Modeling aerosol particles in the atmosphere has some major differences from modeling species such as water vapor or trace gases. For such species, a mass concentration or mixing ratio is sufficient. Particles on the other hand have a size distribution with diameters ranging over several orders of magnitude, from a few nanometers to many micrometers. To represent this size distribution, atmospheric modelers have resorted to two major paradigms. The first of these is a sectional approach in which the size distribution is subdivided into sections covering a small range of particle diameters. This approach has been very popular and has an obvious analogy with particle samplers which measure in size ranges such as a cascade impactor. The second approach assumes that there is an appropriate mathematical functional form which represents the size distribution. Moments of this distribution describe characteristics of the distribution. The zeroeth moment is the total number of particles, the second, and third moments are related to total surface area and volume respectively. Some modelers calculate even higher moments and related them to radiative information which may be gathered from remote sensing.

After a brief review of the two paradigms, most of the presentation will concentrate on the second paradigm as implemented in a three-dimensional chemical-transport model, the EPA Community Multiscale Air Quality (CMAQ) modeling system. In this implementation, particles smaller than 2.5 micrometers in diameter are represented by the superposition of two log-normal subdistributions and larger particles are represented by a single log-normal distribution. In the smaller size range, the total number, total surface area, and the constituent chemical species masses are the predicted variables. For the larger particle range only number and species masses are predicted.

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