would be a grid-based model that uses inverse methods to derive pollutant emission rates from observed pollutant concentrations. This section briefly reviews and provides a critique of some of the key models commonly used in AQM.

Empirical Rollback Model

The empirical rollback model is the simplest model available for AQM. This model assumes that an air pollutant’s concentration in an airshed is directly proportional to the total emission rate of the pollutant in the airshed. In other words, if Po is the current concentration of a pollutant in an airshed, Eo is the current rate of emission, and El is the hypothetical emission rate after the introduction of emission controls, the new pollutant concentration, Pl, predicted by a rollback model would be

(3-3)

where Pbackground is the so-called background concentration of the pollutant that would be found in the absence of any emissions within the airshed. From Equation 3-3, one can solve for Ea, the emission rate needed for attainment of Ps, the pollutant air quality standard or goal:

(3-4)

Although easy to use, rollback models have distinct limitations. Because of the assumption of linearity between emissions and concentrations, these models are only suitable for primary pollutants or secondary pollutants with relatively simple chemical-production mechanisms. Because rollback models only calculate a single concentration for the pollutant in the airshed, they are unable to simulate or account for spatial and temporal variations in pollutant concentrations. As a result, these models are most useful for pollutants that tend to be uniformly mixed in an airshed. They were used extensively in AQM before the mid-1970s and have since been largely supplanted by more sophisticated models. They nevertheless continue to be used in some applications, most notably in the design of urban strategies to meet the NAAQS for carbon monoxide (CO) (NRC 2002b).

Receptor Models

Receptor models are similar to rollback models in their dependence on observed concentrations and their neglect of chemical and meteorological processes. However, instead of being limited to assuming simple linear relationships between a pollutant concentration and its emission rate, re-



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