In general, UV/VIS NO2 retrieval algorithms for spectra from grating spectrometers e.g. have used the DOAS technique to retrieve the slant column densities (SCDs). In the absence of multiple scattering these can be considered to be the integrated trace gas density along the instrument's geometrical line of sight. The technique is based on the principle that a wavelength-dependent absorption signal can be split into two components: the low-frequency, broadband component (representative of features such as aerosol scattering and surface albedo) that can be approximated by a low-order polynomial, and a high-frequency component that is sensitive to trace gas concentrations. In principle the DOAS fit is a least squares fit of the logarithm of the reflectance spectrum (the ratio of the incident and attenuated spectra) over a given wavelength range, using a modified form of the Beer–Lambert law: ln⁡IλI0λ=-∑iσiλNs,i+Pλ. In Eq. () the reference and object spectra are represented by I0 and I respectively, while Ns,i represents the SCD of trace gas i. For satellite retrievals of NO2 I would be the measured Earth radiance spectra, while solar irradiance spectra measured separately by the instrument would be used as I0. In this case the retrieved SCD would be the total slant column density along the line of sight.

Limitations in the instrument design may result in the measured spectra having improper spectral calibration, which can adversely affect the quality of the fitted SCD. To remedy this, additional terms representing a necessary shift and stretch in the wavelength grid can also be included in Eq. (). The resulting solution would then be found through nonlinear least squares fitting of Eq. () .

σi represents the absorption cross-section of the ith trace gas considered in this fit, while P represents the low-order polynomial used to account for the broadband structure in the spectra. Ideally, the trace gas absorption cross-sections and wavelength ranges considered in the fit should be such that the cross-sections are orthogonal to each other to give the best result, though in practice this often does not occur, and can be a large source of error in the fit.

In DOAS retrievals of NO2 from instruments measuring in the UV/Vis range a fitting window is usually selected in the 400–500 nm range. Often used is the 425–450 nm window, which minimises contamination from other species while taking advantage of the distinct NO2 spectral features present in this region . For OMI measurements a wider fit window of 405–465 nm is used to improve the signal-to-noise and therewith improve the fit . For GOME-2 spectra the use of the window 425–497 nm has been tested successfully .

In addition to NO2, trace gas absorption cross-sections such as O3, H2O and the O2–O2 collision complex within the UV/Vis range have also been included in the fit to account for other sources of absorption in the spectra. Furthermore, a synthetic cross-section to account for absorption caused by rotational Raman scattering the Ring effect; is also included in the fit.

SCDs retrieved by DOAS still need to be weighted in order to account for enhancement owing to factors such as optical path length, scattering from clouds/aerosols, and surface albedo. To that end, the SCDs are divided by an air mass factor (AMF) to convert them into VCDs e.g.. The AMFs are in turn created by inputting forward model parameters describing local conditions such as surface albedo, trace gas profile information and cloud cover into a radiative transport model (RTM). Quantifying the uncertainty in the forward model parameters is important for determining the final retrieval error of the derived VCDs .

Launched in 2004 onboard the NASA AURA satellite, the Ozone Monitoring Instrument OMI, produces tropospheric NO2 VCDs at a near-urban spatial resolution (nadir pixel size: 13 × 24 km2, though in its spatial zoom modes this can be reduced to 13 × 12 km2 or even 13 × 3 km2, as discussed in ). As a push-broom spectrometer, OMI has a swath width of 2600 km which is divided into 60 across-track pixels. Each pixel corresponds to a separate viewing angle. OMI follows a sun-synchronous orbit, with a local overpass time of approximately 13:45. The instrument's visible channel has a 350–500 nm spectral range, with an average spectral resolution of 0.63 nm.

The process of deriving tropospheric NO2 VCDs from the Level 1B Earth radiance data (OML1BRVG product, see Sect. 2) via DOAS is briefly described in this section. In the operational OMI DOAS slant column retrieval algorithm OMNO2A , the Earth radiance reflectance spectra are fitted using a 405–465 nm fitting window. The reflectance spectra are fitted with absorption cross-sections for NO2, O3 and H2O, as well as a fifth-order polynomial to account for broadband variations (see Table ).

In the OMNO2A algorithm the Ring effect is treated differently compared with traditional DOAS retrievals. In this case the Ring effect is treated as a source of photons, rather than a pseudo-absorber. Because of this, the algorithm performs a nonlinear least squares fit using the following equation: IλI0λ=Pλexp-∑iσiNs,i×1+CRINGIRINGλI0λ. In Eq. () P represents a fifth-order polynomial, while the IRING term is the Ring radiance spectrum, I0 is the measured solar irradiance spectrum, and CRING is the Ring absorption coefficient determined by the fit.

There are currently two operational algorithms that process the SCDs retrieved by OMNO2A into tropospheric NO2 VCDs; brief descriptions of each are given below.

The goal of this first effort was to demonstrate the theoretical possibility of using an Earth radiance reference in the DOAS fit and show in the absence of noise, aerosol and trace gas contamination that the Earth radiance-retrieved SCD is the difference in NO2 between the reference and observed region. In order to demonstrate the validity of using Earth radiance reference spectra to retrieve tropospheric NO2, the SCIATRAN RTM v 3.1.27, was used to simulate spectra that may typically be observed over the Pacific and China. Vertical profile data for temperature, NO2, O3 and H2O in these scenarios was provided by the CAMELOT data set and are summarised in Fig. . The Pacific is relatively free of tropospheric NO2, which theoretically makes it possible for spectra taken over this region to be used as an estimation of the local stratospheric field over a given location.

An Earth radiance spectrum from the Pacific and polluted Chinese scenarios was modelled, with absorption due to O2-O2 provided by a profile created by SCIATRAN from the pressure profile. Absorption from the Ring effect was calculated by SCIATRAN using the algorithm developed by . While no aerosol information was included, the solar zenith angle in either scenario was varied between 0–80∘ in order to demonstrate the retrieval's accuracy at different diurnal ranges. DOAS fits were carried out on all spectra, using a solar irradiance spectrum as a reference. For Chinese scenarios, the Pacific Earth radiance spectrum was used as a reference as well. The results of this study are discussed in Sect. .

In order to test the validity of the ERrs-DOAS technique using operational satellite spectra, data from the OML1BRVG collection 3, product were used to provide the calibrated, wavelength-corrected spectra for both the reference and object spectra in the DOAS retrieval in this work. Data regarding the ground pixel quality (e.g. cloud cover, surface albedo) were provided by the DOMINO (v. 2.0) product. Tropospheric SCDs retrieved by DOMINO were used to compare with the retrieved NO2, though these had to be reconstructed using the “TroposphericVerticalColumn” and “AirMassFactorTropospheric” fields in the DOMINO data product. Similarly, the tropospheric SCDs retrieved by OMNO2 were derived from the “ColumnAmountNO2Trop” and “AmfTrop” fields in the OMNO2 data product, while the OMNO2A total SCDs were taken from the “SlantColumnAmountNO2” field. For most of this work only data collected before 2008 were considered, as this was largely before the emergence of the “row anomaly” artefacts that have affected OMI data coverage since 2007 . All cross-sections used were convolved with the OMI slit function prior to the DOAS fit .

Prior to the DOAS fit, the reference spectrum is interpolated onto the same wavelength grid as the observed Earth radiance spectrum using the same interpolation technique as used in . The interpolated reference spectrum I0,λ(ES) is calculated using the following equation: I0,λ(ES)=I0,λ(REF)Fλ(REF)Fλ(ES). First, a high-resolution oversampled solar atlas that is convolved to the OMI instrument line shape is interpolated onto both the reference and radiance spectra wavelength grids (Fλ(REF) and Fλ(ES) respectively) using cubic spline interpolation. The ratio of these interpolated spectra is then multiplied by the intensity of the solar irradiance, which therefore gives the desired interpolation.

A wavelength correction is applied to the Earth radiance spectra before the DOAS fit, in order to correct for shifts caused by cloudy scenes . The correction is performed as a single offset, calculated from comparing the 408–423 nm spectral window to the high resolution solar atlas . The offsets applied for each OMI ground pixel can be found in the “WavelengthRegistrationCheck” field in the OMNO2 product. Additionally, spectral pixels flagged as being affected by instrumental defects such as random telegraph signals or dark current behaviour were removed prior to the DOAS fit . In QDOAS this removal can be performed by specifying gaps in the spectral window which are then ignored in the analysis.

The results from the ERrs-DOAS fits of modelled CAMELOT spectra (see Sect. ) are discussed herein. As shown in Fig. , for all solar zenith angles considered the SCD retrieved by DOAS fitting spectra from the Chinese scenario using a Pacific Earth radiance reference was near-identical to the difference in the modelled total SCD between the two scenarios. From Fig.  it appears that the difference in SCD is largely due to differences in tropospheric NO2, though the difference in stratospheric NO2 between the two scenarios would also greatly contribute to the retrieved SCD. Ideally, the reference spectra should be collected from a region where the stratospheric NO2 is similar to the target region to minimise this bias.

Prior to comparing tropospheric SCDs in satellite data, it is essential to determine any inherent biases present in the retrieval algorithm, as QDOAS performs DOAS fits differently to OMNO2A. QDOAS performs a nonlinear DOAS fit by solving a variant of Eq. (), in which the Ring is treated as a pseudo-absorber like other trace gases, and no treatment of elastic scattering is considered. To determine the magnitude of possible biases resulting from these differing assumptions a comparison exercise was established. As with the OMNO2A retrieval, a composite set of solar irradiance reference spectra derived from OMI irradiance data OML1BIRR, collection 3, taken during 2005 were used in this initial test. These were used to retrieve total NO2 SCDs in cloud-free regions (i.e. pixel cloud fraction < 25 %) over the whole globe during June 2005, using the retrieval parameters shown in Table , as care was taken to ensure that the cross-sections, interpolation method and retrieval settings employed were a close approximation to those used in the current OMNO2A retrieval v2006;. The resulting SCDs and uncertainties were then compared with those retrieved by OMNO2A, as shown in Fig. .

The results show an almost constant negative SCD bias between the QDOAS-based retrieval and OMNO2A over all regions (average SCD bias ∼ -1.0 × 1015 molec cm-2). There appear to be no geospatial features other than a slightly stronger bias over mountainous regions, potentially due to possible retrieval sensitivity to surface albedo. The lack of spatial features suggests that this bias is the result of some flaw in the retrieval algorithm, rather than any unforeseen geophysical process. A similar bias has previously been reported in other comparisons between OMNO2A and QDOAS-based retrievals, which appears to be resolved in part through better wavelength and slit function calibration .

Additionally, the bias also exhibits a strong across-track variation, as shown in Fig. . The reason for this effect is currently unknown. One possible cause could be how QDOAS treats spectral pixels flagged for removal due to random telegraph signals or dark current behaviour ; the number of pixels that need to be removed from the DOAS fit for this reason varies between across-track pixels, which may add to the bias caused by the retrieval algorithm differences.

As a result, comparisons between the retrievals covered in this paper with existing retrievals were conducted using only ground pixels in which the QDOAS-based retrieval using solar reference spectra produced total SCDs that were within 5 % of the total SCDs produced by OMNO2A. It was assumed that ERrs-DOAS retrievals of NO2 over such pixels using the QDOAS software would be representative of what would be retrieved if the ERrs-DOAS fits were performed using the OMNO2A algorithm, as they would be relatively free from this bias.

The cross-sections used in this study are identical to those used in the OMNO2A retrieval (see Table ). Following preliminary testing over the Sahara desert (see Sect. ), cross-sections for sand and liquid H2O were also included in the ERrs-DOAS fit.

For the first phase of this study Earth radiance spectra recorded during June 2005 were considered. Daily Earth radiance data from a Pacific reference sector (125–180∘ W, 60∘ S–60∘ N) over this month were binned into a set of 60 reference spectra for each OMI viewing angle, as the stratospheric NO2 present in the observed spectrum will be highly dependent on the scattering path length, and so the viewing geometry. Consequently, all DOAS retrievals were performed using reference spectra measured at the same viewing angle as the observed radiance spectra. To account for latitudinal gradient in stratospheric NO2 and SZA the spectra were also binned into 1∘ latitude bins, such that DOAS retrievals of Earth radiance spectra observed over the rest of the planet made use of the reference spectra obtained from the closest latitude bin.

Using a latitudinal reference sector also resolves potential biases resulting from changes in SZA between the reference and observed region. Observations made with high SZAs will be more sensitive to the stratosphere due to an increase the mean scattering height , which may result in unforseen stratospheric contamination in the SCDs retrieved with this method. However, as OMI follows a sun-synchronous orbit, the ground pixel SZA is dependent on latitude and season. As a result, using a daily, latitudinally binned reference spectrum means that the difference in SZA between the reference and observed region will be negligible, so this effect will be negated.

The choice of reference sector and frequency of data collection will result in unknown uncertainties affecting the overall retrieval accuracy. For instance, pollution transport events (e.g. outflow from the mainland) will result in a negative bias exhibited in the retrieved SCDs. The static reference sector used in this work was to maximise the number of usable spectra which could be binned at all latitudes. Similarly, the temporal frequency of the binned reference spectra will also contribute to the retrieval uncertainty (e.g. accounting for seasonal variation in the stratospheric field). An operational algorithm will therefore need to automatically select remote regions which are assumed to be free of such contamination; possible selection methods are discussed in Sect. .

It was determined that only spectra that were measured over largely cloud-free scenes (i.e. cloud fraction < 25 %) would be binned to this data set. Scattering from clouds would lead to inhomogeneous illumination of the OMI entrance slit, which in turn leads to a change in the position and shape of the instrument slit function. The change in the slit function then results in an observed shift in the wavelength mapping of the Fraunhofer lines on the detector . As the DOAS fit depends on good wavelength calibration, cloudy pixels would need to be avoided to obtain the best possible result in this work. As well as this, using cloudy scenes would otherwise introduce a cloud height dependence on the inherent stratospheric NO2 retrieved.

As shown in Fig. a and b the ERrs-DOAS retrieval shows good agreement with tropospheric SCDs retrieved by DOMINO, particularly showing good spatial similarity with megacities and regions with known anthropogenic activity (e.g. mining), as well as possible biomass burning over central Africa. Overall, the retrieved SCDs highly correlate with those retrieved by the operational DOMINO product (r2=0.85), particularly over heavily polluted regions such as China (r2=0.96, 0.99 for SCDs >1.0×1016 molec cm-2).

However, the retrieval produces significant, broad negative biases over remote regions such as Tibet, particularly at higher northern latitudes over land. This is potentially due to undersampling of reference spectra in the Pacific reference sector resulting from excessive cloud cover at those latitudes, which would result in a degradation in the quality of the DOAS fit and an underestimation of the local stratospheric field; both factors would result in lower SCDs retrieved.

As well as this, Fig. d shows that the stratospheric NO2 field varies considerably with longitude at the latitudes where this bias appears. This variation is especially pronounced in the Pacific reference sector, which has higher stratospheric SCDs compared with other longitudes. The increased NO2 absorption present in the reference sector would therefore lead to lower tropospheric SCDs retrieved over other areas.

One particularly significant positive bias appears over the region (70∘ W–160∘ E, 16–22∘ S) and the Southern Atlantic Ocean, in which the retrieval overestimates the magnitude and spatial spread of the tropospheric NO2 band that is detected in the DOMINO retrieval (Fig. b). According to the assimilated stratospheric NO2 available from DOMINO (Fig. d) these regions had considerable longitudinal variation in stratospheric fields compared with the Pacific reference sector, which would result in the Pacific reference sector being an underestimate of the local stratospheric field. Both of these cases show the need to accurately estimate the stratospheric NO2 field and to have enough cloud-free measurements in the reference sector in order for this type of retrieval to be successful.

In order to determine the sensitivity of this retrieval to the relative difference in NO2 between urban and rural areas a comparison exercise was undertaken between the ERrs-DOAS, OMNO2 and DOMINO retrievals. As shown in Fig. , the mean tropospheric NO2 SCDs retrieved during June 2005 are selected over a latitudinal transect across China, from Hong Kong to Inner Mongolia (20–50∘ N, 114∘ E). The average tropospheric SCD retrieved using an Earth radiance reference spectrum during June 2005 is compared with that retrieved by the DOMINO and OMNO2 algorithms.

The Earth radiance reference retrieval demonstrates sensitivity to NO2 enhancement over urban areas, as the latitudinal variation is very similar to that exhibited by the DOMINO and OMNO2 transects. Over the Pearl River Delta (23∘ N) the SCDs retrieved by all three algorithms appear to be nearly identical, while enhancement over other urban areas is also detected by the Earth radiance retrieval and shows good agreement with the other algorithms. However, further along the transect there is a consistent negative offset associated with the Earth radiance retrieval, particularly over Inner Mongolia (45–50∘ N), though this bias appears to be largely within the mean uncertainty of the DOAS fit as reported by QDOAS. The residual bias is likely the result of longitudinal differences in stratospheric NO2 over the Pacific reference sector and China, which could not be accounted for when collecting reference spectra. Residual biases arising from differences between the OMNO2A and QDOAS algorithms would also contribute to the discrepancy. Despite the presence of such biases, the sensitivity to tropospheric NO2 variability demonstrates that this technique could be used to retrieve spatially resolved tropospheric NO2 over urban areas.

A significant issue when using reference spectra from a single location is that differences in the local tropospheric and stratospheric NO2 field can lead to substantial biases in estimating tropospheric NO2 over other longitudes. One possible solution is to use reference spectra from an area closer to the region of interest in order to provide a better representation of the local stratospheric field. Such regions may also be comparatively cloud-free, which would lead to better sampling of reference spectra. To determine the validity of this technique a comparison exercise is set up over a region covering South Africa. This region is particularly interesting as South Africa has the largest industrialised economy in Africa, with major cities and anthropogenic activities such as mining and agriculture primarily centred around Bushveld and Highveld. Because of this, these regions are considered to be air quality hotspots, and have been the subject of several studies to determine the impact emissions from these regions have on ambient air quality e.g.. The region is an ideal candidate for determining the impact of this technique on retrieval accuracy, as it is distant from other NO2 sources which allows for both point sources and pollution transport to be clearly visible.

For this study Earth radiance spectra measured during June 2005 are analysed over the region (20–40∘ S, 50∘ W–80∘ E). Here, the Earth radiance reference spectra are instead collected from the South Atlantic (20–40∘ S, 0∘ W–30∘ E) for use in the DOAS fit. The reference region was chosen as it was close to the region of interest, while still being distant enough to avoid tropospheric contamination from pollution transport. Figure  shows a comparison between tropospheric SCDs retrieved using this reference sector, the Pacific reference sector and the DOMINO product. Using a nearby reference sector improves correlation with the DOMINO results, while removing the longitudinal bias present beyond ∼ 23∘ S.

In order to determine the impact the ERrs-DOAS technique has on removing across-track striping, all retrievals in a single OMI swath from a region in the Pacific deemed to be distant from tropospheric pollution sources and the reference sector (30∘ S–5∘ N, 90–130∘ W) are analysed. All SCDs retrieved using the multiple Earth radiance reference algorithms over this region for each viewing angle are averaged to form a single data set. The mean is then subtracted in order to determine the across-track variability between pixels. This is then repeated with corresponding data from DOMINO and OMNO2.

As shown in Fig. , the reduction in across-track variability when using multiple Earth radiance reference spectra is greater than the existing destriping algorithms used by OMNO2 and DOMINO, suggesting that this technique could be used to account for biases resulting from instrument design without post hoc filtering. The flat curve of the ERrs-DOAS data also shows that using an Earth radiance reference removes the geometric enhancement of the SCD introduced by off-nadir viewing geometry which is still present in the other curves. The latitudinal reference sector and viewing angle binning ensures that the reference and observed spectra have been measured in similar viewing geometries. Therefore, the enhancement due to path length difference should be nearly identical and so is inherently removed from the retrieved SCD. Traditionally, this enhancement is removed as part of the AMF computation, so VCD estimation based on the ERrs-DOAS technique may require AMFs to only be computed assuming nadir viewing conditions because of this effect.

In order to determine the effect of random noise on the retrievals a statistical approach similar to those conducted by and is adopted. An area over the Pacific that was assumed to be relatively unpolluted is chosen (100–120∘ W, 10∘ N–10∘ S) and the tropospheric NO2 retrieved during June 2005 is analysed. It is assumed that the stratospheric NO2 over this region and timescale is both temporally and spatially invariant, so that the spread in these measurements would primarily originate from the inherent accuracy of the retrieval. To measure this spread the SCDs retrieved over this region using the Earth radiance reference, and OMNO2A algorithms are scaled with a geometric AMF, in order to account for variability introduced by the changing SZA and viewing geometry over this area and period. The resulting VCDs are then binned to 2∘ × 2∘ boxes, from which the deviation from the mean for each SCD is recorded. These deviations are subsequently binned to a histogram to determine the spread of the measurements. It was found that these histograms could be modelled as Gaussian functions, so the retrieval error can represented by the standard deviation, σ, of the distribution.

The OMNO2A SCDs has a σ of 1.1 × 1015 molec cm-2. This value is similar to that derived from the total SCDs retrieved by emulating the OMNO2A algorithm using QDOAS. The Earth radiance retrieval, however, produces a σ of 8.0 × 1014 molec cm-2, which corresponds to a ∼ 27 % reduction in random error using this retrieval. While this may be indicative of improved retrieval sensitivity this reduction is also the result of additional factors, such as the addition of the sand and liquid H2O cross-sections, differences between the QDOAS and OMNO2A treatment of the DOAS fit, and reduction in the across-track striping. Figure  shows the distribution and the fitted Gaussian function for the ERrs-DOAS retrievals.

This analysis was carried out over all pixels retrieved over the specified region between 2005–2008, with the resulting time series shown in Fig. . Both the Earth radiance and solar retrieval uncertainties appear to be subject to an annual cycle, with peak values occurring around June. From regression analysis it was determined that the best fit of the data was achieved when accounting for this cycle (up to the second harmonic in a Fourier series) in addition to a linear trend. This cycle could potentially be related to the periodicity of the insolation observed over the area during the year, though the physical meaning behind the second harmonic is currently unknown. This model also does not fit the solar retrieval uncertainty trends as well as the Earth radiance retrieval, suggesting that DOAS fits using a solar reference are subject to some other factor, such as changes in the solar irradiance reference spectrum. Such changes over time would not be accounted for, as both the OMNO2A and QDOAS solar retrievals only use the composite irradiance reference spectra measured in 2005 previously described in this work.

In addition to the annual cycle there appears to be a statistically significant positive trend for all three time series, which may be the result of instrument degradation during this time period. The trend for the Earth radiance retrieval uncertainty (1.5 × 1013 molec cm-2 month-1) is much lower than that of the solar retrieval uncertainty, (5.8 × 1013 molec cm-2 month-1), potentially demonstrating this technique's resilience to spectral degradation.