Abstract
Abstract. Experience of differential atmospheric absorption spectroscopy (DOAS) shows that a spectral shift between measurement spectra and reference spectra is frequently required in order to achieve optimal fit results, while the straightforward calculation of the optical density proves inferior. The shift is often attributed to temporal instabilities of the instrument but implicitly solved the problem of the tilt effect discussed/explained in this paper. Spectral positions of Fraunhofer and molecular absorption lines are systematically shifted for different measurement geometries due to an overall slope – or tilt – of the intensity spectrum. The phenomenon has become known as the tilt effect for limb satellite observations, where it is corrected for in a first-order approximation, whereas the remaining community is less aware of its cause and consequences. It is caused by the measurement process, because atmospheric absorption and convolution in the spectrometer do not commute. Highly resolved spectral structures in the spectrum will first be modified by absorption and scattering processes in the atmosphere before they are recorded with a spectrometer, which convolves them with a specific instrument function. In the DOAS spectral evaluation process, however, the polynomial (or other function used for this purpose) accounting for broadband absorption is applied after the convolution is performed. In this paper, we derive that changing the order of the two modifications of the spectra leads to different results. Assuming typical geometries for the observations of scattered sunlight and a spectral resolution of 0.6 nm, this effect can be interpreted as a spectral shift of up to 1.5 pm, which is confirmed in the actual analysis of the ground-based measurements of scattered sunlight as well as in numerical radiative transfer simulations. If no spectral shift is allowed by the fitting routine, residual structures of up to 2.5 × 10−3 peak-to-peak are observed. Thus, this effect needs to be considered for DOAS applications aiming at an rms of the residual of 10−3 and below.
Highlights
For a measured structured spectrum s(λ), the tilt effect emerges, because structures do not cancel out completely in the ratio of a measured spectrum t (λ) relative to another spectrum with a different colour, which denotes the broadband spectral dependence
Based on a theoretical analysis as well as on measured and simulated scattered sunlight spectra, we have shown that the tilt effect can cause artificial shifts and enhanced residuals, which are introduced by the fact that any modification of the broadband spectral variation of a spectrum does not commute with the convolution with the instrument slit function
In the context of limb satellite observations, this effect was mathematically described by Rozanov et al (2011)
Summary
For a measured structured spectrum s(λ) (e.g. scattered sunlight), the tilt effect emerges, because structures do not cancel out completely in the ratio of a measured spectrum t (λ) relative to another spectrum with a different colour, which denotes the broadband spectral dependence. Significant spectral shifts are still observed and are related to the telescope elevation angle of the MAX-DOAS observation These can be explained in such cases by the tilt effect as shown in Sect. If a measured spectrum is evaluated relative to a so-called Kurucz Sun spectrum (as e.g. in Burton and Sawyer, 2016; Lübcke et al, 2016), the instrumentally induced tilt change can lead to an apparent relative spectral shift Another interesting aspect is that correction of the measured shifts including the tilt effect will allow the spectral stability of passive DOAS instruments to be estimated more precisely as shown in Sect. We provide examples and estimate its impact on the spectral retrieval
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