A primitive form of air quality modeling which is still used in some very limited situations is commonly referred to as “proportional modeling” or “roll-back” modeling. The basis for this form of modeling is that there is a linear relationship between air quality and emissions that are released into the air that cause the air pollution problem. This approach has more validity in the case of pollutants that are directly emitted as opposed to pollutants that are formed in the atmosphere. Even in the case of secondary pollutants, some insights can be gained through the use of proportional modeling. In the case of proportional modeling, it is assumed that air quality concentrations can be represented as shown in equation 7.1.2-1.

Where c refers to the air quality concentration at a location and Q refers to the total emission rate that contributes to the concentration. K is a proportionality constant that relates the atmospheric concentration of pollutants to the emission rate of pollutants or pollutant precursors. b refers to the background level of air pollution that would occur in the absence of local emissions. K and b must be determined from empirical data. The normal way to calculate K is to first determine a value for b based on local remote air quality monitors such as a monitor upwind of the area of interest and a value for c using the highest impacted air quality monitor in the region of interest. Then K can be estimated as shown in equation 7.1.2-2.

Once K and b are determined then equation 7.1.2-2 can be used to estimate air quality concentrations in the cases where Q is assumed to increase or decrease due to growth and air quality regulations.

Great care should be taken in using proportional modeling. Very inaccurate estimations can result from this approach. Proportional modeling is recommended only for those situations where there is no opportunity to use the more sophisticated modeling approaches discussed in succeeding sections.