The main focus of this paper is NO2 data derived from measurements by OMI , which are compared to NO2 data from the first GOME-2 instrument and from SCIAMACHY . All three instruments measure the backscattered and direct sunlight in the UV and visible ranges from a sun-synchronous polar orbit.

OMI is aboard the EOS-Aura satellite and has been operating since 2004. The overpass is at 13:40 local time (LT), with the satellite flying south to north on the dayside of the Earth. Individual nadir ground pixels are 13 × 24 km2 at the middle of the swath; the size of the pixels increases towards the edges of the swath. The full swath width is about 2600 km and OMI achieves global coverage each day.

The first GOME-2 instrument is aboard the MetOp-A satellite and has been operating since 2007. The overpass is at 09:30 LT, with the satellite flying north to south on the dayside of the Earth. Individual ground pixels are 40 × 80 km2. The full swath width is about 1920 km and GOME-2 achieves nearly global coverage each day. A second, identical GOME-2 instrument was launched aboard the MetOp-B satellite in 2012. In this paper, GOME-2 refers to the instrument aboard MetOp-A, sometimes referred to as GOME-2A.

SCIAMACHY is aboard the satellite ENVISAT and operated in the period 2002–2012. The overpass was at 10:00 LT, with the satellite flying north to south on the dayside of the Earth. Individual ground pixels were 30 × 60 km2. The full swath width was about 960 km and SCIAMACHY achieved global coverage only once every 6 days, because it measured alternatively in a nadir and limb viewing mode.

The DOAS retrieval technique, described in Sect. , is applied to the backscattered spectra measured by the three satellite instruments to obtain the NO2 slant column density (SCD). The SCD is the integrated concentration of NO2 over light paths from the Sun through the Earth's atmosphere to the satellite, weighted with their relative contribution to the radiance.

The standard OMI NO2 SCD data are calculated at NASA by a processor named OMNO2A. The retrieval results of OMNO2A are input for subsequent processing to determine NO2 vertical column densities (VCDs), e.g. for the DOMINO data product of KNMI (e.g. ; ) and NASA's NO2 Standard Product (SP; e.g. ). For the OMI NO2 retrieval, the selected spectral fitting window is 405–465 nm, wider than the often used 425–450 nm window in order to improve the effective signal-to-noise ratio.

For GOME-2 and SCIAMACHY NO2 SCD data, BIRA-IASB uses a processor based on QDOAS , the multi-platform successor of their WinDOAS package; see e.g.  and . The DOAS fit on GOME-2 and SCIAMACHY data uses almost the same wavelength window: 425.0–450.0 and 426.5–451.5 nm respectively (the small difference between the fit windows is related to instrumental issues). The degree of the DOAS polynomial is 3 for GOME-2 and 2 for SCIAMACHY.

Table  provides an overview of the details of the DOAS retrieval for the OMI, GOME-2 and SCIAMACHY sensors used in this study.

The DOAS () technique matches an analytical function that describes the relevant atmospheric physical processes (scattering, reflection and absorption) to the satellite-measured spectrum. In the OMNO2A setup, the modelled reflectance is expressed in terms of intensities, which leads to a non-linear fit problem and allows the effects of inelastic scattering to be described after a scattering event has occurred: Rmod(λ)=P(λ)⋅exp⁡-∑k=1Nkσk(λ)⋅Nscd,k⋅1+CRingIRing(λ)I0(λ). This physical model contains a low-order polynomial P(λ) of degree Np that represents the slowly varying broad-band absorption, as well as Rayleigh and Mie scattering processes in the atmosphere and smooth surface reflection and absorption effects. Furthermore, the physical model includes the spectrally varying absorption signatures σk(λ) and the slant column amount Nscd,k of relevant absorbers k, notably NO2, ozone (O3) and water vapour (H2Ovap).

The physical model accounts for inelastic Raman scattering of incoming sunlight by N2 and O2 molecules that leads to filling-in of the Fraunhofer lines in the radiance spectrum – the so-called “Ring effect” (see ) – by describing these effects as a pseudo-absorber, that is, by including a Ring reference absorption spectrum along with the molecular absorption terms. In Eq. (), CRing is the Ring fitting coefficient and IRing(λ)/I0(λ) the sun-normalised synthetic Ring spectrum. The term between parentheses in Eq. () describes both the contribution of the direct differential absorption (i.e. the 1) and the modification of these differential structures by inelastic scattering (the +CRingIRing(λ)/I0(λ) term) to the reflectance spectrum.

The DOAS procedure minimises the difference between the measured reflectance spectrum Rmeas(λ) and the modelled spectrum Rmod(λ) within a given wavelength window, in the form of minimisation of a chi-squared merit function. The measured reflectance Rmeas(λ) is determined from the radiance measured at top-of-atmosphere I(λ) and the measured extraterrestrial solar irradiance spectrum I0(λ). Some further details on the OMI NO2 DOAS slant column retrieval, such as the merit function that is minimised and the definition of the RMS error, can be found in Sect. S1 in the Supplement.

The set of reference spectra in the current OMNO2A processing has been introduced in August 2006. Since then a number of improved reference spectra data sets have been reported in the peer-reviewed literature. In addition, the reference spectra used in the current OMNO2A processing have been convolved with the OMI slit function, described by a parametrised broadened Gaussian function , but without taking the wavelength and row dependency (i.e. viewing angle dependency) of the slit function into account.

For these reasons all relevant cross sections are generated anew, based on the latest established absorption spectra, and convolved with the OMI slit function while now taking the wavelength and row dependency of the slit function into account in the form of a row-average slit function. The OMI slit function

 The full set of the OMI slit function – the slit functions for the 60 individual rows as well as the average slit function, both for the visible (350–500 nm) and UV (310–380 nm) wavelength ranges – is available for download via the OMI website at http://www.knmi.nl/omi/research/product/ .

Details of the relevant reference spectra used in the current and forthcoming OMNO2A slant column fit are given in Sect. S4. The updated reference spectra are

solar spectrum Iref(λ), from

The reference spectra labelled “v2006” below refer to those used in the current OMNO2A processor (used in, for example, the DOMINO v2.0 data set), while “v2014” refers to the updated reference spectra. The relation between these labels and the official version numbering of OMNO2A is described in Sect. S5.

The measured solar irradiance spectrum I0(λ) used in the OMI NO2 DOAS fit has been constructed from a yearly average of daily solar irradiance measurements by OMI during 2005 and has an accurate wavelength calibration.

From the start of the OMI mission, the level-1b radiance spectra I(λ) of OMI are given on an initial assigned wavelength grid . This assigned wavelength grid – hereafter referred to as “wcA” – was at the time accurate enough for the NO2 retrieval with OMNO2A. After the onset of the first row anomaly

 See http://www.knmi.nl/omi/research/product/rowanomaly-background.php for an explanation and details.

The NO2 fit results were improved by the introduction of a wavelength calibration in OMNO2A in January 2009. This wavelength calibration determines a wavelength shift for each individual radiance spectrum I(λ) from a fit against the reference solar spectrum Iref(λ), taking the Ring effect into account (cf. ), starting from the assigned wavelength grid wcA. The wavelength calibration in the current OMNO2A processing, called “wcB” hereafter, uses 408.0–423.0 nm as the calibration window. This window was chosen because it covers some distinct Fraunhofer features in the solar spectrum. Due to the construction of the OMI detector, a squeezing or stretching of the wavelengths is unlikely (which is confirmed by ongoing tests on OMI data as preparation for the implementation of a wavelength calibration for TROPOMI which includes the possibility of a squeeze/stretch in the calibration), so that the shift found from the calibration window is representative for the whole NO2 fit window. The relation between the wavelength calibration labels and the official version numbering of OMNO2A is described in Sect. S5.

With the update of the solar reference spectrum Iref(λ) and the Ring radiance spectrum IRing(λ), the wavelength shift determined in calibration window wcB turns out to be different from the shift found in the current OMNO2A setup. This change in the wavelength grid of the level-1b spectra directly improves the fit results: both the RMS and the error on the NO2 SCD are reduced. Using the v2006 reference spectra for NO2, O3 and H2Ovap (and not yet including O2–O2 and H2Oliq), the changes due to the introduction of the new solar and Ring reference spectra in the wcB wavelength calibration, averaged between 60∘ S and 60∘ N over the Pacific Ocean test orbit (see Sect. ), are as follows:

wavelength shift from +0.55 to -3.63 × 10-3 nm

Since the spectral sampling of OMI is about 0.21 nm , a shift of -3.62 × 10-3 nm corresponds to 1.7 % of a wavelength pixel.

Given that the NO2 fit results depend so clearly on the wavelength calibration, it was decided to test a range of calibration windows. Both the starting and end point of the calibration window were varied in steps of 0.5 nm, with a minimum size of 10 nm for the window, over the complete 405–465 nm fit window for a total of 5151 possible calibration windows. The fits were performed on the Pacific Ocean test orbit with all new v2014 reference spectra, including O2–O2 and H2Oliq absorption. From these calculations the “optimal calibration window”, defined as the window that results in the lowest RMS and NO2 error in the subsequent DOAS fit, was found to be 409.0–428.0 nm. This new calibration window, hereafter “wcN”, covers one more distinct Fraunhofer line than wcB (cf. Fig. S4 in the Supplement).

Table  lists the calibration shift and the RMS and NO2 error of the subsequent DOAS fit for calibration windows wcB and wcN. For comparison, Table  also gives the fit results using two other calibration windows: one spanning the full fit window (“wcF”) and one more or less at the centre of the fit window (“wcC”). For the other orbits of the same day (not shown), minimal RMS is achieved either in the wcN window or in a slightly different window, but the difference between that RMS and the RMS of wcN is less than 0.05 %. Hence, wcN is selected as the optimal wavelength calibration window to be implemented in the new version of the OMNO2A processor.

For the comparison of the current and updated OMNO2A spectra fit results, the OMI orbit over the Pacific Ocean on 1 July 2005 (orbit number 05121) is used. Other orbits of this day and of some other days in 2005 are used to evaluate the robustness of the findings. Only ground pixels with a solar zenith angle less than 75∘ are considered; in most comparisons using orbit averages, the data are limited to the latitude range [-60∘:+60∘]. Since stratospheric NO2 is the main focus of this study, no filtering of cloudy pixels is applied.

Table  lists the NO2 SCD, the NO2 SCD error and the RMS error values for the step-by-step improvements listed above. The first case in the table represents the current OMNO2A settings for the SCDs used in the DOMINO v2.0 and NASA SP v2.1 NO2 data products; case 2 represents the improved wavelength calibration; and case 4 the implementation of all updates together, i.e. the updated “v2” version of OMNO2A. Figure  shows the absolute values of and differences between cases 0, 2 and 4 in Table  of the RMS error and the NO2 SCD for all 15 orbits of 1 July 2005.

These results show that the wavelength calibration update (case 2) leads to large improvements in the spectral fitting of OMI NO2 and the updates of the relevant reference spectra lead to smaller yet still significant improvements of the fit. The lower panels indicate that differences in RMS and NO2 SCD vary only a little from orbit to orbit. When averaging the 15 orbit averages and giving changes w.r.t. the case-0 averages, the conclusions are that

the wavelength calibration updates reduce the RMS by 23 % and the SCD by 0.85 × 1015 molec cm-2,

The latitudinal dependency of the changes in the NO2 SCD averaged over the 15 orbits is shown in Fig. . The change in NO2 SCD resulting from the update of the wavelength calibration (blue line with squares) shows little variation with latitude, indicating that the imperfect wavelength calibration likely represents an additive offset of 0.85 ± 0.04 × 1015 molec cm-2 in the current “v1 OMNO2A” retrieval.

However, the change in NO2 SCD due to the update of the trace gas reference spectra and the inclusion of absorption by O2–O2 and H2Oliq (black line with triangles in Fig. ) depends clearly on latitude in absolute numbers and as a percentage of the NO2 SCD: the change ranges from 0.1 × 1015 molec cm-2 (3 %) in the tropics to 0.8 × 1015 molec cm-2 (5 %) at high latitudes. The change in the NO2 SCD increases with latitude and reflects the inclusion of O2–O2 absorption, which increases poleward as shown by the green short-dashed line in Fig. .

Overall, the improved OMNO2A NO2 SCD is reduced by 1.0 to 1.8 × 1015 molec cm-2 (10 to 16 %), the NO2 SCD error by 0.2 to 0.3 × 1015 molec cm-2 (16 to 30 %) and the RMS error by 24 to 35 %, depending on latitude.

The above settings of case 0 and case 4 have been evaluated on the 4 test days used in the EU FP7 project QA4ECV

 See http://www.qa4ecv.eu/.

The spectral residual of the NO2 retrieval describes the unexplained portion of the measured spectrum after a selected set of absorption signatures is accounted for in the fit model. Figure  shows the spectral residual of two cloud-free pixels along row 29 (0-based) of the Pacific Ocean test orbit: pixel 425 and pixel 592 using the updated reference spectra without (case 3, red solid lines) and with (case 4, blue dashed lines) taking absorption of O2–O2 and H2Oliq into account. Pixel 425 is over clear open ocean water with a low chlorophyll concentration

 Chlorophyll concentrations are extracted from NASA's daily assimilated total chlorophyll data sets with the Giovanni online data system from NASA GES DISC; data file:  NOBM_DAtot.CR.data.01Jul2005.G3.output.txt.

Figure  shows that the residual of pixel 425 has a clear structure in the range 445–465 nm in case liquid water absorption is not accounted for, while this structure does not appear for pixel 592. If H2Oliq is included in the fit, the residual of pixel 425 is much reduced (the RMS decreases by -35 %), while there is hardly any change in the residual of pixel 592 (by -2 %). For both pixels the NO2 SCD reduces by about 6 % and the retrieved H2Oliq fit coefficients are physically meaningful: for pixel 425 the H2Oliq fit coefficient is 10.49 m and for pixel 592 it is 0.83 m.

Figure  shows the retrieved H2Oliq coefficient (left axis, red solid line) as a function of latitude for all ground pixels of detector row 29 for which a chlorophyll concentration is available. For comparison the graphs also shows the chlorophyll concentration and the cloud fraction for the same pixels (right axis); cloudiness clearly leads to lower H2Oliq coefficients, as expected. The inset of Fig.  shows the relationship between the H2Oliq coefficient and the chlorophyll concentration. The graph makes a distinction between the ground pixels in the latitude range 40∘ S to 40∘ N (red crosses) and outside that range (green circles). Pixels at latitudes above 40∘ N have chlorophyll concentration >0.3 mg m-3 and for that reason low H2Oliq coefficients. Pixels at latitudes <40∘ S at high solar zenith angle (above 70∘) have low H2Oliq coefficients (below about 2 m) even though chlorophyll concentrations are low (<0.2 mg m-3).

Figure  shows a global map of the H2Oliq coefficient retrieved from all OMI orbits of 1 July 2005. Open water areas are clearly visible on the map and land/sea boundaries show up sharply in areas like the Mediterranean Sea, the Gulf of Mexico, around Madagascar and the east coast of South America. Along the west coasts of South America, North America and Africa, for example, the H2Oliq coefficient is very low, consistent with high chlorophyll concentrations there. Note that since the processing is not optimised for the retrieval of the H2Oliq coefficient, it is not possible to say how accurate the coefficient is, but overall its values appear realistic. Positive H2Oliq fit coefficients over areas with little or no liquid water absorption, such as over land or cloudy scenes, are small.

The inclusion of the absorption of H2Oliq and the O2–O2 collision complex in the NO2 fit is justified since their absorption is known to affect the radiance I(λ) – unless their inclusion would reduce the quality of the NO2 fit, which is not the case. Figure  shows the effect of including O2–O2 and H2Oliq in the retrieved O3 SCDs. Without either of the two additional absorbers, ozone slant columns are negative in the regions where absorption in open water is taking place. Adding both absorbers brings the retrieved O3 SCD close to the values given in the official OMI ozone SCD data product OMDOAO3; the improvement is mostly due to including H2Oliq absorption.

Including O2–O2 absorption but not H2Oliq absorption does not result in realistic O3 SCD values. Furthermore, the retrieved O2–O2 SCD values appear realistic compared to the values given in the official OMI cloud data product OMCLDO2 if H2Oliq is included in the fit. Including O2–O2 absorption has a small effect on the retrieved H2Oliq coefficient (bottom-right panel in Fig. ).

In summary, (a) including liquid water absorption leads to significant improvements in the NO2 retrieval fit for pixels over clear open waters, without affecting other pixels, results in physically meaningful H2Oliq and O3 absorption coefficients; and (b) simultaneously including O2–O2 absorption results in realistic O2–O2 SCDs and improves the fit, especially if light paths are long.

Since the OMI, SCIAMACHY and GOME-2 spectral fits have been done with different fitting approaches and fitting windows (cf. Table ), the sensitivity of the NO2 SCD to the spectral fitting approach is studied here. Such estimates are important for satellite intercomparisons and the generation of long-term seamless multi-sensor data records such as the QA4ECV project. The flexible QDOAS package (version 2.105, May 2013), which provides a linear fit approach (cf. the details on DOAS fitting in Sect. S1 in the Supplement), is used for this study with the v2014 reference spectra on the OMI Pacific Ocean test orbit.

Figure  shows that the OMNO2A and QDOAS processors, both applied in the 405–465 nm window, result in small differences in the NO2 SCDs of -0.2 to +0.1 × 1015 molec cm-2. The agreement between these two is therefore quite good considering there are several differences between the processors: the fitting method differs, the Ring effect is included differently and the wavelength calibration of QDOAS differs from the OMNO2A wavelength calibration.

QDOAS has the option to apply a non-linear intensity fitting method instead of the linear optical density fitting method Eq. (S4), similar to the OMNO2A non-linear fitting method Eq. () but with the Ring effect treated as a pseudo-absorber; cf. Eq. (S5). The red line with open circles in Fig.  shows the difference between the results of this approach and the OMNO2A results, which appears to be larger than the difference with the linear fitting method of QDOAS: about -0.3 × 1015 molec cm-2, almost independent of latitude.

The SCIAMACHY and GOME-2 NO2 data are retrieved in the fit window 425–450 nm, using a third-degree polynomial. The difference between the OMI orbit processed with QDOAS in this manner and the OMNO2A data is shown by the blue line with squares in Fig. . At +0.2–0.6 × 1015 molec cm-2, the difference is clearly larger than for the OMNO2A fit window.

In their study to improve the GOME-2 NO2 retrieval, apply the extended fit window 425–497 nm. The black line with triangles in Fig.  shows that OMNO2A is higher by 0.4–0.9 × 1015 molec cm-2 than applying a linear fit in this extended fit window.

The NO2 SCD differences in Fig.  show a clear latitudinal variation around latitudes 20∘ S and 20∘ N – areas of the Pacific Ocean where absorption in liquid water plays a role (cf. Sect. ) – for the three curves where QDOAS was used in the linear fitting mode, while for QDOAS's non-linear fitting mode the differences with OMNO2A are nearly independent of latitude. This may indicate that the linear fitting method deals differently with the polynomial-like signature of H2Oliq and/or O3 and/or O2–O2 absorption (cf. Fig. S6) than the non-linear fitting method, which is possibly due to interference of the reference spectra with the DOAS polynomial (a few further remarks regarding this issue are given in Sect. S6).

In summary, the selection of the fit window (and with that the degree of the polynomial) and the fitting method determines the NO2 fit results, i.e. there is no “true” NO2 SCD but at most a fit window and fit method specific slant column value. Judging from the curves in Fig. , the variability in the fit window and fit method selection introduces differences in the retrieved NO2 SCD between -0.3 and +0.6 × 1015 molec cm-2 (i.e. up to 0.2 × 1015 molec cm-2 in terms of the NO2 VCD). To better understand the “true” NO2 SCD, a comparison with measurements that do not depend on the DOAS technique is needed.

All OMI NO2 slant column data of the year 2005 have been reprocessed to evaluate the consistency of the proposed improvements. Figure  shows the current (case 0) data on the top row and the difference between the current and update data on the bottom row as a function of the updated (case 4) data. The linear relationship between the NO2 SCD of the current and updated retrieval in the top-right panel shows an offset, reflecting the improved wavelength calibration. The slope of the linear fit is 1.04, which implies that high NO2 SCD values will decrease more than low SCDs but not by much. This suggests that the effect of the updated retrieval settings on high (tropospheric) NO2 SCDs will be small compared to the overall decrease of the NO2 values.

Figure  shows a map of the monthly average gridded NO2 slant columns of the updated (case 4) data and the corresponding difference with the current (case 0) data for July 2005. The RMS error data for the same month are shown in Fig. . Similar maps of the month of January 2005 are shown in Sect. S7 in the Supplement. In some areas with high NO2 levels related to pollution, the decrease of the NO2 slant column is relatively large, such as for the Highveld area in South Africa in Fig.  for July. The average change in the RMS error shown in the lower panel of Fig.  is about 0.33 × 10-4. For clear-sky pixels only (not shown), the decrease of the RMS is much smaller, namely 0.14 × 10-4 on average, while for cloudy pixels (not shown) the decrease is much larger: 0.80 × 10-4 on average. Notably above clouds, the quality of the fit is evidently improved by the changes made to the OMNO2A retrieval.

Section S7 in the Supplement shows monthly average maps for July 2005 similar to Figs. – of the results of the other fit parameters.