Departures from the Rayleigh atmosphere assumed in construction of the radiance tables used to derive total ozone tend to display a wavelength dependence that is linear in derived surface reflectivity. This situation was anticipated in the original work of Dave, and has been observed under conditions of sun glint (Zia Ahmad) as well as in the presence of tropospheric aerosols (Omar Torres). This assumption may be formulated by assuming that the residues of the triplet ozone retrieval are due to an error in ozone associated with such a linear dependence in reflectivity. Expressions for the residues at two channels (e.g. 313 nm and 331 nm for the A-triplet) can be written as:

And

These two equations can be solved for the "true" ozone amount that is consistent with the R(lambda) assumption.

Where:

r(l ₎ - Residue reported on current level-2 for channel l

W ₀ - Total ozone reported on current level-2

s(l ₎ - Sensitivity of channel l radiance to changes in ozone

R(l ₎ - Lambertian equivalent surface reflectivity (or reflectivity) for channel l

sr(l ₎ - Sensitivity of channel l radiance to changes in reflectivity

D R(l ₎ - Difference of Rl from reflectivty reported on level-2

D l (l ₎ - Difference of channel l wavelength from 360 nm

This expression for corrected ozone provides a good correction for cases of sun-glint present in the V7 TOMS ozone data as shown in Figure 1. This example is near the equator at equinox and the Earth Probe has a local equator crossing time of about 10:30, so when EP/TOMS scans to the east, it observes the image of the sun reflected in the ocean, centered at around scan position 21. The 331 nm residue shows a fairly broad region (scan positions 14 - 27) to be affected by the glint.

Figure 1. Illustration of glint correction performance showing un-corrected and corrected scan angle dependence in derived ozone relative to the corrected mean. Also shown is the 331 nm residue (or aerosol index) and the derived surface reflectivity, which is approximately 8% over all 35 samples.

The residues resulting from a single retrieval affected by glint are shown in Figure 2 for the case of the Version 7 retrieval and for the Dave assumption. The Version 7 algorithm uses the assumption departures from the Rayleigh forward model are linear with wavelength in units of n-value (or percent radiance). This is illustrated in Figure 2 by the solid line, which connects the V7 residues for the triplet wavelengths used in the retrieval (313 nm, 331 nm, and 360 nm). The Dave assumption is that the effective Lambertian equivalent surface reflectivity is linear with wavelength. Since the sensitivity of the upwelling radiance to surface reflectivity is a function of wavelength, this assumption is non-linear in units of n-value (or percent radiance), as illustrated by the dashed line in Figure 2.

Figure 2. Residues from a TOMS retrieval affected by glint. The solid line and plus (+) indicate the Version 7 retrieval, and the dashed line and asterisks indicate results based on the Dave assumption.

The R(lambda) assumption also provides a fairly good correction for the impact of tropospheric aerosols on TOMS derived ozone as well. This effect has been carefully modeled and studied by Omar Torres (Torres, Moy and Bhartia, 1998, "Impact of Aerosol Absorption on Total Ozone Retrieval from Satellite Measurements of Backscattered Ultraviolet Radiation," J. Geophys. Res., 1999), and in the EP TOMS Data Products User’s Guide.