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<p><span id="page2"/>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 (NO<span class="inline-formula">₂</span>, HCHO, O<span class="inline-formula">₃</span>, HONO, CHOCHO and O<span class="inline-formula">₄</span>). 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).</p> <p>In the presented study, the retrieved CINDI-2 MAX-DOAS trace gas (NO<span class="inline-formula">₂</span>, 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 O<span class="inline-formula">₃</span>, 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.</p> <p>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) <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M6" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>×</mo><msup><mn mathvariant="normal">10</mn><mn mathvariant="normal">14</mn></msup><mspace width="0.125em" linebreak="nobreak"/><mrow class="unit"><mi mathvariant="normal">molec</mi><mo>.</mo><mspace linebreak="nobreak" width="0.125em"/><msup><mi mathvariant="normal">cm</mi><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup></mrow></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="91pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="aeb8dd3db82d1642ebc9ff80080bd950"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1-2021-ie00001.svg" width="91pt" height="14pt" src="amt-14-1-2021-ie00001.png"/></svg:svg></span></span> for trace gas (NO<span class="inline-formula">₂</span>, HCHO) VCDs and (0.3–<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M8" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">8</mn><mo>)</mo><mo>×</mo><msup><mn mathvariant="normal">10</mn><mn mathvariant="normal">10</mn></msup><mspace linebreak="nobreak" width="0.125em"/><mrow class="unit"><mi mathvariant="normal">molec</mi><mo>.</mo><mspace width="0.125em" linebreak="nobreak"/><msup><mi mathvariant="normal">cm</mi><mrow><mo>-</mo><mn mathvariant="normal">3</mn></mrow></msup></mrow></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="104pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="4b532d36724729684a22637d116eb041"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1-2021-ie00002.svg" width="104pt" height="15pt" src="amt-14-1-2021-ie00002.png"/></svg:svg></span></span> for trace gas surface concentrations. These values compare to approximate average optical thicknesses of <span class="inline-formula">0.3</span>, trace gas vertical columns of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M10" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">90</mn><mo>×</mo><msup><mn mathvariant="normal">10</mn><mn mathvariant="normal">14</mn></msup><mspace width="0.125em" linebreak="nobreak"/><mrow class="unit"><mi mathvariant="normal">molec</mi><mo>.</mo><mspace linebreak="nobreak" width="0.125em"/><msup><mi mathvariant="normal">cm</mi><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup></mrow></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="107pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="c24ff433d3afc4a104118b058d990855"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1-2021-ie00003.svg" width="107pt" height="14pt" src="amt-14-1-2021-ie00003.png"/></svg:svg></span></span> and trace gas surface concentrations of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M11" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">11</mn><mo>×</mo><msup><mn mathvariant="normal">10</mn><mn mathvariant="normal">10</mn></msup><mspace width="0.125em" linebreak="nobreak"/><mrow class="unit"><mi mathvariant="normal">molec</mi><mo>.</mo><mspace width="0.125em" linebreak="nobreak"/><msup><mi mathvariant="normal">cm</mi><mrow><mo>-</mo><mn mathvariant="normal">3</mn></mrow></msup></mrow></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="107pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="b0480f3a1b416c859e24bb5513e080c5"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1-2021-ie00004.svg" width="107pt" height="14pt" src="amt-14-1-2021-ie00004.png"/></svg:svg></span></span> 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.</p> <p>For the comparison against supporting observations, the RMSDs increase to a range of 0.02–0.2 against AOTs from the Sun photometer, (11–<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M12" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">55</mn><mo>)</mo><mo>×</mo><msup><mn mathvariant="normal">10</mn><mn mathvariant="normal">14</mn></msup><mspace linebreak="nobreak" width="0.125em"/><mrow class="unit"><mi mathvariant="normal">molec</mi><mo>.</mo><mspace linebreak="nobreak" width="0.125em"/><msup><mi mathvariant="normal">cm</mi><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup></mrow></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="110pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="f33ac9c4ea0e5b4a1ca833515e189ce6"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1-2021-ie00005.svg" width="110pt" height="15pt" src="amt-14-1-2021-ie00005.png"/></svg:svg></span></span> against trace gas VCDs from direct-sun DOAS observations and (0.8–<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M13" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">9</mn><mo>)</mo><mo>×</mo><msup><mn mathvariant="normal">10</mn><mn mathvariant="normal">10</mn></msup><mspace linebreak="nobreak" width="0.125em"/><mrow class="unit"><mi mathvariant="normal">molec</mi><mo>.</mo><mspace linebreak="nobreak" width="0.125em"/><msup><mi mathvariant="normal">cm</mi><mrow><mo>-</mo><mn mathvariant="normal">3</mn></mrow></msup></mrow></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="104pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="cfe20c3ab67b23b083178136948919bb"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-14-1-2021-ie00006.svg" width="104pt" height="15pt" src="amt-14-1-2021-ie00006.png"/></svg:svg></span></span> 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.</p> <p>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 <span class="inline-formula">30 <i>%</i></span> for AOTs, by <span class="inline-formula">180 <i>%</i></span> (<span class="inline-formula">40 <i>%</i></span>) for HCHO (NO<span class="inline-formula">₂</span>) VCDs and by <span class="inline-formula">90 <i>%</i></span> (<span class="inline-formula">20 <i>%</i></span>) for HCHO (NO<span class="inline-formula">₂</span>) surface concentrations.</p> <p>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.</p>