This section introduces the supporting observations that were used for comparison and validation of the MAX-DOAS retrieved results. It shall be pointed out that a general challenge here was to find compromises between (i) using only accurate and representative data with good spatiotemporal overlap and (ii) keeping as much supporting data as possible to have a large comparison dataset. Considerations and investigations on this issue (e.g. comparisons between the supporting observations, spatiotemporal variability and overlap) which lead to the decisions finally taken are mentioned in the following subsections and described in more detail in the Supplement they refer to.

In the case of OEM retrievals, the gain in information on the atmospheric state can be quantified according to . Essentially speaking, this is done by comparing the knowledge before (represented by the a priori profile and its uncertainties) and after the profile retrieval. The gain in information for each individual vertical profile can be represented by the AVK matrix (denoted by A). Aij describes the sensitivity of the measured concentration in the ith layer to small changes in the real concentration in the jth layer. Each row Ai can thus be plotted over altitude providing the following information: (1) the value in the layer i itself (the diagonal element Aii with a value between 0 and 1) gives the gain in information while 1-Aii represents the amount of a priori knowledge which had to be assimilated to obtain a well-defined concentration value. (2) The values in the other layers (off-diagonal elements of A) indicate the cross sensitivity of layer i to layer j. Typically, the cross sensitivity decreases with the distance to the layer i. The length of this decay (note that i can be converted to the corresponding altitude by multiplication with the retrieval layer thickness Δh) is an indicator for the vertical resolution of the retrieval. The trace of A is equal to the DOFS and hence the total number of independent pieces of information gained from the measurements compared to the a priori knowledge. Figure  visualizes the average AVK matrices (median over participants and mean over time) for all five species studied in this work. Note that the AVKs do not necessarily represent the real or total sensitivity and information content of MAX-DOAS observations as they only consider the gain of information with respect to the a priori knowledge. Hence, for stricter a priori constraints, less gain in information will be indicated by the AVKs.

With the a priori profiles and covariances used within this study, the sensitivity is limited to about the lowest 1.5 km of the atmosphere for all species. More information is obtained on the Vis species, as the differential light path increases with wavelength resulting in higher sensitivity. The obtained DOFS values are generally a bit lower as observed in former studies. This is related to the rather small a priori covariance (50%; see Sect. ), which implies a good knowledge on the atmospheric state prior to the retrieval and finally leads to less gain in information from the measurements. Figures S35, S36, S37, S38 and S39 in Supplement Sect. S8.1 show the average AVKs of the individual participants and reveal that there are significant differences (up to 1 DOFS) between the participants even when using the same algorithm (up to 0.5 DOFS in the case of PriAM). This indicates that the information content is not assessed consistently. BOREAS, for instance, states a very low gain in information especially for aerosol Vis. This is related to an additional Tikhonov term used as a smoother which was also applied during AVK assessment. Furthermore, all BOREAS results were retrieved on another grid and interpolated onto the submission grid, which leads to a decrease in all AVKs and therefore the DOFS. On average, the dependence of the total amount of information on the cloud conditions is small (typically decrease of 0.1 DOFS). Examination of the AVKs of individual profiles (not shown here), indicated that there are two competing effects: (1) the presence of clouds can increase the sensitivity to higher layers due to multiple scattering and thus light path enhancement in the clouds, whereas (2) a decrease in the horizontal viewing distance (e.g. due to fog, rain or high aerosol loads) reduces the information content, since the light paths are shorter and their geometry depends less on the viewing elevation.

Figures to show the retrieved profiles of all participants over the whole semi-blind period. They serve as the basis for a general qualitative comparison. For the trace gases, the altitude ranges (full range is 4 km) were reduced to 0–2.5km for better visibility, considering the MAX-DOAS sensitivity range and the occurrence altitude of the respective species.

Considering valid data only, all algorithms detect similar features in the vertical profiles but smoothed to different amounts and sometimes detected at different altitudes. For clear-sky conditions, the observed ASDevs are 3.5×10-2km-1 for aerosol UV, 4.0×10-2km-1 for aerosol Vis, 1.2×1010molec.cm-3 for HCHO, 2.4×1010molec.cm-3 for NO2 UV and 4.4×1010molec.cm-3 NO2 Vis. When regarding participants using the same algorithm, these values are reduced only by about 50%, indicating that significant discrepancies are caused by differences in the user-defined retrieval settings that were not prescribed. The latter are, for instance, the accuracy criteria for the RTMs, the number of iterations in the inversion, the convergence criteria or the decision at which points of the iteration process the forward model Jacobians are (re)calculated. An example are the discrepancies between UTOR/HEIPRO and IUPHD/HEIPRO. In this case, the number of applied iteration steps in the aerosol inversion was identified as the main reason: UTOR and IUPHD used 5 and 20 iterations here, respectively. The consequences are evident throughout the comparison. Another example is the aerosol UV retrieval of AUTH/bePro, where in contrast to other bePRO users oscillations seem to appear. We suspect this to originate for similar reasons, which could not yet be identified.

In general, larger discrepancies appear for the species measured in the Vis spectral range than in the UV. For NO2 (aerosol), the ASDev increases in the Vis by 50% (90%). In the case of OEM algorithms, a reason might be that there is lower information content in the UV, meaning that the retrievals are drawn closer to the collectively used a priori profile. Further, the larger viewing distance of the Vis retrievals (see Supplement Sect. S5) might be problematic, since the exact treatment of the viewing geometries (like the Earth's curvature or the treatment of the instrument field of view) gains influence. Note that the worsened performance in the Vis was also apparent in the study by with synthetic data. The presence of clouds affects ASDevs very differently for different species: for aerosol UV and Vis, it is degraded by factors of 3 and 4, respectively, which is expected since clouds mostly feature high optical depths > 1 and are detected to very different extent by the individual participants. For HCHO, the ASDev decreases by 38%, which can be well explained by the systematically lower (-36%) HCHO concentrations observed under cloudy conditions. ASDevs for NO2 increase by about 20%, while the observed concentrations remain similar (increase <10%).

Considering valid data only, the parameterized approaches are mostly in good agreement with the other algorithms. For MAPA, unrealistic results are reliably identified and flagged as invalid, whereas in the case of MARK some valid profiles do not look plausible, e.g. for aerosol Vis on 22 September 2016. For both algorithms, a large fraction (30% to 70%) of the profiles are discarded as invalid or look unrealistic if the retrieval conditions are not ideal (see also flagging statistics in Sect. ). Gaps in the MARK data appear where no optimum solution could be found at all. For aerosol, OEM algorithms often see elevated layers in the Vis even in clear-sky scenarios that cannot be observed in the UV or the ceilometer profiles. On cloudy days, MMF (see Table 2 for definition) is capable of detecting clouds as very defined features with a good qualitative agreement with the ceilometer data. In the Vis, even high clouds are detected, e.g. on 17 and 22 September 2016, which indeed coincide with high-altitude clouds above the retrieval altitude range of 4km. In contrast to the PAR approaches, OEM and Realtime algorithms yield realistic profiles also under less favourable measurement conditions (e.g. clouds); in particular, the OEM results are in qualitative agreement with the ceilometer profiles for many cases.

Regarding HCHO, the agreement of the profiles is exceptionally good considering the particularly low information content of the measurements (due to higher uncertainties in the dSCD data). This is probably because observed spatial and temporal concentration gradients are much smaller than for NO2, which might partly be related to enhanced smoothing by the retrieval but is also very likely to be real, since HCHO sources (mainly the photolysis of volatile organic compounds) are less localized. High HCHO concentrations coincide with clear-sky conditions and wind from the continent, which is what would be expected from the current knowledge on the origin and chemistry of atmospheric HCHO. As in the case of aerosol, there are significant discrepancies among the bePRO participants, this time with INTA standing out of the group with slight overestimation.

For NO2, very shallow layers and large vertical and horizontal gradients might complicate the retrievals. Nevertheless, good ASDev is achieved in the UV. Weekdays and weekends (17, 18, 24 and 25 September) can clearly be distinguished. The lowest concentrations are observed on 18 September, where a Sunday coincides with northerly winds from the sea.

The agreement with the supporting observations will be discussed in detail in the following sections.

An intrinsic indicator for a successful profile retrieval is a good agreement between the measured and the modelled dSCDs, the latter being the dSCDs obtained from the RTM model for the finally retrieved aerosol and trace gas profiles. Poor agreement might indicate that only a local minimum of the cost function was found (OEM approaches) that inappropriate retrieval settings were chosen (e.g. too-low number of iterations in the minimization) or that the RTM is inaccurate for other reasons, for instance, because it cannot describe horizontal inhomogeneities. Figures  to show the correlation of measured and modelled dSCDs for all profiles and elevations of each participant. The NASA/Realtime algorithm is not included since it does not use an RTM and therefore does not provide simulated dSCDs.

For clear-sky conditions, good agreement is achieved by most participants. Only IUPB/BOREAS, AUTH/bePRO, BSU/PriAM and KNMI/MARK exceed relative RMSDs of 10% and only for O4 and NO2 Vis dSCDs. MMF achieves the best overall performance, being the only algorithm with relative RMSDs <5% for all species. Regarding HEIPRO, UTOR yields larger RMSD values than IUPHD, which is very likely related to the aforementioned smaller number of iterations applied by UTOR. For the trace gases, small relative RMSD values between 8% and 8% are achieved for all cloud conditions.

Regarding aerosol, PriAM and BOREAS feature slightly too-low slopes in the UV (approx. 0.9) and more pronounced in the Vis (0.8 to 0.85), interestingly almost exclusively caused by data recorded on 23 and 27 September where the atmospheric aerosol load is particularly low. RMSDs increase for cloudy scenarios by 10% (HCHO), 30% (NO2 UV) and 50% (NO2 Vis, O4), most likely because the horizontal inhomogeneity cannot be adequately reproduced by the 1-D models. This is supported by the comparison results from synthetic data by , where horizontal homogeneity is inherently assured and the scatter remains similar for all cloud scenarios. KNMI/MARK has problems reproducing O4 dSCDs (relative RMSD>30%), while for trace gases the performance is comparable to the other algorithms. Regarding Vis species, M3 shows outliers under cloudy conditions (while performing excellently in the UV) and bePRO seems to have convergence problems, which was also evident in the synthetic data . This problem is overcome by flagging of approx. 10% of the data, reducing the RMSD by >50%. PriAM (except MPIC) shows outliers, in particular for NO2 Vis. The O4 scaling factor of 0.8 for MAPA improves O4 dSCD agreement in the UV by about 35% (for clear-sky and valid data) but not in the Vis spectral range (see also Supplement Sect. S2).

This section compares vertically integrated MAX-DOAS aerosol extinction profiles with the AOTs observed by the nearby Sun photometer. In former publications e.g. and also during this comparison study, it was found that MAX-DOAS vertically integrated aerosol profiles systematically underestimate AOTs. It has already been proposed by , and but not proven that this is related to smoothing effects, namely the reduced sensitivity of MAX-DOAS observations to higher altitudes and associated a priori assumptions. Even though the sensitivity to elevated layers was observed to be increased by the presence of optically thick aerosol layers at the corresponding altitudes ( and Sect.  of this study), high-altitude abundances of trace gases and aerosol typically cannot be reliably located and quantified by ground-based MAX-DOAS observations, while aerosol aloft may even introduce systematic errors . Integrated profiles rather provide “partial AOTs” which basically only consider low-altitude aerosol and which are additionally biased by a priori assumptions on the aerosol extinctions at higher altitudes (for OEM algorithms defined by the a priori profile and covariance, for PAR algorithms partly in the form of prescribed profile shapes). Therefore, a comparison between MAX-DOAS and Sun photometer is not necessarily meaningful. However, for OEM approaches, information on the true aerosol extinction profile x (which is available from the ceilometer as described in Sect. ) and the AVKs A can be used to account for this effect: inserting x and A into Eq. () yields a smoothed profile x̃ that can be used to estimate which fraction fτ of the aerosol column is expected to be detected by the OEM retrievals: 10fτ=τs′τs=∑ix̃i∑jxj, with τs′ being the actually detectable “partial AOT”. The left panel of Fig.  shows an example of an extreme case during the campaign from 15 September, 15:00 UT. Shown are a ceilometer backscatter profile (x, black) and the same profile smoothed by the MAX-DOAS median OEM averaging kernels for aerosol UV and aerosol Vis (xUV and xVis, blue and green), respectively. In this particular case, it is expected that a large fraction of the aerosol above 1km altitude will hardly be detected by the MAX-DOAS instruments, resulting in factors fτ=τs′τs of 0.67 and 0.78 for the UV and the Vis AOT, respectively. Note, however, that corresponding information actually seems to be present in the measurements, since part of the high-altitude aerosol appears to be shifted to lower altitudes which are accessible within the constraints of the a priori covariance. Multiplying the AOT observed by the Sun photometer with fτ significantly improves the agreement between MAX-DOAS and Sun photometer observations in particular in the UV. In the following, this is referred to as the PAC. The right panels in Fig.  show information on fτ and the improvement in the UV and Vis results (second and third columns of the figure) over the whole campaign. Average values are fτ=0.81±0.16 in the UV and (0.9±0.13) in the Vis (using the median AVKs of all OEM retrievals). It shall be pointed out that for OEM algorithms the necessity for the PAC can generally be reduced by using improved a priori profiles and covariances (e.g. from climatologies, supporting observations and/or model data). Also the values for fτ will differ, when other a priori profiles and covariances than the ones prescribed for this study (see Sect. ) are used.

Parameterized and analytical approaches typically do not quantify the sensitivity, the effective resolution or the amount of assimilated a priori knowledge. For these algorithms, the correction could not be performed and the total Sun photometer AOT τs had to be used for the comparison in this section. However, the comparison results and further investigations in Supplement Sect. S2 indicate that a scaling of the measured O4 dSCDs prior to the retrieval with SF≈fτ might be used to at least partly account for the PAC for MAPA and probably other PAR and ANA algorithms (see Supplement Sect. S2), even though the motivations for the application of the PAC and the SF are different: the application of the PAC is necessary solely for mathematical reasons related to the concept of OEM and prior constraints applied therein. In contrast, publications that suggest or discuss the application of an SF (e.g. ; , Sect. 2.2; ; ) directly compare forward-modelled O4 dSCDs (using an atmosphere derived from supporting observations to reproduce the real conditions to the best knowledge) to measured O4 dSCDs. For the determination of the SF, they do not make use of optimal estimation or prior constraints similar to those used in our study. Thus, their findings can be in general regarded as independent from any kind of PAC, even though PAC and SF have a similar impact on the MAX-DOAS AOT results with the a priori assumptions applied in this study. Particularly, it shall be pointed out that our findings regarding the PAC have no implications on whether elevated aerosol layers explain the necessity of the SF as proposed by or not.

Figure shows the time series of the MAX-DOAS retrieved AOTs in comparison to their median and the Sun photometer data. For the Sun photometer, both the total AOT τs and the partial AOT τs′ are shown. For the calculation of τs′ in Fig. , the median AVKs of all OEM participants were used for the smoothing according to Eq. (). In the correlation analysis (Fig. ), AVKs of the individual participants and the individual profiles were applied. Keep in mind that the non-OEM approaches (NASA/Realtime, KNMI/MARK and MPIC/MAPA) are correlated against τs and are therefore expected to generally achieve worse agreement. For correlations of OEM algorithms against τs, please refer to Supplement Sect. S8.3. Correlation parameters, RMSD and bias values were derived as described in Sect. .

Under clear-sky conditions, average RMSD values against the MAX-DOAS median are 0.028 in the UV and 0.032 in the Vis. In the presence of clouds, they increase by about 30% and 80%, respectively, which is to mainly due to the periods of particularly large scatter between 16 and 19 September 2016. As already shown in Sect. , different algorithms detect clouds to a very different extent. Especially in the presence of optically thick clouds (AOT > 10), this easily induces discrepancies of several orders of magnitudes. The observed average RMSDs are similar to the specified uncertainties (average is 0.025) that are derived from propagated measurement noise and smoothing effects. Keeping in mind that the retrievals were performed on a common dSCD dataset, this indicates that the choice of the retrieval algorithm and the remaining free settings have a severe impact on the results.

For the comparison to the Sun photometer, it shall be noted that the PAC induces further uncertainties, as it incorporates the extinction profiles derived from the ceilometer and the algorithms' AVKs, both being error prone. Further, the comparison to Sun photometer data under cloudy conditions might not be very meaningful as (1) there are only 13 measurements available in the presence of clouds and (2) it is very likely that these measurements were made by looking through very local cloud holes, such that they will not be representative of the MAX-DOAS retrieved AOTs with a typical horizontal sensitivity range of several kilometres (see Supplement Sect. S5). The following discussion of the Sun photometer comparison therefore refers to clear-sky conditions and valid data only. In general, there is reasonable agreement of the MAX-DOAS retrieved AOT with the Sun photometer, with average observed RMSDs of 0.08 (0.06) for aerosol UV (Vis). Best performance in the UV is observed for IUPHD/HEIPRO and LMU/M3 with RMSDs around 0.05; in the Vis, it is the participants using the bePRO (BIRA and INTA), the HEIPRO (IUPHD and UTOR) and the BOREAS (IUPB) algorithms. For all participants except MPIC-0.8/MAPA, negative biases <-0.03 in the UV remain, even though the PAC has been applied for the OEM algorithms. The average bias in the UV is -0.06, indicating that the systematic underestimation dominates over random deviations here. Note that the slopes and intercepts vary significantly among the participants, however, in an anti-correlated manner, finally resulting in similar bias values.

The average bias in the Vis is only 0.02. Bias magnitudes are much smaller than RMSDs for many participants here, indicating that in these cases Vis AOTs mainly suffer from random discrepancies. BePRO suffers the aforementioned convergence problems during inversion in the Vis (see Sect. ) but the affected results are reliably flagged. KNMI/MARK, NASA/Realtime and MPIC-1.0/MAPA feature the highest RMSDs around 0.1 and strongest biases below -0.1 in the UV. A particular case is KNMI/aerosol Vis with RMSD>0.2, with and without flagging being applied.

As described in Supplement Sect. S2, the PAC and the application of an O4 dSCD scaling factor of SF≈fτ have a very similar impact on the AOT correlation. Consequently, the application of SF=0.8 in the case of MPIC-0.8/MAPA significantly improves the agreement to the Sun photometer total AOT in the UV (fτ≈0.8), whereas in the Vis (fτ≈0.9) it leads to an overcompensation with a bias of about 0.05.

This section assesses the consistency of the VCDs for each of the trace gases HCHO and NO2. Independent observations of VCDs are the direct-sun DOAS observations but also integrated columns of radiosonde and lidar profiles (NO2 only). Time series comparisons of all observations are shown in Figs.  and . For the statistical evaluation in Fig. , from the supporting observations only direct-sun observations were considered, as they provide the most complete dataset.

As for AOTs, smoothing effects potentially affect the comparability of MAX-DOAS and direct-sun observations. In contrast to aerosol, only scarce (NO2) or no (HCHO) information on the true profile is available, and a correction similar to the PAC cannot be performed. However, for NO2, the available radiosonde profiles could be used for an impact estimate. Ignoring one problematic radiosonde profile on 27 September at 07:00 UT (where NO2 concentration was close to the radiosonde detection limit and thus instrumental offsets became particularly apparent), correction factors of 1.06±0.05 in the UV and 1.03±0.03 in the Vis are obtained, indicating that the MAX-DOAS retrieved tropospheric NO2 VCD is affected by smoothing effects to only a few percent. This is expected since NO2 mostly appears close to the ground. Also in Figs.  and , NO2 appears to be confined to the lowermost retrieval layers with concentrations dropping to around zero already at altitudes where MAX-DOAS sensitivity is still significant. Profiles from the NO2 lidar were not used in this investigation as they often suffer from artefacts at higher altitudes. Regarding HCHO, the MAX-DOAS profiling results on some days show large concentrations over the whole altitude range where the information content of the measurements is significant (compare Figs.  and ), indicating that there might be “invisible” HCHO at even higher altitudes. This is supported in Fig. , where MAX-DOAS observations tend to yield smaller VCDs than the direct-sun observations in particular in scenarios with high HCHO abundance.

Under clear-sky conditions, average RMSD values against the MAX-DOAS median are 5×1014molec.cm-2 for HCHO and 7×1014molec.cm-2 for NO2 (both UV and Vis). In contrast to AOTs, these values do not increase significantly (<15%) in the presence of clouds. For HCHO, it is even reduced by 25% for the same reasons as discussed already in Sect. . Bias values are approximately of half the magnitude of RMSDs for all trace gases.

For HCHO, the comparison against the direct-sun DOAS observations yields an average RMSD of 1.4×1015molec.cm-2. Note, however, that the two observations are not fully independent, as for the direct-sun data, the residual HCHO amount in the reference spectrum was adapted from the MAX-DOAS VCD (see Sect. ). Bias values are of the order of 35% of the RMSDs, indicating that the deviations are mostly random.

For NO2 UV (Vis), the comparison to the direct-sun DOAS yields an average RMSD of 3.7×1015molec.cm-2 (3.8×1015molec.cm-2), which is about 5 times the average RMSD of the MAX-DOAS median comparison. Between 12 and 14 September, the direct-sun VCDs but also most radiosonde and lidar observation are systematically lower than the MAX-DOAS VCDs. This is also reflected in the correlation statistics: RMSDs and bias values of different participants appear strongly correlated in Fig.  and bias magnitudes are >70% of the RMSDs for both UV and Vis. The reason could not yet be identified. Interestingly, this contrasts with findings on the surface concentration in the following section, where discrepancies to the LP-DOAS are dominated by random deviations.

In contrast to the AOTs, the RMSDs against the MAX-DOAS median here are smaller than the specified retrieval errors, which are 1.3×1015molec.cm-2 for HCHO, 1.3×1015molec.cm-2 for NO2 UV and 1.2×1015molec.cm-2 for NO2 Vis. On the other hand, NO2 RMSDs against the direct-sun observations are about 3 times larger. For the less abundant HCHO, the signal-to-noise ratio in the median dSCDs is smaller than for other species, such that the specified uncertainties derived from the dSCD noise are larger and more representative of the actual retrieval accuracy.

This section compares the number concentration of NO2 and HCHO observed at the surface. Note that in this paper “surface concentration” refers to the average concentration in the lowest MAX-DOAS retrieval layer extending from 0 to 200 m altitude. Independent observations are the LP-DOAS (NO2 and HCHO) and the surface values of radiosonde and lidar profiles (NO2), as well as integrated values of in situ measurements in the tower (described in Sect. ). Comparisons of all observations are shown in Figs.  and . For the statistical evaluation (Fig. ), only LP-DOAS data were considered since they provide a very accurate, representative and complete dataset (see Sect. ). The impact of profile smoothing during the retrieval on the retrieved surface concentration was estimated for NO2 in Supplement Sect. S9 from available radiosonde and lidar NO2 profiles and was found to be around 5.5×109molec.cm-3 (4×109molec.cm-3) in the UV (Vis). Typical RMSD values in the comparison with the LP-DOAS are about 1 order of magnitude larger, indicating that the impact of smoothing on the NO2 surface concentration is negligible in this study.

The comparisons of surface concentrations are particularly useful, because the largest set of validation data is available here and because in contrast to the comparison of AOT and VCDs, the surface concentration comparison requires an isolation of the surface layer from the layers above and therefore reflects the MAX-DOAS ability to actually resolve vertical profiles at least close to the surface.

Figures and show good qualitative agreement between all observations most of the time, even in the presence of clouds. Apparent exceptions for NO2 are the fog event on 16 September (strong scatter among the participants) and at forenoon on 22 September (MAX-DOAS median shows large deviations compared to the tower measurements probably due to a very local NO2 emission event close to the tower).

Under clear-sky conditions average RMSDs observed for the comparison to the MAX-DOAS median results are 8.8×109molec.cm-3 for HCHO, 1.8×1010molec.cm-3 for NO2 UV and 2.7×1010molec.cm-3 for NO2 Vis. For the comparison to the LP-DOAS, these values increase to 1.8×1010molec.cm-3, 4.7×1010molec.cm-3 and 5.6×1010molec.cm-3, respectively. For the median comparison, bias magnitudes are about 40% of the RMSD values. In contrast to the VCDs, deviations to the supporting observations (LP-DOAS) seem to be random to a large part, as bias magnitudes are about 3 times smaller than RMSDs. Significant biases are only observed for some participants, e.g. UTOR/HEIPRO in the UV.

Clouds have very different impacts on the results: the average RMSD to the median increases by 15% for HCHO, 26% for NO2 UV and 38% for NO2 Vis, whereas the average RMSD to the LP-DOAS is even reduced by 4%, 15% and 17%, respectively. A large fraction of the scatter in the comparison to the LP-DOAS might be related to the spatiotemporal variability of the gas concentrations, in particular in the Vis spectral range, where the MAX-DOAS viewing distance is large. The good agreement of the surface concentrations with the supporting observations during the first days is opposite to the VCD comparison, which at least for NO2 points to a problem with the retrieval results in higher layers or the direct-sun data. For NO2 Vis, the agreement is generally worse than for NO2 UV. Convergence problems of bePRO appear again in the form of outliers (see in particular the RMSD values), which are efficiently removed by flagging. INTA shows strong systematic outliers over whole days (e.g. on 18 September), which are not observed for other bePRO users and are very likely produced by technical problems. Again, as for AOTs and VCDs, the scatter among the participants is similar to or larger than the specified errors even for clear-sky conditions (factors of about 1 for HCHO, 2 for NO2 UV and 3 for NO2 Vis; see Figs.  and ).

As described in Sect. , the results compared so far were retrieved from a common set of median dSCDs. Thus, the results only illustrate the performance of the different retrieval techniques. However, it is also interesting to compare colocated MAX-DOAS measurements which are fully independent to obtain an estimate of the reliability of a typical MAX-DOAS profile measurement undergoing the whole spectra acquisition and data processing chain. Therefore, the study above was once more conducted with each participant using their own measured dSCDs seefor dataset details. Supplement Sect. S10 shows further details by means of figures that are equivalent to those shown before in the course of the median dSCD comparison. A summary is given in Table , which shows the increase in the average RMSD and average bias magnitude for the most important comparisons (as described in the preceding subsections for the median dSCDs) when participants use their own instead of the median dSCDs. Only valid data of participants appearing in both studies were considered, and BIRA/bePRO and KNMI were excluded because in contrast to the median dSCD study BIRA/bePRO and KNMI did not submit flags for the own dSCD study, which heavily impacted the results.

Regarding only the increase in RMSD in the MAX-DOAS median comparison (hence the degradation of consistency among the participants) is qualitatively consistent with what one would expect from the findings by on the CINDI-2 dSCD consistency: for NO2, almost all participating instruments were able to deliver good-quality dSCDs suitable for profile inversion, while for HCHO the quality was much more variable, resulting in the stronger degradation given in Table . identified instrumental characterization (e.g. detector non-linearity and stray light in the spectrometer) and pointing issues as the main sources of discrepancy between the participant's own dSCD datasets. The degradation is smaller for the surface concentrations than for the trace gas VCDs and is very similar for different cloud conditions.

For the comparison to the supporting observations, the increase in the average RMSD is smaller (second and fourth columns of Table ). This means that even though using their own dSCDs induces differences among the participants, the average quality of the dSCDs is basically maintained or at least small compared to the discrepancies induced by the retrieval techniques. Interestingly, the RMSD and bias values for the UV AOT and NO2 VCD even decrease, indicating that the median dSCDs suffer from systematic errors. Under clear-sky conditions, low impact (≤10%) was found for aerosol UV AOTs and NO2 data products. Particularly large impact is observed for HCHO VCDs (66%). Under cloudy conditions, the impact on NO2 products remains small (again <10%), whereas for all other products, the increase in the average RMSD exceeds 20%.

It is also of interest to explicitly estimate which fractions of the total observed discrepancies among MAX-DOAS observations are caused either by the use of different retrieval algorithms or by inconsistencies in the dSCD acquisition. Note that the RMSD values from the median dSCD comparison represent the error arising solely from using different algorithms, while the RMSD values from the own dSCD comparison represent the combined effect of both aspects. For simplicity, we assume that the contributions of both aspects are random and independent so that the effect of using own dSCDs can be isolated by simple RMSD error calculations. For clear-sky conditions, we find that the differences in the measured dSCDs are responsible for approximately 40% (for AOTs), 85% (HCHO VCDs), 70% (HCHO surface concentrations), 50% (NO2 VCDs), 40% (NO2 UV surface concentrations) and 20% (NO2 Vis surface concentrations) of the total variance observed among the participants. The residual variance can be attributed to the choice and setup of the retrieval algorithm.