Abstract. The results of a comparison exercise of radiative transfer models (RTM) of various international research groups for Multiple AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) viewing geometry are presented. In contrast to previous comparison exercises, box-air-mass-factors (box-AMFs) for various atmospheric height layers were modelled, which describe the sensitivity of the measurements as a function of altitude. In addition, radiances were calculated allowing the identification of potential errors, which might be overlooked if only AMFs are compared. Accurate modelling of radiances is also a prerequisite for the correct interpretation of satellite observations, for which the received radiance can strongly vary across the large ground pixels, and might be also important for the retrieval of aerosol properties as a future application of MAX-DOAS. The comparison exercises included different wavelengths and atmospheric scenarios (with and without aerosols). The results were systematically investigated with respect to their dependence on the telescope's elevation angle and the azimuth angle. For both dependencies, a strong and systematic influence of aerosol scattering was found indicating that from MAX-DOAS observations also information on atmospheric aerosols can be retrieved. During the various iterations of the exercises, the results from all models showed a substantial convergence, and the final data sets agreed for most cases within about 5%. Larger deviations were found for cases with low atmospheric optical depth, for which the photon path lengths along the line of sight of the instrument can become very large. The differences occurred between models including full spherical geometry and those using only plane parallel approximation indicating that the correct treatment of the Earth's sphericity becomes indispensable. The modelled box-AMFs constitute an universal data base for the calculation of arbitrary (total) AMFs by simple convolution with a given trace gas concentration profile. Together with the modelled radiances and the specified settings for the various exercises, they can serve as test cases for future RTM developments.

SupplementThe first part of the supplement presents a modified version of Fig. 4. In contrast to the original figure, in Fig. S1 the error bars are shown for the retrievals assuming a box-profile (shape parameter = 1).The second part of the supplement (Figs. S2 -S11) presents the individual graphs of the correlation analyses between the MAX-DOAS results versus independent measurements as well as between MAX-DOAS results of the different telescopes.In the third part of the supplement, the results of the normalised radiance and the normalised O 4 dAMF α (Fig. S12) are shown for the whole campaign.The fourth part of the supplement (Fig. S13) presents results for individual days (individual elevation sequences) are shown. For comparison, AOD from the AERONET station at Ispra, NO 2 and HCHO mixing ratios from the long path DOAS instrument, and HCHO mixing ratios from the Hantzsch instrument are also included.