Systematic errors

Uncertainties in the literature absorption cross-sections

Different literature absorption cross-sections exist for each absorber. The systematic error that arises when using different literature absorption cross-sections can be estimated to be approximately up to 10 % (e.g. for the spectral retrieval of O₄ in the UV, see Section 8.2.1).

Temperature dependence of the literature absorption cross-sections

The shape and absolute values of the various literature absorption cross-sections show a strong dependence on temperature due to the temperature-dependent occupation of the vibrational and rotational bands and since absorption occurs at different altitudes in the atmosphere and thus at different temperatures (e.g. Platt and Stutz, 2008). This effect can be accounted for by including several absorption cross-sections of the same trace gas species in the DOAS retrieval measured at different temperatures. The absorption cross-sections of the same species have to be orthogonalised to each other, in order to avoid correlations (Van Roozendael and Fayt, 2001). In this thesis, a correction for the temperature dependence of the O₃ absorption cross-section is implemented in the DOAS retrieval, i.e. O₃ absorption cross-sections at two different temperatures are included in the DOAS spectral retrieval.

Influence of the slit function

It is typically assumed in DOAS evaluations that the slit function is constant over the whole wave-length range. Figure 8.32 shows a comparison of the shape of the different mercury and cadmium emission lines that can be detected by the present instrument.

Figure 8.32: Comparison of the shape of the mercury and cadmium lines in the UV (left panel) and in the visible wavelength range (right panel) for a spectrum recorded on 16 November 2011. The wavelength and intensity axes are normalised and given in arbitrary units.

The background intensity is subtracted from each line, i.e. the minimum intensity in the wave-length range around the emission line. If the background signal below the emission line is not correctly subtracted, an offset in the inferred dSCDs might occur. A Gauss function is further fitted to the emission line to define the centre wavelength. The wavelength range of the line is then shifted to this centre position. The intensity of each emission line is then area-normalised as well

as normalised to one. It has to be noticed that not all lines are single emission lines, some emission lines are double emission lines (Table 8.1), which are not fully resolved by the instrument. The shape and FWHM of the single emission lines in the UV (326 nm, 334 nm, 340 nm, 346 nm) and in the visible wavelength range (467 nm, 480 nm, 508 nm) do not change significantly over the total spectral range, respectively. The double emission lines in the UV (361 nm, 365 nm) are slightly broader than the single emission lines, whereas the double emission line at 435 nm has a different shape and is significantly broader than the single emission lines in the visible wavelength range. The baseline of the background signal below each slit function is not always identical on both sides of the emission line. The minimum signal of the emission line might not be representative for the total range of the peak. A possible reason for small changes in the convolved absorption cross-sections and thus in the inferred dSCDs might be due to this remaining baseline in the background signal after subtracting the minimum signal. Thus, for further applications, it is recommended to fit a straight line to the background baseline and subtract this line from the intensity instead of simply subtracting the minimum intensity.

Figure 8.33 shows the absorption cross-sections of O₄, HCHO and NO₂ convolved with the different slit functions. In the UV, the absorption cross-sections of O₄ and HCHO convolved with a single emission line are almost identical, whereas the absorption cross-sections convolved with a double emission line are much smaller. In the visible wavelength range, the absorption cross-sections of O₄ and NO₂ convolved with the slit function at 480 nm and 508 nm are almost identical.

The absorption cross-section convolved with the slit function at 467 nm shows a smaller absorption structure than the other absorption cross-sections convolved with a single emission. The absorption cross-sections convolved with the double emission line at 435 nm shows a similar shape than the absorption cross-sections convolved with the slit function at 467 nm.

Figure 8.33: Cross-sections of O₄, HCHO and NO₂ convolved with the different slit functions from Figure 8.32.

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In Figure 8.34, the different slit functions are used to evaluate O₄ and HCHO in the UV as well as O₄ and NO₂ in the visible wavelength range. Obviously, the resulting dSCDs differ depending on the slit function that is used to convolve the absorption cross-sections. It can be expected that for a broad slit function, the differential structures are smaller and thus the resulting dSCDs are larger than for a narrow slit function. The O₄ and HCHO dSCDs in the UV convolved with a single emission line agree very well with each other with an average deviation of less than 1 %.

When using a double emission line as a slit function (361 nm, 365 nm), the dSCDs increase showing the largest values for the slit function at 365 nm. The O₄ dSCDs in the UV show a maximum deviation of approximately (0.1 − 0.2) · 10⁴³ molec²cm⁻⁵ (≈ 7 %) and the HCHO dSCDs result in a maximum deviation of approximately 1 · 10¹⁶ molec cm⁻² (≈ 30 %) between the dSCDs evaluated with a single emission and a double emission line. In the visible wavelength range, the difference between the dSCDs convolved with a single emission line is larger than in the UV and results in a maximum deviation of roughly 0.1 · 10⁴³molec² cm⁻⁵(≈ 3 %) for O₄ and approximately (0.5) · 10¹⁵ molec cm⁻² (≈ 4 %) for NO₂. Largest dSCDs are received for the slit function at 435 nm, which is a double emission line. However, the NO₂ dSCDs evaluated with the slit function at 467 nm are almost as large as the dSCDs evaluated using the double emission line at 435 as a convolution kernel. The reason for this remains unclear. It is recommended to only use single emission lines as a slit function. The dSCD variations due to a different slit function are smaller or of the order of the dSCD error. Thus, the influence of the shape of the slit function on the inferred dSCDs can be neglected in the analysis.

Figure 8.34: Inferred dSCDs of O₄, HCHO and NO₂ for the different slit functions from Figure 8.32 for a period of 20 minutes on 16 November 2011.

Influence of the WinDOAS convolution tool

A minor error has been detected in the convolution tool of the software WinDOAS (Caroline Fayt, IASB/BIRA, Brussels, personal communication June 2014). This error has been fixed in the software QDOAS, which is the successor of WinDOAS. In order to estimate the systematic error of this error, the absorption cross-sections are convolved with WinDOAS, QDOAS and DOASIS, respectively and compared to each other (Figure 8.35). Obviously, the absorption cross-sections convolved with QDOAS and DOASIS agree very well with each other, whereas the absorption cross-sections convolved with WinDOAS are slightly shifted to higher wavelengths by approximately 0.08 nm. In order to assess the total dSCD error that results from the error in the WinDOAS convolution, the dSCDs of an exemplary flight (16 November 2011) are inferred in WinDOAS using the absorption cross-sections convolved with WinDOAS, QDOAS and DOASIS, respectively. Figure 8.36 shows a section of five minutes of that flight. Overall, the dSCDs inferred with absorption cross-sections that are convolved with QDOAS and DOASIS are similar. For the O₄ dSCDs, the average deviation between the dSCDs inferred with the WinDOAS convolution tool and retrieved with the QDOAS /DOASIS convolution tool vary by less than 1 % and can thus be neglected. The HCHO dSCDs inferred with the WinDOAS convolution are approximately 6 % smaller than the dSCDs inferred with the QDOAS convolution tool, whereas the NO₂ dSCDs are approximately 2 to 3 % larger. The dSCD error divided by the dSCD average over the whole flight results in approximately 2 % for O₄ in the UV and visible wavelength range, 13 % for HCHO and 12 % for NO₂. The variations due to the error in the WinDOAS convolution tool are smaller than the averaged dSCD errors and lie within the error bars of the dSCD error. Nevertheless, for future DOAS evaluations, the software WinDOAS should be replaced by the software QDOAS to avoid this systematic error.

Figure 8.35: Absorption cross-sections of O₄, HCHO and NO₂ convolved with WinDOAS, QDOAS and DOASIS using the slit function at 334 nm for the UV (left panels) and at 467 nm for the visible wavelength range (right panels).

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Figure 8.36: O₄ and HCHO dSCDs in the UV (left panels) and O₄ and NO₂ dSCDs in the visible wavelength range (right panels) inferred with the WinDOAS programme and using the absorption cross-sections convolved with WinDOAS, QDOAS and DOASIS programmes from Figure 8.35, respectively.

Influence of spectrometer stray light

Possible stray light of the instrumental set-up can be accounted for in the DOAS spectral fitting procedure by including an additional stray light polynomial. In order to estimate the systematic error that arises due to instrumental stray light, an exemplary flight (sortie 1 on 16 November 2011) is evaluated without using a stray polynomial, including a constant stray light polynomial as well as a polynomial of first and second order. Figure 8.37 shows the results of this analysis for O₄, HCHO and NO₂. As it can be seen from this Figure, the RMS is largest when no offset is included.

In the UV, including a stray light polynomial reduces the RMS by approximately (0.5 - 1) ·10⁻⁴, i.e. by approximately 10 - 15 %, whereas in the visible wavelength range the RMS is only reduced by approximately 0.2 ·10⁻⁴, i.e. by approximately 2 - 6 %, excluding the stray light polynomial of the order of two. For O₄ in the UV as well as in the visible wavelength range, the order of the polynomial is rather not relevant, as a constant polynomial leads to almost the same dSCDs as a polynomial of the order of one or two. For HCHO, the RMS and dSCDs slightly change when using a different order of polynomial with the lowest RMS values for the case using a stray light polynomial of first order. For NO₂ it is not unambiguous, which polynomial order leads to the optimal result. Basically, the order of the polynomial should be as small as possible and as large as necessary. In this study, a polynomial of the order of one is chosen for the spectral analysis.

(a)

(b)

Figure 8.37: Influence of the stray light polynomial (a) on the RMS and (b) on the inferred dSCDs of O₄ and HCHO in the UV (left panels) and of O₄ and NO₂ in the visible wavelength range (right panels), respectively for sortie 1 on 16 November 2011.

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