In September 2016, 36 spectrometers from 24 institutes measured a number of key atmospheric pollutants for a period of 17 d during the Second Cabauw Intercomparison campaign for Nitrogen Dioxide measuring Instruments (CINDI-2) that took place at Cabauw, the Netherlands (51.97^∘ N, 4.93^∘ E). We report on the outcome of the formal semi-blind intercomparison exercise, which was held under the umbrella of the Network for the Detection of Atmospheric Composition Change (NDACC) and the European Space Agency (ESA). The three major goals of CINDI-2 were (1) to characterise and better understand the differences between a large number of multi-axis differential optical absorption spectroscopy (MAX-DOAS) and zenith-sky DOAS instruments and analysis methods, (2) to define a robust methodology for performance assessment of all participating instruments, and (3) to contribute to a harmonisation of the measurement settings and retrieval methods. This, in turn, creates the capability to produce consistent high-quality ground-based data sets, which are an essential requirement to generate reliable long-term measurement time series suitable for trend analysis and satellite data validation. The data products investigated during the semi-blind intercomparison are slant columns of nitrogen dioxide (NO₂), the oxygen collision complex (O₄) and ozone (O₃) measured in the UV and visible wavelength region, formaldehyde (HCHO) in the UV spectral region, and NO₂ in an additional (smaller) wavelength range in the visible region. The campaign design and implementation processes are discussed in detail including the measurement protocol, calibration procedures and slant column retrieval settings. Strong emphasis was put on the careful alignment and synchronisation of the measurement systems, resulting in a unique set of measurements made under highly comparable air mass conditions. The CINDI-2 data sets were investigated using a regression analysis of the slant columns measured by each instrument and for each of the target data products. The slope and intercept of the regression analysis respectively quantify the mean systematic bias and offset of the individual data sets against the selected reference (which is obtained from the median of either all data sets or a subset), and the rms error provides an estimate of the measurement noise or dispersion. These three criteria are examined and for each of the parameters and each of the data products, performance thresholds are set and applied to all the measurements. The approach presented here has been developed based on heritage from previous intercomparison exercises. It introduces a quantitative assessment of the consistency between all the participating instruments for the MAX-DOAS and zenith-sky DOAS techniques.

The second Cabauw Intercomparison of Nitrogen Dioxide measuring Instruments (CINDI-2) took place in Cabauw (the Netherlands) in September 2016 with the aim of assessing the consistency of multi-axis differential optical absorption spectroscopy (MAX-DOAS) measurements of tropospheric species (NO₂, HCHO, O₃, HONO, CHOCHO and O₄). This was achieved through the coordinated operation of 36 spectrometers operated by 24 groups from all over the world, together with a wide range of supporting reference observations (in situ analysers, balloon sondes, lidars, long-path DOAS, direct-sun DOAS, Sun photometer and meteorological instruments). In the presented study, the retrieved CINDI-2 MAX-DOAS trace gas (NO₂, HCHO) and aerosol vertical profiles of 15 participating groups using different inversion algorithms are compared and validated against the colocated supporting observations, with the focus on aerosol optical thicknesses (AOTs), trace gas vertical column densities (VCDs) and trace gas surface concentrations. The algorithms are based on three different techniques: six use the optimal estimation method, two use a parameterized approach and one algorithm relies on simplified radiative transport assumptions and analytical calculations. To assess the agreement among the inversion algorithms independent of inconsistencies in the trace gas slant column density acquisition, participants applied their inversion to a common set of slant columns. Further, important settings like the retrieval grid, profiles of O₃, temperature and pressure as well as aerosol optical properties and a priori assumptions (for optimal estimation algorithms) have been prescribed to reduce possible sources of discrepancies. The profiling results were found to be in good qualitative agreement: most participants obtained the same features in the retrieved vertical trace gas and aerosol distributions; however, these are sometimes at different altitudes and of different magnitudes. Under clear-sky conditions, the root-mean-square differences (RMSDs) among the results of individual participants are in the range of 0.01–0.1 for AOTs, (1.5–15) $\times {\mathrm{10}}^{\mathrm{14}}\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{2}}$ for trace gas (NO₂, HCHO) VCDs and (0.3–$\mathrm{8})\times {\mathrm{10}}^{\mathrm{10}}\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ for trace gas surface concentrations. These values compare to approximate average optical thicknesses of 0.3, trace gas vertical columns of $\mathrm{90}\times {\mathrm{10}}^{\mathrm{14}}\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{2}}$ and trace gas surface concentrations of $\mathrm{11}\times {\mathrm{10}}^{\mathrm{10}}\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ observed over the campaign period. The discrepancies originate from differences in the applied techniques, the exact implementation of the algorithms and the user-defined settings that were not prescribed. For the comparison against supporting observations, the RMSDs increase to a range of 0.02–0.2 against AOTs from the Sun photometer, (11–$\mathrm{55})\times {\mathrm{10}}^{\mathrm{14}}\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{2}}$ against trace gas VCDs from direct-sun DOAS observations and (0.8–$\mathrm{9})\times {\mathrm{10}}^{\mathrm{10}}\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ against surface concentrations from the long-path DOAS instrument. This increase in RMSDs is most likely caused by uncertainties in the supporting data, spatiotemporal mismatch among the observations and simplified assumptions particularly on aerosol optical properties made for the MAX-DOAS retrieval. As a side investigation, the comparison was repeated with the participants retrieving profiles from their own differential slant column densities (dSCDs) acquired during the campaign. In this case, the consistency among the participants degrades by about 30 % for AOTs, by 180 % (40 %) for HCHO (NO₂) VCDs and by 90 % (20 %) for HCHO (NO₂) surface concentrations. In former publications and also during this comparison study, it was found that MAX-DOAS vertically integrated aerosol extinction coefficient profiles systematically underestimate the AOT observed by the Sun photometer. For the first time, it is quantitatively shown that for optimal estimation algorithms this can be largely explained and compensated by considering biases arising from the reduced sensitivity of MAX-DOAS observations to higher altitudes and associated a priori assumptions.

Multi-axis differential optical absorption spectroscopy (MAX-DOAS) is a widely used measurement technique for the detection of a variety of atmospheric trace gases. Using inverse modelling, the observation of trace gas column densities along different lines of sight enables the retrieval of aerosol and trace gas vertical profiles in the atmospheric boundary layer using appropriate retrieval algorithms. In this study, the ability of eight profile retrieval algorithms to reconstruct vertical profiles is assessed on the basis of synthetic measurements. Five of the algorithms are based on the optimal estimation method, two on parametrised approaches, and one using an analytical approach without involving any radiative transfer modelling. The synthetic measurements consist of the median of simulated slant column densities of O₄ at 360 and 477 nm, as well as of HCHO at 343 nm and NO₂ at 477 nm, from seven datasets simulated by five different radiative transfer models. Simulations are performed for a combination of 10 trace gas and 11 aerosol profiles, as well as 11 elevation angles, three solar zenith, and three relative azimuth angles. Overall, the results from the different algorithms show moderate to good performance for the retrieval of vertical profiles, surface concentrations, and total columns. Except for some outliers, the root-mean-square difference between the true and retrieved state ranges between (0.05–0.1) km⁻¹ for aerosol extinction and (2.5–5.0) ×10¹⁰ molec cm⁻³ for HCHO and NO₂ concentrations.

Airborne imaging differential optical absorption spectroscopy (DOAS), ground-based stationary DOAS, and car DOAS measurements were conducted during the S5P-VAL-DE-Ruhr campaign in September 2020. The campaign area is located in the Rhine-Ruhr region of North Rhine-Westphalia, western Germany, which is a pollution hotspot in Europe comprising urban and large industrial sources. The DOAS measurements are used to validate spaceborne NO₂ tropospheric vertical column density (VCD) data products from the Sentinel-5 Precursor (S5P) TROPOspheric Monitoring Instrument (TROPOMI). Seven flights were performed with the airborne imaging DOAS instrument for measurements of atmospheric pollution (AirMAP), providing measurements that were used to create continuous maps of NO₂ in the layer below the aircraft. These flights cover many S5P ground pixels within an area of 30 km × 35 km and were accompanied by ground-based stationary measurements and three mobile car DOAS instruments. Stationary measurements were conducted by two Pandora, two Zenith-DOAS, and two MAX-DOAS instruments. Ground-based stationary and car DOAS measurements are used to evaluate the AirMAP tropospheric NO₂ VCDs and show high Pearson correlation coefficients of 0.88 and 0.89 and slopes of 0.90 ± 0.09 and 0.89 ± 0.02 for the stationary and car DOAS, respectively. Having a spatial resolution of about 100 m × 30 m, the AirMAP tropospheric NO₂ VCD data create a link between the ground-based and the TROPOMI measurements with a nadir resolution of 3.5 km × 5.5 km and are therefore well suited to validate the TROPOMI tropospheric NO₂ VCD. The observations on the 7 flight days show strong NO₂ variability, which is dependent on the three target areas, the day of the week, and the meteorological conditions. The AirMAP campaign data set is compared to the TROPOMI NO₂ operational offline (OFFL) V01.03.02 data product, the reprocessed NO₂ data using the V02.03.01 of the official level-2 processor provided by the Product Algorithm Laboratory (PAL), and several scientific TROPOMI NO₂ data products. The AirMAP and TROPOMI OFFL V01.03.02 data are highly correlated (r=0.87) but show an underestimation of the TROPOMI data with a slope of 0.38 ± 0.02 and a median relative difference of −9 %. With the modifications in the NO₂ retrieval implemented in the PAL V02.03.01 product, the slope and median relative difference increased to 0.83 ± 0.06 and +20 %. However, the modifications resulted in larger scatter and the correlation decreased significantly to r=0.72. The results can be improved by not applying a cloud correction for the TROPOMI data in conditions with high aerosol load and when cloud pressures are retrieved close to the surface. The influence of spatially more highly resolved a priori NO₂ vertical profiles and surface reflectivity are investigated using scientific TROPOMI tropospheric NO₂ VCD data products. The comparison of the AirMAP campaign data set to the scientific data products shows that the choice of surface reflectivity database has a minor impact on the tropospheric NO₂ VCD retrieval in the campaign region and season. In comparison, the replacement of the a priori NO₂ profile in combination with the improvements in the retrieval of the PAL V02.03.01 product regarding cloud heights can further increase the tropospheric NO₂ VCDs. This study demonstrates that the underestimation of the TROPOMI tropospheric NO₂ VCD product with respect to the validation data set has been and can be further significantly improved.

We present a new MAX-DOAS profiling algorithm for aerosols and trace gases, BOREAS, which utilizes an iterative solution method including Tikhonov regularization and the optimal estimation technique. The aerosol profile retrieval is based on a novel approach in which the absorption depth of O₄ is directly used in order to retrieve extinction coefficient profiles instead of the commonly used perturbation theory method. The retrieval of trace gases is done with the frequently used optimal estimation method but significant improvements are presented on how to deal with wrongly weighted a priori constraints and for scenarios in which the a priori profile is inaccurate. Performance tests are separated into two parts. First, we address the general sensitivity of the retrieval to the example of synthetic data calculated with the radiative transfer model SCIATRAN. In the second part of the study, we demonstrate BOREAS profiling accuracy by validating the results with the help of ancillary measurements carried out during the CINDI-2 campaign in Cabauw, the Netherlands, in 2016. The synthetic sensitivity tests indicate that the regularization between measurement and a priori constraints is insufficient when knowledge of the true state of the atmosphere is poor. We demonstrate a priori pre-scaling and extensive regularization tests as a tool for the optimization of retrieved profiles. The comparison of retrieval results with in situ, ceilometer, NO₂ lidar, sonde and long-path DOAS measurements during the CINDI-2 campaign always shows high correlations with coefficients greater than 0.75. The largest differences can be found in the morning hours, when the planetary boundary layer is not yet fully developed and the concentration of trace gases and aerosol, as a result of a low night-time boundary layer having formed, is focused in a shallow, near-surface layer.

In this study the consistency between MAX-DOAS measurements and radiative transfer simulations of the atmospheric O₄ absorption is investigated on 2 mainly cloud-free days during the MAD-CAT campaign in Mainz, Germany, in summer 2013. In recent years several studies indicated that measurements and radiative transfer simulations of the atmospheric O₄ absorption can only be brought into agreement if a so-called scaling factor (<1) is applied to the measured O₄ absorption. However, many studies, including those based on direct sunlight measurements, came to the opposite conclusion, that there is no need for a scaling factor. Up to now, there is no broad consensus for an explanation of the observed discrepancies between measurements and simulations. Previous studies inferred the need for a scaling factor from the comparison of the aerosol optical depths derived from MAX-DOAS O₄ measurements with that derived from coincident sun photometer measurements. In this study a different approach is chosen: the measured O₄ absorption at 360 nm is directly compared to the O₄ absorption obtained from radiative transfer simulations. The atmospheric conditions used as input for the radiative transfer simulations were taken from independent data sets, in particular from sun photometer and ceilometer measurements at the measurement site. This study has three main goals: first all relevant error sources of the spectral analysis, the radiative transfer simulations and the extraction of the input parameters used for the radiative transfer simulations are quantified. One important result obtained from the analysis of synthetic spectra is that the O₄ absorptions derived from the spectral analysis agree within 1 % with the corresponding radiative transfer simulations at 360 nm. Based on the results from sensitivity studies, recommendations for optimised settings for the spectral analysis and radiative transfer simulations are given. Second, the measured and simulated results are compared for 2 selected cloud-free days with similar aerosol optical depths but very different aerosol properties. On 18 June, measurements and simulations agree within their (rather large) uncertainties (the ratio of simulated and measured O₄ absorptions is found to be 1.01±0.16). In contrast, on 8 July measurements and simulations significantly disagree: for the middle period of that day the ratio of simulated and measured O₄ absorptions is found to be 0.82±0.10, which differs significantly from unity. Thus, for that day a scaling factor is needed to bring measurements and simulations into agreement. Third, recommendations for further intercomparison exercises are derived. One important recommendation for future studies is that aerosol profile data should be measured at the same wavelengths as the MAX-DOAS measurements. Also, the altitude range without profile information close to the ground should be minimised and detailed information on the aerosol optical and/or microphysical properties should be collected and used. The results for both days are inconsistent, and no explanation for a O₄ scaling factor could be derived in this study. Thus, similar but more extended future studies should be performed, including more measurement days and more instruments. Also, additional wavelengths should be included.