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.

The atom–bond pairwise additive approach, recently introduced by us to describe the potential energy surface for atom–molecule cases, is extended here for the first time to molecule–molecule systems. The idea is to decompose the van der Waals interaction energy into bond–bond pair contributions. This must be considered an improvement with respect to the familiar atom–atom pairwise additive representation since, still using a simple formulation, it indirectly accounts for three body effects. Such an approach also allows to include, in a straightforward way, the effect of the bond length on the intermolecular interaction energy. Cases of study are the weakly bound complexes involving the H₂ and N₂ molecules, namely N₂–H₂ and N₂–N₂, here described as a single bond–bond pair. For both systems ab initio calculations and experimental molecular beam scattering data, as well as second virial coefficients, have been employed to test the accuracy of the chosen representation of the interaction and to improve the obtained potential energy surfaces. The results of this work are important also for the generalization to the cases involving molecular ions and polyatomic molecules.

Nitrogen oxides (${\mathrm{NO}}_x\equiv \mathrm{NO}+{\mathrm{NO}}_{\mathrm{2}}$ ) in the NO_x-limited upper troposphere (UT) are long-lived and so have a large influence on the oxidizing capacity of the troposphere and formation of the greenhouse gas ozone. Models misrepresent NO_x in the UT, and observations to address deficiencies in models are sparse. Here we obtain a year of near-global seasonal mean mixing ratios of NO₂ in the UT (450–180 hPa) at $\mathrm{1}{}^{\circ }\times \mathrm{1}{}^{\circ }$ by applying cloud-slicing to partial columns of NO₂ from TROPOMI. This follows refinement of the cloud-slicing algorithm with synthetic partial columns from the GEOS-Chem chemical transport model. TROPOMI, prior to cloud-slicing, is corrected for a 13 % underestimate in stratospheric NO₂ variance and a 50 % overestimate in free-tropospheric NO₂ determined by comparison to Pandora total columns at high-altitude free-tropospheric sites at Mauna Loa, Izaña, and Altzomoni and MAX-DOAS and Pandora tropospheric columns at Izaña. Two cloud-sliced seasonal mean UT NO₂ products for June 2019 to May 2020 are retrieved from corrected TROPOMI total columns using distinct TROPOMI cloud products that assume clouds are reflective boundaries (FRESCO-S) or water droplet layers (ROCINN-CAL). TROPOMI UT NO₂ typically ranges from 20–30 pptv over remote oceans to >80 pptv over locations with intense seasonal lightning. Spatial coverage is mostly in the tropics and subtropics with FRESCO-S and extends to the midlatitudes and polar regions with ROCINN-CAL, due to its greater abundance of optically thick clouds and wider cloud-top altitude range. TROPOMI UT NO₂ seasonal means are spatially consistent (R=0.6–0.8) with an existing coarser spatial resolution (5^∘ latitude × 8^∘ longitude) UT NO₂ product from the Ozone Monitoring Instrument (OMI). UT NO₂ from TROPOMI is 12–26 pptv more than that from OMI due to increase in NO₂ with altitude from the OMI pressure ceiling (280 hPa) to that for TROPOMI (180 hPa), but possibly also due to altitude differences in TROPOMI and OMI cloud products and NO₂ retrieval algorithms. The TROPOMI UT NO₂ product offers potential to evaluate and improve representation of UT NO_x in models and supplement aircraft observations that are sporadic and susceptible to large biases in the UT.

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.