Dependence of Contrast Transmittance Tr on Atmospheric Optical Variables

Because the contrast transmittance is the one variable that contains all the information required to describe how various physical descriptors of scenic landscape features are modified as a function of aerosol loading, illumination, and observer-vista geometry, it is of interest to examine how sensitive ir is to changes in atmospheric aerosol loading as a function of aerosol mass and average scene radiance. The average scene radiance, N, was identified as a^ in Eq. (23).

Malm and Henry (1987) examined how the xr changes with changing image reflectivity, image distance, aerosol size distribution, and aerosol mass loading. For a sulfate aerosol, bext is almost entirely due to scattering and, as such, bext is proportional to aerosol mass. Therefore, the variation of xr with respect to bext is proportional to its variation with respect to aerosol mass. Figures 4a and 4b show 5 = |ArrA/)ext| as a function of bext.

Figure 4a corresponds to a typical sulfate aerosol mass size distribution, scattering angle 9S — 15°, and ¡V0 = 0.13NS, where Ns is the Rayleigh sky radiance. Figure 4b is also for a sulfate aerosol but with (Js — 125° and ¡V0 = 0.5iVv. An immediately evident trend shown in Figures 4a and 4b is that there is a distance where S is maximum; S decreases to zero as R —0 and as R oo. Secondly, the distance at which S is maximum increases as N0 increases (brighter landscapes). In a forward scattering situation where landscapes are in a shadow (C0 ~ —0.90), S is maximum in the 5- to 10-km range. Although not explicitly shown in Figure 4a, in a back-scatter geometry (6S = 125°), the most sensitive distance is still around 5 to 10 km if the landscape is dark. However, the maximum sensitivity drops by about a factor of 2 and is not nearly as sensitive to distance. On the other hand, Figure 4b shows that when the landscape is highly reflective and illuminated (C0 ~ 0.50 and 9S — 125°) the distance of maximum sensitivity increases, is quite sensitive to background bext, and remains sensitive to changes in bsxt long after dark targets have lost their sensitivity (dark targets will have disappeared, while bright targets can still be seen).

Figure 5 examines in more detail the relative contribution of N* and T to S. Figure 5 shows contributions of N* and T to S for the case shown in Figure 4a at T = 10 km (forward scattering, sulfate aerosol, and dark target). Changes in N* are primarily responsible for changes in Mt{ a as aerosol is added or subtracted from a clean atmosphere. As background aerosol loading is increased (larger bext), the relative importance of T to S increases to a point where T dominates the effect on S. However, it should be emphasized that this only occurs after the Mt{ a has increased to a point where landscape features would be barely visible. Figure 5b shows N* and T contributions to S for the Figure 4b case at R = 70 km (backscatter, sulfate aerosol, and bright target). With this geometry, attenuation of image-forming information, T, is responsible for much of the change in Mtf a. In fact, N* can

(a) 0.020 0.032 0.044 0.056 0.068 0.080

bext (krrT1)

Figure 5 Sensitivity (S) expressed as changes in the modulation transfer function increase of 5ext = 0.01 km"' plotted against bex[ for a sulfate aerosol. In (a) 9S = 15°, R = 70 km, and N0 = 0.13 Ns, while in (b) 0, = 125°, R = 70 km, and ,\'0 = 0.5 Ns. Parts (a) and (b) show the relative contributions of path radiance and atmospheric transmittance to changes in Mxi a as a function of 5ext.

Figure 5 Sensitivity (S) expressed as changes in the modulation transfer function increase of 5ext = 0.01 km"' plotted against bex[ for a sulfate aerosol. In (a) 9S = 15°, R = 70 km, and N0 = 0.13 Ns, while in (b) 0, = 125°, R = 70 km, and ,\'0 = 0.5 Ns. Parts (a) and (b) show the relative contributions of path radiance and atmospheric transmittance to changes in Mxi a as a function of 5ext.

dominates changes in Mtf a. On the other hand, when looking at brightly colored landscape features with the sun behind the observer's back (backscatter), the relative importance of N* to visibility becomes smaller and changes in Nr as a result of increased bcx[ are more dependent on image-forming radiance being attenuated over the sight path. However, for a specific scene under static illumination conditions, contributions of N* and T to change in Mtf a as a function of aerosol concentration tend to track each other.

Because most research to date has focused on apportionment of ¿>ext, and therefore T, to aerosol species, it is fortunate that for scattering aerosols, such as sulfates, an understanding of this relationship yields significant insight into how aerosols affect visibility under a wide range of viewing conditions. However, under not uncommon circumstances, the major cause of visibility degradation can be associated with path radiance, and path radiance explicitly requires knowledge of the volume scattering function in addition to bext. Almost no effort has been expended on examining how path radiance is affected as a function of aerosol characteristics or on apportioning path radiance to aerosol species. Aerosols that absorb light contribute to path radiance differently than aerosols that only scatter light (such as sulfates), so the impact of scatterers and absorbers on path radiance is not additive. Conversely, the effect of scattering and absorbers in bext is additive. Therefore, when appreciable concentrations of light-absorbing particles or gases are present, knowledge of just bext (transmittance) may not be adequate to describe changes in visibility.

The concepts discussed above are summarized in Figure 6. Those variables enclosed in the box on the left side of Figure 6 are dependent on illumination observer geometry, while those on the right are not. Path radiance, a geometry-

Aerosol Chemical and Physical Characteristics

Aerosol Chemical and Physical Characteristics

Figure 6 Flow diagram showing how aerosol physical-chemical characteristics relate to the optical variables required to completely specify the atmospheric modulation transfer function.

dependent variable, is combined with atmospheric transmittance, a geometry-independent parameter, and average scene luminance to yield contrast transmittance or modulation transfer function.

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