Ring Effect

First noticed by Grainger and Ring (1962), the Ring effect is the phenomenon whereby the relative depths of Fraunhoffer absorption lines are observed to be greater in direct sunlight than in skylight. Early suggestions as to its source include daytime airglow (Grainger and Ring, 1962) and aerosol fluorescence (Noxon and Goody, 1965). Recent studies have ruled these out in favour of molecular inelastic, or Raman, scattering (e.g.: Conde et al., 1992).

Raman scattering is inelastic scattering by particles which are much smaller than both the incident and scattered wavelengths. Initially unpolarized light which undergoes Raman scattering will only be slightly polarized as the phase function is proportional to $1+\frac{1}{13} \cos^2\Theta$. In UV and visible spectroscopy, only rotational Raman scattering is considered; the vibrational component results in wavelength shifts large enough that they are usually not considered (Chance and Spurr, 1997).

Generally, the Ring phenomenon is accounted for by treating it as an absorber. A number of empirical methods have been suggested in order to obtain an effective Raman cross-section for use in the DOAS fitting process. The simplest is to assume the spectrum of the Raman scattered light is unstructured. If this is valid, the Ring spectrum can be approximated as the reciprocal of the reference spectrum (Fish, 1994), such that,

$$\sigma_{\rm Ring}(\lambda) \propto \frac{1}{I_{\rm ref}(\lambda)}.$$ (11.8)

Another method is to assume single scattering is valid and that the unpolarized photons have been Raman scattered and the polarized photons have been Rayleigh scattered. The effective Ring cross-section is then (Solomon et al., 1987; Fish, 1994),

$$\sigma_{\rm Ring}(\lambda) \propto \frac{R(\lambda) - \frac{1-\rho}{1+\rho}\cos^2\Theta} {1-R(\lambda)}$$ (11.9)

where $R=I_{\parallel}/I_{\perp}$ and $\rho$ is the depolarization factor (discussed in Section 2.4.3).

 

Both these methods make important assumptions, the validity of which are questionable. In particular, in the reciprocal reference spectrum method, the spectrum of inelastically scattered light is structured and in the measured polarization method, the assumption of the single-scattering polarization is not valid, at least in the troposphere. Another approach is to forward model the Raman scattering in an inelastic radiative transfer code and extract from it the Ring cross-sections (Fish and Jones, 1995; Vountas et al., 1998). This is quite computationally intensive due to the large number of wavelengths involved and so at present this has only been done for single scattering (Vountas et al., 1998).

A fourth approach, and the one used in this study, is outlined below. Detailed rotational Raman N₂ and O₂ scattering cross-sections, taken from Chance and Spurr (1997) and shown in Figure 6.5, were convolved with a high-resolution solar spectrum to produce an effective Ring cross-section, (Chance and Spurr, 1997),

$$\sigma_{\rm Ring}(\lambda) \propto \pi F_o(\lambda) \otimes \sigma_{\rm Raman}(\lambda)$$ (11.10)

where $\sigma_{\rm Raman}(\lambda)$ is the combined N₂ and O₂ mixing ratio weighted cross-sections of Figure 6.5a and 6.5b and $\otimes$ denotes convolution. Tests using single-scattered GOMETRAN (or the radiative transfer model designed for the GOME instrument) simulated spectra, including Raman scattering, indicate that using this type of ring cross-section used in the retrieval of NO₂ is accurate to 2% for ${\rm SZA}<70^{\circ}$ and 4% for ${\rm SZA}<90^{\circ}$ (relative to that obtained using the single-scattered GOMETRAN ring cross-section) (Vountas et al., 1998).

Once the effective Ring cross-section is known, the differential cross-section is determined. An example is shown in Figure 6.5c between 480 and 540 nm.