Shipborne MAX-DOAS measurements for validation of TROPOMI NO2 products

Tropospheric NO2 and stratospheric NO2 vertical column densities are important TROPOMI data products. In order to validate the TROPOMI NO2 products, KNMI MAX-DOAS instruments have measured NO2 on ship cruises over the Atlantic and the Pacific oceans. The MAX-DOAS instruments have participated in five cruises on-board RV Sonne (in 2017 and 2019) and RV Maria S. Merian (in 2018). The MAX-DOAS measurements were acquired in 7 months and spanned about 300◦ in longitude and 90◦ in latitude. During the cruises there were also aerosol measurements from Microtops sun-photometers. 5 The MAX-DOAS measured stratospheric NO2 columns between 1.5× 10 and 3.5× 10 molec cm−2, and tropospheric NO2 up to 0.6× 10 molec cm−2. The MAX-DOAS stratospheric NO2 vertical column densities have been compared with TROPOMI stratospheric NO2 vertical column densities and the stratospheric NO2 vertical column densities simulated by TM5-MP model. Good correlation is found between the MAX-DOAS and TROPOMI and TM5 stratospheric NO2 vertical column densities, with a correlation coefficient of 0.93 or larger. The TROPOMI and TM5 stratospheric NO2 vertical column 10 densities are about 0.4× 10 molec cm−2 (19%) higher than the MAX-DOAS measurements. The TROPOMI tropospheric NO2 has also good agreement with the MAX-DOAS measurements. The tropospheric NO2 vertical column density is as low as 0.5× 10 molec cm−2 over remote oceans.

days. Because the ship sails over remote oceans, we mainly measured the background tropospheric NO 2 and the stratospheric 60 NO 2 .
In this paper we show the results of the MAX-DOAS measurements during the five cruises and compare the MAX-DOAS measurements with the TROPOMI measurements and TM5-MP model simulations. This paper has the following structure: Section 2 describes the data sets used in the paper, Section 3 describes the data analysis method, the results and some discussions are shown in Section 4, and Section 5 presents the conclusions. This section describes ship-based data sets used in this paper, i.e.: the scientific data sets of the MAX-DOAS and Microtops, as well as data measured by the ship's instruments (GPS system and automatic weather station).

Ship cruises and weather data 70
The RV Sonne and RV Maria S. Merian provide extensive position and ship state data as well as weather station data at high time resolution during the cruises. The data sets include time, latitude, longitude, and course from the ship's GPS, and heading, pitch and roll of the ship from its compass and inertial systems. The weather data consists of absolute and relative wind speed, absolute and relative wind direction, air temperature, pressure, relative humidity, water temperature, short wave and long wave radiation. The short wave and long wave radiation are only measured outside of the exclusive economic zones (EEZ) of 75 the countries that the ship sailed through. The time, latitude and longitude are important to obtain an accurate ship position and calculate the local solar zenith angle. The heading is used to calculate the viewing azimuth angle of the MAX-DOAS instruments. We downloaded the ship data at 1 minute time resolution.
The ships were quite stable measurement platforms, with pitch values mainly within ±1 • and roll values within ±2 • during the cruises. For most of the cruises, the relative wind direction was mostly from the front of the ship. However, in cases where 80 the relative wind direction was from the stern (back) of the ship, there was a risk that the exhaust gases of the ship's smoke stack came into the field of view of the MAX-DOAS, which could contaminate the measurement. The ship speed was usually 22 km h −1 during the transit cruises. Cruises with a oceanographic purpose had more stationary time. An example is Sonne cruise SO268/1 in March 2019, which was mainly stationary at two locations in the Pacific Ocean. The air temperature in the tropical regions ranged mainly between 25 and 30 • C. There were a few cloud-free days, but most days were partly cloudy. 85 There were also several days with rain during the cruises.

MAX-DOAS data
Two similar compact Airyx MAX-DOAS instruments have been used in the cruises. One MAX-DOAS instrument was used in the cruise on-board RV Sonne from December 2017 to January 2018. Another MAX-DOAS instrument was used in four cruises, the RV Maria S. Merian (MSM for short hereafter) cruise in December 2018 and three Sonne cruises in 2019. The 90 compact MAX-DOAS instrument contains of an Avantes spectrometer, a scanning mirror, a computer, a web camera, and a GPS. Similar instruments have been used in the Cabauw Intercomparison of Nitrogen Dioxide Measuring Instruments 2 (CINDI2) campaign (Kreher et al., 2019).  When the solar zenith angle was between 84 • and 97 • , the MAX-DOAS performed zenith measurements (90 • elevation angle) only. When the SZA was greater than 100 • , MAX-DOAS performed dark current and offset measurements. The dark current and offset measurements are used to check the stability of the instruments.
The temperature of the spectrometer was stabilized at 20 • C during the trips. The telescope has a heating unit to prevent ice 110 but the temperature of the telescope is not stabilized. During the cruises, MAX-DOAS performed measurements automatically every day, except for the days sailing inside the EEZ. Sometimes MAX-DOAS measured the emissions from the ship itself but these data were not used in this paper.

Aerosol data
Aerosol data were measured using a hand-held Microtops sun-photometer (Smirnov et al., 2009). The measurements were 115 performed manually by pointing the sun-photometer to the sun when there were no clouds in the viewing direction of the sun, roughly every 20 minutes. The Microtops measures aerosol optical thickness (AOT) at five wavelengths and total water vapour column. The Angstrom coefficients are calculated from the AOTs. The data derived from the Microtops directly are called level 1 data which are sent to NASA Maritime Aerosol Network (MAN) for cloud screening and quality control. This process generates Microtops level 1.5 and level 2 data, which we downloaded from the NASA MAN website after the cruises.

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These Microtops data include daily time series and daily mean for AOTs, Angstrom coefficients, and total water vapour column density.
The daily aerosol optical thickness time series data were used in the MAX-DOAS data analysis. For each day, the AOT time series were interpolated at the MAX-DOAS measurement time. On the days without aerosol data, an AOT of 0.05 was used in the data analysis. The Microtops daily mean AOT at 500 nm is shown in Fig. 1 AOT was about 1.5; the AOT was ≥ 1 for three days when the visibility was a few hundred meters and the ship was covered by dust. During the other cruises the AOT values were low, about 0.1 or less at 500 nm, mainly due to sea salt aerosols. The lowest AOT value was about 0.03 at 500 nm during one of the cruises.

TROPOMI data
The TROPOMI NO 2 product was developed at KNMI and is generated within the TROPOMI ground segment (PDGS) operational at the German Aerospace Centre (DLR) (van Geffen et al., 2019). The TROPOMI NO 2 product provides tropospheric, stratospheric, and total vertical column densities (VCDs) and their precision, as well as detailed results for example NO 2 slant column densities and precision, airmass factors.

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The KNMI TROPOMI NO 2 retrieval algorithm is based on a retrieval/data-assimilation system, following the approach introduced for the OMI NO 2 retrievals (the DOMINO approach) (Boersma et al., 2007(Boersma et al., , 2011 and also applied for the OMI retrievals within the QA4ECV project . The total NO 2 slant column densities are derived using the Differential Optical Absorption Spectroscopy (DOAS) method (Platt and Stutz, 2008). Then the total slant column densities are assimilated in the TM5-MP model to determine the stratospheric NO 2 slant column densities. The tropospheric NO 2 slant 140 column density is the total slant column density minus the stratospheric slant column density, after which these slant column densities are converted to the tropospheric and stratospheric NO 2 VCDs using appropriate air mass factors (AMFs).
The TROPOMI overpass is at about 13:30 local time. On any given day the TROPOMI measurement closest in space and time to one of the MAX-DOAS measurements was selected as the overpass pixel. The mean and standard deviation of the 3 × 3 and 5 × 5 pixels around the overpass pixel were also determined. TROPOMI data was not available for the cruise from 145 December 2017 to January 2018 when the instrument was still in its in-orbit test phase. Only data with Quality Assurance (QA) value of > 0.75 (i.e. cloud radiance fraction < 0.5) were selected.

TM5-MP model data
The baseline method in the TROPOMI NO 2 algorithm to separate stratospheric and tropospheric contributions to the NO 2 total slant column densities is by data assimilation of slant column densities in the TM5-MP chemistry transport model (Huijnen 150 et al., 2010;Williams et al., 2017). The TM5-MP NO 2 profiles are simulated globally at 1 • × 1 • (latitude x longitude) grids at 35 levels from surface to about 0.01 hPa. The time interval of the output is 30 minutes. The TM5-MP NO 2 profiles are kept in archive at KNMI. We selected the NO 2 profiles along the ship tracks every day. The number of grid cells from the TM5-MP model collocated with the ship in space and time varied from 1 to 6 per day, depending on the speed of the ship and its activities. The total, stratospheric, and tropospheric NO 2 vertical column densities were integrated using the TM5-MP 155 NO 2 profiles. The tropopause level provided in the TM5-MP data was used to separate the stratospheric and tropospheric NO 2 column densities. The collocated TM5-MP data are available for four cruises. There are no TROPOMI NO 2 data for the first cruise, therefore also no TM5-MP data.
3 Data analysis for MAX-DOAS 3.1 Fitting of NO 2 slant column densities 160 The NO 2 slant column densities were retrieved with the DOAS technique (Platt and Stutz, 2008) using software developed at KNMI. The MAX-DOAS spectra were corrected for the dark current and offset measured on the same day. For some days without the dark current and offset spectra measurements, the dark current and offset spectra from nearby days were used.
Wavelength calibration was performed using the measurement at the 15 • elevation angle in every measurement series. The full width half maximum (FWHM) of the instrument spectral response function was fitted during the wavelength calibration. The

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FWHM is about 0.6 nm for the MAX-DOAS instruments.
For the DOAS fit we used the settings commonly used in the MAX-DOAS community (e.g., Piters et al., 2012;Kreher et al., 2019). The fitting window was 425-490 nm. For the stratospheric NO 2 fit, the cross sections included were NO 2 at 220 K (Vandaele et al., 1998), O 3 at 223 K (Bogumil et al., 2003), water vapour (Rothman et al., 2010), O 2 -O 2 (Hermans et al., 2001), Ring cross section based on a solar spectrum from Kurucz et al. (1984). For the tropospheric NO 2 fit, the O 3 , water 170 vapour, O 2 -O 2 , and Ring cross sections were the same as those used in the stratospheric NO 2 fit but the NO 2 cross section at 298 K (Vandaele et al., 1998) and the NO 2 cross section at 220 K which was made orthogonal with the 298 K cross section were used. A fifth order polynomial of the wavelength was also included in the fits.
In the DOAS fit, one removes the solar Fraunhofer lines by using the ratio of the measured spectrum and a reference spectrum. Because both spectra are influenced by the instrument spectral response function, the solar Fraunhofer lines cannot 175 be removed completely in the ratio. Since this effect comes from the solar spectrum I 0 , it is referred to as "I 0 effect". Detailed explanation and corrections for the I 0 effect was presented by Alliwell et al. (2002). The NO 2 and O 3 cross sections have been corrected for the I 0 effect.
For the fit of tropospheric NO 2 , the reference spectrum was the measurement at 90 • elevation angle (zenith) at every scanning series. For the stratospheric NO 2 , the reference spectrum for the MAX-DOAS measurements from December 2017 to January 180 2018 was taken on 3 January 2018. The reference spectrum for the MAX-DOAS measurements in December 2018 and 2019 was taken on 3 February 2019. These two reference spectra were measured at solar zenith angle 17 • and 24 • in the afternoon, at 90 • elevation angle, and in cloud free situations. We did not use spectra measured at solar zenith angle close to 0 • because of saturation of the detector.
The NO 2 slant column densities present the amount of NO 2 along the effective light path from the sun to the MAX-DOAS.
In order to convert the slant column densities to the vertical column densities, air mass factors (AMFs) were calculated using the Doubling-Adding KNMI radiative transfer codes (DAK) (De Haan et al., 1987;Stammes, 2001), with a pseudo-spherical correction (because of the large solar zenith angles up to 89 • ) and tropical atmospheric profiles of temperature and pressure (Anderson et al., 1986). The NO 2 profile was taken from the TM5-MP model simulations and interpolated at the tropical 190 atmospheric profile levels. For the stratospheric AMF, the tropospheric NO 2 mixing ratio was set to zero at the altitude from 0 to 18 km, which is about the tropopause height from the model for the tropical regions. The NO 2 total column density in the tropical atmospheric profile is about 2.0×10 15 molec cm −2 . NO 2 photolysis at twilight was not taken into account in the AMF calculations. The uncertainty of the AMFs caused by the neglecting of the NO 2 photolysis has been shown by (Van Roozendael and Hendrick, 2012) and will be discussed in Sect. 4.5. Aerosols were specified in a well-mixed layer from 0 to 1 km with 195 aerosol optical thickness values from 0 to 2 in 20 intervals. A Henyey-Greenstein phase function was used for aerosols in the computations.
AMFs for the stratospheric and tropospheric NO 2 were calculated off-line separately and stored in look-up tables. The AMF is a function of elevation angle, solar zenith angle, relative azimuth angle, aerosol optical thickness, surface albedo and surface height. For the ship measurements, we set the surface albedo to 0.05 and the surface height to 0 km. The solar zenith 200 angles ranged from 0 • to 89 • . The AMFs were calculated at the wavelength of 460 nm. The method for the calculation of the tropospheric AMFs is described by Vlemmix et al. (2010).
Clouds were not taken into account in the AMF computations. According to Van Roozendael and Hendrick (2012) clouds are not important for the stratospheric NO 2 retrievals using MAX-DOAS. The impact of clouds on tropospheric NO 2 retrievals has been analysed by Vlemmix et al. (2015), by analysing the fully cloudy scenes (both zenith and off-axis elevation having 205 clouds) and partly cloudy scenes (one elevation having clouds, either zenith or off-axis). They have reported that for the fully cloudy scenes, the impact of clouds on the sensitivity of MAX-DOAS tropospheric NO 2 measurement is small. For the partly cloudy scenes, the clouds have strong impact on the MAX-DOAS tropospheric NO 2 measurements, but the impact can be reduced if the MAX-DOAS data are averaged in time.
The viewing azimuth angles of the MAX-DOAS measurements were corrected using the heading data of the ship. The 210 elevation angles were not explicitly corrected for the pitch and roll of the ship in our calculations because the MAX-DOAS instruments had an automatic continuous adjustment of the elevation angles during the measurements. Because we use 15 • (165 • ) and 30 • (150 • ) elevation angles in the NO 2 retrievals, the 1 degree of pitch and roll are not important for these elevation angles. The solar zenith angles and relative azimuth angles have been re-computed using the ship GPS data because the internal GPS of the MAX-DOAS instrument was malfunctioning.

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The stratospheric NO 2 vertical column densities (VCD strat ) are calculated using Eq. 1.
where DSCD is the differential slant column density between the actual slant column density and the slant column density in the reference spectrum. SCD ref is the slant column density in the reference spectrum which is calculated using the total VCD multiplied with the cosine of the SZA. AMF strat is the stratospheric NO 2 AMF. 220 We obtained the total NO 2 VCDs in the MAX-DOAS reference spectra from collocated OMI/QA4ECV NO 2 data (version 1.1 off-line, at http://www.temis.nl/) . The total NO 2 column density was 1.5 × 10 15 molec cm −2 in the reference spectrum on 3 January 2018 and was 1.7 × 10 15 molec cm −2 in the reference spectrum on 3 February 2019.
The tropospheric NO 2 vertical column densities (VCD trop ) are calculated using Eq. 2.
where DSCD 90 is the differential slant column densities between a given elevation angle and 90 • elevation angle in the same scanning series, and DAMF is the difference between the NO 2 AMFs at the given elevation angle and at 90 • elevation angle. densities. There is no enhanced tropospheric NO 2 on this day, which is the case for most of the cruises. At SZA larger than 60 • , some tropospheric NO 2 VCDs are larger than at noon, which may be the impact of the stratospheric NO 2 .
As shown in Fig. 3, when the solar zenith angles are larger than 70 • , in the morning the VCDs at the elevations of 150 • and 245 165 • decrease with the increasing SZA; in the evening the VCDs at the elevations of 15 • and 30 • decrease with the increasing SZA. The decrease of tropospheric NO 2 VCDs with increasing SZA at relatively large SZA is an artefact which is caused by the rapid changing of the stratospheric NO 2 at large SZA and by using the spectrum measured at 90 • elevation angle as the reference spectrum in every scanning series. The measurements started from the 15 • elevation angle and finished at the 165 • elevation angle. In the morning, the spectra at the 150 • and 165 • elevation angles are measured later than the reference 250 spectrum and the stratospheric NO 2 decreases rapidly in the morning, therefore less NO 2 is measured at the 150 • and 165 • elevation angles than in the reference spectrum. In the evening, the stratospheric NO 2 increases rapidly as SZA increasing and the spectra at the 15 • and 30 • elevation angles are measured earlier than the reference spectrum, consequently, less NO 2 is measured at the 15 • and 30 • elevation angles than in the reference spectrum. If there is more NO 2 in the reference spectrum than in the actual measurement, the DOAS fit may yield a negative NO 2 slant column density. This artefact has no impact on   Table 2. 280 We also compared the TROPOMI stratospheric NO 2 VCDs with the TM5-MP model simulated stratospheric NO 2 VCDs.
They are almost the same, the mean difference is about −2.49 × 10 13 molec cm −2 (about 1%). This is expected because the TROPOMI NO 2 total column densites are assimilated in TM5-MP model to separate the stratospheric and tropospheric NO 2 . This is a good consistency check for the TROPOMI stratospheric NO 2 VCDs.   molec cm −2 . The linear fit of the TROPOMI and TM5 interpolated stratospheric NO 2 VCDs has a slope of 1.083 and an offset of 2.653 × 10 14 molec cm −2 , which is similar to that of Fig. 7. The mean and standard deviation values for TROPOMI and MAX-DOAS stratospheric NO 2 VCDs are presented in Table 3.

Comparison of MAX-DOAS and TROPOMI
The MAX-DOAS and TROPOMI stratospheric NO 2 VCDs for all cruises are shown as a function of latitude in Fig. 9. Both data sets illustrate the latitudinal dependency of the stratospheric NO 2 VCDs, with low values in tropical region (20 • S to 10 • 320 N) and higher values at mid-latitudes (10 • N -40 • N). Note that the MAX-DOAS data were taken in four cruise in different months, not in a single cruise. The latitudinal dependency is well-known in satellite stratospheric NO 2 VCD data (Belmonte-Rivas et al., 2014). In the tropics the low stratospheric NO 2 VCDs are caused by upward and poleward transport in the Hadley cell (Noxon, 1979).

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The tropospheric NO 2 VCDs for the cruise in February 2019 across the Pacific is shown in Fig. 10. There are no anomalous high tropospheric NO 2 VCDs during this cruise. As shown in the figure, most MAX-DOAS tropospheric NO 2 VCDs are close to zero. And the TROPOMI tropospheric NO 2 VCDs are also very low, 7 × 10 14 molec cm −2 , with large error bars because of the low NO 2 concentrations (van Geffen et al., 2019). Figure 11 shows the scatter plot of TROPOMI tropospheric NO 2 VCD versus MAX-DOAS tropospheric NO 2 VCD at the 330 closest overpass time. The vertical error bar is the uncertainty of the TROPOMI tropospheric NO 2 VCD, which is taken from the TROPOMI data. The horizontal error bar is for the MAX-DOAS tropospheric NO 2 VCD, which is assumed to be 100% of the NO 2 VCD. We can see that the MAX-DOAS and TROPOMI data both show low tropospheric NO 2 during these cruises.
The TROPOMI and MAX-DOAS tropospheric NO 2 VCDs are in the same range, most of the points are between 0 and 5×10 14 molec cm −2 . Because of very low tropospheric NO 2 , there is almost no correlation between the tropospheric NO 2 VCDs. The 335 mean difference and standard deviation are 4.00 × 10 14 and 5.08 × 10 14 molec cm −2 , respectively.
The negative values in the MAX-DOAS tropospheric NO 2 are mostly due to the low NO 2 values and the detection limit of the MAX-DOAS. The negative tropospheric NO 2 VCD values may also be caused by the clouds in the reference spectrum but not in the off-axis spectrum. The best root mean square error in the DOAS fit for tropospheric NO 2 is 1.2 × 10 −4 . The NO 2 cross section is about 1 × 10 −19 cm 2 molec −1 . If we assume that twice of the RMS can be detected, the detection limit for the 340 slant column density is 2.4×10 15 molec cm −2 . The AMF for the 15 • elevation angle is about 2.2, hence the detection limit for the vertical column density is 1.1 × 10 15 molec cm −2 . This estimation of the detection limit is similar to that used by Peters et al. (2012). They proposed this value as an upper limit, the actual detection limit can be better than this. During the cruises, tropospheric NO 2 slant column densities larger than 2.4 × 10 15 molec cm −2 were rarely detected.

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Because the reference spectra were measured by the MAX-DOAS during the cruises, there was background NO 2 absorption in the reference spectra. The NO 2 VCD in the reference spectrum was estimated using the collocated OMI/QA4ECV NO 2 VCD, which may cause an uncertainty (offset) in the MAX-DOAS stratospheric NO 2 VCDs. Zara et al. (2018) reported that the uncertainty of the OMI NO 2 SCD in remote ocean region was about 8 × 10 14 molec cm −2 . The uncertainty of the NO 2 VCD in the reference spectrum is estimated to be 4×10 14 molec cm −2 because the AMF is about 2 at noon. The NO 2 VCD in 350 the reference spectrum has a larger impact on the stratospheric NO 2 VCD at the TROPOMI overpass time, for example in the comparison of MAX-DOAS NO 2 VCD with TROPOMI at the collocated pixels. Since the same reference spectrum is used for the MAX-DOAS analysis, the impact of the reference spectrum on the MAX-DOAS stratospheric NO 2 VCD is the same for all trips. The NO 2 in the reference spectrum has less impact on the MAX-DOAS stratospheric NO 2 VCD at the SZA range of 75 • -89 • , because the mean AMF in this SZA range is about 7 time the AMFs of the reference spectrum (due to the long 355 light path at large SZAs).
Neglecting the NO 2 photo-dissociation may lead to 10% uncertainty in the AMFs at twilight because of the change of the NO 2 profiles (Van Roozendael and Hendrick, 2012). Since we only used the measurements at SZA smaller than 89 • , the impact from the photo-dissociation may be smaller in our analysis. We have calculated the stratospheric NO 2 AMFs using a range of NO 2 profiles from the TM5 output. The AMFs for the stratospheric NO 2 are very similar and the differences are within 5%. For the tropospheric NO 2 VCDs, assuming the AMF of 2.0 with an uncertainty of 10%, the uncertainty of the tropospheric NO 2 VCD is estimated to be 2.1×10 14 molec cm −2 . However, Bais et al. (2016) recommended that the NO 2 differential AMF uncertainties to be used for MAX-DOAS at 15 • and 30 • elevations were 41% and 22%, respectively. In reality the uncertainty of the MAX-DOAS tropospheric NO 2 VCDs is larger than the values given here.

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The comparison of MAX-DOAS and TROPOMI stratospheric NO 2 VCDs has also been analysed using averaged TROPOMI data over 3 × 3 and 5 × 5 ground pixels around the collocated pixels. The mean differences between TROPOMI and MAX-DOAS stratospheric NO 2 VCDs are 4.34, 4.57, 4.55 ×10 14 molec cm −2 for 1, 3 × 3, and 5 × 5 pixels, respectively. The best agreement between the TROPOMI and MAX-DOAS stratospheric NO 2 VCDs occurs for the single pixel cases presented in this paper.

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The comparisons of TROPOMI stratospheric NO 2 VCDs with MAX-DOAS collocated stratospheric NO 2 VCD and with the The differences of the MAX-DOAS and TROPOMI NO 2 VCDs do not depend on the cloud radiance fraction. The MAX-DOAS tropospheric NO 2 VCDs are close to the detection limit. The negative values can also be due to clouds observed in the of the lowest TROPOMI tropospheric NO 2 values; such clean cases are not easily observed over land.
Similar to Peters et al. (2012) and Behrens et al. (2019), we also measured the latitude dependent shape of stratospheric NO 2

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VCDs. Because the TROPOMI overpass time is close to noon, we cannot use the morning or evening MAX-DOAS values to compare with TROPOMI data directly. The morning and evening MAX-DOAS NO 2 were calculated from the SZA of 88 • to 92 • by Peters et al. (2012) and Behrens et al. (2019). We used the NO 2 VCDs until solar zenith angle of 89 • . Peters et al. (2012) reported that the tropospheric NO 2 VCDs were only above the detection limit when there were ship emissions or close to land. This agrees with our tropospheric NO 2 measurements although we do not have measurements close to land. Because the cruises were mostly in remote ocean areas, the MAX-DOAS tropospheric NO 2 values were quite low, often 400 close to 0 or slightly negative as a result of low detection limit or impact of clouds. Daily AOD at 500 nm