Ring effect correction

To test whether this linearization approach works the Ring effect operator, which is described in the next paragraph, is applied toI0, which results inI1, if the correction works correctly. Figure 6.5 shows I0, I1, I2 and I1 recalculated from I0

for a sample spectrum and bothI1 in Fig. 6.5 are nearly identical.

2841 284.5 285 285.5 286 286.5 287

2 3 4 5 6 7 8 9 10 11x 10¹⁰

Wavelength in nm Limb radiance in ph cm−2 s−1 nm−1 sr−1

I₁ I₂ I₀

Ring effect applied to I₀

Fig. 6.5: Ring effect correction for the Mg 285.2 nm line for a limb measurement with a tangent altitude of 53.5 km. The Ring effect is forward simulated using the measured spectrumI1(λ) to obtain I2(λ). The filling-in effect is assumed to be small and differences between the first and the second application are, therefore, also small. Under this assumption the differences are nearly the same I0(λ)−I1(λ) ≈ I1(λ)−I2(λ). And by adding I1(λ) the corrected spectrum I0(λ) is obtained as I0(λ) = 2I1(λ)−I2(λ).

A 3.3 nm wide boxcar function with a central peak at Δλ= 0 shown in Fig. 6.6 is used as the Ring effect operator. The central peak represents the 96% Rayleigh scattering, while the boxcar function represents the Raman scattered part. Note, that actually the Raman spectra ofN2 and O2 show discrete narrow lines. However, when smoothing a Raman spectrum (e.g., from Penney et al., 1974) with the SCIA-MACHY resolution of 0.22 nm it is very similar to a boxcar function. The boxcar function, therefore, is adequate for a rough estimation of the Ring effect as long as the correction is not so strong, that a more exact method is necessary.

The fraction of Raman scattering is estimated to be between 3 and 6%. To test whether the Ring effect correction works correctly, nearby Fraunhofer lines of metals with very low emission signals in the mesosphere, e.g., the Si line at 288 nm, are used. It is assumed, that these apparent “emission lines” in the limb radiance

−2 −1 0 1 2 10⁻³

10⁻² 10⁻¹ 10⁰

Δ wavelength in nm

Relative part to the new pixel

Fig. 6.6: Ring effect smoothing function. 96 % of the background light is Rayleigh scattered. The Raman scattered part is approximated with a boxcar for the remain-ing 4 %.

to solar irradiance ratio result only from Raman scattering and should disappear if the correct percentage of Raman scattering is chosen. If the line is still an apparent emission line after the correction, the correction is too weak, while if the line is an apparent absorption line after the correction the correction is too strong.

The Ring effect is especially strong for Mg compared to Mg⁺ as the Mg line is a single Fraunhofer line and can be filled in from both the longer and shorter wavelength edge, while the Ring effect is much weaker for the Mg⁺double line, where the line is wide enough that filling-in comes only from one edge of the spectrum.

Ratio spectra of Ring effect corrected limb radiances and solar irradiance for different percentages of Raman scattering and different altitudes are shown in Figs. 6.7 and 6.8. The Ring effect correction influence on the vertical slant column emission profile is shown in Fig. 6.9.

For the Mg 285.2 nm line the Ring effect influence is nearly negligibly small above 90 km. Below 90 km the Ring effect influence steeply increases and the ratio of contribution to the spectral peak from the Ring effect and the actual emission becomes larger than 1 between 80 and 70 km. Below 70 km the Ring effect contri-bution to the peak in the spectrum dominates the emission signal. Therefore, only measurements with tangent altitudes above 70 km are used for the Mg and Mg⁺ retrieval.

The situation is much better for the Mg⁺double lines, where the Ring effect can nearly be neglected above 70 km. Furthermore, the Ring effect correction algorithm

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1.4 1.6 1.8 2 2.2 2.4 2.6x 10

−3

Wavelength in nm

Limb radiance/solar irradiance in sr−1

1% inelastic scattering 2% inelastic scattering 3% inelastic scattering 4% inelastic scattering 5% inelastic scattering 6% inelastic scattering 7% inelastic scattering no correction

Fig. 6.7: Result of the Ring effect correction for a tangent altitude of 53.5 km for the ratio I/F. Shown are the uncorrected spectrum and the corrected spectra with different percentages of Raman scattering in the applied method. The emission signals become smaller with this correction and the Mg line at 285.2 nm, as well as the Si line at 288 nm, which cannot be observed in the region between 90 to 100 km and originates probably purely from Ring effect, nearly vanish for the Ring correction with 4 % of inelastic scattering in the background signal.

produces a small systematic error in the peak altitude region of Mg⁺. This is, because the signal to background ratio is high there. For the case of a pure emission spectrum the Ring effect smoothing reduces the peak value of the emission by 4%.

Therefore, it is better to not to do the Ring effect correction at all for the Mg⁺lines, but also neglect altitudes below 70 km (Not doing the Ring effect correction above a certain altitude or including the emission feature into the consideration of the Ring effect correction was another option here).

The Ring effect correction was also compared to the more sophisticated and exact calculations of SCIATRAN (see, e.g., Rozanov et al., 2014), showing very similar results, so that the use of the simpler approach is justified above 70 km.

SCIATRAN allows to forward model radiative transfer with and without inelastic scattering. However, when comparing these to measured spectra, there are small differences in this wavelength region. These differences may originate partly from simplifications in the models on the one hand side and spectrometer calibration is-sues on the other hand side. Whatever the reason for these differences is, it makes it hard to apply the SCIATRAN corrections directly to the measured spectra with-out making significant systematic errors. Therefore, the simpler approach of the Ring effect correction is not just simpler, but also not worse than using the more

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1 1.5 2 2.5 3 3.5x 10

−4

Wavelength in nm

Limb radiance/solar irradiance in sr−1

1% inelastic scattering 2% inelastic scattering 3% inelastic scattering 4% inelastic scattering 5% inelastic scattering 6% inelastic scattering 7% inelastic scattering no correction

Fig. 6.8: Result of the Ring effect correction for a tangent altitude of 90 km for the ratio I/F. The background signal is low at this altitude and the Ring effect correction is only very small.

sophisticated method, at this point.