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Abstract

Experience of differential atmospheric absorption spectroscopy (DOAS) shows that a spectral shift between measurement spectra and reference spectra is frequently re- quired in order to achieve optimal fit results, while the straightforward calculation of the optical density proves in- ferior. 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 ge- ometries due to an overall slope – or tilt – of the intensity spectrum. The phenomenon has become known as the tilt ef- fect for limb satellite observations, where it is corrected for in a first-order approximation, whereas the remaining com- munity is less aware of its cause and consequences. It is caused by the measurement process, because atmo- spheric absorption and convolution in the spectrometer do not commute. Highly resolved spectral structures in the spec- trum will first be modified by absorption and scattering pro- cesses in the atmosphere before they are recorded with a spectrometer, which convolves them with a specific instru- ment function. In the DOAS spectral evaluation process, however, the polynomial (or other function used for this pur- pose) 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. Assum- ing typical geometries for the observations of scattered sun- light 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 con- firmed in the actual analysis of the ground-based measure- ments of scattered sunlight as well as in numerical radiative transfer simulations. If no spectral shift is allowed by the fit- ting 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.