Extinction by an Ensemble of Particles

FIGURE 15.4 Aerosol scattering phase function for (NH SQ particles at 80% relative humidity at X = 550 nm (Nemesure et al. 1995). Incident beam enters from the left. 

If F0 is the incident flux at z = 0, taken to represent, say, the top of the layer, then intensity at any distance z into the layer is 

As noted in Chapter 4, the dimensionless product x = beM z is called the optical depth of the layer, and (15.26) is called the Beer-Lambert law. In the visible portion of the spectrum, optical depth of tropospheric aerosols can range from less than 0.05 in remote, pristine environments to close to 1.0 near the source of intense particulate emissions such as in the plume of a forest fire. 

For a population of monodisperse, spherical particles at a number concentration of N, the extinction coefficient is related to the dimensionless extinction efficiency by 

The extinction coefficient can be expressed as the sum of a scattering coefficient / scat and an absorption coefficient b s 

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