Evaluation of SCIAMACHY Level-1 data versions using nadir ozone profile retrievals in the period 2003–2011

Ozone profile retrieval from nadir-viewing satellite instruments operating in the ultraviolet–visible range requires accurate calibration of Level-1 (L1) radiance data. Here we study the effects of calibration on the derived Level-2 (L2) ozone profiles for three versions of SCanning Imaging Absorption spectroMeter for Atmospheric ChartograpHY (SCIAMACHY) L1 data: version 7 (v7), version 7 with m-factors (v7mfac) and version 8 (v8). We retrieve nadir ozone profiles from the SCIAMACHY instrument that flew on board Envisat using the Ozone ProfilE Retrieval Algorithm (OPERA) developed at KNMI with a focus on stratospheric ozone. We study and assess the quality of these profiles and compare retrieved L2 products from L1 SCIAMACHY data versions from the years 2003 to 2011 without further radiometric correction. From validation of the profiles against ozone sonde measurements, we find that the v8 performs better than v7 and v7mfac due to correction for the scan-angle dependency of the instrument’s optical degradation. Validation for the years 2003 and 2009 with ozone sondes shows deviations of SCIAMACHY ozone profiles of 0.8– 15 % in the stratosphere (corresponding to pressure range ∼ 100–10 hPa) and 2.5–100 % in the troposphere (corresponding to pressure range ∼ 1000–100 hPa), depending on the latitude and the L1 version used. Using L1 v8 for the years 2003–2011 leads to deviations of ∼ 1–11 % in stratospheric ozone and ∼ 1–45 % in tropospheric ozone. The SCIAMACHY L1 v8 data can still be improved upon in the 265–330 nm range used for ozone profile retrieval. The slit function can be improved with a spectral shift and squeeze, which leads to a few percent residue reduction compared to reference solar irradiance spectra. Furthermore, studies of the ratio of measured to simulated reflectance spectra show that a bias correction in the reflectance for wavelengths below 300 nm appears to be necessary.

ozone. We study and assess the quality of these profiles and compare retrieved L2 products from L1 SCIAMACHY data versions from the years 2003-2011 without further radiometric correction. From validation of the profiles against ozone sonde measurements, we find that the v8 performs better than 15 v7 and v7 mfac due to correction for the scan-angle dependency of the instrument's optical degradation.
Validation for the years 2003 and 2009 with ozone sondes shows deviations of SCIAMACHY ozone profiles of 0.8% − 15% in the stratosphere and 2.5%−100% in the troposphere, 20 depending on the latitude and the L1 version used. Using L1 v8 for the years 2003-2011 leads to deviations of ∼ 1% − 11% in stratospheric ozone and ∼ 1% − 45% in tropospheric ozone.
The SCIAMACHY L1 v8 data can still be improved upon 25 in the 265-330 nm range used for ozone profile retrieval. The slit function can be improved with a spectral shift and squeeze, which leads to a few percent residue reduction compared to reference solar irradiance spectra. Furthermore, a bias correction in the reflectance for wavelengths below 30 300 nm appears to be necessary.

Introduction
Ozone (O 3 ) is one of the most important trace gases in our atmosphere. Stratospheric O 3 absorbs the dangerous solar ultra-violet (UV) radiation making it an important protector 35 of life. A small amount of O 3 is found in the troposphere originating from stratospheric intrusions and from air pollution and photochemistry -this ozone is considered a healthrisk.
Daily ozone monitoring using satellites dates back to the 40 late 1970s with the Total Ozone Monitoring Spectrometer (TOMS, 1979) and Solar Backscatter Ultra Violet (SBUV) instruments, and since the mid-1990s also by the full UV/VIS spectral coverage instruments Global Ozone Monitoring Experiment (GOME, GOME-2) (e.g. Burrows et al., 1999;45 Munro et al., 2016), SCanning Imaging Absorption spec-troMeter for Atmospheric CHartographY (SCIAMACHY) (Bovensmann et al., 1999), and Ozone Monitoring Instrument (OMI) (Levelt et al., 2006). These successions of instruments allow us to compare long term global ozone layer 50 behaviour and cross-check the quality of the measured data. Long-term monitoring of the ozone layer is primarily driven by global measurements of total ozone time series of such satellite data.
The vertical profile of ozone has traditionally been mea-55 sured by in-situ electrochemical instruments attached to balloons, so-called ozone sondes (Deshler et al., 2008), (Smit et al., 2007). Although ozone sondes provide an accurate method for ozone profile measurement, they are limited in the heights they can reach (< 35 km), and their geographical 60 coverage is limited to approximately 70 stations worldwide (Staehelin, 2007). Ozone sondes provide weekly ozone profiles, and only few stations have a higher than weekly measurement frequency.
Satellite measurements provide an alternative means for 65 obtaining global vertical ozone profiles. Ozone profile re-trievals from nadir SBUV-type satellite instruments span for more than 40 years (Bhartia et al., 1996), (Bhartia et al., 2013). Successful retrievals are being performed from limb viewing instruments, like MLS, MIPAS, OSIRIS and OMPS-LP, as well as from occultation instruments like ACE-FTS, 5 GOMOS and SAGE II. In general limb and occultation mode satellite instruments can well resolve the vertical distribution in stratospheric ozone. However, they are limited in their horizontal resolution, and they have no sensitivity to ozone in the middle and lower troposphere. For that purpose satellite measurements in nadir mode by high-resolution spectrometers are required in the thermal IR, like TES (Worden et al., 2007) and IASI (Clerbaux et al., 2009), and in the UV/VIS, like GOME, GOME-2 (e.g. Cai et al., 2012;van Peet et al., 2014;Keppens et al., 2015;Miles et al., 2015), OMI (e.g. Liu 15 et al., 2010;Kroon et al., 2011), and SCIAMACHY.
The observation principle of nadir ozone profile retrieval in the UV/VIS is based on the strong spectral variation of the ozone absorption cross-section in the UV-visible wavelength range, combined with Rayleigh scattering. The key here 20 is that the short UV wavelengths (265-300 nm) are backscattered from the upper part of the atmosphere whereas the longer UV wavelengths (300-330 nm) are mostly backscattered from the lower part of the atmosphere. This transition in the ozone cross-section between 265-330 nm is useful 25 in retrieving its vertical profile. Nadir UV and visible spectra provide a good horizontal resolution in ozone although their observations can only be carried out in daytime. In the thermal infra-red measurements can be done during both night and day. 30 SCIAMACHY had both limb and nadir mode capability. There have been several studies of ozone profiles using SCIAMACHY limb data (e.g. Brinksma et al., 2006;Mieruch et al., 2012;Hubert et al., 2017). Brinksma et al. (2006) found biases in stratospheric ozone profiles of < 10%. 35 Also Mieruch et al. (2012) in their analysis of limb ozone profiles from SCIAMACHY for 2002-2008 found stratospheric ozone biases of ∼ 10% against correlative data sets; the bias increased up to 100% in the troposphere for the tropics. Similarly Hubert et al. (2017) in their more recent study 40 of limb profiles found that the SCIAMACHY ozone biases are about ∼ 10% or more in the stratosphere with short-term variabilities of ∼ 10%. There has been very little published work on ozone profile retrieval from SCIAMACHY nadir mode, probably due to calibration issues. In this paper we 45 compare and evaluate the three most recent versions of the SCIAMACHY L1 product. The comparison is based on the retrieval of the nadir ozone profiles from the SCIAMACHY UV reflectance spectra, showing the impact of L1 calibration improvements. The three different L1 data versions used 50 are: v7, v7 mfac , and v8. The primary difference between them is the implementation of degradation correction. These data versions are described in Sect. 2. The result of this paper shows the improved quality of the latest L1 dataset version.
The results presented here highlight the need for further 55 corrections of the L1 data. However, a detailed study of radiometric bias corrections in L1 data is beyond the scope of this paper. The focus of this study is to assess the quality of L1 data by analysing the retrieved ozone profiles. We do this for almost the entire mission length of 2003-2011 and 60 we perform validation for the latest version of the L1 data (v8). The OPERA retrieval algorithm is briefly reviewed in Sect. 2.2. Results of the ozone profiles, and the comparison between the level-1 datasets are shown in Sect. 3. This is followed by comparison to sondes in Sect. 4 for the most recent 65 dataset from the years 2003-2011. We discuss the possible effects of L1 radiometric bias corrections and applying slit function corrections in Sect. 5, and finally conclude in Sect. 6.
2 Instrument, data and methods

70
SCanning Imaging Absorption spectroMeter for Atmospheric ChartograpHY (SCIAMACHY) is a space-borne spectrometer on board ESA's Environmental Satellite Envisat (Burrows et al., 1995;Bovensmann et al., 1999) that was launched in March 2002and lasted until April 2012 The instrument measures the sunlight reflected by the Earth's atmosphere over a wide spectral range from 212 nm (UV) to 2386 nm (shortwave infrared, SWIR) spread over 8 channels. SCIAMACHY can perform measurements in both nadir and limb viewing modes (Gottwald and Bovensmann, 2011). 80 These modes usually alternate and the data collected are stored in blocks known as "states". Each nadir state is essentially an observed area on the Earth's surface, consisting of multiple ground-pixels.
The nadir viewing mode of the instrument corresponds 85 to an Instantaneous Field of View (IFoV) of 0.045 • (across track) × 1.8 • (along track). The observed area is determined by the scan speed of the nadir mirror in the across-track direction, the spacecraft speed in the along-track direction, and the integration time (IT). This gives typical ground-90 pixel sizes of 240 km × 30 km corresponding to an IT of 1.0 s and 60 km × 30 km for an IT of 0.25 s ( Gottwald and Bovensmann, 2011). Typically, a nadir state is an area of 960 km× ≈ 500 km (across × along track), consisting of 64 pixels containing the spectra to which ozone profile retrieval 95 algorithm was applied. In order to perform radiometric calibration, SCIAMACHY also observes the Sun once per day.
The L1 data provided to users are generated from raw, uncalibrated Level-0 (L0) data by spectral and radiometric calibration ( (Lichtenberg et al., 2006)). In this paper we re-100 trieve the vertical distribution of the ozone using the 265-330 nm L1 data. This wavelength range spreads over Channels 1 and 2 of SCIAMACHY, with a partial overlap. We use wavelengths 265-314 nm from Channel 1 and 314-330 nm from Channel 2. The spectrum of each channel is divided 105 into spectral clusters which are groups of wavelengths with a common integration time. These spectral clusters, and not the channels, are the organization structure of the data. The mapping of wavelengths to clusters, the spectral resolution, and IT are listed in Table 1.
The main input quantity for retrieving the ozone profile is 5 the Earth's reflectance spectrum, derived from the L1 product. In this paper the measured reflectance spectrum is defined as: where λ is the wavelength, I is the top-of-atmosphere ra-10 diance reflected by the Earth's atmosphere and surface, and E is the incident solar irradiance at top-of-atmosphere perpendicular to the solar beam. We note that this definition of reflectance is also called the sun-normalized radiance. An example of a SCIAMACHY measured reflectance spectrum is 15 shown in Fig. 1 for the spectral range used for the ozone profile retrieval.

Versions of Level-1 data
The uncalibrated L0 data are processed into two sub-levels of L1: Levels 1b and 1c. The SCIAMACHY specific calibra-20 tions applied to the L0 data are described in Slijkhuis et al. (2001). The two sublevels differ in the application of calibration steps: L1c data is processed by full calibration and contains geo-located, spectral radiance and irradiance products. Specifically the calibrated L1c data are produced using 25 ESA's SciaL1C program of v3.2.6. We make use of three different versions of L1c (hereafter called L1) data products described below: 1. v7: This is SCIAMACHY L1 version 7.04−W released in early 2012, where 'W' means the processing stage 30 flag and 7.04 is the software version number used for converting L0 into L1 data.
2. v7 mfac : This version is identical to the one above, except here we use the degradation correction factors, so-called "m-factors", that were provided independently as aux- 35 iliary data files 1 . The data structure allows to turn on and turn off the degradation correction independent of other calibrations. The m-factors are determined by the monitoring of the light path which is given by the ratio of the measured spectrum of a constant source (Sun) 40 to that obtained for the same optical path at a given time. This gives therefore the degradation of the optical path as the instrument ages. These m-factors are simple multiplication factors to the solar spectrum after the absolute radiometric calibration (Gottwald and Bovens-45 mann, 2011).
3. v8: This is version v8.02, which is the 2016 version of the SCIAMACHY L1 product. The main difference between this version and the one above is the implicit implementation of a standard degradation correction with 50 scan angle dependence. Specifically the radiometric calibration uses a scan mirror model which takes into account the physical effect of the contamination layers on the mirror. The degradation using this model gives a scan angle dependence (Bramstedt, 2014

OPERA retrieval algorithm
The Ozone ProfilE Retrieval Algorithm (OPERA), developed in KNMI (van Oss and Spurr, 2002;van der A et al., 2002), retrieves the vertical ozone profile using nadir satellite observations of scattered UV light from the atmosphere. The 5 algorithm makes use of radiative transfer computations of the top-of-atmosphere radiances given the atmospheric scattering and absorption parameters. The ozone absorption crosssection decreases from 265 nm to 330 nm which allows us to retrieve the amount of ozone as a function of atmospheric 10 height. In OPERA, the retrieval of ozone profiles uses the maximum a-posteriori approach Rodgers (2000). The state of the atmosphere and the measurement are given by the vectors x and y respectively, and the two vectors are related by the for-15 ward model F, according to y = F(x). The solution is given by the following three equations: wherex is the retrieved state vector, x a is the a priori, A is the averaging kernel, x t is the "true" state of the atmosphere,Ŝ is the retrieved covariance matrix, I is the identity matrix, S a is the a priori covariance matrix, K is the weighting function matrix or Jacobian (which gives the sensitivity of the forward model to the state vector) and S is the measurement covariance matrix. The matrices A andŜ provide valuable information on the retrieval. The sum of the diagonal elements of A (i.e. the trace) is called the Degrees of Freedom for Signal (DFS). The higher the DFS, the more the retrieval has learned from the 15 measurement. On the other hand, with a low DFS most information in the retrieval is coming from the a-priori. The total DFS gives the number of independent pieces of information present in the retrieval. The rows of A are called the smoothing functions, since they give an indication of how x t is 20 smoothed out over the layers of the retrieval. The diagonal elements of the covariance matrix give the variance at the corresponding altitude, while the off-diagonal elements are related to the correlation between the layers in the retrieval. For a comprehensive algorithm overview and retrieval configu-25 ration, along with application of the algorithm to GOME-2 data, we refer to (Mijling et al., 2010;van Peet et al., 2014).
The OPERA configuration chosen for application to SCIAMACHY data is given in Table 2. The ozone profile retrieval grid is chosen according to the Nyquist criterion. 30 For SCIAMACHY data we find that setting the retrieval grid to 31 layers or more gives the same value for the DFS. Following (van Peet et al., 2014), we have used the (McPeters et al., 2007) a-priori ozone profiles, because it is a recent climatology (includes ozone depletion) and unlike other clican also use the (Fortuin and Kelder, 1998) climatology. The reflectance measurement errors are provided in the SCIA-MACHY L1 data; a systematic relative error in the measured reflectance ("noise floor") of 0.015 is added to the measurement errors. The noise-floor is assumed the same for all L1 45 data.
In practice, the measured reflectance spectrum R meas (λ) (see Eq. 1) is prepared in the beginning of the OPERA algorithm, which is then passed to the forward model. This model contains vertical atmospheric profiles, like temperature and 50 a-priori ozone profile, geolocation, cloud data, and surface characteristics. The forward model computes sun-normalized radiances at top-of-atmosphere at wavelengths determined from the measured instrumental spectral data. After multiplication with a high-resolution solar irradiance reference 55 spectrum and convolution of simulated radiances and irradiances with the instrumental slit function, the simulated reflectance spectrum R sim (λ) is obtained. The inversion step that follows is based on the Optimal Estimation method requiring measurement, simulation and measurement errors in 60 vector/matrix forms. An inversion using derivatives of simulated reflectances with respect to the desired parameter to be solved is carried out until convergence is reached or until the maximum number of iterations is reached. For a comprehensive description of the implementation, configuration 65 and the model parameters of the algorithm we refer to the OPERA manual . As mentioned above, the averaging kernel (AK) of a retrieval represents the measurement sensitivity with respect to the true state of the atmosphere Rodgers (2000). In Fig. 2 we show an example of 70 the AK for an individual OPERA ozone profile retrieval for a SCIAMACHY state on 2004/01/07. The AK rows represent the smoothing of the true profile as a function of the ozone retrieval layers. These smoothing functions should peak at the corresponding retrieval level and the half-width is a mea-75 sure for the vertical resolution of the retrieval at that altitude. For an ideal retrieval, the curve of each row will peak at the nominal layer height with a spread that gives the vertical resolution of the retrieval. It is clear from Fig. 2 that information on the ozone amount in a certain layer is also coming from 80 other heights.  Figure 2. Example of the averaging kernel shape for a subset of seven layers from a 31-layer SCIAMACHY ozone profile retrieval. The triangles are the nominal altitudes of the retrieval layers. This subset of seven retrieval layers was selected uniformly ranging from top to bottom for clarity.   Table 3. The maximum number of iterations, n_iter, is set to 10 (see Table 2). The decreasing DFS value going from 2003 to 2009 is further illustrated in Fig. 4  Here we validate SCIAMACHY ozone profile retrievals with ozone sondes. We first compare the three different SCIAMACHY dataset versions as done above in Sect. 4.1, followed by validation results using v8 dataset for all the years, 2003-2011. The aim is to analyse the quality 65 of SCIAMACHY nadir ozone profile retrievals using v7, v7 mfac , and v8 L1 data. With a UV-visible instrument it is very hard to retrieve an accurate ozone profile in the troposphere. This is clearly shown in Fig. 4, where the DFS in the troposphere, at pressure levels from ∼ 1000 − 100 hPa, 70 is at most 1. That means that there is at most one piece of information in the troposphere. Therefore, we focus the validation on the stratospheric part of the ozone profile between ∼ 100 − 10 hPa.  . We summarize it briefly here and refer to that paper for details.
An ozone sonde profile generally has a higher vertical resolution than a satellite retrieval, and can therefore observe 15 more details in the ozone distribution. The validation should be done with the sonde profile as it would have been observed by the satellite, i.e. the sonde profile should be convolved according to the information present in the averaging kernel. The convolved (or smoothed) sonde profile is calculated 20 by convolving the original sonde profile with the AK from the retrieval according to: The smoothed sonde profile is then compared to the retrieved profiles from SCIAMACHY. Using a smoothed sonde profile instead of the original sonde profile to compare with the 25 satellite retrieved profiles influences the results in Figs. 6-7. This is discussed below. To get an impression of the shape of the SCIAMACHY averaging kernels, we refer to Figure 2. In Figure 8 a comparison between satellite and sonde profiles is shown for both cases: sonde profile convolved with 30 the averaging kernel and not convolved. The validation comparison is clearly better in the first case.

Ozone profile validation comparison between
versions v7, v7 mfac , and v8 In Fig. 6 Table 4 we see that the retrieved profile deviations (median differences in [%]) in the stratosphere are systematically smaller than in the troposphere. These large spreads in deviations of satellite retrievals from sondes are also visible 30 in Fig. 6. Any deviation above ∼ 15% in the stratosphere  [%] in the stratosphere, Column 3: Median of relative differences for the stratosphere over the specified altitude range and latitude zone, Column 4,5: Same as Column 2,3 but for the troposphere. and above 20% in the troposphere are shown in bold numbers for reference, as these are the required accuracy levels in the ESA Ozone CCI project (http://www.esa-ozonecci.org/). This behaviour is probably not only due to the rel-35 atively worsening sensitivity of UV instruments in the troposphere. Rather, it might be due to the limited quality of the SCIAMACHY L1 data. Deviations in retrieved ozone profiles in the upper troposphere and lower stratosphere have been reported due to the ozone variability in a previous study 40 of GOME-2 data (Cai et al., 2012)

Validation of v8 ozone profiles for 2003-2011
In Fig. 7 Table 2). The number of collocated pixels for all the latitude bands for each year are listed in Table 5 along with median DFS, median number of iterations required to achieve convergence, the median solar 15 zenith angle and the median deviations in % for each zone in stratosphere and troposphere. From Fig. 7 we note that validation for all latitude bands show in general smaller deviations from the zero line for earlier years than for later years.      pecially for tropics and NH bands. The median deviations given in Table 5 show often values higher than 20% (in boldface) for the troposphere whereas these values are less than 15% for the stratosphere deeming them within specifications according to the Ozone CCI requirements (see Sect. 4.1). It should be noted, however, that the large deviations in tropospheric ozone are systematically higher than those for the stratosphere for all zones and the years even for v8, whereas such deviations are not observed for instance with GOME-2 nadir profiles (van Peet et al., 2014).
It can be seen from Fig. 7 that the vertical pattern of differences has changed significantly (and not just the absolute differences) over the instrument lifetime. This important to consider when applying the profiles for ozone layer studies.
This validation of ozone profiles based on L1 v8 suggests 15 that the quality of nadir SCIAMACHY L1 data can still be improved upon. It affects the lowest troposphere in the beginning of the mission and gets worse due to instrument degradation. This is still uncorrected in the UV wavelength range. Please also note the higher deviations in the year 2003 in 20 NH and Tr latitude zones in Fig. 7 as compared to other early years. This is a unique behaviour for 2003; the cause is not clear, but it is probably related to calibration or instrument changes in the early mission. Further improvements are needed (see Sect. 5).

25
The deviations found in SCIAMACHY v8 ozone profiles can be compared, for instance, with GOME-2 ozone profile validation by van Peet et al. (2014). Their validation of tropospheric ozone showed deviations ranging from a few percent to ∼ −30% for the Northern Hemisphere, whereas we 30 find deviations that range from ∼ −10% to −45%) for the year 2008 (blue line in right panels Fig. 7). In the Southern Hemisphere, however, we find the deviations for year 2008 to range from a few percent to ∼ 20%, which is more comparable to the range of a few percent to ∼ −15% found by 35 van Peet et al. (2014).
In Fig. 8 and smoother for the case where the AK was applied to the ozone sondes. For all validations presented in this section AK smoothing of ozone sonde profiles was used.

Discussion of remaining L1 corrections
The accuracy of the retrieved ozone profile is primarily 45 driven by the spectral and radiometric calibration of the measured L1 spectra. In this section we describe two potential L1 corrections that could further improve the quality of the SCIAMACHY L1 spectra: (1) retrieval of the instrumental slit function (SF) using solar spectra; (2) radiometric bias 50 correction.

In-flight slit function calibration using solar measurements
One of the spectral calibrations often performed to assess the behaviour of an instrument in-flight is a fit of the instrumental 55 slit function (also called instrumental spectral response function). The SF parameters of SCIAMACHY were measured pre-flight and are provided as key data in the L1 product.
The slit function S of the instrument has different functional forms depending on the channel. For Channels 1-2 (relevant 60 for our ozone profile retrieval) S is described by a single hyperbolic function: The L1 key data provides the full width half maximum (FWHM), which is related to the a parameter in the equa-65 tion above. This parameter can be solved in terms of the FWHM by using the fact that at the central point (λ 0 ) we have S(λ 0 ) = 1/a 2 . Thus, a = FWHM 2 2 . At each given solar spectrum wavelength, λ i , this functional shape is numerically computed between [-1,1] nm centred at λ i . This shape 70 can be manipulated with the following four parameters: additive constant (Offset O), multiplication factor (Gain G), displacement of the spectral peak (Shift D) and expansion and contraction of the spectral peak (Squeeze S). The high resolution solar reference spectrum from Dobber et al. (2008) 75 is modified with these four parameters to best match the SCIAMACHY measured solar irradiance (E(λ)). First the spectral parameters, shift D and squeeze S, are applied to Eq. 5: 80 followed by the radiometric parameters, gain G and offset O: The unit of D is nm whereas O, G and S are numeric factors. All four parameters depend on wavelength. The parameters FWHM and λ 0 at each wavelength, taken from the v8 85 L1 key data, were identical for all the solar spectra throughout the mission. These values are given at certain wavelengths spread throughout Channels 1 and 2 and were interpolated for the wavelengths in-between. An Optimal Estimation (OE) algorithm was used to solve for the best parame-90 ter values fitting the solar spectrum measurements in-flight.
The retrieved values of the four parameters at the solar spectrum wavelengths were then also applied to the Earth radiance spectra I(λ) interpolated at the solar spectrum wavelengths.

95
Thus for each wavelength of the solar spectrum the parameter values are computed using the above slit function model. Each spectral peak of the solar reference spectrum can be transformed by manipulating the SF using Offset, Gain, Shift, and Squeeze until it fits the measured spectrum.    . Comparison between SCIAMACHY retrieved ozone profiles and ozone sonde profiles with applying averaging kernels (AK, solid lines) and without applying averaging kernels (dashed lines). Here the L1 v8 data set is used.
These spectral manipulations can be modelled as a polynomial of order n at the desired channels. The fit is checked by evaluating the relative difference between the solar irradiance measurement and simulation, which is the relative residual. The relative residuals for the best fit are shown in Fig. 9. Each curve is a residual for one solar spectrum, where the blue line is achieved by using only Gain and Offset in the model and the red line is achieved by including the Shift and Squeeze.
We find that the wavelength range 265-308 nm is the optimal range for obtaining the smallest residuals in Channel 1.
However, the ozone profile retrieval algorithm requires spectra from 260 nm onwards. Because the part of Channel 1 above 308 nm is known to suffer of calibration problems, the SF fit in Channel 1 is performed for the range 260-308 nm. We ran the optimal estimation on all solar measurements of the SCIAMACHY mission for each day, which amounts to 3463 solar spectra. We convolved all spectra with {Offset, Gain, Shift, Squeeze} of polynomial order of = {2, 15, 2, −} and found that the cost function for the majority of cases reaches less than 1 (as expected) within 10 iterations in the 20 Optimal Estimation routine. By using a spectral shift in the range 265-308 nm instead of in the entire band 265-314 nm the residuals were significantly reduced (see left-panel in Fig. 9). No SF fit was possible between 308-314 nm. Thus, from 308 nm onwards we used the Channel 2 spectra. 25 The residuals in Channel 2 are somewhat larger than those in Channel 1 (see Fig. 9). The dashed lines in both panels of the figure mark the ±2% residuals for reference. Dividing the relevant range of 308-330 nm into smaller ranges to get smaller residuals did not reduce the residuals any further. 30 For the optimal wavelength divisions, we found the smallest residuals given by the polynomial orders of the set of {Offset, Gain, Shift, Squeeze} = {1, 4, 1, 2}. In Channel 2, we find that using spectral shift and squeeze in the range 308-330 nm reduces the relative residuals significantly. The relative er- 35 rors of the L1 solar irradiance in the wavelength range used for ozone profile retrieval, 265-330 nm, are only in the order of 10 −5 . However, the relative residuals are in the order of a few percent. So we expect this error to propagate into the ozone profile retrieval. There are strong residuals at around 40 279 nm, 280 nm and 285 nm, due to the MgI and MgII lines in the solar spectra. These spectral windows were therefore not used in the ozone profile retrieval (see Sect. 2). Figure 10 shows the temporal behaviour of the slit function parameters for Channel 1 (top row) and Channel 2 (bot-45 tom row) as density plots; the fitted parameter value for each wavelength and each day of the year is shown. The seasonal dependence of solar irradiance is observed, as expected, in the Gain parameter for both channels. The other parameters do not show a clear seasonal dependence or a clear trend over 50 the mission time.

Radiometric bias correction
As shown above, spectral corrections like shift and squeeze at UV wavelengths can further improve the solar spectra by several percent (see Fig. 9). However, the expected improve-55 ment from this is less than the degradation and other remaining potential biases for the L1 data, which are increasing with the mission time. A preliminary analysis of this is shown in Fig. 11, where the mean ratio of observed to simulated reflectance spectra (R meas /R sim ) is plotted for the day of June 60 24 for years 2003-2011. There is a strong deviation of this ratio from one below 300 nm and this becomes worse for later years. A detailed study of this radiometric bias is beyond the scope of this paper. Please note the odd behaviour of the reflectance ratio around 283 nm. This was found to be due to 65 a jump in the value of the Earth radiance at the transition of cluster 3 to cluster 4 owing to the difference in integration time. This region is therefore blocked in our retrieval algorithm.
A L1 reflectance bias correction can significantly improve 70 the quality of L1 data and will influence the validation and other results in this paper from their ozone retrievals. Furthermore applying these bias corrections would also make it meaningful to apply the spectral slit function corrections that can potentially improve the ozone retrievals further. Thus a 75 detailed study of the effect of such bias corrections on the L1 data can be investigated against the quality of the ozone retrieval algorithm to better understand the quality of the SCIAMACHY nadir data. 80 We have performed SCIAMACHY nadir ozone profile retrievals using the OPERA algorithm from three L1 data sets, namely v7, v7 mfac and v8. We have used the latest complete dataset v8 for almost the entire SCIAMACHY mission length from 2003 to 2011. Differences between L1 datasets 85 with and without degradation corrections (m-factors) were analysed in the wavelength range of 265-330 nm and show that the degradation correction including the scan-angle dependence in the v8 dataset gives the most smooth ozone profiles. This improved quality is also reflected in the global 90 validation of retrieved ozone profiles against ozone sondes. The comparison between different L1 versions shows that v7 gives significantly worse ozone profiles, especially later in the mission compared to v7 mfac and v8, where the profiles of v7 show a double peak for the year 2009 and an over-all 95 reduced amount of ozone. Thus L1 v8 should be used for the nadir ozone profile applications of SCIAMACHY data. We have found that further improvement of L1 data is possible. Retrieving the instrument slit function in the UV range for the v8 data set gives an improvement of a few percent 100 in the solar data through the mission length. The measured reflectance spectra show that the degradation in v8 is still significant for some wavelengths, because the ratio of the measured to simulated reflectance spectra below 300 nm can range from ∼ 1.1 − 1.4. This could be corrected empirically by including a bias correction in the ozone profile retrievals.