Is a scaling factor required to obtain closure between measured and 1 modelled atmospheric O 4 absorptions ?-A case study for two days during 2 the MADCAT campaign 3 4

Abstract. In this study the consistency between MAX-DOAS measurements and radiative transfer simulations of the atmospheric O4 absorption is investigated on two mainly clear 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 (


absorptions is found to be 1.010.16). In contrast, on 8 July measurements and simulations 54 significantly disagree: For the middle period of that day the ratio of simulated and measured 55 O 4 absorptions is found to be 0.71 0.12, which differs significantly from unity. Thus for that 56 day a scaling factor is needed to bring measurements and simulations into agreement. One 57 possible reason for the comparison results on 18 June is the rather large aerosol extinction 58 (and its large uncertainty) close to the surface, which has a large effect on the radiative 59 transfer simulations. Besides the inconsistent comparison results for both days, also no 60 explanation for a O 4 scaling factor could be derived in this study. Thus similar, but more 61 extended future studies should be performed, which preferably include more measurement 62 days, more instruments and should be supported by more detailed independent aerosol 63 measurements. Also additional wavelengths should be included. The MAX-DOAS 64 measurements collected during the recent CINDI-2 campaign are probably well suited for that 65 purpose. as the most probable atmospheric aerosol profile (for more details, see e.g. Frieß et al., 2006 While with the application of a SF the consistency between forward model and measurements 99 was substantially improved, both studies could not provide an explanation for the physical 100 mechanism behind such a SF. In the following years several research groups applied a SF in 101 their MAX-DOAS aerosol profile retrievals. However, a similarly large fraction of studies 102 (including direct sun measurements and aircraft measurements, see Spinei et al. (2015)) did 103 not find it necessary to apply a SF to bring measurements and forward model simulations into 104 agreement. An overview on the application of a SF in various MAX-DOAS publications after 105 2010 is provided in Table 1. Up to now, there is no community consensus on whether or not a 106 SF is needed for measured O 4 DSCDs. This is a rather unfortunate situation, because this 107 ambiguity directly affects the aerosol results derived from MAX-DOAS measurements and 108 thus the general confidence in the method. 109 110 So far, most of the studies deduced the need for a SF in a rather indirect way: aerosol 111 extinction profiles derived from MAX-DOAS measurements using different SF are usually 112 compared to independent data sets (mostly AOD from sun photometer observations) and the 113 SF leading to the best agreement is selected. In many cases SF between 0.75 and 0.9 were 114 derived. 115 In this study, we follow a different approach: similar to Ortega  (2) 130 131 The conversion of the measured O 4 SCDs into AMFs is carried out to ensure a simple and 132 direct comparison between measurements and forward model simulations. Here it should be 133 noted that in addition to the AMFs also so-called differential AMFs (dAMFs) will be 134 compared in this study. during which the variation of the aerosol profiles was relatively small (see Table 2). In 145 addition to the aerosol profiles, also other atmospheric properties are averaged during these 146 periods before they are used as input for the radiative transfer simulations. 147 of the extraction results derived from different groups/persons (see Table 3). 158 b) Calculation of O 4 (d)AMFs from radiative transfer simulations: 159 Besides differences between the different radiative transfer codes, the dominating error 160 sources are the uncertainties of the input parameters. They are investigated by sensitivity 161 studies and by the comparison of extracted input data by different groups/persons. Also the 162 effects of operating different radiative transfer models by different groups are investigated. 163 c) Analysis of the O 4 (d)AMFs from MAX-DOAS measurements: 164 Uncertainties of the spectral analysis results are caused by errors and imperfections of the 165 measurements/instruments, by the dependence of the analysis results on the specific fit 166 settings, and the uncertainties of the O 4 cross sections. They are investigated by systematic 167 variation of the DOAS fit settings (for measured and synthetic spectra), and by comparison of 168 analysis results obtained from different groups and/or instruments. 169 The paper is organised as follows: in section 2, information on the selected days during the 170 MADCAT campaign, on the MAX-DOAS measurements, and on the data sets from 171 independent measurements is provided. Section 3 presents initial comparison results for the 172 selected days using standard settings. In section 4 the uncertainties associated with each of the 173 various processing steps of the spectral analysis and the forward model simulations are 174 quantified. Section 5 presents a summary and conclusions. was towards north-west (51° with respect to North). Measurements at this viewing direction 192 were the main focus of this study, but a few comparisons using the 'standard settings' (see 193 section 3) were also carried out for three other azimuth angles (141°, 231°, 321°, see Fig. A2 I 194 in appendix A1). Each elevation sequence contains the following elevation angles: 1, 2, 3, 4, 195 5, 6, 8, 10, 15, 30 and 90°. In this study, in addition to the MPIC instrument, also spectra from 196 3 other MAX-DOAS instruments were analysed. The instrumental details are given in Table  197 Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2018-238 Manuscript under review for journal Atmos In order to constrain the radiative transfer simulations, independent measurements and data 203 sets were used. In particular, information on atmospheric pressure, temperature and relative 204 humidity, as well as aerosol properties is used. In addition to local in situ measurements from 205 air quality monitoring stations and remote sensing measurements by a ceilometer and a sun 206 photometer, also ECMWF reanalysis data were used. An overview on these data sets is given 207 in Several radiative transfer models are used to calculate O 4 (d)AMFs for the selected days. As 213 input, vertical profiles of temperature, pressure, relative humidity and aerosol extinction 214 extracted from the independent data sets (see section 2.2 and 4) were used. The vertical 215 resolution is high in the lowest layers and decreases with increasing altitude (see Table A1 in 216 appendix A1). The upper boundary of the vertical grid is set to 1000 km. The lower boundary 217 of the model grid represents the surface elevation of the instrument (150 m above sea level). 218 For the 'standard run', a surface albedo of 5% is assumed and the aerosol optical properties 219 are described by a Henyey-Greenstein phase function with an asymmetry parameter of 0.68 220 and a single scattering albedo of 0.95. Both values represent typical urban aerosols (see e.g. 221 Dubovik et al., 2002). Ozone absorption was not considered, because it is very small at 360 222 nm. The MADCAT campaign took place around summer solstice. Thus the same dependence 223 of the solar zenith angle (SZA) and relative azimuth angle (RAZI) on time is used for both 224 days (see Table A2 in the appendix A1). The input data used for the radiative transfer 225 simulations are available at the website http://joseba.mpch-mainz.mpg.de/d_doc_zip.htm. In 226 the following sub-sections the different radiative transfer models used in this study are 227 described.  In addition to AMFs and dAMFs, also synthetic spectra were simulated. They are analysed in 274 the same way as the measured spectra, which allows the investigation of two important 275 aspects: 276 a) The derived O 4 dAMFs from the synthetic spectra can be compared to the O 4 dAMFs 277 obtained directly from the radiative simulations using the same settings. In this way the 278 consistency of the spectral analysis results and the radiative transfer simulations is tested. 279 b) Sensitivity tests can be performed varying several fit parameters, e.g. the spectral range or 280 the DOAS polynomial, and their effect on the derived O 4 dAMFs can be assessed. 281 Synthetic spectra are simulated using SCIATRAN taking into account rotational Raman 282 scattering. The basic simulation settings are the same as for the RTM simulations of the O 4 283 (d)AMFs described above. In order to minimise the computational effort, for the profiles of 284 temperature, pressure, relative humidity and aerosol extinction the input data for only two 285 periods (18 June: 11:00 -14:00, 08 July: 7:00 -11:00, see Table 2) are used for the whole. 286 Thus 'perfect' agreement with the measurements can only be expected for the two selected 287 periods. Aerosol optical properties (phase function and single scattering albedo) are taken 288 from AERONET measurements of the two selected days. Although the wavelength 289 dependencies of both quantities (and also for the aerosol extinction) are considered, it should 290 be noted that the associated uncertainties are probably rather large, since the optical properties 291 in the UV had to be extrapolated from measurements in the visible spectral range. Moreover, 292 the phase functions were not available as fully consolidated AERONET level 2.0 data, but 293 only as level 1.5 data. 294 Spectra were simulated at a spectral resolution of 0.01 nm and convolved with a Gaussian slit 295 function of 0.6 nm full width at half maximum (FWHM), which is similar to those of the 296 measurements. For the generation of the spectra the trace gas absorptions of O 3 , NO 2 , HCHO, 297 and O 4 are considered (see Table A3 in appendix A1 indicates that possible uncertainties of the calibration of the elevation angles of the 337 instruments can be neglected. Here it is interesting to note that on 18 June even slightly lower 338 O 4 (d)AMFs are found for the low elevation angles. This is in agreement with the finding of 339 high aerosol extinction in a shallow layer above the surface (see Fig. 1 profiles from ECMWF ERA-Interim re-analysis data (see Table 5). Both data sets are used to 397 derive the O 4 concentration profiles for the three selected periods on both days. The general 398 procedure is that first the temperature profiles are determined. In a second step, the pressure 399 In this altitude range the accuracy of the temperature profile is not critical and thus the 415 ECMWF temperature profile for 00:00 UTC of the respective day is used for simplicity. 416 The temperature profiles for 8 July 2013 extracted in this way are shown in Fig. 4 (left). Close 417 to the surface the temperature variation during the day is about 10 K. 418 In the next step, the pressure profiles are determined from the surface pressure (obtained from 419 the in situ measurements) and the extracted temperature profiles according to the ideal gas 420 law. In principle the effect of atmospheric humidity could also be taken into account, but the 421 effect is very small for surface-near layers and is thus ignored here. The derived pressure 422 profiles for 8 July 2013 are shown in Fig. 4  Next the effect of the aerosol extinction profile is investigated. In this study, aerosol 527 extinction profiles are derived from the combined ceilometer and sun photometer 528 measurements (see Table 5). In short, the ceilometer measurements of the attenuated 529 backscatter are scaled by the simultaneously measured aerosol optical depth (AOD) from the 530 sun photometer to obtain the aerosol extinction profile. Also the self-attenuation of the aerosol 531 is taken into account. The different steps are illustrated in Fig. 8 and described in detail in 532 appendix A5. In the extraction procedure, several assumptions have to be made: First, the 533 ceilometer profiles have to be extrapolated for altitudes below 180 m, for which the 534 ceilometer is not sensitive. Furthermore, they have to be averaged over several hours and are 535 in addition vertically smoothed (above 2 km) to minimise the rather large scatter. Finally, 536 above 5 to 6 km (depending on the ceilometer profiles) the extinction is set to zero because of 537 the further increasing scatter and the usually small extinctions. Another assumption is that the 538 LIDAR ratio is independent of altitude, which is typically not strictly fulfilled (the LIDAR 539 ratio describes the ratio between the extinction and backscatter probabilities of the molecules 540 and aerosol particles). 541 Some of these uncertainties are quantified by sensitivity studies, in particular the effect of the 542 extrapolation below 180 m and the altitude above which the aerosol extinction is set to zero. 543 Other uncertainties, like the effect of the assumption of a constant LIDAR ratio are more 544 difficult to quantify without further information. While a constant LIDAR ratio is probably a 545 good assumption for 8 July, for 18 June the surface measurements indicate that the aerosol 546 properties strongly change with time. Thus the LIDAR ratio might also vary stronger with 547 altitude on that day. The effect of temporal averaging and smoothing is probably negligible 548 for 8 July, because similar height profiles are found for all three periods of that day, but on 18 549 June the effect might be more important. 550 Fig. 9 shows a comparison of the aerosol extinction profiles extracted by the different groups 551 for the three periods on both days. Especially on 8 July systematic differences are found. 552 were extracted for a larger altitude range ( Fig. A7 and Table A5 in the appendix A4). Here it 558 is interesting to note that these differences are not related to the direct effect of the aerosol 559 extinction at high altitude, but to the corresponding (via the scaling with the AOD) decrease 560 of the aerosol extinction close to the surface. Larger deviations (up to 4%) are found for 8 561 July, while the deviations on 18 June are within 3%. 562 In Fig. A8 and The impact of the aerosol phase function is investigated in two ways: First, simulation results 569 are compared for Henyey Greenstein phase functions with different asymmetry parameters. 570 The corresponding results are shown in Fig. A10 and it should be noted that the actual deviations from the true phase function might be even larger. 575 In order to better estimate these uncertainties, also simulations for phase functions derived 576 from the sun photometer measurements based on Mie theory (in the following referred to as 577 Mie phase functions) were performed. A comparison of these Mie phase functions with the 578 Henyey Greenstein phase functions is shown in Fig. 10 settings (see Table 6) derived by MPIC using MCARTIM. 608 In general, larger uncertainties are found for the O 4 dAMFs compared to the O 4 AMFs. This is 609 expected because the uncertainties of the O 4 dAMFs contain the uncertainties of two 610 simulations (at 90° elevation and at low elevation). Another general finding is that the 611 uncertainties on 18 June are larger than on 8 July. This finding is mainly related to the larger 612 uncertainties due to the aerosol phase function, which has an especially strong forward peak 613 on 18 June. Also the error contributions from the O 4 profile extraction, the choice of the 614 radiative transfer model and the extrapolation of the aerosol extinction below 180 m are larger 615 on 18 June than on 8 July. These higher uncertainties are probably mainly related to the high 616 aerosol extinction close to the surface on 18 June (see section 5.1, and appendices A2 and 617 A5). 618 For the total uncertainties two values are given in Table 9: The 'average deviation' is the sum 619 of all systematic deviations of the individual uncertainties (the corresponding mean of the 620 maximum and minimum values). The second quantity (the 'range of uncertainties) is 621 calculated from half the individual uncertainty ranges by assuming that they are independent. 622 Finally, it should be noted that for some error sources (e.g. the effects of the surface albedo or 623 the single scattering albedo) the given numbers probably overestimate the true uncertainties, 624 while for others, e.g. the uncertainties related to the aerosol extinction profiles or the phase 625 functions they possibly underestimate the true uncertainties (although reasonable assumptions 626 were made). The two latter error sources are especially large for 18 June. The differences 627 between both days are discussed in more detail in section 5. Synthetic spectra for both selected days were simulated using the radiative transfer model 645 SCIATRAN (for details see section 2.4 and Table A3 in appendix A1). While spectra for the 646 whole day are simulated (for the viewing geometry see Table A2 in appendix A1) it should be 647 noted that the aerosol properties during the middle periods are used also for the whole day (to 648 minimise the computational efforts cross section. Also one version of synthetic spectra with added random noise is processed. 655 First, the synthetic spectra are analysed using the standard settings (see Table 7). Examples of 656 the O 4 fits for synthetic (and measured) spectra are shown in Fig. 11. 657 In Fig. 12  the spectra without noise (Fig. 12 b) are found but the results now show a large scatter. From 675 these results and also the spectral analyses ( Fig. 11) we conclude that the noise added to the 676 synthetic spectra overestimates that of the real measurements. 677 In Table A13  found for both measured (-12%) and synthetic spectra (-5%) for the spectral range 335 to 374 693 nm. On 8 July the corresponding differences are smaller (-6% and -2% for measured and 694 synthetic spectra, respectively). For the spectral range 345 -374 nm, smaller differences of 695 only up to 1% are found for both days. The reason for the larger deviations on 18 June for the 696 spectral range 335 -374 nm is not clear. One possible reason could be the differences of the 697 Ångström parameters (see Fig. 1) and phase functions (see Fig 10). 698 In Fig. A16 and Table A15 the results for different degrees of the polynomial used in the 699 spectral analysis are shown. For the measured spectra systematically higher O 4 (d)AMFs (up 700 to 6%) than for the standard analysis are found when using lower polynomial degrees. For the 701 synthetic spectra the effect is smaller (<3%). 702 In Fig. A17 and Table A16 the results for different intensity offsets are shown. Again, for the 703 measured spectra systematically higher O 4 (d)AMFs (up to 16%) than for the standard 704 analysis are found when reducing the order of the intensity offset, while for the synthetic 705 spectra the effect is smaller (<3%). 706 In Fig. A18 and Table A17 the results for spectral analyses with only one Ring spectrum are 707 shown. In contrast to the standard analysis, which includes two Ring spectra (one for clear 708 and In Fig. A19 and Table A18 the results for using two NO 2 cross sections (294 and 220 K) 717 compared to the standard analysis (using only a NO 2 cross section for 294 K) are shown. The 718 results are almost the same as for the standard analysis. 719 In Fig. A20 and Table A19 the results for using an additional wavelength-dependent NO 2 720 cross section compared to the standard analysis (using only one NO 2 cross section) are shown. 721 The second NO 2 cross section is calculated by multiplying the original cross section with 722 wavelength (Pukite et al., 2010). Again, only small deviations of the results from the standard 723 analysis (1% for the measured spectra, and 2% for the synthetic spectra are found. 724 In Fig. A21 and Table A20  are almost identical to those from the standard analysis (within 1%). 734 In Fig. A23 and Table A22 the results for including a HCHO cross section (Polyansky et al.,735 2018) compared to the standard analysis (using no HCHO cross section) are shown. 736 Especially for 18 June a large systematic effect is found: the O 4 dAMFs are by 4 % or 6 % 737 smaller than for the standard analysis for measured and synthetic spectra, respectively. On 8 738 July the underestimation is smaller (2% and 3% for measured and synthetic spectra, 739 respectively for 18 June rather large differences (between -6% / +5%) to the MPIC standard analysis are 851 found. Interestingly the largest differences are found in the morning when the aerosol 852 extinction close to the surface was strongest. On 8 July smaller differences (between -6% and 853 -1%) are found. 854 In Fig. 14b and properties and retrievals can be estimated. Interestingly, the observed differences are only 864 slightly larger than those for the analysis of the spectra from the different instruments by 865 MPIC (Fig. 14b) contain the uncertainties of two analyses (at 90° elevation and at low elevation). Also, the 879 uncertainties on 18 June are again larger than on 8 July. This finding was not expected, but is 880 possibly related to the higher trace gas abundances (see Fig. 1 and Table A3 Tables  1060  1061  Table 1 Overview on studies which did not apply a scaling factor (upper part) or did apply a 1062 scaling             The backscatter profiles are converted into extinction profiles by scaling with the AOD from the sun photometer.
The self attenuation of the aerosol is accounted for.
Below 180m, the profiles are extrapolated (constant value, or constant or double slope).
Extinction profiles at 360 nm derived by different groups      Measurements are from 4 different instruments, but analysed by MPIC using the standard 1668 settings (see Table 7). Simulations are performed by three different groups using Mie phase 1669 functions and otherwise the standard settings (see Table 6).    The settings for the simulation of the synthetic spectra are given in Table 6 and Tables A1,  1713 A2, and A3 in appendix 1. Measurements are analysed using the standard settings (see Table  1714 7). For T1 and T4 azimuth direction, no measurements at 1°elevation were possible due to obstacles.
For T1 and T4 azimuth direction, no measurements at 1°elevation were possible due to obstacles. For T1 and T4 azimuth direction, no measurements at 1°elevation were possible due to obstacles.