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).

The TROPOMI NO2 product was developed at KNMI and is generated within the TROPOMI ground segment (PDGS) operating at the German Aerospace Centre (DLR) . The TROPOMI NO2 product provides tropospheric, stratospheric, and total vertical column densities (VCDs) and their precision, as well as detailed results of, for example, NO2 slant column densities and precision air mass factors.

The KNMI TROPOMI NO2 retrieval algorithm is based on a retrieval and data assimilation system, following the approach introduced for the OMI NO2 retrievals (the DOMINO approach) and also applied for the OMI retrievals within the QA4ECV project . The total NO2 slant column densities are derived using the Differential Optical Absorption Spectroscopy (DOAS) method . The total slant column densities are then assimilated in the TM5-MP model to determine the stratospheric NO2 slant column densities. The tropospheric NO2 slant 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 NO2 VCDs using appropriate air mass factors (AMFs).

The TROPOMI overpass is at about 13:30 LT. 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 were not available for the cruise from December 2017 to January 2018 when the instrument was still in its in-orbit test phase. Only data with a quality assurance (QA) value of >0.75 (i.e. cloud radiance fraction <0.5) were selected.

The baseline method in the TROPOMI NO2 algorithm to separate stratospheric and tropospheric contributions to the NO2 total slant column densities is by data assimilation of slant column densities in the TM5-MP chemistry transport model . The TM5-MP NO2 profiles are simulated globally in 1∘ × 1∘ (latitude × longitude) grids at 35 levels from surface to about 0.01 hPa. The time interval of the output is 30 min. The TM5-MP NO2 profiles are kept in archive at KNMI. We selected the NO2 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 d-1, depending on the speed of the ship and its activities. The total, stratospheric, and tropospheric NO2 vertical column densities were integrated using the TM5-MP NO2 profiles. The tropopause level provided in the TM5-MP data was used to separate the stratospheric and tropospheric NO2 column densities. The collocated TM5-MP data are available for four cruises. There are no TROPOMI NO2 data for the first cruise, and therefore there were no TM5-MP data either.

The NO2 slant column densities were retrieved with the DOAS technique 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 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.. The fitting window was 425–490 nm. For the stratospheric NO2 fit, the cross sections included were NO2 at 220 K , O3 at 223 K , water vapour , O2–O2 , and a Ring cross section based on a solar spectrum from . For the tropospheric NO2 fit, the O3, water vapour, O2–O2, and Ring cross sections were the same as those used in the stratospheric NO2 fit, but the NO2 cross section at 298 K and the NO2 cross section at 220 K that 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, the solar Fraunhofer lines are removed 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 be removed completely in the ratio. Since this effect comes from the solar spectrum I0, it is referred to as “I0 effect”. Detailed explanation and corrections for the I0 effect were presented by . The NO2 and O3 cross sections have been corrected for the I0 effect.

For the fit of tropospheric NO2, the reference spectrum was the measurement at 90∘ elevation angle (zenith) at every scanning series. For the stratospheric NO2, the reference spectrum for the MAX-DOAS measurements from December 2017 to January 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 in cloud-free situations. We did not use spectra measured at a solar zenith angle close to 0∘ because of saturation of the detector.

The NO2 slant column densities present the amount of NO2 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) , with a pseudospherical correction (because of the large solar zenith angles up to 89∘) and tropical atmospheric profiles of temperature and pressure . The NO2 profile was taken from the TM5-MP model simulations and interpolated at the tropical atmospheric profile levels. For the stratospheric AMF, the tropospheric NO2 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 NO2 total column density in the tropical atmospheric profile is about 2.0×1015 moleccm-2. NO2 photolysis at twilight was not taken into account in the AMF calculations. The uncertainty of the AMFs caused by the neglecting of the NO2 photolysis has been shown by and will be discussed in Sect. 4.5. Aerosols were specified in a well-mixed layer from 0 to 1 km, with 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 NO2 were calculated separately offline 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 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 .

Clouds were not taken into account in the AMF computations. According to clouds are not important for the stratospheric NO2 retrievals using MAX-DOAS. The impact of clouds on tropospheric NO2 retrievals has been analysed by , by analysing the fully cloudy scenes (both zenith and off-axis elevation having 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 NO2 measurement is small. For the partly cloudy scenes, the clouds have strong impact on the MAX-DOAS tropospheric NO2 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 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∘), 30∘ (150∘), and 90∘ elevation angles in the NO2 retrievals, the 1∘ 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.

The stratospheric NO2 vertical column densities (VCDstrat) are calculated using Eq. (). 1VCDstrat=(DSCD+SCDref)/AMFstrat, where DSCD is the differential slant column density between the actual slant column density and the slant column density in the reference spectrum. SCDref is the slant column density in the reference spectrum, which is calculated using the total VCD multiplied with the cosine of the SZA. AMFstrat is the stratospheric NO2 AMF.

We obtained the total NO2 VCDs in the MAX-DOAS reference spectra from collocated OMI/QA4ECV NO2 data (version 1.1 offline, at http://www.temis.nl/, last access: 23 March 2020) . The total NO2 column density was 1.5×1015 moleccm-2 in the reference spectrum on 3 January 2018 and was 1.7×1015 moleccm-2 in the reference spectrum on 3 February 2019.

The tropospheric NO2 vertical column densities (VCDtrop) are calculated using Eq. (). 2VCDtrop=DSCD90/DAMF, where DSCD90 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 NO2 AMFs at the given elevation angle and at 90∘ elevation angle.

Stratospheric NO2 vertical column densities derived from all viewing directions on 5 February 2019 are shown in Fig. . On this day, RV Sonne sailed in the Pacific ocean (1.37–2.08∘ N, 142.08–140.58∘ W). It was good weather with lots of scattered clouds, which was the normal weather condition during the cruises. The stratospheric NO2 VCDs derived from different elevation angles are quite close to each other, but the VCDs are slightly larger at small elevation angles. The NO2 VCD shows a typical diurnal evolution pattern in the stratosphere, with low values in the morning, increasing during the day, and high values in the evening. These features can be explained by the NOx-related stratospheric chemistry, as mentioned in the Introduction. The stratospheric NO2 VCD is about 1.5×1015 moleccm-2 at noon and 2.6×1015 moleccm-2 at SZA of 89∘. The values are in the same range as those measured by satellite instruments reported by .

Figure  shows tropospheric NO2 VCDs on 24 June 2019. The measurement was taken over the Pacific ocean (25.12–24.40∘ N, 137.83–134.44∘ E) with scattered clouds. The tropospheric NO2 vertical column densities are between 0 and 0.5×1015 moleccm-2 and similar at different elevation angles. Therefore, we do not need to separate different elevation angles when comparing MAX-DOAS tropospheric NO2 vertical column densities with TROPOMI tropospheric NO2 vertical column densities. There is no enhanced tropospheric NO2 on this day, which is the case for most of the cruises. At SZA larger than 60∘, some tropospheric NO2 VCDs are larger than at noon, which may be the impact of the stratospheric NO2.

As shown in Fig. , when the solar zenith angles are larger than 70∘, in the morning the VCDs at the elevations of 150 and 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 in tropospheric NO2 VCDs with increasing SZA at relatively large SZA is an artefact that is caused by the rapid changing of the stratospheric NO2 at large SZA and 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 spectrum and the stratospheric NO2 decreases rapidly in the morning, therefore less NO2 is measured at the 150 and 165∘ elevation angles than in the reference spectrum. In the evening, the stratospheric NO2 increases rapidly as SZA is increasing, and the spectra at the 15 and 30∘ elevation angles are measured earlier than the reference spectrum; consequently, less NO2 is measured at the 15 and 30∘ elevation angles than in the reference spectrum. If there is more NO2 in the reference spectrum than in the actual measurement, the DOAS fit may yield a negative NO2 slant column density. This artefact has no impact on the comparison with TROPOMI tropospheric NO2 because the SZAs are small at the TROPOMI overpass time during the four cruises.

The TM5-MP-simulated NO2 profiles were integrated vertically from the tropopause level to the highest level of the model to get the stratospheric NO2 vertical column densities. If there were several TM5 latitude–longitude grid cells crossed by the ship in a day, the NO2 column densities in the morning (evening) from the first (last) TM5 grid were used to compare with the MAX-DOAS morning (evening) measurements. The SZA values of the TM5 NO2 profiles were calculated at the centre of the latitude and longitude grids. The variation in the NO2 column densities in different grid cells crossed by the ship per day was usually small. Figure  shows 1 d of the stratospheric NO2 column densities simulated by TM5 and measured by MAX-DOAS on 22 March 2019, when the ship was stationary in the Pacific at 14.5∘ N, 125.5∘ W. On this day, the NO2 vertical column densities from one TM5 grid cell were selected. The largest SZA in the MAX-DOAS NO2 VCD data is 89∘ in the morning and evening. The MAX-DOAS stratospheric NO2 vertical column densities have a similar diurnal variation to the TM5-simulated stratospheric NO2 column densities. The TM5 stratospheric NO2 vertical column densities have a positive offset compared to the MAX-DOAS stratospheric NO2 VCDs. Plots of other days show a similar pattern.

Figure  shows the scatter plot of the MAX-DOAS stratospheric NO2 VCDs measured in the morning and evening versus TM5-simulated stratospheric NO2 VCDs for four cruises. The morning and evening NO2 values are the average of NO2 VCD measured from SZA 75 to 89∘, respectively. This solar zenith angle range is used throughout the paper to define the morning and evening NO2. At large SZA, the light path in the stratosphere is longer than that at noon; consequently, the MAX-DOAS measurements are more sensitive to the stratospheric NO2. The MAX-DOAS and TM5 stratospheric NO2 VCDs have a good linear correlation, with a correlation coefficient R=0.97. The mean differences are 3.34×1014 (±1.88×1014) moleccm-2 (16.5 %) in the morning and 5.69×1014 (±3.12×1014) moleccm-2 (17.4 %) in the evening. The TM5 stratospheric NO2 VCDs are slightly higher than the MAX-DOAS stratospheric NO2 VCDs.

Additionally, we have compared the MAX-DOAS and TM5 stratospheric NO2 VCDs at the SZA ranges of 0–30∘, 30–60∘, and 60–75∘. At smaller SZA angles, TM5-simulated stratospheric NO2 VCDs are mostly larger than the MAX-DOAS measurements. The results of the comparison are presented in Table .

We also compared the TROPOMI stratospheric NO2 VCDs with the TM5-MP model-simulated stratospheric NO2 VCDs. They are almost the same, and the mean difference is about -2.49×1013 moleccm-2 (about 1 %). This is expected because the TROPOMI NO2 total column densities are assimilated in TM5-MP model to separate the stratospheric and tropospheric NO2. This is a good consistency check for the TROPOMI stratospheric NO2 VCDs.

Because the reference spectra were measured by the MAX-DOAS during the cruises, there was background NO2 absorption in the reference spectra. The NO2 VCD in the reference spectrum was estimated using the collocated OMI/QA4ECV NO2 VCD, which may cause an uncertainty (offset) in the MAX-DOAS stratospheric NO2 VCDs. reported that the uncertainty of the OMI NO2 SCD in remote ocean regions was about 8×1014 moleccm-2. The uncertainty of the NO2 VCD in the reference spectrum is estimated to be 4×1014 moleccm-2 because the AMF is about 2 at noon. The NO2 VCD in the reference spectrum has a larger impact on the stratospheric NO2 VCD at the TROPOMI overpass time, e.g. in the comparison of MAX-DOAS NO2 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 NO2 VCD is the same for all trips. The NO2 in the reference spectrum has less impact on the MAX-DOAS stratospheric NO2 VCD at the SZA range of 75–89∘ because the mean AMF in this SZA range is about 7 times the AMFs of the reference spectrum (due to the long light path at large SZAs).

Neglecting the NO2 photodissociation may lead to 10 % uncertainty in the AMFs at twilight because of the change of the NO2 profiles . Since we only used the measurements at SZA smaller than 89∘, the impact from the photodissociation may be smaller in our analysis. We have calculated the stratospheric NO2 AMFs using a range of NO2 profiles from the TM5 output. The AMFs for the stratospheric NO2 are very similar and the differences are within 5 %.

In the DOAS fit, the uncertainty of the MAX-DOAS stratospheric NO2 slant column densities is about 0.5×1014 moleccm-2 at SZA of 20∘ and increases to 1×1014 moleccm-2 at SZA of 80∘. These uncertainties are given in the output of our DOAS fit program. The uncertainty of the NO2 VCD in the reference spectra is about 4×1014 moleccm-2 based on the OMI data. The stratospheric NO2 AMFs are about 1.2 and 5.5 at 20 and 80∘ of the SZA, with an uncertainty of 10 %. Using the uncertainty estimation method presented by , in total we estimate that the uncertainty of the stratospheric NO2 VCD is about 4×1014 moleccm-2 and 1×1014 moleccm-2 at SZA of 20 and 80∘, respectively.

For the tropospheric NO2 VCDs, assuming an AMF of 2.0 with an uncertainty of 10 %, the uncertainty of the tropospheric NO2 VCD is estimated to be 2.1×1014 moleccm-2. However, recommended that the NO2 differential AMF uncertainties to be used for MAX-DOAS at 15 and 30∘ elevations are 41 % and 22 %, respectively. In reality the uncertainty of the MAX-DOAS tropospheric NO2 VCDs is larger than the values given here.

The comparison of MAX-DOAS and TROPOMI stratospheric NO2 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 NO2 VCDs are 4.34, 4.57, and 4.55 ×1014 moleccm-2 for 1, 3×3, and 5×5 pixels, respectively. The best agreement between the TROPOMI and MAX-DOAS stratospheric NO2 VCDs occurs for the single-pixel cases presented in this paper.

The comparisons of TROPOMI stratospheric NO2 VCDs with MAX-DOAS-collocated stratospheric NO2 VCD and with the TM5-MP-interpolated stratospheric NO2 VCDs show consistent results: TROPOMI stratospheric NO2 VCDs are higher than the other two products. The TROPOMI stratospheric NO2 VCDs have good linear correlation with the MAX-DOAS-collocated and TM5-interpolated stratospheric NO2 VCDs. The linear fit of the TROPOMI stratospheric NO2 VCDs and MAX-DOAS-collocated stratospheric NO2 VCDs or TM5-interpolated stratospheric NO2 VCDs have similar slopes and offsets.

The differences between the MAX-DOAS and TROPOMI NO2 VCDs do not depend on the cloud radiance fraction. The MAX-DOAS tropospheric NO2 VCDs are close to the detection limit. The negative values can also be due to clouds observed in the 90∘ elevation angle but not in the off-axis elevation angle. These MAX-DOAS tropospheric NO2 VCDs provide an evaluation of the lowest TROPOMI tropospheric NO2 values; such clean cases are not easily observed over land.

Similar to and , we also measured the latitude-dependent shape of stratospheric NO2 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 NO2 were calculated from the SZA of 88 to 92∘ by and . We used the NO2 VCDs up to a solar zenith angle of 89∘. reported that the tropospheric NO2 VCDs were only above the detection limit when there were ship emissions or they were close to land. This agrees with our tropospheric NO2 measurements, although we do not have measurements close to land.