Accounting for the photochemical variation of stratospheric NO 2 in the SAGE III/ISS solar occultation retrieval

. The Stratospheric Aerosol and Gas Experiment (SAGE) III has been operating on the International Space Station (ISS) since mid 2017. Nitrogen dioxide ( NO 2 ) number density proﬁles are routinely retrieved from SAGE III/ISS solar oc-cultation measurements in the middle atmosphere. Although NO 2 density varies throughout the day due to photochemistry, the standard SAGE NO 2 retrieval algorithm neglects these variations along the instrument’s line of sight by assuming that the number density has a constant gradient within a given vertical layer of the atmosphere. This assumption will result in a 5 retrieval bias for a species like NO 2 that changes rapidly across the terminator. In this work we account for diurnal variations in retrievals of NO 2 from the SAGE III/ISS measurements, and determine the impact of this algorithm improvement on the resulting NO 2 number densities. The ﬁrst step in applying the diurnal correction is to use publicly available SAGE III/ISS products to convert the retrieved number density proﬁles to optical depth proﬁles. The retrieval is then re-performed with a new matrix that applies photochemical scale factors for each point along the line of sight according to the changing solar zenith 10 angle. In general NO 2 that is retrieved by accounting for these diurnal variations is more than 10% lower than the standard algorithm below 30 km. This effect is greatest in winter at high latitudes, and generally greater for sunrise occultations than sunset. Comparisons with coincident proﬁles from the Optical Spectrograph and InfraRed Imager System (OSIRIS) show that NO 2 from SAGE III/ISS is generally biased high, however the agreement improves by up to 20% in the mid stratosphere when diurnal variations are accounted for in the retrieval.


Introduction
The Stratospheric Aerosol and Gas Experiment (SAGE) III on the International Space Station (ISS) uses solar occultation to measure the attenuation of sunlight through the middle atmosphere (Cisewski et al., 2014). These measurements are used 20 to retrieve vertical profiles of nitrogen dioxide (NO 2 ), as well as other atmospheric constituents, mainly ozone and aerosol NO2 number density calculated with PRATMO photochemical box model. latitude, longitude, and date. These input parameters are kept constant. The model then calculates a set of chemical reactions 55 over a single day, iterating until the start and end values converge (Prather, 1992). This results in a 24 hour steady-state system of each species in the model. The model outputs are the NO 2 profiles at any predetermined SZAs. These values can be used to scale the measured NO 2 to different solar times in order to account for variations in SZA along the measurement LOS (Section 4). PRATMO scaling was used in several previous studies (e.g. Adams et al., 2017;Park et al., 2017;Dubé et al., 2020)  The irradiances are used in the standard SAGE III/ISS retrieval (version 5.1, SAGE III Algorithm Theoretical Basis Document, 2002) to determine the number density of several species, as well as the aerosol extinction at several wavelengths.
The first step in the algorithm is to calculate slant path transmission profiles for each wavelength channel from the measured irradiance. Each slant path transmission profile is converted to a slant path optical depth profile that contains contributions from Rayleigh scattering, aerosol extinction, and absorption by at least one species. With this information NO 2 and O 3 slant path number density profiles are solved for simultaneously using multiple linear regression. NO 2 is retrieved from channel 75 S3, covering 433 to 450 nm. The slant path number density is converted to vertical number density profiles using a global fit method that assumes each layer of the atmosphere is a spherical shell with a constant gradient. The final NO 2 number density is available from 10 to 45 km on a 0.5 km grid with a vertical resolution of about 1.5 km. The reported uncertainty in the SAGE III/ISS NO 2 is around 5% at 30 km, and increases to up to 20% at 10 km and 40 km. This uncertainty is due to measurement noise only, and does not account for systematic bias due to the horizontal homogeneity assumption.

OSIRIS
OSIRIS has been in sun-synchronous orbit on the Odin satellite since October 2001 (Murtagh et al., 2002;Llewellyn et al., 2004). There are 100 to 400 vertical profiles of limb-scattered solar irradiance measured each day, at wavelengths from 280 to 800 nm. NO 2 is retrieved by spectral fitting in the wavelength range from 435 to 477 nm for altitudes from the cloud top to 39.5 km with a resolution of 2 km.  The OSIRIS LOS is approximately aligned with the terminator so the variation in SZA along the LOS is much smaller than for occultation instruments. McLinden et al. (2006) studied the effect of the diurnal error on NO 2 from OSIRIS and found that it is only significant when the SZA is near 90 • and the solar azimuth angle varies significantly from 90 • . These extreme conditions occurred in 16% of profiles from 2004, resulting in errors of up to 35% in the OSIRIS NO 2 below 25 km. Sioris et al.
(2017) used PRATMO to create a 2D OSIRIS NO 2 retrieval to further assess the impact of diurnal variations on the results.

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They found minimally improved agreement between OSIRIS NO 2 and NO 2 from balloon measurements, particularly below 20 km. Owing to the minimal effect for OSIRIS, the standard NO 2 data product is produced neglecting the NO 2 photochemical gradient.
its altitude. Figure 2 illustrates this geometry. The black arrow represents the LOS, pointing from the instrument to the sun.
The SZA at a given location is the angle between the dashed line and the LOS.
The SAGE III/ISS retrieval assumes that the number density of each chemical constituent is either constant or has a constant gradient within a shell (SAGE III Algorithm Theoretical Basis Document, 2002). This assumption is generally valid for species such as ozone that undergo minimal diurnal variation in the stratosphere, however it is not true for NO 2 . This can be  Figure 3). The right panel of Figure 3 shows 110 that the NO 2 concentration at 32 km and the two SZAs where the 22 km LOS passes through that shell are both different from the concentration when the SZA is 90 • . In addition, the NO 2 does not change linearly across the terminator so deviations from linearity on either side of the LOS do not cancel out. Therefore using the 32 km NO 2 at 90 • to retrieve the 22 km NO 2 is inaccurate, and it cannot be assumed that the number density has a constant gradient across the terminator within a layer of the atmosphere when performing the retrieval. This lack of spherical homogeneity can be accounted for by adding factors to the 115 retrieval that scale the NO 2 according to SZA, at each location along the LOS.
Ideally we would incorporate the scale factors by redoing the conversion of slant path optical depth, obtained directly from the solar transmission measurements, to number density. As the SAGE III/ISS NO 2 optical depth profiles are not publicly available, we instead start by undoing the SAGE III/ISS retrieval to revert the number densities to optical depths. This is done where τ is the vertical profile of slant path optical depths from NO 2 , σ is the NO 2 cross section, and n 0 is the number density profile. X 0 is the path length matrix where each row represents a LOS for a particular tangent point altitude and each column represents a different altitude through which the LOS passes. Each element of X 0 is the path length distance between subsequent shells along the LOS. The path lengths on opposite sides of the tangent point are the same (i.e. the distance from 125 shell 1 to 2 on the instrument side of the tangent point is the same as the distance from shell 1 to 2 on the sun side) which allows X 0 to be written as an upper triangular matrix where values from opposite sides of the tangent point are added together.
These optical depths are used to find the number densities accounting for diurnal variations, n dv , using a new matrix, X dv , In this matrix each path length includes a factor, explained below, that depends on the SZA at that location. Note that the NO 2 130 cross section is the same in both equations 1 and 2 and so it cancels out when finding n dv . Although this is not strictly the case, using a constant cross section is a reasonable approximation as the cross section has a weak temperature and pressure dependence. The equations also assume that optical depth is constant within each layer of the atmosphere.
For a given SAGE III/ISS scan we know the date and time, the tangent point position, the spacecraft position, and the NO 2 number density from the SAGE v5.1 retrieval. This information is all that is needed to construct X 0 . To build the matrix we  The LOS for a particular tangent altitude intersects all of the shells above it. To find the scale factors for a given LOS we first find the apparent local solar time at the midpoint of each path created by the intersection of that LOS with the shells.
PRATMO is then run with input ozone, temperature, and pressure from the SAGE III/ISS Level 2 scan data. The model NO 2

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is computed at each calculated LST and at a SZA of 90 • , corresponding to the exact time of sunrise or sunset. For each shell altitude along the LOS, the scale factor is the PRATMO NO 2 at that altitude (corresponding to the LST at that location) divided by the PRATMO NO 2 at the tangent point altitude for that LOS (the scale factor is 1 for the shell containing the tangent point).
There is no scaling done above 40 km as the low amount of NO 2 can lead to unphysical scale factors and we want to prevent abnormal values from influencing the results at lower altitudes.  It is also useful to look at the scale factor as a function of altitude along each LOS ( Figure 5). Lower lines of sight pass through more layers of the atmosphere, resulting in greater scale factors. For lines of sight below about 30 km the change in scale factor with altitude becomes non-linear. This is because the shape of NO 2 cycle across the terminator changes with altitude (right panel of Figure 3). At higher altitudes the NO 2 increases along the whole LOS; below about 30 km the NO 2 starts to level out on the night-side (the curve on either side of the terminator becomes different), changing the slope of the 155 scale factor curves in Figure 5.