the plume source is calculated.  The calculated plume rise is added to the height of the plume's source point to obtain the so-called 'effective stack height', also known as the plume centerline height or simply the emission height.

Then, the ground-level pollutant concentration beneath the plume at the given downwind distance is predicted using the Gaussian dispersion equation.

Assumptions and Constraints

A host of assumptions and constraints are required to derive the Gaussian dispersion equation for modeling a continuous, buoyant plume from a single point-source in flat terrain ... which is still a long way from the more sophisticated models now in use for multiple sources in complex terrain.  The most important assumptions and constraints are related to:

The accuracy of predicting the plume rise since that affects the emission height used in the Gaussian dispersion equation.

The accuracy of the dispersion coefficients (i.e., the vertical and horizontal standard deviations of the emission distribution) used in the Gaussian dispersion equation.

The assumption of the averaging time period represented by the calculated ground-level pollutant concentrations as determined by the dispersion coefficients used in the Gaussian equation.  In other words, do the calculated ground-level concentrations represent a 5-minute, 10-minute, 15-minute, 30-minute or 1-hour average concentration?

Besides the assumptions and constraints in deriving the Gaussian equation, the methods for obtaining certain parameters used in the Gaussian models are also subject to many assumptions and constraints.  Those methods include: obtaining the atmospheric stability classifications (which characterize the degree of turbulence available to enhance dispersion), determining the profiles of windspeed versus emission height, and converting ground-level short-term concentrations from one averaging time to another.  This discussion of shortcomings in the Gaussian dispersion models is not unique.  The literature abounds with such discussions. (2,3,4,5,6)  Unfortunately, despite those discussions, there is a widespread belief that dispersion models can predict dispersed plume concentrations within a factor of two or three of the actual concentrations in the real world.  Indeed, there are some who believe the models are even more accurate than that.

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