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We present the inter-comparison of delta slant column densities (SCDs) and vertical profiles of nitrous acid (HONO) derived from measurements of different multi-axis differential optical absorption spectroscopy (MAX-DOAS) instruments and using different inversion algorithms during the Second Cabauw Inter-comparison campaign for Nitrogen Dioxide measuring Instruments (CINDI-2) in September 2016 at Cabauw, the Netherlands (51.97∘ N, 4.93∘ E). The HONO vertical profiles, vertical column densities (VCDs), and near-surface volume mixing ratios are compared between different MAX-DOAS instruments and profile inversion algorithms for the first time. Systematic and random discrepancies of the HONO results are derived from the comparisons of all data sets against their median values. Systematic discrepancies of HONO delta SCDs are observed in the range of ±0.3×1015 molec. cm−2, which is half of the typical random discrepancy of 0.6×1015 molec. cm−2. For a typical high HONO delta SCD of 2×1015 molec. cm−2, the relative systematic and random discrepancies are about 15 % and 30 %, respectively. The inter-comparison of HONO profiles shows that both systematic and random discrepancies of HONO VCDs and near-surface volume mixing ratios (VMRs) are mostly in the range of ∼±0.5×1014 molec. cm−2 and ∼±0.1 ppb (typically ∼20 %). Further we find that the discrepancies of the retrieved HONO profiles are dominated by discrepancies of the HONO delta SCDs. The profile retrievals only contribute to the discrepancies of the HONO profiles by ∼5 %. However, some data sets with substantially larger discrepancies than the typical values indicate that inappropriate implementations of profile inversion algorithms and configurations of radiative transfer models in the profile retrievals can also be an important uncertainty source. In addition, estimations of measurement uncertainties of HONO dSCDs, which can significantly impact profile retrievals using the optimal estimation method, need to consider not only DOAS fit errors, but also atmospheric variability, especially for an instrument with a DOAS fit error lower than ∼3×1014 molec. cm−2. The MAX-DOAS results during the CINDI-2 campaign indicate that the peak HONO levels (e.g. near-surface VMRs of ∼0.4 ppb) often appeared in the early morning and below 0.2 km. The near-surface VMRs retrieved from the MAX-DOAS observations are compared with those measured using a co-located long-path DOAS instrument. The systematic differences are smaller than 0.15 and 0.07 ppb during early morning and around noon, respectively. Since true HONO values at high altitudes are not known in the absence of real measurements, in order to evaluate the abilities of profile inversion algorithms to respond to different HONO profile shapes, we performed sensitivity studies using synthetic HONO delta SCDs simulated by a radiative transfer model with assumed HONO profiles. The tests indicate that the profile inversion algorithms based on the optimal estimation method with proper configurations can reproduce the different HONO profile shapes well. Therefore we conclude that the features of HONO accumulated near the surface derived from MAX-DOAS measurements are expected to represent the ambient HONO profiles well.
