comes less restrictive when the model is applied to larger, three-dimensional, and spatially averaged concentrations rather than to concentrations at individual points in a geographic region. Thus, the model is especially useful for spatially averaged problems, such as regional haze.

A speciated rollback model for airborne particles is an aggregation of several separate rollback models for each individual chemical component of the atmospheric particle complex. In almost all cases, the anthropogenic materials in the dry particle mass almost entirely consist of five components: sulfates, organics, elemental carbon, nitrates, and crustal material (e.g., soil dust and road dust). Organics can be further subdivided into primary organic and secondary organic particles. In the simplest case, it is assumed that linear rollback models can relate each primary particle component (elemental carbon, crustal material, and primary organics) to its regionwide emission level and each secondary aerosol component (sulfates, nitrates, and secondary organics) to the emission level of its controlling gas phase precursor (e.g., SO2, NOx, NH3, and VOC).

In considering the ambient nature of airborne particles (not only the measured dry fine-particle mass), particle-bound water is an additional important component. Certain chemical constituents of anthropogenic particles—such as sulfates, nitrates, and some organics—have an affinity for water. The constituents acquire water vapor from the atmosphere and form a liquid phase at relative humidities well below the 100% level normally associated with condensation. If the concentration of hygroscopic particles (i.e., those that retain water) is reduced, there is a corresponding reduction in the particle-bound water. Accordingly, water retention is usually incorporated into the rollback models for the hygroscopic airborne particles (i.e., sulfate-bound water is assumed to change in proportion to sulfate concentrations at a particular relative humidity, nitrate-bound water in proportion to nitrate concentrations, etc.). For example, if one is considering a rollback model for visibility effects, the total light-extinction contribution from nonbackground sulfate particles plus sulfate-associated water is assumed to change in proportion to SOx emissions.

The speciated rollback model incorporates a very restrictive assumption in addition to the assumption about the spatial homogeneity of emission changes. The restrictive assumption is that there is only one controlling precursor for each secondary airborne particle component and that transformation and deposition processes are completely linear with



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