About one fourth of the population in the United States lives in areas which experience episodes of photochemical air pollution, and in 1990 almost 100 cities were out of compliance with the National Ambient Air Quality Standard (NAAQS) (NRC, 1992). Air pollution abatement would reduce the risks of adverse human health effects and vegetation damage and may slow the rate of material degradation as well. However, it is desirable to achieve these environmental standards in a cost-effective manner. Advanced computer models follow pollutant species emitted from anthro­ pogenic and biogenic sources as they are transported downwind to receptor areas and simulate their complex chemical interactions with other species in the atmosphere. Currently these models represent the most scientifically sound foundation for testing alternative control strategies; thus, they are increasingly being used as the basis for regulations. Billions of dollars may be spent to comply with these regulations, so it is important to understand the uncertainty in the underlying models. While many (if not most) of the uncertainty in model predictions comes from uncertainty in the model inputs, there is some introduced by the model itself, e.g., by the numerical advection routines employed.