Atmospheric Aerosols and Log-Normal Distributions

Ideally, one would like to describe various size distributions by some relatively simple mathematical function. Because there is no single theoretical basis for a particular function to describe atmospheric aerosols, various empirical matches have been carried out to the experimentally observed size distributions some of these are discussed in detail elsewhere (e.g., see Hinds, 1982). Out of the various mathematical distribution functions for fitting aerosol data, the log-normal distribution (Aitchison and Brown, 1957 Patel et al., 1976) has emerged as the mathematical function that most frequently provides a sufficiently good fit, and hence we briefly discuss its application to the size distribution of atmospheric aerosols. 

Most readers will be familiar with the bell-shaped normal distribution plotted in Fig. 9.12. When applied to the size distribution of particles, for example, such a distribution is fully characterized by the arithmetic mean D and the standard deviation a, where a is defined such that 68% of the particles have sizes in the range D a In the log-normal distribution, the logarithm of the diameter D is assumed to have a normal distribution. (Either logarithms to the base 10 or loga- 

TABLE 9.2 Some Typical Tropospheric Aerosols and Their Associated Properties  

Type Typical number concentration (cm 3) Typical characteristics 

Marine 100-400 Three modes Dp 0.1, 0.1-0.6, and 0.6 p,m most ( 95%) of particle mass but only 5-10% of total number in largest mode large particles mainly sea salt aerosol, smallest are products (e.g., SO ) of gas (e.g., DMS) to particle conversion 

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