In Eq. (BB), C() is the contrast relative to the horizon (or background) of an object seen at the observation point itself, that is, at a distance L 0, and C is the contrast at the distance L. The contrast is defined as the ratio of the brightness of the object (Ba) to that of the horizon or background (Bu) minus one:
For example, a black object at zero distance has a brightness of zero (e.g., it absorbs all the visible light) and hence has a C() of f.0. bcn in Eq. (BB) is the total extinction as defined in Eq. (V). Observers typically can differentiate objects on the horizon if C C() ~ 0.02-0.05. A contrast of 0.02, corresponds, using Eq. (BB), to a visual range VR of contribution from light absorption by suspended particulate matter.
It should be noted that the definition of visual range in Eq. (DD) is not always in accord with visual ranges reported from qualitative sightings of surrounding landmarks, as is done, for example, at airport observation towers. There are a number of factors that might influence this, such as the targets not being black or there being differences between various observers. In general, the airport visual ranges are less than those predicted from Eq. (DD) (Stevens et al., 1983; Waggoner, 1983; Lodge, 1983). Indeed, on the basis of airport visual range observations, Ozkaynak et al. (1985) suggest that the use of the coefficient 3.9 in Eq. (DD) is optimistic and that a value less than half that, 1.8, may be more appropriate in urban areas. Other methods of assessing visibility in the atmosphere are discussed by Richards et al. (1988, 1989).
Most of the light scattering by particles in the atmosphere is due to particles in the size range 0.1-1 ¡xm as shown by calculations carried out during World War II for screening smoke particle sizes (Sinclair, 1950). This can be seen in Fig. 9.22, which shows the scattering coefficient of a single particle per unit volume as a function of the particle diameter for spheres with a refractive index of f.50 and light of wavelength 550 nm. The portion of the total extinction coefficient due to particle scattering, 6sp, can be obtained by combining the curve in Fig. 9.22 with the particle volume size distribution, that is, by the curve of AK A log D vs log D.
In a clean, particle-free atmosphere, some light scattering occurs due to the Rayleigh scattering by gases. For this scattering, bsg 1.5 X fO 5 m 1 integrated over the solar spectrum at sea level and 25°C (Ouimette et al., 1981). If light absorption by gases is negligible, as it usually is unless significant concentrations of NOz are present, then bcxl bsg 1.5 X 10 5 m ', and the visual range is ~ 200-260 km for contrasts of 0.05-0.02. While this is an approximation that depends on the nature of the object and on the observer, it does give some idea of the visual range that can be expected in clean air.
Visual ranges can vary from hundreds of kilometers in remote areas to only a few kilometers in heavily polluted urban areas. In the latter case, most of the loss in visibility is due to light scattering, with some
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