Improved spectral fitting of nitrogen dioxide from OMI in the 405 – 465 nm window

An improved nitrogen dioxide (NO2) slant column density retrieval for the Ozone Monitoring Instrument (OMI) in the 405–465 nm spectral region is presented. Since the launch of OMI on board NASA’s EOS-Aura satellite in 2004, differential optical absorption spectroscopy (DOAS) retrievals of NO2 slant column densities have been the starting point for the KNMI DOMINO and NASA SP NO2 vertical column data as well as the OMI NO2 data of some other institutes. However, recent intercomparisons between NO2 retrievals from OMI and other UV/Vis and limb spectrometers, as well as ground-based measurements, suggest that OMI stratospheric NO2 is biased high. This study revises and, for the first time, fully documents the OMI NO2 retrieval in detail. The representation of the OMI slit function to convolve high-resolution reference spectra onto the relevant spectral grid is improved. The window used for the wavelength calibration is optimised, leading to much-reduced fitting errors. Ozone and water vapour spectra used in the fit are updated, reflecting the recently improved knowledge of their absorption cross section in the literature. The improved spectral fit also accounts for absorption by the O2–O2 collision complex and by liquid water over clearwater areas. The main changes in the improved spectral fitting result from the updates related to the wavelength calibration: the RMS error of the fit is reduced by 23 % and the NO2 slant column by 0.85× 10 molec cm, independent of latitude, solar zenith angle and NO2 value. Including O2–O2 and liquid water absorption and updating the O3 and water vapour cross-section spectra further reduces NO2 slant columns on average by 0.35× 10 molec cm, accompanied by a further 9 % reduction in the RMS error of the fit. The improved OMI NO2 slant columns are consistent with independent NO2 retrievals from other instruments to within a range that can be explained by photochemically driven diurnal increases in stratospheric NO2 and by small differences in fitting window and approach. The revisions indicate that current OMI NO2 slant columns suffered mostly from an additive positive offset, which is removed by the improved wavelength calibration and representation of the OMI slit function. It is therefore anticipated that the improved NO2 slant columns are most important to retrievals of spatially homogeneous stratospheric NO2 rather than to heterogeneous tropospheric NO2.


Introduction
Nitrogen dioxide (NO 2 ) and nitrogen oxide (NO) -together usually referred to as nitrogen oxides (NO x = NO + NO 2 )are important trace gases in the Earth's atmosphere.They enter the atmosphere due to anthropogenic (e.g.fossil fuel combustion, biomass burning) and natural (e.g.microbiological processes in soils, wild fires, lightning) processes.Over remote regions NO 2 is primarily located in the stratosphere.Stratospheric NO 2 columns range from about 2 × 10 15 to Published by Copernicus Publications on behalf of the European Geosciences Union.
7 × 10 15 molec cm −2 between the tropics and high latitudes.For polluted regions, up to 90 % of the total NO 2 column may be located in the troposphere.Tropospheric NO 2 columns over polluted areas are usually considerably higher, in places even higher than 30 × 10 15 molec cm −2 .For typical levels of OH, the lifetime of NO x in the lower troposphere is less than 1 day (e.g.Schaub et al., 2007;Beirle et al., 2011).
Boundary layer NO 2 directly affects human health (WHO, 2003).In addition, nitrogen oxides are essential precursors for the photochemical formation of ozone (Sillman et al., 1990): they influence concentrations of OH and thereby influence the lifetime of methane (Fuglestvedt et al., 1999) and other gases.NO 2 itself is a minor greenhouse gas, but the indirect effects of NO 2 on global climate change are probably larger, with a presumed net cooling effect mostly driven by oxidation-fuelled aerosol formation (Shindell et al., 2009).Stratospheric NO 2 originates mainly from oxidation of N 2 O in the middle stratosphere, which leads to NO x , which in turn acts as a catalyst for ozone destruction (Crutzen, 1970;Hendrick et al., 2012).Stratospheric NO x can also suppress ozone depletion by converting reactive chlorine and hydrogen compounds into unreactive reservoir species (such as ClONO 2 and HNO 3 ; Murphy et al., 1993).
The important role of NO 2 in both troposphere and stratosphere requires monitoring of its concentration distribution on a global scale.Observations from satellite instruments provide global coverage complementary to sparse measurements by ground-based and in situ (balloon, aircraft) instruments.NO 2 column densities have been retrieved using the differential optical absorption spectroscopy (DOAS) technique from space since the mid-1990s from data acquired by the nadir-viewing UV/Vis backscatter instruments GOME (Burrows et al., 1999), SCIAMACHY (Bovensmann et al., 1999), OMI (Levelt et al., 2006) and the GOME-2 instruments (Munro et al., 2006) aboard MetOp-A and MetOp-B.TROPOMI (Veefkind et al., 2012), scheduled for launch in 2016, will extend the record of these observations.The retrieval of NO 2 from satellite measured spectra with DOAS is certainly possible but not easy: the structure of the NO 2 differential absorption is weak and there are interfering signals from the surface, atmosphere and instrumental issues.Most retrievals of NO 2 concentrations are performed in the visible range between 400 and 500 nm, taking into account other absorbers and processes relevant in this wavelength range.Early satellite retrievals of NO 2 focused on the dominant absorbers NO 2 , ozone and water vapour, as well as rotational Raman scattering (the so-called "Ring effect").Recent years have shown continuous improvements in the NO 2 retrieval by accounting for weaker absorbers, notably the O 2 -O 2 collision complex and liquid water.
This paper describes a revision of NO 2 slant column retrieval from level-1b spectra measured by OMI since 2004, performed by a processor named OMNO2A.The study was prompted by the observation, reported first by N. Krotkov at the EOS-Aura meeting in October 2012 (Krotkov et al., 2012), that OMI stratospheric NO 2 concentrations are systematically higher than those derived from SCIAMACHY and GOME-2 measurements by 0.5-1 × 10 15 molec cm −2 , after accounting for the daytime increase in stratospheric NO 2 (Dirksen et al., 2011).Recently, Belmonte-Rivas et al. (2014) confirmed the high bias in OMI stratospheric columns compared to an ensemble of stratospheric NO 2 retrievals from satellite-based limb-sounding sensors.Section 3 presents a further comparison of OMI, SCIAMACHY and GOME-2 data, as well as a comparison using groundbased measurements at the Jungfraujoch station, to confirm the high bias in OMI NO 2 data.
The revision of the OMNO2A settings and input is further motivated by a number of issues regarding the absorption reference spectra (Sect.4.1): (a) the need to update the spectra of ozone and water vapour; (b) the need to account for the wavelength and row dependency of the OMI slit function in the convolution of the spectra; (c) the need to investigate whether including absorption by O 2 -O 2 (so far omitted from OMNO2A; cf.Bucsela et al., 2006) and liquid water (cf.Richter et al., 2011;Lerot et al., 2010) improves the NO 2 retrieval results.In addition, the effects on the DOAS NO 2 retrieval of the wavelength calibration of the OMI radiance spectra, introduced in OMNO2A following the first appearance of the so-called row anomaly in 2007 but not yet evaluated, has been investigated and the calibration settings have been optimised (Sect.4.2).Lastly, it was recognised that it is important for users of the OMI NO 2 data to document the essential elements, both the current and the updated, of the slant column retrieval in one easily referable paper.

UV/Vis satellite-based NO 2 observations
The main focus of this paper is NO 2 data derived from measurements by OMI (Levelt et al., 2006), which are compared to NO 2 data from the first GOME-2 instrument (Munro et al., 2006) and from SCIAMACHY (Bovensmann et al., 1999).All three instruments measure the backscattered and direct sunlight in the UV and visible ranges from a sunsynchronous 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 km 2 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 km 2 .The full swath width is about 1920 km and GOME-2 achieves nearly global coverage each day.A sec- 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 km 2 .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.2.2, is applied to the backscattered spectra measured by the three satellite instruments to obtain the NO 2 slant column density (SCD).The SCD is the integrated concentration of NO 2 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 NO 2 SCD data are calculated at NASA by a processor named OMNO2A.The retrieval results of OMNO2A are input for subsequent processing to determine NO 2 vertical column densities (VCDs), e.g. for the DOMINO data product of KNMI (e.g.Boersma et al., 2007Boersma et al., , 2011;;Dirksen et al., 2011) and NASA's NO 2 Standard Product (SP; e.g.Bucsela et al., 2006Bucsela et al., , 2013)).For the OMI NO 2 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 NO 2 SCD data, BIRA-IASB uses a processor based on QDOAS (Danckaert et al., 2012), the multi-platform successor of their WinDOAS package; see e.g.Van Roozendael et al. (2006) and Lerot et al. (2009).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 SCIA-MACHY.
Table 1 provides an overview of the details of the DOAS retrieval for the OMI, GOME-2 and SCIAMACHY sensors used in this study.

DOAS retrieval of NO 2 slant column densities
The DOAS (Platt, 1994;Platt and Stutz, 2008) 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: This physical model contains a low-order polynomial P (λ) of degree N p 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 σ k (λ) and the slant column amount N scd,k of relevant absorbers k, notably NO 2 , ozone (O 3 ) and water vapour (H 2 O vap ).
The physical model accounts for inelastic Raman scattering of incoming sunlight by N 2 and O 2 molecules that leads to filling-in of the Fraunhofer lines in the radiance spectrum -the so-called "Ring effect" (see Grainger and Ring, 1962;Chance and Spurr, 1997) -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. ( 1), C Ring is the Ring fitting coefficient and I Ring (λ)/I 0 (λ) the sun-normalised synthetic Ring spectrum.The term between parentheses in Eq. (1) describes both the contribution of the direct differential absorption (i.e. the 1) and the modification of these differential structures by in- elastic scattering (the +C Ring I Ring (λ)/I 0 (λ) term) to the reflectance spectrum.
The DOAS procedure minimises the difference between the measured reflectance spectrum R meas (λ) and the modelled spectrum R mod (λ) within a given wavelength window, in the form of minimisation of a chi-squared merit function.The measured reflectance R meas (λ) is determined from the radiance measured at top-of-atmosphere I (λ) and the measured extraterrestrial solar irradiance spectrum I 0 (λ).Some further details on the OMI NO 2 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.

Intercomparisons of stratospheric NO 2 columns
NO 2 data from OMI, GOME-2 and SCIAMACHY are evaluated for 2007.Stratospheric NO 2 concentrations are best detected over the Pacific Ocean, where tropospheric contributions to the NO 2 column are small in the absence of substantial sources of pollution.The Pacific Ocean area is defined here as the area from 60 • S to 60 • N and from 140 to 180 • W. DOMINO v2.0 data are used for OMI (Boersma et al., 2011), TM4NO2A v2.1 for GOME-2 and TM4NO2A v2.0 for SCIAMACHY (Boersma et al., 2004).
Figure 1 shows the monthly average stratospheric NO 2 column for the three instruments and their mutual differences as a function of latitude for March 2007; for other months (not shown) the comparisons look quite similar.The OMI stratospheric columns are clearly higher than those of GOME-2 by about 1.0 × 10 15 molec cm −2 , consistent with Belmonte-Rivas et al. (2014), who reported a similar high Figure 1 shows that there is only a weak variability of the intra-sensor differences with latitude and that the differences are similar to within 0.2 × 10 15 molec cm −2 .This weak variability with latitude and independence of the month indicates that the differences between the instruments is dominated by an additive offset.Table 2 lists the annual averaged 2007 intra-sensor differences over the Pacific Ocean area.The difference of 1.1-1.3× 10 15 molec cm −2 between OMI (overpass at 13:40 LT) and the two mid-morning sensors is considerably larger than the increase of stratospheric NO 2 between the respective measurement times.Photochemical models suggest a latitude-dependent increase of 10-30 % in stratospheric NO 2 between 09:30 and 13:40 LT.This increase reflects the production of NO 2 from N 2 O 5 photodissociation and corresponds to an increase of 0.1-0.6 × 10 15 molec cm −2 (Dirksen et al., 2011;Belmonte-Rivas et al., 2014).
The comparison of data from the ground-based SAOZ and FTIR instruments at the Jungfraujoch station with satellite data by Hendrick et al. (2012) was repeated, now also including OMI data and extending the GOME-2 and SCIA-MACHY data sets to the end of 2012 (see Sect.S2 in the Supplement).The results of the comparisons also strongly suggest that OMI stratospheric NO 2 is biased high.Since the air-mass factor calculations for NO 2 in the stratosphere are straightforward (with an error of less than 1 %), the high bias in OMI stratospheric columns originates from the slant column retrieval.As a result of this finding, the details of the OMI NO 2 spectral fitting OMNO2A were revisited.
4 Improvements to the OMI NO 2 retrieval

Reference spectra
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 (Dirksen et al., 2006), 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 function1 and the implementation of the convolution are given in Sect.S3 in the Supplement.
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 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.

Other absorption features
Over tropical forests, detectable contributions from glyoxal (CHOCHO) have been reported, and its retrieval requires the inclusion of NO 2 absorption (e.g.Lerot et al., 2010).Conversely, however, glyoxal absorption is only a very minor interference for NO 2 absorption, so that it can be safely neglected.Richter et al. (2011) have investigated absorption signatures attributable to sand, e.g. over deserts, but this signature is broadband in the OMI NO 2 fit window (any structure in the signature lies well beyond the fit window) and is therefore not accounted for here.
Absorption by vibrational Raman scattering (VRS; e.g.Vasilkov et al., 2002;Vountas et al., 2003) is known to play a role over open waters and thus may have an impact on the NO 2 retrieval; however, it is unclear whether including VRS improves the retrieval results, partly because its signature is apparent over areas where it certainly is not playing a role, e.g. over deserts (A. Richter, personal communication, 2014).In addition, the VRS signature does not seem to be independent from the signature of liquid water absorption (Peters et al., 2014).For these reasons, absorption by VRS is not investigated here.

Wavelength calibration
The measured solar irradiance spectrum I 0 (λ) used in the OMI NO 2 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 (Voors et al., 2006).This assigned wavelength grid -hereafter referred to as "wcA" -was at the time accurate enough for the NO 2 retrieval with OMNO2A.After the onset of the first row anomaly2 in June 2007 and the subsequent growth of this issue after May 2008, however, the assigned wavelength grid appeared to be less accurate and, consequently, hampered sufficiently accurate NO 2 retrievals in all rows, including those not affected by the row anomaly.
The NO 2 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 I ref (λ), taking the Ring effect into account (cf.Voors et al., 2006), starting from the assigned wavelength grid wcA.The wavelength calibration in the current OMNO2A processing, called "wcB" hereafter, uses 408.0-423.0nm 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 wave- With the update of the solar reference spectrum I ref (λ) and the Ring radiance spectrum I Ring (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 NO 2 SCD are reduced.Using the v2006 reference spectra for NO 2 , O 3 and H 2 O vap (and not yet including O 2 -O 2 and H 2 O liq ), 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. 5.1), are as follows: -wavelength shift from +0.55 to −3.63 × 10 −3 nm -RMS error from 1.39 to 1.15 × 10 −4 (−17.4 %) -NO 2 error from 1.29 to 1.17 × 10 15 molec cm −2 (−9.2 %) -NO 2 SCD from 8.54 to 8.04 × 10 15 molec cm −2 (−5.8 %).
Since the spectral sampling of OMI is about 0.21 nm (Levelt et al., 2006), a shift of −3.62 × 10 −3 nm corresponds to 1.7 % of a wavelength pixel.
Given that the NO 2 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 O 2 -O 2 and H 2 O liq absorption.From these calculations the "optimal calibration window", defined as the window that results in the lowest RMS and NO 2 error in the subsequent DOAS fit, was found to be 409.0-428.0nm.This new calibration window, hereafter "wcN", covers one more distinct Fraunhofer line than wcB (cf.Fig. S4 in the Supplement).Table 3 lists the calibration shift and the RMS and NO 2 error of the subsequent DOAS fit for calibration windows wcB and wcN.For comparison, Table 3 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.

Uncertainty in NO 2 SCD related to calibration
Figure 2 shows the relationship between the RMS error (horizontal axis) and the resulting NO 2 SCD (left exist) for all calibration windows of the Pacific Ocean test orbit.The minimum RMS is achieved for calibration window wcN (409.0-428.0).There are 112 possible calibration windows with an RMS within 0.5 % of the RMS of wcN, and these calibration windows all have an end-wavelength below 430 nm.For these windows, the NO 2 error ranges from 0.97 (the value for wcN) to 0.98 × 10 15 molec cm −2 , and the NO 2 SCD ranges from 7.23 to 7.47 × 10 15 molec cm −2 .The latter variation can be considered a measure for the uncertainty in the NO 2 SCD related to the wavelength calibration: 0.12 × 10 15 molec cm −2 (0.05 × 10 15 molec cm −2 in terms of the NO 2 VCD when using a geometric air-mass factor).There appears to be an almost perfectly linear relationship between the NO 2 SCD and the shift of the calibration for the investigated range of wavelength shifts: NO 2 SCD [× 10 15 molec cm 2 ] = 2.325 • shift [× 10 −2 nm] + 8.470, with a correlation coefficient of r = 0.99997.This linear relationship implies that an error in the wavelength shift of 1 × 10 −3 nm (0.5 % of a detector pixel) corresponds to a change in the NO 2 SCD of about 0.2 × 10 15 molec cm −2 .Depending on the desired accuracy of the retrieved NO 2 column, e.g. for future satellite missions, the relationship poses firm requirements on the accuracy of the wavelength grid.The effect of spectral misalignments, i.e. a mismatch between the wavelengths of the measured spectra and the reference spectra, on DOAS fit results has also been investigated, e.g. by Stutz and Platt (1996) and Beirle et al. (2013).

Results of the OMI NO 2 retrieval improvements
The improvements for the OMNO2A NO 2 SCD retrieval discussed above comprise four steps: 1. the update of the high-resolution solar reference spectrum and the Ring spectrum used for the wavelength calibration; 2. the change of the wavelength calibration window from wcB to wcN; 3. the update of the reference spectra of NO 2 , O 3 and H 2 O vap ; 4. the inclusion of absorption by the O 2 -O 2 collision complex and by liquid water.
The current OMNO2A processing system is referred to as "v1" below, while the processing using the updated spectral fit settings is named "v2".

Current vs. updated NO 2 fit results
For the comparison of the current and updated OMNO2A spectra fit results, the OMI orbit over the Pacific Ocean on 1  4. The difference "case 0 -case 2" (blue line) refers to the updates of the wavelength calibration, "case 2 -case 4" (black line) to the updates of the reference spectra, and "case 0 -case 4" (red line) to all updates put together.

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Figure 3. Absolute values (top row) and absolute differences (bottom row) of the orbit average RMS error (left column, × 10 −4 ) and NO 2 SCD (right column, × 10 15 molec cm −2 ) as a function of the OMI orbit number on 1 July 2005; the Pacific Ocean orbit is number 14.The case numbers refer to the cases listed in Table 4.The difference "case 0 -case 2" (blue line) refers to the updates of the wavelength calibration, "case 2 -case 4" (black line) to the updates of the reference spectra, and "case 0 -case 4" (red line) to all updates put together.
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 NO 2 is the main focus of this study, no filtering of cloudy pixels is applied.
Table 4 lists the NO 2 SCD, the NO 2 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 NO 2 data products; case 2 represents the improved wavelength calibration; and case 4 the implementation of all updates together, i.  4, similar to the bottom panels of Fig. 3.For comparison, the concentration of O 2 -O 2 as a function of latitude is shown in arbitrary units (green short-dashed line).
OMNO2A. Figure 3 shows the absolute values of and differences between cases 0, 2 and 4 in Table 4 of the RMS error and the NO 2 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 NO 2 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 NO 2 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 × 10 15 molec cm −2 , -updates in the reference spectra further reduce the RMS by 9 % and the SCD by 0.35 × 10 15 molec cm −2 , -in total the RMS improves by 31 % and the SCD is smaller, on average, by 1.20 × 10 15 molec cm −2 .
The latitudinal dependency of the changes in the NO 2 SCD averaged over the 15 orbits is shown in Fig. 4. The change in NO 2 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 × 10 15 molec cm −2 in the current "v1 OMNO2A" retrieval.
However, the change in NO 2 SCD due to the update of the trace gas reference spectra and the inclusion of absorption by O 2 -O 2 and H 2 O liq (black line with triangles in Fig. 4) depends clearly on latitude in absolute numbers and as a percentage of the NO 2 SCD: the change ranges from 0.1 × 10 15 molec cm −2 (3 %) in the tropics to Overall, the improved OMNO2A NO 2 SCD is reduced by 1.0 to 1.8 × 10 15 molec cm −2 (10 to 16 %), the NO 2 SCD error by 0.2 to 0.3 × 10 15 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 QA4ECV3 to evaluate the robustness of the improvements for other days of the test year (2 February and 16 August 2005) and for more recent OMI data (4 February and 4 August 2013).Figure 5 shows the orbit average values of the RMS error and the NO 2 SCD the updated retrieval values and the differences between the current and the updated values.The other fit coefficients (not shown), such as ozone and water vapour, as well as the associated error terms, show no systematic differences between the results of the current and updated settings either.This comparison confirms that the improvements are robust over time and can therefore be used for reprocessing the entire OMI record.
To facilitate a comparison of the improved spectral fit for OMI with data from SCIAMACHY, the NO 2 slant columns of both instruments are converted to vertical columns with the geometric air-mass factor M geo , taking the curvature of the Earth's atmosphere into account (Leue, 1999).This conversion ensures that the considerable differences in viewing angles between the two instruments do not affect the comparison.
Figure 6 shows a comparison of the OMI Pacific Ocean test orbit using the "v1 OMNO2A" and the "v2 OMNO2A" retrieval and of the SCIAMACHY data over the Pacific Ocean of the same day (lines with symbols).Given SCIAMACHY's poor geographic coverage, the data of its three orbits over the Pacific are averaged for this comparison.The figure shows that the discrepancy between OMI and SCIAMACHY has been reduced from 1.2 to 0.8 × 10 15 molec cm −2 .
The remaining offset between the new v2 OMNO2A and the SCIAMACHY NO 2 VCDs of 0.8 × 10 15 molec cm −2 can be explained in part by the difference of about 0.5 × 10 15 molec cm −2 expected due to the diurnal cycle of stratospheric NO 2 .It should, furthermore, be kept in mind that SCIAMACHY has a negative bias of 0.1-0.2× 10 15 molec cm −2 w.r.t.GOME-2 (Sect. 3;Hendrick et al., 2012) and w.r.t. an ensemble of stratospheric NO 2 limb sensor measurements (Belmonte-Rivas et al., 2014).In addition, the OMI NO 2 is retrieved by OMNO2A with a nonlinear fit approach in the 405-465 nm window, while the SCIAMACHY NO 2 is retrieved by QDOAS with a linear fit approach in the 425-450 nm window (cf.Table 1).The difference in fit window and fit approach explains another 0.1-0.2× 10 15 molec cm −2 in the difference between OMNO2A and SCIAMACHY, as is shown in Sect.5.3.To clarify the graph, the wavelengths of three detector pixels are averaged, thus mimicking the fact that OMI's spectral resolution is about 3 times its spectral sampling.

About including O 2 -O 2 and liquid water
The spectral residual of the NO 2 retrieval describes the unexplained portion of the measured spectrum after a selected set of absorption signatures is accounted for in the fit model.Figure 7 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 O 2 -O 2 and H 2 O liq into account.Pixel 425 is over clear open ocean water with a low chlorophyll concentration4 (0.028 mg m −3 ), while pixel 592 is over ocean water with a relatively high chlorophyll concentration (0.351 mg m −3 ).An anti-correlation between the chlorophyll concentration and the liquid water absorption coefficient is expected, because the higher the chlorophyll concentration the more opaque the water is and therefore the shorter the penetration depth of light will be.
Figure 7 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 H 2 O liq 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 NO 2 SCD reduces by about  Figure 8 shows the retrieved H 2 O liq 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 H 2 O liq coefficients, as expected.The inset of Fig. 8 shows the relationship between the H 2 O liq coefficient and the chlorophyll concen- Figure 9 shows a global map of the H 2 O liq 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 H 2 O liq coefficient is very low, consistent with high chlorophyll concentrations there.Note that since the processing is not optimised for the retrieval of the H 2 O liq coefficient, it is not possible to say how accurate the coefficient is, but overall its values appear realistic.Positive H 2 O liq 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 H 2 O liq and the O 2 -O 2 collision complex in the NO 2 fit is justified since their absorption is known to affect the radiance I (λ) -unless their inclusion would reduce the quality of the NO 2 fit, which is not the case.Figure 10 6) with QDOAS retrievals using different fit windows with a linear fitting approach (filled symbols) and using a non-linear fitting approach in the standard fit window (open circles) for the Pacific Ocean test orbit.The size of the steps along the vertical scale is the same as in Fig. 4 to ease comparison of the SCD differences.

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Figure 11.Differences of the NO 2 SCD values of the new v2 OMNO2A fit results (i.e. the red line with circles in Fig. 6) with QDOAS retrievals using different fit windows with a linear fitting approach (filled symbols) and using a non-linear fitting approach in the standard fit window (open circles) for the Pacific Ocean test orbit.The size of the steps along the vertical scale is the same as in Fig. 4 to ease comparison of the SCD differences.

Comparison between OMNO2A and QDOAS
Since the OMI, SCIAMACHY and GOME-2 spectral fits have been done with different fitting approaches and fitting windows (cf.Table 1), the sensitivity of the NO 2 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 Supple-ment), is used for this study with the v2014 reference spectra on the OMI Pacific Ocean test orbit.
Figure 11 shows that the OMNO2A and QDOAS processors, both applied in the 405-465 nm window, result in small differences in the NO 2 SCDs of −0.2 to +0.1 × 10 15 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. (1) but with the Ring effect treated as a pseudo-absorber; cf.Eq. (S5).The red line with open circles in Fig. 11 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 × 10 15 molec cm −2 , almost independent of latitude.
The SCIAMACHY and GOME-2 NO 2 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. 11.At +0.2-0.6 × 10 15 molec cm −2 , the difference is clearly larger than for the OMNO2A fit window.
In their study to improve the GOME-2 NO 2 retrieval, Richter et al. (2011) apply the extended fit window 425-497 nm.The black line with triangles in Fig. 11 shows that OMNO2A is higher by 0.4-0.9× 10 15 molec cm −2 than applying a linear fit in this extended fit window.
The NO 2 SCD differences in Fig. 11 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.5.2) -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 H 2 O liq and/or O 3 and/or O 2 -O 2 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 NO 2 fit results, i.e. there is no "true" NO 2 SCD but at most a fit window and fit method specific slant column value.Judging from the curves in Fig. 11, the variability in the fit window and fit method selection introduces differences in the retrieved NO 2 SCD between −0.3 and +0.6 × 10 15 molec cm −2 (i.e. up to 0.2 × 10 15 molec cm −2 in terms of the NO 2 VCD).To better understand the "true" NO 2 SCD, a comparison with measurements that do not depend on the DOAS technique is needed.

Reprocessed OMI NO 2 data of 2005
All OMI NO 2 slant column data of the year 2005 have been reprocessed to evaluate the consistency of the proposed improvements.Figure 12 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 NO 2 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 NO 2 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) NO 2 SCDs will be small compared to the overall decrease of the NO 2 values.
Figure 13 shows a map of the monthly average gridded NO 2 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. 14.Similar maps of the month of January 2005 are shown in Sect.S7 in the Supplement.In some areas with high NO 2 levels related to pollution, the decrease of the NO 2 slant column is relatively large, such as for the Highveld area in South Africa in Fig. 13 for July.The average change in the RMS error shown in the lower panel of Fig. 14 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. 13-14 of the results of the other fit parameters.

Concluding remarks
The OMI NO 2 slant column density retrieval, OMNO2A, lies at the basis of the stratospheric and tropospheric NO 2 vertical column data products of OMI, notably the Dutch OMI NO 2 (DOMINO) and NASA SP data sets.This paper describes important updates for OMNO2A in order to improve the quality of the OMI NO 2 SCD data.The investigation was triggered by the high bias in OMI stratospheric NO 2 columns w.r.t.other satellite sensors and ground-based measurements as well as the need to investigate a number of other elements of the OMNO2A processor.The improvements for the OMNO2A processor are  NO 2 SCD retrievals for other satellite and ground-based instruments employ different spectral fit windows and use different implementations of the DOAS technique, which leads to small differences in the resulting SCD values.A short investigation of this using the QDOAS software (Danckaert et al., 2012) shows that the uncertainty in NO 2 SCD related to the choice of the fit window and fit method may be as large as 0.3 × 10 15 molec cm −2 .
The combination of improvements to the OMNO2A spectral fit lead to an overall reduction of the NO 2 SCD by about 1.2 × 10 15 molec cm −2 , a reduction of the NO 2 fitting error by 0.2-0.3× 10 15 molec cm −2 and a reduction of the RMS by 24-35 %.The reduction of the SCD is largely an additive offset, implying that the improvements in OMNO2A will probably affect stratospheric NO 2 most and smaller effects may be expected on tropospheric NO 2 .
Comparing the updated OMNO2A data with SCIA-MACHY data over the Pacific Ocean shows that the discrepancy between the two instruments is reduced from 1.2 to 0.8 × 10 15 molec cm −2 .The remaining difference can be explained largely by the difference expected due to the diurnal cycle of stratospheric NO 2 , which is higher by about 0.5 × 10 15 molec cm −2 at 13:40 LT (when OMI measures) than at 09:30 (when SCIAMACHY measures), the different choice of the fitting window and the low bias of SCIA-MACHY relative to other instruments.
The updates to the OMNO2A retrieval systems are sufficient to remove the bias between the stratospheric NO 2 columns from OMI and those from other satellite and ground-based instruments.A final test of this requires the conversion of the retrieved SCD to the separate stratospheric and tropospheric NO 2 columns.This issue will be discussed in a forthcoming study that describes improvements to the data assimilation system of DOMINO, leading to a new DOMINO v3.0 data set for the entire OMI period.The settings of the updated OMNO2A processing will be the initial configuration of the NO 2 retrieval for TROPOMI for reasons of consistency (van Geffen et al., 2014).
The Supplement related to this article is available online at doi:10.5194/amt-8-1685-2015-supplement.

Fig. 1 .Figure 1 .
Fig. 1.Monthly average stratospheric NO2 VCD values (left axis; filled symbols) and absolute differences (right axis; open symbols) in 10 15 molec/cm 2 of OMI, GOME-2 and SCIAMACHY in March 2007 over the Pacific Ocean area (60 • S -60 • N, 140 • W -180 • W), as function of latitude.The error bars at the data points near the equator mark for that latitude bin the average standard deviation of the total VCD.[Data source: http://www.temis.nl/]

Fig. 2 .Figure 2 .
Fig. 2. Pacific Ocean test orbit average relationship between the RMS error and the NO2 SCD for the 5151 wavelength calibration windows investigated.The right axis of the main plot is an approximation: it gives the wavelength shift constructed from the linear relationship with the NO2 SCD mentioned in the text.

Fig. 3 .
Fig. 3. Absolute values (top row) and absolute differences (bottom row) of the orbit average RMS error (left column, ×10 −4 ) and NO2 SCD (right column, ×10 15 molec/cm 2 ) as function of the OMI orbit number on 1 July 2005; the Pacific Ocean orbit is number 14.The case numbers refer to the cases listed in Table4.The

Fig. 4 .Figure 4 .
Fig. 4. Absolute differences in the NO2 SCD as function of latitude averaged over all 15 orbits.The case numbers refer to the cases listed in Table4, similar to the bottom panels of Fig.3.For comparison, the concentration of O2-O2 as function of latitude is shown in arbitrary units (green short-dashed line).

Fig. 5 .Figure 5 .
Fig. 5. Absolute values of the updated data (case 4, top row) and absolute differences between the current and the updated data (bottom row) of the orbit average RMS error (left column, ×10 −4 ) and NO2 SCD (right column, ×10 15 molec/cm 2 ) as function of the OMI orbit number on 4 selected days.The case numbers refer to the cases listed in Table4.Measurements from the rows affected by the row anomaly in the 2013 (rows 25-48 and 53) have been omitted from all data in this comparison.

Fig. 6 .Figure 6 .
Fig. 6.Comparison of the NO2 VCD values (lines with symbols) of the new v2 OMNO2A (red circles) and old v1 OMNO2A (blue squares) retrieval for the Pacific Ocean orbit of 1 July 2005, and the average SCIAMACHY data (black triangles) over Pacific Ocean of the same day.The two lines without symbols show differences between the NO2 VCD values.A comparison between OMI and SCIAMACHY should be limited to latitudes below 45 • , because for higher latitudes the instrument cover different geographic areas.

Fig. 7 .Figure 7 .
Fig. 7. Spectral residual of the NO2 retrieval fit with the updated reference spectra without (case 3, red solid lines) and with (case 4, blue dashed lines) O2-O2 and H2Oliq absorption included for two ground pixels along row 29 (0-based): pixel 425 (located at 20.2 • S, 135.4 • W; top two curves, left axis) and pixel 592 (0.0 • S,139.8 • W; bottom two curves, right axis) of the Pacific Ocean test orbit.To clarify the graph, the wavelengths of three detector pixels are averaged, thus mimicing the fact that OMI's spectral resolution is about three times its spectral sampling.

Fig. 8 .Figure 8 .
Fig. 8. Retrieved H2Oliq coefficient (in m; red solid line, left axis) as function of latitude for row 29 of the Pacific Ocean test orbit, showing only ground pixels for which chlorophyll concentration data is available.Also shown, with values along the right axis, are the chlorophyll concentration (in mg/m 3 ; blue dashed line) and the cloud cover fraction (magenta dotted line).The inset shows the H2Oliq coefficient as function of the chlorophyll concentration separately for ground pixels with latitudes between ±40 • (red crosses) and higer latitudes (green circles).

Fig. 9 .Figure 9 .
Fig. 9. World map of the H2Oliq coefficient (in m) based on all 15 OMI orbits of 1 July 2005; the Pacific Ocean test orbit is marked by a black triangle.All ground pixels with solar zenith angle less than 75 • are plotted; no filtering for cloudy pixels was applied.

Fig. 10 .Figure 10 .
Fig. 10.Retrieved values for the O3 SCD (top-left), the O2-O2 SCD (bottom-left) and H2Oliq coefficient (bottom-right) as function of latitude for the Pacific Ocean test orbit for retrievals without and with absorption by O2-O2 and H2Oliq included in the fit as specified by the legend in the top-right corner; case numbers 3 (black dashed) and 4 (red solid) refer to the cases listed in Table4.Also plotted are the O3 SCD value from the OMI ozone slant column product OMDOAO3 (magenta long-dash-dotted) and the O2-O2 SCD value from the OMCLDO2 cloud product (blue short-dash-dotted).

Fig. 11 .
Fig. 11.Differences of the NO2 SCD values of the new v2 OMNO2A fit results (i.e. the red line with circles in Fig.6) with QDOAS retrievals using different fit windows with a linear fitting approach (filled symbols) and in the regions where absorption in open water is taking place.Adding both absorbers brings the retrieved O 3 SCD close to the values given in the official OMI ozone SCD data product OMDOAO3; the improvement is mostly due to including H 2 O liq absorption.Including O 2 -O 2 absorption but not H 2 O liq absorption does not result in realistic O 3 SCD values.Furthermore, the retrieved O 2 -O 2 SCD values appear realistic compared to the values given in the official OMI cloud data product OM-CLDO2 if H 2 O liq is included in the fit.Including O 2 -O 2 absorption has a small effect on the retrieved H 2 O liq coefficient (bottom-right panel in Fig. 10).In summary, (a) including liquid water absorption leads to significant improvements in the NO 2 retrieval fit for pixels over clear open waters, without affecting other pixels, results in physically meaningful H 2 O liq and O 3 absorption coefficients; and (b) simultaneously including O 2 -O 2 absorption results in realistic O 2 -O 2 SCDs and improves the fit, especially if light paths are long.

Fig. 12 .Figure 12 .
Fig. 12. Scatter plots of current data (case 0, top row) and absolute differences between the current and the updated data (bottom row) of the RMS error (left column,×10 −4 ) and NO2 SCD (right column,×10 15 molec/cm 2 ) as function of the updated data (case 4) using the July 2005 average gridded data.Dashed blue lines show linear fits through the data; the fit and correlation coefficients are shown in the top-left of each graph.

Fig. 13 .Figure 13 .
Fig. 13.Monthly average gridded updated (case 4; top panel) NO2 slant column data for July 2005 and the corresponding difference with the current (case 0) data (lower panel).

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implementation of the wavelength and viewing angle dependency of the OMI slit function, -optimisation of the wavelength calibration window based on minimising RMS and NO 2 errors, -an update of the reference spectra of the trace gases included in the spectral fit, -inclusion of absorption by O 2 -O 2 and H 2 O liq to further reduce the RMS error.

Fig. 14 .Figure 14 .
Fig. 14.Monthly average gridded updated (case 4; top panel) RMS error data for July 2005 and the corresponding difference with the current (case 0) data (lower panel).

Table 1 .
Main settings of the DOAS retrieval of NO 2 slant column densities of the data versions used in this paper for the satellite instruments OMI, GOME-2 and SCIAMACHY; for OMI the current settings and the settings resulting from the discussion in this paper are given.

Table 2 .
Average differences in stratospheric NO 2 columns over the Pacific Ocean area (60 • S-60 • N, 140-180 • W) of 2007 of OMI, GOME-2 and SCIAMACHY, where the averages are computed from monthly latitudinally binned data.The relative difference (right column) is given as percentage of the column values of the second instrument in the difference, e.g.w.r.t.SCIA in the difference OMI − SCIA (data source: http://www.temis.nl/).

Table 3 .
Pacific Ocean test orbit average main results of the wavelength calibration and spectral fit, using the v2014 reference spectra for the wavelength calibration windows mentioned in Sect.4.2.

Table 4 .
Results of the NO 2 SCD fit for the different steps of the updates of the OMNO2A processing for the Pacific Ocean orbit.Case 0 represents the current OMNO2A version (v1) and case 4 is the updated version (v2) settings.Cases 1 through 4 follow the updates listed at the beginning of Sect. 5.The numbers between parentheses are percentage changes w.r.t.case 0. The NO 2 SCD error is given in absolute value and as percentage of the NO 2 SCD column.The NO 2 VCD in the last column is determined from the SCD and the geometric air-mass factor.