Abstract. Methods of UV/VIS absorption spectroscopy to determine the constituents in the Earth's atmosphere from measurements of scattered light are often based on the Beer-Lambert law, like e.g. Differential Optical Absorption Spectroscopy (DOAS). While the Beer-Lambert law is strictly valid for a single light path only, the relation between the optical depth and the concentration of any absorber can be approximated as linear also for scattered light observations at a single wavelength if the absorption is weak. If the light path distribution is approximated not to vary with wavelength, also linearity between the optical depth and the product of the cross-section and the concentration of an absorber can be assumed. These assumptions are widely made for DOAS applications for scattered light observations.

For medium and strong absorption of scattered light (e.g. along very long light-paths like in limb geometry) the relation between the optical depth and the concentration of an absorber is no longer linear. In addition, for broad wavelength intervals the differences in the travelled light-paths at different wavelengths become important, especially in the UV, where the probability for scattering increases strongly with decreasing wavelength.

However, the DOAS method can be extended to cases with medium to strong absorptions and for broader wavelength intervals by the so called air mass factor modified (or extended) DOAS and the weighting function modified DOAS. These approaches take into account the wavelength dependency of the slant column densities (SCDs), but also require a priori knowledge for the air mass factor or the weighting function from radiative transfer modelling.

We describe an approach that considers the fitting results obtained from DOAS, the SCDs, as a function of wavelength and vertical optical depth and expands this function into a Taylor series of both quantities. The Taylor coefficients are then applied as additional fitting parameters in the DOAS analysis. Thus the variability of the SCD in the fit window is determined by the retrieval itself.

This new approach provides a description of the SCD the exactness of which depends on the order of the Taylor expansion, and is independent from any assumptions or a priori knowledge of the considered absorbers.

In case studies of simulated and measured spectra in the UV range (332–357 nm), we demonstrate the improvement by this approach for the retrieval of vertical profiles of BrO from the SCIAMACHY limb observations. The results for BrO obtained from the simulated spectra are closer to the true profiles, when applying the new method for the SCDs of ozone, than when the standard DOAS approach is used. For the measured spectra the agreement with validation measurements is also improved significantly, especially for cases with strong ozone absorption.

While the focus of this article is on the improvement of the BrO profile retrieval from the SCIAMACHY limb measurements, the novel approach may be applied to a wide range of DOAS retrievals.