Stratospheric Extinction Profiles from SCIAMACHY Solar Occultation

Abstract. The SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric CHartographY) instrument on ENVISAT provided between August 2002 and April 2012 measurements of solar and Earthshine spectra from the UV to the SWIR spectral region in multiple viewing geometries. We present a new approach to derive stratospheric aerosol extinction profiles from SCIAMACHY solar occultation measure5 ments based on an onion peeling method similar to the Onion Peeling DOAS (Differential Optical Absorption Spectroscopy) retrieval, which has already been successfully used for the derivation of greenhouse gas profiles. Since the retrieval of aerosol extinction requires as input measured transmissions in absolute units, an improved radiometric calibration of the SCIAMACHY solar occultation measurements has been developed, which considers various instrumental and atmospheric effects specific to solar occultation. 10 The extinction retrieval can in principle be applied to all wavelengths measured by SCIAMACHY. As a first application, we show results for 452 nm, 525 nm and 750 nm. The whole SCIAMACHY solar occultation time series has been processed, covering a latitudinal range of about 50–70◦N. Reasonable extinctions are derived between about 15 and 30 km with typically larger uncertainties at higher altitudes due to decreasing extinction. Comparisons with collocated SAGE II and SCIAMACHY limb aerosol data products revealed a good agreement with 15 essentially no mean bias. However, depending on altitude differences of up to±20–30% to SAGE II at 452 nm and 525 nm are observed. These differences are mainly caused by systematic vertical oscillations in the SCIAMACHY occultation data. The agreement with SCIAMACHY limb data is even better (typically within 5–10% between 17 and 27 km). Major volcanic eruptions as well as occurrences of PSCs can be identified in the time series of extinction data and related anomalies. Influence of the Quasi-Biennial-Oscillation (QBO) are visible above 25 km. Estimated linear changes of extinction 20 between 2003 and 2011 reach 20–30% per year at 15 km, mainly because all relevant volcanic eruptions (above 50◦N) occurred after 2006.


SCIAMACHY spectra
The SCIAMACHY solar occultation data used in this study were extracted from the SCIAMACHY Level 1 Version 8 product with all calibrations applied except for polarisation correction as solar irradiances are unpolarised. Additional pointing corrections as described in Bramstedt et al. (2017) have been applied such that the tangent height knowledge is better than 26 m.
These radiance measurements are then converted into transmissions using additional corrections as will be described in detail 70 in section 3.

ECMWF ERA Interim
ECMWF ERA Interim model data (Dee et al., 2011) are used in the retrieval to account for actual pressure and temperature profiles (see section 4.1). These data are available every 6 hours on a 0.75 • horizontal grid and on 60 altitude levels.

SAGE II profiles 75
The SAGE II instrument performed solar occultation measurements from 1984 to 2005 and provided extinction profiles at several wavelengths (386 nm, 452 nm, 525 nm, 1020 nm) as well as profiles of O 3 , NO 2 and H 2 O. In this study we use SAGE II V7.00A sunset extinction data (Damadeo et al., 2013) from the overlap period with SCIAMACHY (2002SCIAMACHY ( to 2005 at 452 nm and 525 nm for comparisons. We selected collocated data within a maximum spatial distance of 800 km and a maximum temporal distance of 9 h. However, the latter is no major restriction; since both data sets are based on sunset measurements, the 80 actual temporal differences are always smaller than 1 h.

SCIAMACHY limb aerosol
The SCIAMACHY limb aerosol extinction product V1.4 was obtained by using the algorithm described in Rieger et al. (2018).
It comprises stratospheric profiles derived from SCIAMACHY limb measurements at 750 nm. The data have been filtered according to the recommendations given by the data providers in the accompanying README file; especially, invalid data 85 and data points with a vertical resolution larger than 7 km or extinctions exceeding 0.1 km −1 have not been used. The spatial collocation criterion is the same as for SAGE II, but we used a maximum temporal distance of 10 h. This is necessary to achieve also collocations in summer. 2. Switch-on the so-called sun follower in azimuthal direction to horizontally align the viewing direction to the intensity centre of the sun.
3. Follow the rising sun while scanning vertically around the (predicted) centre of the sun until about a tangent altitude of 100 100 km.
Above 100 km either special solar calibration measurements are performed or the scan over the sun is continued up to about 250 km. In this study, we concentrate on data below 100 km, such that all available solar occultation measurements can be used.

105
The extinction retrieval (see below) requires as input atmospheric transmissions. In order to derive these transmissions, the individual SCIAMACHY spectra are in a first step normalised to a reference spectrum obtained at a high tangent altitude of about 90 km. This is done independently for up-and downward scans. With this, all possibly erroneous multiplicative calibration factors (e.g. most degradation effects or systematic errors in radiometric calibration) cancel out, which is why occultation measure-110 ments are sometimes called 'self-calibrating'.
However, this is not really the case for SCIAMACHY because of the scan over the sun. The width of the instantaneous field of view (IFOV) of SCIAMACHY is in solar occultation mode about 0.7 • , the height about 0.045 • . As the diameter of the sun is about 0.5 • , this implies a strongly varying signal over the scan as different parts of sun are seen at each readout. Furthermore, altitude range than a downward scan. However, as can be seen in the bottom right figure, the variation of the signal becomes very similar when plotted as function of angular (vertical) distance from the centre of the sun. The thick black line in this figure shows the result of a simple geometrical model of the varying area when assuming a circular sun disk of diameter 0.26 • with homogeneous brightness. The overall shape of the measurements is reproduced quite well by the black line; the deviations are caused by the facts that 1) the real sun does not have the same brightness everywhere (mainly because of limb darkening 130 effects) and 2) the measured signal is an integral over the IFOV in vertical direction (0.045 • correspond to about 2.6 km) which smears out the black curve along the x axis.
The left plots of Fig. 3 show the corresponding measured transmissions for various scans at lower tangent altitudes as function of tangent height (top left) and distance to the sun centre (bottom left). The normalisation is the same as for the right plots, i.e. all upward/downward scans (even/odd numbers) are normalised to the maximum value of of the reference 135 measurement (green/red curve in the right plot). Due to increased atmospheric absorption and scattering the transmissions decrease at lower altitudes. In addition, as can be seen in the bottom left plot, the maximum signal of the scan shifts to the right with decreasing altitude due to increasing refraction.
The plots of Fig. 3 also show that the measured signal for one scan is not symmetrical relative to the sun centre, i.e. the signal drops to zero only on one side. This is because the position and elevation rate of the sun assumed in the commanding 140 of the measurement was derived from predicted orbital information. This results in a scan which is not exactly centred on the (true) sun. This may also lead to azimuthal offsets (see right plot of Fig. 2), which are corrected by use of the sun follower (see above), but this can introduce jumps in the signal at altitudes around 17 km which require special treatment (see Appendix A).
To correct for the scan effect, we define a (numerical) sun shape function S, which is the interpolated measured transmission (T m ) for a scan around a reference altitude of about 90 km as function of angular distance from the centre of the sun (α), as 145 shown in Fig. 3 (bottom right). This is done for each measurement and independently for both up-and downscan in order to reduce possible systematic effects caused by the scan direction.
The actual α is then calculated for each measurement by using the viewing direction (defined by the line-of-sight (LOS) zenith angle γ) and the direction of the 'true' sun (i.e. without refraction) β. The latter is essentially the solar zenith angle (SZA) at the satellite, i.e. β = 180 • − SZA. The LOS zenith angle γ and the solar zenith angle are given in the SCIAMACHY

150
Level 1 product for the centre of the IFOV. As we assume a horizontally homogeneous atmosphere (within the range of one measured profile) azimuthal differences are not relevant in this context. However, as mentioned before, possible azimuthal jumps at lower altitudes need to be considered, see Appendix A.
To account for refraction effects we use a simple model similar to the one used in the SAGE II project (Damadeo et al., 2013), see Fig. 4. It is assumed that refraction occurs only at the tangent point with the basic parameter being the bending angle 155 (δ). This bending angle decreases with altitude and is essentially a function of pressure. In the stratosphere, the overall altitude variation of δ can therefore be described by an exponential function of tangent height z: The parameters a and b depend on atmospheric conditions (and also on wavelength) and are different for each measured profile. b is typically negative, as refraction effects decrease with altitude. Therefore we determine these parameters from the 160 measurements (see Appendix B). From these we then get for each measurement the bending angle δ from which we calculate the distance α of the observed point on the sun to the sun centre via: The expected transmission corresponding to this distance is then given by the sun shape function S(α) derived from the reference scans (see above). The scan-corrected transmission T as function of tangent altitude z i for readout i of an occultation 165 measurement is then given by:

Selection of subset of readouts
Prior to the retrieval (see Section 4.1) the measured transmissions need to be interpolated to a fixed altitude grid. Therefore it is sufficient to use only a subset of the measured spectra for this. This subset is basically selected by using readouts with the 170 highest (uncorrected) transmission signal, which corresponds e.g. to the envelope of the data points shown in the top left plot of Fig. 3. As an additional criterion, we only take data points with an altitude difference of 0.5 km or larger (when starting at the top and then going downwards in altitude). An example showing the results of this procedure is given in section 5.1.

Retrieval method
The basic idea for the aerosol extinction retrieval is to use a two step approach: 175 1. Apply the Onion Peeling DOAS (Differential Optical Absorption Spectroscopy) retrieval method to correct the measured transmissions for Rayleigh scattering and gas absorptions.
2. Use an onion peeling method to determine extinctions from corrected transmissions for different altitude layers, starting with the highest layer.
These two steps are described in more detail in the following sub-sections.

180
With this approach it is possible to determine extinctions even at wavelengths where gases absorb (since this absorption is fitted). In addition, the method also delivers profiles of the absorbing gases. However, these derived stratospheric gas profiles (in the present case for O 3 and NO 2 ) are not the primary focus of the current study as retrieval settings are optimised for aerosol extinction.

185
The Onion Peeling DOAS (ONPD) retrieval method has been originally developed to derive stratospheric profiles of greenhouse gases. So far, it has been applied to the retrieval of water vapour, CO 2 and methane (Noël et al., 2010(Noël et al., , 2011(Noël et al., , 2016(Noël et al., , 2018. The retrieval method is described in detail in these publications; we therefore give here only a basic summary and the specific settings used in the context of this study.

Description of method 190
In the ONPD approach the atmosphere is divided into layers. All measured transmission spectra are interpolated to this grid. For each tangent height j a weighting function DOAS fit (see e.g. Coldewey-Egbers et al., 2005) is performed using the following formula: Here, T interp j is the (interpolated) measured transmission for tangent height j. T j,ref is a reference transmission derived for the 195 same viewing geometry from a radiative transfer model, in our case SCIATRAN V3.7 (Rozanov et al., 2013) in occultation mode. The index i refers to the atmospheric layers, k to the different absorbers considered in the fit. w ij,k is the relative weighting function, which is also derived by the radiative transfer model. It describes how the (logarithmic) transmission for tangent height j changes if the amount of absorber k is changed by 100% in layer i. a i,k is a scalar factor, which describes the actual change of absorber k in layer i relative to the assumptions in the radiative transfer model. Spectrally broadband 200 absorption and scattering (especially due to aerosols) is described by a polynomial P j .
The factors a i,k and the polynomial P j are fitted for each layer j, starting at the top layer and then propagating downwards. In considered in the present study and with the improved calibration performed here we expect that this validity range can be extended even to somewhat lower altitudes, see also below.

210
The general ONPD settings are the same as described in Noël et al. (2018). We use a vertical layering from 0 to 50 km with 1 km steps. In general, the ONPD method uses a fixed data base of reference transmissions derived with SCIATRAN assuming conditions of the 1976 US standard atmosphere (NASA, 1976). We correct for the actual conditions by using corresponding weighting functions via Eq. (4). For pressure and temperature this is done by using as input data from the ECMWF ERA Interim model. We select the profiles spatially and temporally closest to the measurements and interpolate them to the ONPD 215 altitude grid.
In the current study, we have performed calculations for three different extinction wavelengths λ ext (452, 525 and 750 nm).
The degree of the fitted polynomial is 2 in these cases. For consistency reasons and because the fitting windows are optimised for the extinction retrieval we use a specific sequence of retrievals such that information obtained in one retrieval can be used in other retrievals. Therefore we start with the retrieval for λ ext =525 nm, from which we obtain O 3 and NO 2 profiles which 220 are then used in the other retrievals. The detailed settings for each retrieval are summarised in Table 2.

Extinction retrieval
The standard ONPD method does not require fully calibrated data as input as the fitted polynomials P j also account for possible multiplicative radiometric offsets, i.e. as caused by the scan over the sun.
In the present study we use fully calibrated transmissions as input. Therefore, the polynomials P j should essentially contain 225 information about extinction in the atmosphere. This can be described by the following formula: P j (λ ext ) is the value of the polynomial P J derived from the ONPD retrieval at the wavelength λ ext , at which we want to determine the extinction. l ij is a (fixed) geometric factor which describes the length of the occultation light path in layer i when looking layer j. These path lengths are also derived from SCIATRAN for each atmospheric layer and viewing direction and 230 consider refraction. They therefore also depend slightly on wavelength. i is the extinction in layer i; this is the quantity we want to derive. This is done -consistently with the ONPD approach -by use of an onion peeling method: We start at the top layer and then propagate downwards while taking into account the results from above. Contributions from below the current tangent j (due to refraction and vertical size of the IFOV) are considered by assuming i = j for i < j when determining j . Since extinction 235 typically increases with decreasing altitude this results in a small over-estimation, but gives a stable solution.

Example 11 September 2003
To illustrate the outcome of the different calibration and retrieval parts described in the previous section we present in this subsection as an example the results for orbit 8014 (on 11 September 2003). This orbit has been selected due to a close 240 collocation of a corresponding SAGE II measurement, such that a direct comparison of extinction results is possible (see below). The right column of Fig. 5 shows the selected transmissions after the corrections explained above, which now smoothly decrease with altitude as it is expected. The variation of transmission with altitude is different for each wavelength due to different absorbing and scattering effects. In general transmissions at shorter wavelengths are lower at lower altitudes mainly due to ozone absorption and stronger Rayleigh scattering. Below 10 km transmissions are close to zero due to the low input 250 signal, which gives a lower limit for the later retrieval. At altitudes above about 30 km transmissions are close to one. Since extinction information is obtained from the difference of the transmission to one, this also implies an upper limit for the retrieval (see below).
The selected and corrected spectra are then fed into the ONPD retrieval (see section 4.1), in which the background polynomial is fitted considering gas absorptions and Rayleigh scattering. The results of this retrieval for orbit 8014 are shown in -The corrected measured logarithmic transmission at 25 km (thick grey line).
-The SCIATRAN reference model spectrum for US standard atmosphere conditions, incl. Rayleigh scattering (green line).
-The model spectrum corrected for actual temperature, pressure and absorption of gases as derived from the fit (blue line).
-The fitted spectrum, i.e. the combination of the contributions of reference spectrum, absorption and polynomial (red line).
As the fit result (red) is very close to the measurement (grey) the right column of Fig. 6 shows the residual of both (measurement -fit), which is quite low (standard deviation below 0.002) indicating a good fit.

265
The white circles on the pink lines in Fig. 6 mark the value of the polynomial at the wavelength to be used for extinction retrieval. This is the value for 25 km; the complete profiles from 10 to 50 km are presented in the top of Fig. 7. These profiles show the remaining transmission after effects of Rayleigh scattering and gas absorption have been subtracted. The difference to one can thus be interpreted as the effect of extinction.
The profiles of Fig. 7 are used as input for the extinction retrieval (see section 4.2). The resulting extinction profiles are given 270 in Fig. 8. For comparison, we also plotted collocated SAGE II (at 452 and 525 nm) and SCIAMACHY limb aerosol extinction (at 750 nm) profiles. The error bars correspond to the error given in the product files. For SCIAMACHY occultation, this error is derived from the propagation of the transmission errors (Fig. 7 bottom). It does not consider any systematic contributions and is therefore only a lower estimate.
The overall agreement between SCIAMACHY occultation and SAGE II is quite good. Above about 30 km transmissions are 275 close to one (see Fig. 7). Thus, SCIAMACHY occultation errors typically increase and the retrieved extinctions become very noisy. Furthermore, at higher altitudes vertical oscillations occur, which are artefacts probably introduced by the onion peeling method; similar effects have been seen in greenhouse gas retrievals (see e.g. Noël et al., 2018).
At 750 nm, the retrieved SCIAMACHY limb and aerosol extinctions are also quite similar. The vertical sampling of the limb data is however much sparser. Noise and error of the occultation data is smaller; oscillations at higher altitudes are more 280 pronounced than at lower wavelengths. The extinction minimum in the limb data at about 15 km is not seen in the occultation data.

Validation
In this section we show the results of a comparison between the SCIAMACHY solar occultation V5.1.1 extinction data and corresponding profiles from the SAGE II V7.00A and the SCIAMACHY limb aerosol extinction product V1.4. Collocation Because of the larger random and/or systematic errors at higher altitudes (see previous subsection) we currently consider only SCIAMACHY solar occultation extinction data below 30 km as reliable. In addition, SCIAMACHY occultation data 290 below about 15 km have to be treated with care, as e.g. the greenhouse gas occultation retrievals are known to give less accurate results there because of tropospheric influences not covered by the retrieval method (like increased refraction and strong vertical gradients at the tropopause). For the validation activities described in this section and later analyses we will therefore concentrate on the altitude range 15-30 km.
The results from the comparison with SAGE II at 452 and 525 nm are shown in Fig. 9.

295
Since extinctions exponentially decrease with altitude, mean differences and standard deviations of the differences decrease towards higher altitudes whereas relative differences increase. In general, there is no obvious bias between the SCIAMACHY occultation results and the correlative data sets visible, but especially at 452 nm the mean occultation profile shows an oscillation with altitude which is not present in the SAGE II data. This results in an oscillation of the differences with an amplitude of about 20-30% and an estimated period of about 10 km. For upper altitudes (above about 25 km) at 525 nm this oscillation 300 even causes mean differences larger than 50% to SAGE II.
These kind of oscillating features have been observed in other ONPD products (see e.g. Noël et al., 2018). It is assumed that these are related to the onion peeling method which does not include e.g. regularisation on these vertical scales.
The mean error of the SCIAMACHY occultation product is at all wavelengths smaller than the standard deviation of the differences confirming that this error is indeed only a lower estimate. The standard deviation of the mean profiles is very similar 305 for all comparisons. This indicates that all instruments / viewing geometries observe a comparable atmospheric variability.
For the comparison of SCIAMACHY occultation data with limb extinctions at 750 nm we divided the collocation data set into two parts corresponding to background conditions (defined by maximum extinctions below 0.001) and perturbed conditions (all others). The results are shown in Fig. 10.
Because of the large number of collocations the error of the mean difference is very small (dotted and solid red lines are 310 almost on top of each other).
For the background case, the comparison reveals a very good agreement below 27 km within ±5-10%. The standard deviations of the mean profiles are very similar for occultation and limb data, so variability is also comparable.
Under perturbed conditions, the atmospheric variability is much higher both in the spatial and temporal domain. The time offset of up to 10 h between occultation and limb measurements therefore results in a larger scatter between the two data sets 315 and significantly increased standard deviations of differences and mean profiles of more than 100%. This is why the lower limit lines of the standard deviations are not always visible in the logarithmic profile plot (d). The variability for limb is even larger than for occultation, possibly because occultation measurements occur always at the same local time (sunset). However, the average agreement of the two data sets is very good between about 17 and 27 km.
Below 17 km deviations up to 50% are observed. This is in line with comparisons of OSIRIS and SCIAMACHY limb 320 extinctions with SAGE II data (Rieger et al., 2018), which also revealed discrepancies of similar magnitude and sign at higher latitudes. It is assumed that these differences are due to the assumptions on particle sizes made in the limb retrievals, which are most crucial for high Northern latitudes because of low scattering angles.
Above 27 km deviations increase with occultation data being typically larger. This is most likely also related to oscillations in the occultation profiles (see Fig. 8).

Extinction time series
The complete time series of SCIAMACHY solar occultation data has been processed for the three extinction wavelengths investigated in the present study. After filtering out invalid data (from times of non-nominal instrument performance, e.g. during decontamination periods) in total 43686 profiles (from August 2002 to April 2012) remained, from which daily average 330 extinction profiles were created. Because of the sun fixed ENVISAT orbit, all measurements of one day occur at essentially the same latitude but different longitudes. Thus, the geographic latitude of the measurements varies systematically with season and the daily averages are also zonal means (see also Noël et al., 2018). Higher latitudes (∼65-70 • ) typically occur in winter and lower latitudes (∼50-60 • ) in summer. The observed extinctions also vary with season, which is partly caused by the systematic coupling between time and latitude mentioned above and the related variations in tropopause height.

Anomalies
To further investigate the temporal behaviour and to reduce the influence of possible systematic features in the data (e.g. vertical 345 oscillations, see above) we computed monthly relative anomalies of the extinction. We concentrate here on the years 2003 to 2011 to avoid possible influences of missing months in the first and the last year on the weighting of data points.
For this, we first generated for each altitude monthly means from the daily average profiles. From these monthly averages we then subtracted the 2003 to 2006 average value for each month to obtain absolute anomaly profiles. These data are then divided by the mean of the monthly average extinction profiles from 2003 to 2006 to remove the overall vertical shape of the 350 extinction profiles (especially the exponential decrease with altitude). We do not use data after 2006 to determine the mean extinction profiles to avoid influences of the prominent volcanic eruptions at lower altitudes (as seen in Fig. 11). The reference for the anomalies can therefore be interpreted as a "background time" mean.
The resulting relative anomalies may then be plotted using a common linear scale for all altitudes which facilitates the interpretation of the data. As already seen in the extinction plots ( Fig. 11) extinctions increased during times of volcanic 355 influences by more than a factor of 10. These events are of course also clearly visible in the relative anomalies, but here we want to focus on smaller effects which cannot directly be inferred from the extinction time series. Therefore we concentrate on the range of relative anomalies between ±4. Fig. 12 shows the monthly relative anomalies generated by the procedure described above using this scale.
Below 20 km, in addition to the three periods of volcanic influences after mid 2008 the "background time" before 2007 can 360 be clearly identified. During this time interval relative anomalies are close to zero, but slightly increasing with time.
Especially at the lower wavelengths a small increase of relative extinction anomaly at the beginning of 2007 is observed. Changes smaller than the 2σ error derived from the fit (indicated by shaded areas around the lines) are considered to be insignificant. The results are quite similar for all wavelengths and also for limb data (green) and occultation data (red). Comparisons with SAGE II data products show a good agreement with essentially no mean bias but altitude dependent 400 differences in the order of 20-30%. These differences are mainly due to unexpected vertical oscillations in the SCIAMACHY extinction profiles with a period of about 10 km. It is assumed that these oscillations are caused by the onion peeling retrieval method, as similar effects have been seen in the analysis of greenhouse gas profiles derived from SCIAMACHY solar occultation measurements (Noël et al., 2018). The overall agreement with SCIAMACHY limb data at 750 nm is quite good between about 17 and 27 km (5-10%). At higher and lower altitudes deviations up to about 50% are observed, which are caused by 405 oscillations in the occultation data (above 27 km) and deficiencies of the limb data at higher latitudes (below 17 km). The scatter in the data is especially large during perturbed / high aerosol load conditions. Time series of SCIAMACHY solar occultation extinctions and related anomalies show the expected influences of major volcanic eruptions reaching the stratosphere, which cause a sudden increase of extinction by one magnitude or more below 20 km followed by a gradually decrease / downward transport over several months. Furthermore, some enhanced extinctions 410 during polar winter time were detected between 20 and 30 km which are attributed to the presence of PSCs.
A systematic variation of extinctions with season is observed, which is caused by the spatial/temporal coupling of the SCIAMACHY solar occultation measurements resulting in a regular variation of the tropopause height over the year. At altitudes above 25 km also QBO effects are seen, which is in line with the results of greenhouse gas studies (Noël et al., 2018). These results show, that the new SCIAMACHY solar occultation extinction data products are of reasonable quality and 420 useful for geophysical interpretations. As for the corresponding greenhouse gas data the quality of the products seems to be mainly limited by systematic effects, especially by vertical oscillations at altitudes above 30 km.

Appendix A: Azimuth correction
Switching to the sun follower (SF) in azimuth at about 17 km tangent height may result in different azimuthal positions of the IFOV before/after the switch, resulting in a jump of the measured signal to a higher value. Azimuth mispointing may also 425 occur due to a mismatch between the predicted (commanded) and true sun position. This is only critical, if the angular shift is so large that part of the sun is not inside IFOV (see right plot in Fig.2). The effect on the signal due to this missing area can be corrected using the known position of the IFOV on the sun (see above), but this requires the knowledge about the width of the IFOV. Unfortunately, there is not much information from SCIAMACHY on-ground calibration about the IFOV in solar occultation geometry, because this uses a smaller aperture than in the standard Earthshine measurements. This small aperture 430 reduces the light by 3-4 orders of magnitude, which makes measurements with typical on-ground light sources difficult as they would require long integration times. Usually, a typical value of 0.72 • is given for the small aperture IFOV width (see e.g Gottwald and Bovensmann, 2011).
To investigate the impact of azimuthal jumps in the signal after switching on the SF on the final aerosol product we looked at discontinuities in the retrieved extinctions around 17 km as function of IFOV width. It turned out that only data a few 435 kilometres around 17 km are affected by the azimuth jumps. Smoothest profiles are achieved when assuming an IFOV width of 0.68 • , which is why we used this value in our study.

Appendix B: Bending angle fit
The underlying assumption for the determination of the bending angle is that the atmosphere does not change during one occultation measurement. This, however, is a general assumption of the retrieval method. The bending angle can then be 440 determined using the fact that altitudes of adjacent upward/downward scans overlap. This is illustrated in Fig. A1, which shows as example the (uncorrected) measured transmissions T m 1 and T m 2 of two upward scans (nos. 18 and 20). These two measurements are centred around different tangent heights, but the covered altitude ranges overlap. Let P 1 be the point where the transmission of scan 18 is highest. This occurs at a tangent altitude z 1 of about 33.5 km. If we interpolate the transmissions of scan 20 to this altitude, we get point P 2 . The points (P 1 ,P 2 ) therefore correspond to an observation of the same tangent 445 altitude, but for different viewing directions (γ 1 , γ 2 ) and for different sun positions (β 1 , β 2 ). Since the observed point in the atmosphere is the same, the scan-corrected transmissions should also be the same, i.e.: The fact that we observe different transmissions (T m 1 (z 1 ) > T m 2 (z 1 )) is due to refraction, i.e. the (same) bending angle δ(z 1 ) at this altitude.

450
Combining Eqs. (B1) and (3) leads to: This equation can be solved numerically to derive δ(z 1 ). In principle, this procedure can be applied to all pairs of scans; however, it is practically limited by the low transmissions at lower altitudes and too small refraction at higher altitudes. We therefore restrict the application to the altitude range 15 to 35 km, which gives us about five data points of δ for different 455 tangent altitudes z.
We then fit a straight line to log δ(z) to derive the parameters a and b from Eq. 1. This is done independently for each considered wavelength. An example for this is show in Fig. A2.