The NO2 retrievals of TROPOMI and OMI use the three step approach that was introduced for the OMI NO2 retrieval and named DOMINO (). The first step is a DOAS retrieval to determine the SCD, Ns – see Sect.  for details. Next, NO2 vertical profile information from the TM5-MP chemistry transport model / data assimilation system that assimilates the SCDs is used to determine the stratospheric vertical column density (VCD) Nvstrat. Finally, the tropospheric VCD, Nvtrop, is determined using stratospheric and tropospheric air-mass factors (AMFs), which depend on surface albedo, surface pressure, cloud fraction, cloud pressure, the shape of the NO2 vertical profile (not of the absolute concentration levels), and the viewing geometry of the satellite ground pixel in question. A description of the last two steps falls outside the scope of this paper; for details see . Since the SCD depends strongly on the along-track and across-track variation in the solar and viewing zenith angles, it is often easier to consider the geometric column density (GCD), Nvgeo, defined as the SCD divided by the geometric AMF, Mgeo, which depends only on the solar (θ0) and viewing (θ) zenith angles: Mgeo=(1/cos⁡θ0)+(1/cos⁡θ).

To make the use of the TROPOMI data easier, a so-called qa_value (where “qa” stands for “quality assurance”) is assigned to each ground pixel, which serves as an easy filter of the NO2 observations. The usage of the qa_value is detailed in the Product User Manual (PUM;). For most applications, the recommended filter is qa_value>0.75, which removes scenes with large cloud fractions (cloud radiance fraction >0.5) and snow/ice scenes that are not considered cloud-free. In this paper “cloud-free”, “clear-sky” or just “clear” thus refers to qa_value>0.75, while ”cloudy” refers to 0.50<qa_value<0.75. Details of how the NO2 qa_value is constructed are given in the ATBD Appendix E.

A section of orbit 08516 over the Atlantic Ocean (“atl” for short as id in figures and tables), with nadir latitudes [+10°:+40°] was locally reprocessed so as to store the DOAS fit residuals and from this six clear-sky ground pixels with large RL and large negative RD were arbitrarily picked.

The top panel of Fig.  shows the fit residual from one example as a thin red line and a smoothed version of that as a thick red line. Results of the runs test for this fit residual are RD=-6.3, i.e. really in the tail of the distribution, and RL=33 (at λ=[432.28:436.58]nm).

The bottom panel of Fig.  shows smoothed residuals of the six examples as thin lines and a smoothed average residual (“all”) as a thick line. All examples are around longitude -40°, latitude +26°; scanline and row numbers of these and of the other example pixels in this paper are listed in Appendix .

Clearly noticeable in the fit residuals is the large peak around 430nm. Both the RMS error and the χ2 of the fit do not have suspiciously large values: those two quantities give no cause for alarm. Yet, the 430nm peaks is clearly systematic and will have some impact on the NO2 DOAS fit results.

To investigate the magnitude and occurence of this peak further, consider the ratio of the RMS of the peak – i.e. the wavelength range [429:432]nm, indicated in the bottom panel of Fig. , which spans about 15 spectral pixels – and the RMS of the rest of the fit window: 7QRMS430=RRMS(λ∈[429:432])RRMS(λ∉[429:432]) (Like the fit residual, this ratio is not part of the nominal level-2 files). The values of the RMS elements in Eq. () and the full-window RMS error of the average residual (“atl_all”) in Fig.  are given in Table ; for the individual residuals the ratio varies between 2.3 and 2.8. The higher the ratio, the more pronounced the 430nm peak stands out against the noise in the fit residual. Although RMS values are continuous quantities, a ratio QRMS430≥2.0 likely indicates there is a problem with the NO2 SCD.

The top-left panel of Fig.  shows for the above mentioned orbit section the QRMS430 ratio as function of the cloud radiance fraction: by far most pixels with a ratio ≥2.0 are clear-sky pixels (left part of the panel). In fact, the ratio is large only for clear-sky pixels for which the full-window RMS error of the fit is small. For these clear-sky pixels, where the satellite sees the ocean waters, the RMS_430 ratio increases with increasing value of the liquid water fit coefficient (top-right panel of Fig. ): the deeper the light reaches into the ocean waters, the larger the effect of VRS on the retrieval and therefore the more pronounced the peak around 430nm.

For pixels with higher cloud radiance fraction the RMS error of the fit is higher and the RMS_430 ratio is lower. In other words: for most cloudy pixels, any problem with the fit residual around 430nm is possibly hidden between the larger noise on the residual due the presence of those clouds; the higher the cloud radiance fraction, the larger the range of RMS error values, i.e. of noisiness of the fit residual. The RMS_430 ratio does not show a dependency with either the solar or the viewing zenith angle, neither for clear-sky nor for cloudy pixels.

For comparison of what goes on over land, consider a section of orbit 08514 over Northern Africa, with nadir latitudes [+10°:+30°], which is slightly smaller than the Atlantic Ocean section used above to avoid including the Mediterranean Sea, but otherwise covers the same latitudes.

As the middle row of Fig.  shows, there are only a few pixels with QRMS430>1.5 (about 4% from the orbit section), while the full-window RMS has roughly the same range as for the Atlantic Ocean section. Apparently there is no issue around 430nm over this area of land. But this does not hold everywhere over land.

When inspecting other land areas where QRMS430>2.0 occurs in the 5 June 2019 orbits, several pixels stood out over Western Australia, though quite scattered. To look at this in more detail, consider the land pixels of a section of orbit 08510 with nadir latitudes [-45.2°:-7.5°], which covers half of Australia west of about +135°, most of which is free of clouds.

The bottom-left panel of Fig.  shows the scatter plot of the RMS_430 ratio as function of the cloud radiance fraction: about 2% of the really cloud-free pixels (i.e. with a very small cloud radiance fraction) have a ratio larger than 2.0, with a maximum of 2.43; for the Atlantic Ocean section the maximum ratio found is 3.45. None of the Australian land pixels is signaled by the runs test, with |RD|<3.5 and RL<20.

Figure  shows fit residuals of six ground pixels around longitude +120°, latitude -27° with RMS_430 ratios around 2.3; the bottom row of Table  lists the values of the RMS elements of Eq. () for the average (“aus_all”) over the six example residuals. There clearly is a peak around 430nm that stands out above the noise in the fit residual, which definitely is not caused by VRS: the pixels are all classified as “shrubland”. Perhaps this indicates that the effect of RRS is not completely accounted for in the fit.

Figure  shows a map of the locations where QRMS430≥2.0 for all TROPOMI orbits of 5 June 2019. Almost all these locations are over open water; over land there are only scattered pixels, as mentioned in the preceeding sections. Cloudy pixels tend to have a low RMS_430 ratio and therefore do not show up in the map. The outer 22 (20) rows at the left (right) edge of the swath have a larger spectral uncertainty, which is reflected in larger SCD and RMS errors, as a result of which the RMS_430 ratio is somewhat lower there.

Maps for other days (not shown) look similar, with a seasonal variation in the overall North-South pattern over the oceans and an apparent small decrease in time of the number of pixels with QRMS430≥2.0. To investigate this further, Fig.  shows the frequency distribution of the RMS_430 ratio for cloud-free pixels of three selected days over water and over land separately.

From 5 June 2019 to 7 June 2020, the RMS_430 ratio decreases somewhat, clearly visible over water (blue lines) and less clearly over land (red lines). The reason for this decrease is likely the fact that due to the along-track pixel size reduction in August 2019 the uncertainties have increased (Sect. ), i.e. the noise in the fit residual has increased, as a result of which the 430nm peak stands out less clearly.

After that, the uncertainties of the NO2 retrieval remain almost the same, as illustrated in Fig. , but Fig.  indicates that the 430nm peak decreases in magnitude between 2020 and 2024, in particular over water but also over land. This is likely caused by the fact that in 2024 the Sun is more active than in 2020, as a result of which the 430nm structure is less deep, in particular the calcium line there – see Appendix  for a brief investigation of the line depth over time. The irradiance and radiance are affected directly by the varying depth at that wavelength, while in addition to that the radiance over water is also indirectly affected by the change of the depth of the Ca+ lines around 395nm which are shifted to around 430nm by VRS (Sect. ).

In other words: because the structure in the irradiance around 430nm varies with the solar activity cycle, the effects of RRS are never really fully compensated around that wavelength, since the Ring reference spectrum (Sect. ) is determined from a fixed irradiance reference spectrum, and over water things are made worse by the effects of VRS.

For ground pixels over clouds (not shown), the frequency distribution is slightly narrower than for the land pixels in Fig. , with a peak value at about the same RMS_430 ratio, also with a small narrowing over time and a small increase of the peak value.

To investigate the RMS_430 ratio for OMI collection-4 measurements, Atlantic Ocean orbits similar to the TROPOMI one of 5 June 2019, where selected on or close to 5 June of 2005, 2009, 2014, 2019 and 2024.

Fit residuals of clear-sky pixels of the 5 June 2019 orbit (not shown) look very similar to those shown in Fig. , but on the whole the RMS_430 ratio is lower, the reason no doubt being that the noise on the OMI measurements is in general larger than on TROPOMI measurements: ratios above 2.5 are rare, most pixels have ratios well below 2.0, as can be seen from the red solid line in Fig. .

That figure also shows that the change over time of the RMS_430 ratio for OMI is quite different than for TROPOMI (cf. Fig. ) in relation to the solar activity cycle: the higher activity of 2024 leads for TROPOMI to lower RMS_430 ratios than for the lower activity of 2020, while for OMI the higher activity of 2014 and 2024 (dotted lines in Fig. ) leads to higher RMS_430 ratios than for the lower activity of 2009 and 2019 (dashed lines). The increase of the overall SCD error for OMI over time (Fig. ) and thus of the RMS error, may be visible in Fig.  in the difference between the two low-activity (dashed) lines as a small shift to lower RMS_430 ratios, whereas in the two high-activity (dotted) lines it seems to show up as an small shift to higher RMS_430 ratios; these differences, however, could also be due to differences in atmospheric circumstances.

The reason for the different behaviour of TROPOMI and OMI is not clear, but it may be related to the fact that for OMI NO2 retrievals the 2005 average irradiance is used, while for TROPOMI the daily measured irradiance is used (cf. Sect. ), as a result of which the effect of the 430nm issue on the reflectance and hence on the fit residual is quite different for the two instruments.

For cloudy pixels (not shown), the situation is more like TROPOMI: at low activity, the RMS_430 ratios are on the whole a little larger than at high activity.

Figure  shows smoothed residuals of the Atlantic Ocean example from the top panel of Fig.  using the full-window fit (red line) and using the NO₂-gap fit (blue line): especially on either side of the gap the residual is reduced. Table  lists for the six Atlantic Ocean examples the change in the NO2 SCD value, SCD error, RMS error and χ2 of the fit. A reduction of the latter three – in these cases of 10% or more – is generally considered to indicate that the fit has improved and one then assumes that the resulting SCD value has become more reliable.

The NO₂-gap fit also leads to improved fits for the Western Australian land pixels, as can be seen from the results listed in Table , which shows that in some cases the SCD value may increase due to the improvements. For the Northern Africa land pixels (not shown), changes in the SCD and RMS error are for by far most pixels no more than ±2%; for clear-sky pixels the changes are less than for cloudy pixels.

Figure  shows a map of the relative change in percent of the NO2 SCD error and the GCD value due to the NO₂-gap fit instead of the full-window fit for all orbits of 5 June 2019 – changes occur there where the RMS_430 ratio is large (cf. Fig. ). Scatter plots of the changes in the NO2 SCD error and GCD value are shown in Fig.  for clear-sky pixels over water and land and for all cloudy pixels, separately, as function of the RMS_430 ratio. For pixels over water, the reduction of the SCD error is evident, while over land there is also a decrease of the SCD error for a lot of pixels but some pixels show a small increase as result of the NO₂-gap fit. The GCD values show a small decrease over water, while over land they remain mostly the same. For cloudy pixels, the SCD error and GCD value changes are relatively small, where one has to keep in mind that for cloudy pixels with a cloud radiation fraction just above 0.5 part of the light still comes from the water or land surface.

Frequency distributions of the changes for clear-sky pixels in the NO2 SCD error and GCD value are shown by solid lines in Fig. , along with the changes for the other two test days mentioned above. The changes in the SCD error due to the NO₂-gap fit become a little smaller over time, along with what is seen for the RMS_430 ratio in Fig. , but on the whole there clearly is in improvement in the fit over water and a small improvement over land. The GCD value changes are more or less the same over time: a decrease over water and on average no change over land.

For the initial evaluation of the impact of the NO₂-gap fit on the stratospheric and tropospheric columns, two full months were processed: July 2023 and January 2024 – see Sect. . The Pacific Ocean orbits of these two months can be used to check the impact on the slant column uncertainties discussed in Sect. . Given that there is quite some day-to-day variation, Table  lists the monthly average ratios of the uncertainties of the NO₂-gap over the full-window fit, as well as the average SCD value over the same latitude range (the difference between the two months is related to the seasonal cycle in the uncertainties; see the graphs on the webpages https://www.temis.nl/tropomi/no2scd/, last access: 15 June 2026).

The NO₂-gap fit is included in the operational TROPOMI processor since 22 November 2025 (cf. Sect. ), hence we can compare results after that up to what is available at the moment of writing, i.e. up to 30 April 2026, with v2.8.0 data of the same 160-d period one year earlier. The ratios of the averages over these two periods, listed in the last column of Table , agree quite well with those of the two test months.

As expected from the above reported changes in the SCD error, the DOAS uncertainty improves, in particular for clear-sky scenes. For those scenes the statistical uncertainty does not change much, but the NO₂-gap fit appears to have an impact on the statistical uncertainty over cloudy scenes with changes up to -10%. It is not fully clear why the latter decrease occurs. As the bottom-right panel in Fig.  shows, the GCD does on average not change over clouds, but there is quite some scatter, even for low RMS_430 ratio. In particular over bright clouds and at edges of clouds the illumination of the instrument slit may be inhomogeneous, which is likely to have greatest effect on strong Fraunhofer lines. Perhaps the removal of the 430nm peak therefore gives better, more consistent results over clouds due to the incomplete handling of that peak by the Ring correction in the full-window retrieval. The main message, though, is that the NO₂-gap approach reduces the uncertainties, in some cases more than in other cases, without a deterioration of the results.

Inspecting OMI fit residuals of individual clear-sky Atlantic Ocean pixels with a relatively high RMS_430 ratio of the 2005 orbit without and with the NO₂-gap leads to graphs similar to Fig.  and the changes in the SCD and RMS error are of the same order as those listed in Table . For pixels from the 2024 orbit the changes in the SCD and RMS error appear to be smaller, probably because the 430nm peak is relatively less strong in 2024 than in 2005 due to the increased solar activity (Sect. ) and/or the increased measurement uncertainties (Sect. ).

An evaluation of the data for water pixels only in the latitude range [-40°:+40°], which covers the area where the largest changes are expected to occur, and filtering out the rows suffering from the row anomaly (also for the 2005 data, to have equal viewing geometry coverage), reveals that for most pixels the NO2 SCD error is reduced in the NO₂-gap approach: the changes lie roughly between -12% and +2%. For clear-sky pixels the distribution of the SCD error changes peaks at about -0.5% for the orbits of 2009 and 2019, i.e. when solar activity is low, with a frequency a 10th of the peak-frequency for a change of -5.5%. For the high-activity years 2014 and 2024 the peak of the distribution lies at about -1.5% and a frequency a 10th of the peak-frequency is found for a change of -9%. For the 2005 orbit, a year of medium solar activity, the peak lies at roughly the same change but the tail is somewhat longer: a frequency a 10th of the peak-frequency is found at -10%. In other words, for low-activity years the SCD error changes of clear-sky pixels have a narrower distribution than for high-activity years. The reverse is the case for cloudy pixels, and for these pixels the peaks lie between -1.5% and -0.5% for all years.

The changes of GCD values for these Atlantic Ocean pixels (which in general have low GCD values to begin with) have a wide distribution, roughly between -15% and +10% for most clear-sky pixels, with a peak at about -0.5%, with only a little difference between low- and high-activity years. For cloudy pixels the GCD appears to increase a little on average: the changes range from about -10% to +15%, with peaks around +1% to +2%.

Since most of the NO2 over the oceans, away from emission sources, is found in the stratosphere, a change in the SCD in those regions will primarily lead to changes in stratospheric NO2. For the vast majority of the grid cells the change of the stratospheric column is in the range -5% (-2 µmol m⁻² or 1.2×1014 molec. cm⁻²) to 0%; cf. the top panel of Fig. . For some individual grid cells the changes may be a bit larger, while for very few grid cells stratospheric NO2 may increase a little. Most of the change is found in the latitude range [-40°:+40°], the same range where the largest changes in SCD and SCD error occur.

Since tropospheric NO2 column values over oceans are usually small and over land they can vary quite a bit, it is best just to consider absolute differences; cf. the bottom panel of Fig. . For by far most clear-sky water grid cells the tropospheric column decreases: average changes are between -2.0 and +0.5 µmol m⁻², with a peak around -1.0 µmol m⁻². Clear-sky land scenes and all cloudy scenes, on the other hand, show an overall increase of the tropospheric column: average changes are between -0.5 and +2.0 µmol m⁻². Some individual grid cells show much larger (monthly average) changes though: between -20 and +15 µmol m⁻² for clear-sky scenes, while for cloudy scenes the changes may range between -40 and +40 µmol m⁻² (2.4×1015 molec. cm⁻²).

On average we expect that the impact on tropospheric columns is small, since the data assimilation will remove average biases. The lower stratospheric columns above tropical seas are transported over land, as is particularly visible over Eastern Asia and over South-East USA and Mexico (top panel of Fig. ), where tropospheric columns will increase since the SCD over land remains more or less the same. Since over polluted areas the AMF is much smaller than the stratospheric NO2, tropospheric columns may increase more than the stratospheric columns decrease. The data assimilation with the NO₂-gap retrieval results reduces the entire column over oceans, leading to a small decrease of the tropospheric columns there.

Routine validation of TROPOMI tropospheric, stratospheric and total column data with ground-based measurements is being carried out by the Validation Data Analysis Facility (VDAF, https://mpc-vdaf.tropomi.eu/; last access: 15 June 2026), with support from the S5P Validation Team (S5PVT), which issues Quarterly Validation Reports, such as .

The VDAF data of a given station could be compared to the new results by selecting the same ground pixel from the orbit files, as a repetition of the validation. But that probably does not provide clear answers, given that (a) ground-based measurements are not available on each day of the two months, (b) in view of the spin-up the first seven days of each months need to be skipped, and (c) a large day-to-day variation is observed in the validation results, which is larger than the differences discussed here. Instead it seems a better idea to considered the data from the full-window and NO₂-gap retrievals at the VDAF locations in the gridded data.

The results of this comparison are shown in Fig.  in the form of monthly averages of daily absolute differences, where vertical dashed lines separate the three groups of stations for the validation of the stratospheric (15 locations; left), total (75 locations; middle) and tropospheric (8 locations; right) column; a few locations at high latitudes have no data in the local winter month.

For most locations, the average SCD error (ΔNs; top panel) is reduced by about 0.1 µmol m⁻² (0.6×1013 molec. cm⁻²) or about 1 %; the standard deviation of the averaging is smaller than the average for most stations. These reductions are quite small, because the stations are located on land, where the impact of the NO₂-gap approach is small. The largest change in ΔNs occurs for the first stratospheric column station (Bauru, Brazil): -0.6 (-0.4) µmol m⁻² for the month July 2023 (January 2024), or -5.8% and -3.7%, respectively.

For that station, the average GCD column (Nvgeo; 2nd panel) goes down by 2.0 (1.3) µmol m⁻² in July 2023 (January 2024), or about -3.3 % for both months, while the third stratospheric column station (Dumont d'Urville, Antartica) shows a decrease of Nvgeo by 1.3 µmol m⁻² in January 2024. For most other stations, the change in Nvgeo is between -1% and +1%.

The average stratospheric column (Nvstrat; 3rd panel) decreases for almost all stations, from -0.2 to -1.0 µmol m⁻² (0.6×1014 molec. cm⁻², or up to -2%), with a standard deviation lower than 0.3 µmol m⁻², i.e. the decrease of Nvstrat is fairly robust. The 14th stratospheric column station (St. Denis, Reúnion) shows the largest decrease: -1.9 µmol m⁻² in January 2024 (about -4.5%), followed by the 47th total column station (Mauna Loa, Hawaï): -1.6 µmol m⁻² in January 2024 (about -5.1%). As the routine validation mentioned above shows, TROPOMI slightly underestimates the stratospheric column, but those results are latitude dependent. with a possible small overestimation in the tropics where the NO₂-gap approach is most prominent. It looks like the NO₂-gap approach reduces the latitude dependency a little, but the impact on the biases is difficult to estimate in view of the large uncertainties in the validation comparisons.

The average tropospheric column (Nvtrop; 4th panel) of the MAX-DOAS stations – all of which lie on the Northern hemisphere – does not change much and the same holds for most of the stratospheric column stations. For the total column stations the change of Nvtrop has a quite varied distribution, with little to no change for some locations and changes +4.0 to +6.0 µmol m⁻² (3.6×1014 molec. cm⁻²) for other locations. Given that the tropospheric column values for some stations are small, relative changes can be large, but for most stations the relative change is less than ±15%.

The average total column (Nvtotal; 5th panel), i.e. the sum of the tropospheric and total column, shows changes similar to those in the Nvtrop.

All in all the changes in the vertical columns are on average small and are not likely to affect the main conclusions of the VDAF validation reports.

As mentioned at the beginning of Sect. , unexpectedly large TROPOMI tropospheric NO2 columns over Tibetan lakes, attributed by to sources in those lakes, are likely due to unreliable NO2 slant column retrievals , as indicated by the presence of broad-band structures in the fit residuals and large negative water vapour (H2Ovap) coefficients over those lakes. For that study, orbit 08511 of 5 June 2019 was selected – the first orbit in June 2019 that has fully clear-sky pixels over two major lakes: Lake Siling and Lake Nam, but also other lakes in and around Tibet were investigated. For this paper, we focus on those two large lakes (located at about 4.5–4.7km altitude), as well as on Issyk-Kul in Kyrgyzstan (at about 1.6km altitude), as these cover multiple TROPOMI ground pixels.

The top panel of Fig.  shows the fit residual of a pixel over Lake Siling. Like the residuals over the Atlantic Ocean, shown in Fig. , there are broad-band structures in the residual above about 430nm, but there are striking differences: the peak around 430nm that lead to the NO₂-gap approach is much less pronounced here, the “downward wave top” between 430 and 440nm is much deeper, and there is a strong negative “peak” at about 442.7nm (indicated by an arrow). That peak can be attributed to the fact that the DOAS fit has, in order to minimise the residual, among others resulted in a strongly negative H2Ovap coefficient of -1.419±0.280×103molm-2 for this example, as opposed to an average of +0.235×103molm-2 outside the lake.

Both the broad-band structures and the large negative H2Ovap coefficient were tell-tale signs to conclude that the higher GCD values over the lakes (0.71µmolm-2 on average), compared to surrounding values (0.66µmolm-2 on average; cf. the maps in ), are probably due to unrealiable fit results rather than due to NO2 emissions from the lakes: since stratospheric NO2 is more or less constant over the short distances involved here, any elevation in the retrieved SCD value will end up as an enhancement of the tropospheric NO2 column.

Residuals of other ground pixels over Lake Siling, Lake Nam and Lake Issyk-Kul look similar, with some difference in the details of the broad-band structures and the H2Ovap values. The bottom panel of Fig.  shows for the three lakes the smoothed fit residual averaged over six ground pixels with surface classification “Water” – even in these smoothed versions, the downward peak related to the negative H2Ovap coefficient can be seen.

The broad-band structure between 430 and 440nm is picked up by the runs test: RL>20, as is visible in the maps on the top row of Fig. , and RD<-5 for most pixels. For Lake Siling, the RMS_430 peak is barely visible, while for Lake Nam and Lake Issyk-Kul part of the water pixels have QRMS430≥2.0 (red patches in the bottom row maps of Fig. ).

The lower RMS_430 ratio over these lakes as opposed to the ratio over the Atlantic Ocean indicates that for the lakes the effects of VRS are less important and in some cases apparently absent. Liquid water fit coefficients over the Atlantic Ocean are usually around several metres (cf. top-right panel of Fig. ), whereas for Lake Siling and Lake Issyk-Kul they are around +1m, while Lake Nam has values around -3.5m; the latter is another indication that the DOAS fit is not really going well here. Differences in the overall broad-band structures in the fit residual may be due to the fact that the characteristics of the material dissolved in the water of the lakes differs from what is dissolved in the oceans.

Looking at results for the three lakes when using the NO₂-gap fit introduced above reveals that for Lake Siling the changes are small and erratic: for some pixels the RMS and SCD error and the GCD value go down by one or two percent, while for other lake pixels they go up a little. For Lakes Nam and Issyk-Kul, the RMS and SCD error appears to go down by five to ten percent, and the GCD value by one to four percent. In other words, the NO₂-gap approach improves the fit quality somewhat but does not solve the issue of the observed bias in the slant column values over these lakes. To solve the bias additional reference spectra, describing the characteristings of the material dissolved in lakes, need to be added to the fit, but such spectra are currently not known.

Several DOAS applications include an intensity offset correction (IOC for short), constant or linear in wavelength, to improve the retrievals in some spectral ranges. This correction has been implemented in the TROPOMI NO2 processor in the form of an addional term to Eq. (): 8Rmod(λ)=…+∑cmλmE0(λ),m=0,1,…,noff with cm fit parameters; in most applications noff=0 or 1. The option has, however, not been turned on, mainly because the precise physical origin of such an intensity offset is not known – it is thought to be related to instrumental issues (e.g. incomplete removal of stray light or dark current in Level-1b spectra, neither of which is deemed necessary for TROPOMI measurements) and/or atmospheric issues (e.g. incomplete removal of Ring spectrum structures and VRS in clear ocean waters); see, for example, , , , .

The blue line in Fig.  shows the smoothed fit residual in case the IOC is turned on in the full-window fit with noff=0: the IOC clearly decreases the 430nm issue and gives close to it a slightly better fit residual, quite similar to the NO₂-gap fit (black dotted line); the shape of the IOC term is indicated by the thin grey line at the bottom of the panel. The change in the NO2 SCD value, SCD error, RMS error and χ2 for the six Atlantic Ocean example pixels are listed in Table  – these changes are similar to but somewhat less than those for the NO₂-gap fit listed in Table .

The IOC is proportional to one over the irradiance and the Fraunhofer peak in the irradiance is much narrower than the 430nm residual issue, hence the IOC can never fully compensate for the issue. In addition to that, the 1/E0(λ) spectrum has additional structures and shows a slope above 440nm, which may be introducing artifacts in the retrieval.

All things considering, the NO₂-gap fit seems to be a physically better justifiable approach than including the IOC in the fit to solve the 430nm issue. Neither of the two approaches, however, are able to deal with the broad-band structures at higher wavelengths.

The NO₂-gap fit was introduced to remove the systematic residual feature around 430nm. This does not deal with issues at higher wavelengths visible in the fit residuals (e.g. Fig. ), which are related on the one hand to wavelength shifts caused by VRS effects () and on the other hand by the presence in the water of, for example, chlorophyll and dissolved organic matter (DOM), which are known to absorb light in the visible region (), and particulate matter that may be scattering UV radiation. Chrolophyll and DOM come in different flavours, each with their own slightly different reference spectrum . It is unclear whether these structures remaining in the fit residual mean that the retrieved NO2 SCD is affected, but the results of the lakes discussed in Sect.  suggest they may well be.

The broad-band structures visible in the fit residual themselves do not represent the missing reference spectrum, because the shape of the residual is the result of DOAS adjusting all fit parameters so as to minimise the residual, i.e. possibly using incorrect fit coefficients – cf. the downward peak in Fig.  due to the large negative water vapour coefficient. Note further that the reference spectra σk(λ) are in the exponent of the modelled reflectance of Eq. (), rather than directly in the residual.

Over relatively small areas like the lakes in Sect. , where one may assume the stratosphere to be more or less constant, one could try to reconstruct the missing reference spectrum by assuming that the fit coefficients found outside the lake are valid over the lake as well, with some sensible assumption of what the liquid water coefficient might be, although it is then unclear what one should assume for the polynomial coefficients. An attempt in that direction falls outside the scope of the present paper. In addition, the approach would not work over oceans, as there are no neighbouring values for the fit coefficients available.