Air mass factors (AMFs) relate apparent column densities (ACDs)
to vertical column densities, VCDs, through,
In general, air mass factors depend on a number of factors, including: solar zenith angle, height of the layer being perturbed, wavelength, the type and abundance of aerosols, and the altitude and direction of observation. The effects of these variables have been examined in some detail for zenith-sky geometry (Perliski and Solomon, 1993; Slusser et al., 1996) but, to date, their effects on nadir and limb geometry have not been assessed. Air mass factors will also depend on how the absorber profile varies within the perturbed layer itself.
Air mass factor calculations made using the model developed for this work compare well with Monte Carlo-calculated AMFs for zenith-sky geometry (Slusser et al., 1996). A brief survey of how solar zenith angle, height of the ER-2, height of the absorbing layer, wavelength, and aerosols impact both limb and nadir geometry is carried out. Nadir air mass factors are considered first. Refer to Figure 6.2 for an illustration of the the nadir geometry.
Figure 6.11 shows nadir AMFs for an albedo of 0.6 and 0.3 using different absorbing layer heights as a function of solar zenith angle. These calculations are for BrO at 350 nm, although the optical depths are small enough that they are applicable for any absorber at this wavelength. For the layers nearer to the surface, the AMF increases slightly with SZA and then decreases. This is due primarily to the increasing pathlength, and hence increasing extinction, of the direct solar beam. At larger SZAs, most of the energy will have been scattered out before reaching these levels. For this same reason, the lower the layer, the smaller the AMF. The higher layers tend to continually increase with SZA due to the increase in overall pathlength. A larger albedo will increase the AMF as a larger fraction of the signal will have passed through the absorbing layer (at least) twice (as long as the atmosphere is not too thick). The dashed lines in Figure 6.11 refers to the optically-thin, plane-parallel, geometric AMF of . The 8-20 km layer resembles this but only in a qualitative way.
The impact of changing other variables is summarized in Table 6.4. Lowering the height of the observation tends to increase the AMF as the signal contains a larger fraction of photons which have sampled the absorbing layer. The exception is for the 8-20 km layer where the AMF decreases as less of the absorber is below the observation point. Removing the aerosols from the planetary boundary layer (PBL) acts to decrease the AMF, especially if the absorbing layer overlaps the PBL, due to the reduced scattering. Similarly, without stratospheric aerosols, the AMF may increase if the absorbing layer is low, or decrease if it overlaps the aerosol layer. Comparisons with single scattering AMFs indicates that multiple scattering is important, although less so for 8-20 km layer.
Air mass factors are now examined as a function of where the absorbing layer is placed for limb and nadir viewing angles. The limb viewing geometry is illustrated in Figure 6.2. A set of ten limb scan steps, starting at , are used which represent a typical CPFM scan. These angles are given in Table 6.5. The thickness of the perturbed layer was 1 km. Figure 6.12 shows the calculations at 500 nm. The first five steps are shown in panel (a). Steps 0 to 3 all have peaks, indicating the height to which they are most sensitive, near 20 km, the altitude of the ER-2. This is due simply to the fact that the largest pathlength enhancements occur for all near 20 km. Step 4 has its peak slightly below 20 km, near its tangent height of 19 km. Panel (b) has the remaining steps, including the nadir. Step 5 also peaks near its tangent height, 13.9 km, but steps 6 to 9 all peak near the 20 km. The reason for this is that while the pathlengths are longer closer to the surface, the optical depths are large enough that the majority of the signal is originating from layers near the observation point. The nadir AMF is nearly constant with a slight maximum just above the surface.
Similar calculations were carried out at 350 nm and are presented in Figure 6.13. The increase in Rayleigh scattering acts to push the heights at which the maximum AMF occurs closer to 20 km. This also leads to an overall decrease in AMF peak values and an increase in width. With the exception of the nadir, which had a peak at 8-9 km, the maximum occurs at all angles between 18-21 km. The heights at which each angle has a maximum in AMF are summarized in Table 6.5.