A convenient concept to encompass the complex light path geometries in MAX-DOAS applications is the airmass-factor (AMF), defined as A s (λ, Ω) = S s (λ, Ω)/V s , in terms of the vertical column density V s and the SCD S s (λ, Ω) for trace gas s. We further define the "AMF eccentricity" 5 which quantifies the relative change in AMF obtained with a polariser in a distinct viewing direction. Figure S1 shows values of the AMF eccentricities over the sky hemisphere; these were simulated for a

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... gh atmosphere through application of the RAPSODI forward model described in Section 5.3. The largest eccentricities occur in the Vis spectral range, for species with comparably large scale height values (like O 4 ) and in directions of strong polarisation (compare skylight polarisation patterns e.g. by Emde et al., 2010). 10