ExoMars TGO/NOMADUVIS vertical profiles of ozone: Part 1 – Seasonal variation and comparison to water

ExoMars TGO/NOMADUVIS vertical profiles of ozone: Part 1 – Seasonal variation and comparison to water Journal Item How to cite: Patel, M. R.; Sellers, G.; Mason, J.; Holmes, J.A.; Brown, M. A. J.; Lewis, S. R.; Rajendran, K.; Streeter, P. M.; Marriner, C.; Hathi, B. D.; Slade, D. J.; Leese, M. R.; Wolff, M. J.; Khayat, A. S. J.; Smith, M. D.; Aoki, S.; Piccialli, A.; Vandaele, A. C.; Robert, S.; Daerden, F.; Thomas, I. R.; Ristic, B.; Willame, Y.; Depiesse, C.; Bellucci, G. and LopezMoreno, J.J. (2021). ExoMars TGO/NOMADUVIS vertical profiles of ozone: Part 1 – Seasonal variation and comparison to water. Journal of Geophysical Research: Planets (Accepted Manuscript Online).


Introduction
Ozone (O3) is a highly reactive trace gas in the martian atmosphere, where odd-hydrogen (OH, HO2, H, H2O2) catalytic products of water vapor photolysis dominate Mars photochemistry (Parkinson and Hunten, 1972;McElroy and Donahue, 1972), and contribute the primary loss mechanism for Mars O3. As a consequence, large spatial and temporal changes in Mars O3 were quickly recognized to be associated with condensation-driven variations in atmospheric water vapour (Barth et al., 1973;Kong andMcElroy, 1977, Shimazaki andShimizu, 1979;Clancy and Nair, 1996). Mars atmospheric water variations result from seasonal/spatial variations in loss or supply to seasonal and residual polar ice caps (Jakosky and Farmer, 1982;Smith, 2004Smith, , 2009Fedorova et al., 2006;Steele et al., 2014;Pankine and Tamppari, 2019;Khayat et al., 2019); and by the large spatial/temporal variations in ice cloud saturation conditions in the Mars atmosphere Montmessin et al., 2004;Navarro et al., 2014;Neary et al., 2020).

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Mariner 7 made the first detection of O3 in the martian atmosphere (Barth and Hord, 1971) and later Mariner 9 showed O3 to be seasonally variable (Barth et al., 1973). Subsequent missions and ground-based observations have characterised the geographical and seasonal variability of O3 extensively (e.g. Blamont and Chassefière, 1993;Clancy et al. 1999;Fast et al., 2006;Lebonnois et al., 2006;Montmessin and Lefèvre, 2013;Clancy et al. 2016;Lefèvre et al., 2017;Lefèvre et al., 2021). This has led to the well-established O3 climatology of increased column abundances in the cold, dry atmospheric conditions of the fall and winter high latitude regions; and reduced substantially in abundance over warmer, wetter low latitude and summer high latitude regions. In addition, a distinct-low latitude, mid-altitude peak in O3 arises from ~20 K colder atmospheric (and surface) temperatures present around Mars aphelion (Clancy and Nair, 1996), when Mars is furthest from the Sun in its eccentric orbit (at the current epoch, this occurs around Mars northern summer at a solar longitude, LS, of 71°). These basic temporal and spatial behaviours of Mars atmospheric O3 and H2O column abundances are qualitatively reproduced in Mars global circulation models (GCM) (e.g. Lefèvre et al. 2004Lefèvre et al. , 2008Holmes et al, 2017;Holmes et al, 2018;Holmes et al, 2020;Daerden et al., 2019).
However, most of the above behaviours are primarily characterized in terms of column O3 measurements, due to the limited extent of vertical profile measurements for O3 Clancy et al., 2017;Gröller et al., 2018;Olsen et al., 2020;Piccialli et al., 2021) or H2O (Maltagliati et al., 2013;Fedorova et al, 2018). This is a significant limitation given the importance of vertical profile dependences in characterizing these photochemical and water vapor saturation (cloud microphysical) processes in any detail. Surprisingly, our understanding of such a fundamental relationship as the anti-correlation of Mars atmospheric O3 and H2O is obscured by uncertainties associated with column O3 and H2O measurement comparisons. Current model-data comparisons for these column data sets have implied significant (50-100%) excesses in observed atmospheric O3, while reproducing observed water column abundances more closely (Lefèvre et al., 2008). Heterogenous reduction of HOx on Mars water ice clouds has been proposed to account for such elevated O3 abundances relative to homogeneous (gas-phase only) photochemical predictions (Lefèvre el al., 2008). Subsequent Mars O3 observations have not yet indicated a heterogenous solution but the model underestimations of O3 columns remain unresolved (Clancy et al., 2016;Daerden et al., 2019). It is possible, perhaps likely, that inaccurate model simulations of water vapor (and O3) profiles contributes significantly to this issue (Clancy et al., 2017). Column O3 measurements are heavily weighted by O3 abundances in the lower scale height (~10 km), a region untouched by profile measurements to date. Column H2O measurements do not provide significant guidance to temperature-sensitive, process-complicated simulations of cloud microphysics, necessary to simulate water vapor profiles accurately (e.g., Navarro et al., 2014).
Consequently, ExoMars TGO sensitive and accurate determinations for O3 profiles through UV (260 nm Hartley band) solar occultations (this paper), and water vapor profiles through near-IR solar occultations (NOMAD-Vandaele et al., 2019, Aoki et al., 2020ACS-Fedorova et al., 2020), represent a major observational advance in the study of Mars photochemistry. On their own, NOMAD O3 profile retrievals yield a unique vertical dimension to our definition of Mars photochemistry. Coincident with NOMAD water profile retrievals, they enable an intrinsically diagnostic study of Mars Ox (O + O3) and HOx chemistry. Remaining contradictions on the presence of atmospheric methane (Korablev et al, 2019) and recent ExoMars detections of atmospheric HCl (Korablev et al., 2020;Aoki et al., 2020) lead to renewed importance in establishing a detailed understanding of Mars photochemistry.

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Here, we present retrieved NOMAD O3 profiles, with an emphasis on generating a global view of Mars photochemistry (O3) in the vertical dimension. Preliminary comparisons of these NOMAD O3 profile retrievals are provided with published NOMAD water profile retrievals (over LS = 163-345° in MY34, Aoki et al., 2019) and modelled water profiles  extending over the remaining LS range of presented O3 profiles. An initial comparison of modelled O3 profiles indicates the degree to which existing models, without assimilated NOMAD water profile retrievals, correspond to the NOMAD O3 profile measurements. Following studies of the combined NOMAD water and O3 profile data sets will employ data assimilation of NOMAD water profile measurements to fully realize anticipated advances in Mars photochemistry associated with NOMAD O3 and H2O profile data.
Vertical profile measurements by the Nadir and Occultation for MArs Discovery (NOMAD) spectrometer suite, aboard the ESA/Roscosmos ExoMars Trace Gas Orbiter (TGO) mission have now been taken for over 1.5 Mars Years (MY), allowing the first glimpse into the vertical distribution of O3 in the atmosphere of Mars. In this paper, we present O3 vertical profiles from April 2018 to November 2020, covering over 1.5 MY of O3 measurements. This period includes the MY34 global dust storm, as well as the occurrence of a regional storm . The companion paper to this study (Khayat et al. 2021) studies the high-altitude enhancement observed in more detail. The details of the NOMAD observations and the retrievals method are described in sections 2 and 3 respectively, and the observational results are discussed in section 4.

ExoMars and NOMAD-UVIS
The Ultraviolet and Visible Spectrometer (UVIS) is one of three channels that comprise the NOMAD spectrometer suite, aboard ExoMars TGO. The other two channels of NOMAD are infrared (IR) spectrometers: the Solar Occultation (SO) channel and the Limb Nadir and Occultation (LNO) channel. A full description of the SO and LNO channels can be found in Vandaele et al. (2015). UVIS covers the spectral range of 200-650 nm with a spectral resolution of < 2 nm and is capable of (mutually exclusive) observations in both solar occultation and nadir viewing geometries using a single spectrometer with the aim to provide a comprehensive understanding of the climatology and vertical distribution of ozone, dust aerosols and ice aerosols in the martian atmosphere. At the time of writing, the UVIS nadir ozone retrievals are not yet published. The occultation channel provides the capability to not only measure these species in the vertical and spatial dimension but to also measure changes on seasonal and diurnal timescales. A full description of the NOMAD-UVIS channel can be found in Patel et al. (2017) TGO is in a near-circular 74° inclined orbit with a periapsis of 380 km and apoapsis of 420 km and an orbital period of approximately 2 hours. NOMAD occultations come in four flavours: two different pointing modes and two different spacecraft manoeuvres. When the -angle, the angle between the orbital plane and the direction to the Sun, is <20° TGO will actively track the Sun during an occultation, keeping the instrument boresight fixed on the Sun centre. Within each planning period (approximately 1 month) around two of these suntracking occultations will be led using the UVIS boresight (i.e. the UVIS boresight is held centred on the Sun centre); the rest are led by the NOMAD SO IR channel. At -angles >20°, spacecraft angular momentum constraints prohibit suntracking and TGO rotates around the instrument pointing vector. This has minimal

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This article is protected by copyright. All rights reserved. effect on UVIS-led occultations, however, on SO-led occultations the UVIS occultation boresight (2 arcmin field of view) traces an arc around the solar disc at a distance from the solar centre of approximately 0.3 solar radii. In general, there is no discernible impact on the calculated transmissions, since the UVIS boresight remains at the same radial distance from the centre of the Sun, and the top of atmosphere reference transmission is defined over a range of altitudes using a linear regression method (see section 2.3).

Data set
Data acquired by the UVIS spectrometer from the start of the TGO science phase in April 2018 to November 2020 were used in this study, covering a period of just over one full martian year (MY 34, LS = 163° to MY 35, LS = 320°). This dataset comprises 5990 solar occultations (3051 egresses, 2939 ingresses) and corresponds to the Level 1.0 data made available through the NOMAD PI institute. The derived retrieval data dataset can be accessed freely through the Open Research Data Online (ORDO) repository (Patel, 2021).
The geographical distribution of the occultation measurements is shown Figure 1. Due to TGO's orbital characteristics and the terminator geometry for solar occultations, the majority of occultations are to be found clustered symmetrically around ±63 ∘ latitude bands ( Figure 1) in the northern and southern hemispheres, with minimally slanted (vertical) atmospheric profiles. Relatively few occultations penetrate the equatorial latitudes; those that do tend to exhibit very long ground tracks reflecting a highly slanted atmospheric profile. The latitudinal progression of the occultations over the duration of the current dataset is shown in Figure 2 and is controlled by the changing -angle of the spacecraft orbit. The -angle varies in a cyclic pattern, moving between low and high -angle phases. At low -angles an orbit will typically consist of both an ingress and egress occultation, alternating between high latitudes in the northern and southern hemispheres. As the -angle increases the occultations tend towards equatorial latitudes until the orbital geometry (-angles > 60°) prohibits occultation pointing and results in a period of no occultation observations. Each individual occultation occurs over a period of between approximately 1-7 minutes, with equatorial occultations generally having longer durations as a result of the longer slant paths. The total integration time of each individual measurement was 45 ms or 75 ms. In the initial phase of the science mission (LS = 163-345°) the UVIS sampling frequency was set to 3 s providing a spectral resolution of < 2 nm. Since the altitude resolution is also dependent on the occultation duration, the 3 s sampling frequency initially gave vertical resolutions that varied between 0.7 km and 4.4 km. This somewhat coarse altitude resolution for occultations with short durations was a result of the 3 s measurement rhythm which is set by the CCD readout time and the data transfer time from UVIS to the NOMAD data processing unit. The CCD read time is fixed and cannot be changed but the data transfer time can be reduced by sending less data. After LS = 345°, UVIS was modified to spectrally bin the CCD array from 1024 pixels to 128 pixels, a factor of 8 reduction in the data volume, allowing an increase in the sampling frequency to 1 s, a factor of three improvement, and a corresponding increase to the altitude resolution in the range 0.2 km to 1.4 km. The spectral features of ozone, water ice aerosols, and dust aerosols are all broad band features, as such an increase in the spectral resolution to 4 nm had no impact on the retrievals.
A great benefit of the solar occultation technique is that it does not rely on laboratory radiometric calibration, and it is a self-calibrating measurement. During a solar occultation, the line of sight (LoS) between the instrument and the Sun is maintained as the LoS passes through the atmosphere, from a very high altitude (200-250 km) down to the surface (or vice versa). Relative transmission is then calculated using a reference spectrum obtained from high up in the atmosphere where no atmospheric contribution is expected (typically ~110 km), resulting in a consistently self-calibrated transmission profile through the atmosphere for each individual occultation. Additionally, no correction for UV airglow is required, given the significantly higher signal intensity from the line-of-sight Sun illumination with respect to atmospheric emission at these wavelengths.

Atmospheric Transmittance
This transmission is defined as the spectral radiance observed through the atmosphere at a given tangent altitude, , above the surface, ( , ), taken as a proportion of the total (above atmosphere) solar radiance, 0 ( ).
( , ) = ( , ) 0 ( ) S0() is determined using the algorithm defined by Trompet et al. (2016), as discussed in Vandaele et al. (2018) as the standard occultation procedure for NOMAD transmissions. This method uses an iterative algorithm to define a mean value for spectra above 120 km, where it is assumed there is no absorption due to martian atmospheric gases, thus defining a unique reference for each occultation.
The spectral transmission obtained from the data can be related to the number density of all absorbing agents in the LoS through the atmosphere through the Beer-Lambert law: where, is the cross-section of the ℎ absorbing chemical species and = ∫ . is the integrated total number density per species along the LoS column. Given the small field of view, the signal contribution from forward scattering was modelled to be approximately two orders of magnitude lower than the direct solar signal and is considered negligible. A single transmission spectrum yields a transmission ratio for each wavelength in the detector range of 200-650 nm at a spectral resolution varying between approximately 1.5-3.5 nm (depending on observation configuration). An example of the corresponding set of transmission spectra obtained during a single occultation is shown in Figure 3, representing the observed transmission through different layers of the martian atmosphere. Transmission values below 1% are not considered in the retrieval process.

Spectral Inversion
The transmission spectra observed by the instrument at successive tangent altitudes above the surface are converted into number densities of different species by a spectral inversion process. These number density profiles, or slant densities, are a measure of the total integrated number of a given species in the line-of-sight column of each observation.

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The line-of-sight points
A schematic of the location of the LoS between the TGO spacecraft and the Sun for each observation is shown in Figure 4. The tangent height point, denoted by , is defined as the point along the LoS that has the shortest distance from the LoS to the centre of the planet. The geometry parameters recorded in each observation specify the height of TGO above the centre of the planet , together with the planetocentric latitude and longitude of the TGO position. They also give the height of the tangent point above the MGM1025 areoid (Lemoine et al., 2001), defining the term 'altitude' used throughout this paper.
It is useful to define a cartesian coordinate system with origin at the centre of the planet, the positive axis cutting the 0 ∘ meridian, and the positive axis passing through the north pole. Then, using the geometry of the ellipsoid, it is possible to calculate the cartesian coordinates ] of the point on the ellipsoid corresponding to the position ( , ). This is done by first calculating the corresponding radial distance of the point from the centre of the ellipsoid Since is collinear with the centre of the planet and the location of the satellite , a simple rescaling then gives the cartesian coordinates of the satellite location

= .
Similarly, it is possible to calculate the cartesian coordinates of the tangent height point, by rescaling the cartesian coordinates of the point on the ellipsoid corresponding to the

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position ( , ). The procedure is as described above for the case of , except that the final rescaling is given as follows = + .
Once the cartesian coordinates of and are known, the LoS points are readily calculated as points that lie along the line joining and . It is noted that the effect of refraction in low pressure atmospheres has been found to be small by previous studies (e.g. Hubbard et al., 2001;Bellucci et al., 2009;Bétrémieux and Kaltenegger (2015)) and therefore refraction effects are not considered here.

GCM and re-analysis
To perform the spectral fitting (described in the next section), initial estimates of aerosol opacity and ozone abundance along the LoS points are determined. These initial estimates are not strictly needed to perform the initial opacity retrieval, but are used for subsequent mixing ratio calculations, and were therefore used as initial estimates to optimise the fitting process since they were available. These values were extracted from outputs of the Open University (OU) modelling group Mars GCM coupled to the Analysis Correction assimilation scheme that has a strong heritage in data assimilation on Mars (Holmes et al. 2018, Lewis et al. 2005, Montabone et al., 2006, Streeter et al. 2020). The GCM is comprised of physical parameterisations (Forget et al. 1999) and a photochemical module (Lefèvre et al., 2004(Lefèvre et al., , 2008 shared with the Laboratoire de Météorologie Dynamique (LMD) modelling group, alongside a spectral dynamical core and semi-Lagrangian advection scheme (Newman et al., 2002). It includes the latest sub-models to provide the most realistic modelling of the turbulent processes in the planetary boundary layer (Colaïtis et al., 2013), and a water-ice cloud microphysics package (Navarro et al., 2014) that includes radiatively active water ice clouds and supersaturation. The OU modelling group GCM has been developed in a collaboration between the Open University, the LMD, the University of Oxford and the Instituto de Astrofisica de Andalucia. Initial O3 values originate from a model run that assimilated O3 column data measured by the SPICAM instrument during MY 27 (Holmes et al 2018). Although this model run is for a different year, it produces a good initial estimate of ozone for the beginning of the model run assuming that the seasonal O3 distribution is repeatable from year to year. For temperature, dust and aerosol fields, a different model run was used, that assimilated contemporaneous temperature profiles and column dust data measured by the Mars Climate Sounder (MCS) instrument (Streeter et al. 2020). The basis of the dust distribution for this period is presented in Montabone et al. (2020).

Cross-sections
The three primary absorption features acting on the observed atmospheric transmissions in the observational wavelength region between 200 and 650 nm are those due to carbon dioxide (CO2), aerosols and O3. Only the cross-section of O3 is of relevance in this study since wavelengths close to CO2 absorption are not considered, and the O3 cross-section values at 218 K of Malicet et al. (1995) are used here. The spectral absorption characteristics of aerosols exhibit a continuum attenuation in the transmission spectra so an increase in aerosol abundance can in principle be modelled as a fit to any part of the spectra well separated from the reserved O3 band. Due to the spectral shape changes at longer wavelengths due to aerosol particle size these wavelengths are avoided for modelling the aerosol content in the spectra.

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Spectral fitting
A least-squares ( 2 ) procedure involving minimizing the sum of the squares of the residual differences between the measured transmissions and a best fit model across a range of wavelengths, is performed utilising the Levenberg-Marquardt algorithm to obtain the best fit solution. Modelled values for aerosol opacity and ozone abundance are extracted for each LoS from the assimilated data set described earlier as a priori values for the iterative fitting process, purely to reduce the number of iterations required.
The first iteration of the fitting is performed in the region between 320-360 nm (i.e. outside the O3 absorption band) for the aerosol abundance determination (Clancy et al. 2016) ), with an optional additional region at 220-230 nm to adjust for CO2 Rayleigh scattering (Ityaksov et al. 2008) across the O3 band when required. Due to the reduced performance of the detector in this shorter wavelength fit region, in instances when the measured transmission in this region results in negative retrieved values of CO2 Rayleigh scattering, an aerosol re-fit constrained solely to the 320-360 nm region is performed around the initial obtained aerosol value and the re-fitted aerosol fit is extrapolated over the O3 band. All parameters in the model were initially fixed except for the CO2 Rayleigh scattering contribution and aerosol abundances along with the Angstrom coefficient, which were treated as free parameters over each iteration to determine an aerosol abundance, after CO2 Rayleigh scattering, on convergence. The fitting procedure for O3 abundance then follows, with updated CO2 Rayleigh scattering and aerosol values fixed in the model, within the wavelength range 240-320 nm on the positive gradient of the O3 Hartley band. This wavelength range was used since it permits an accurate representation of O3 abundance based on a measure of the depth of this feature in the spectrum, whilst avoiding the CO2 Rayleigh scattering fit region and the less well characterised transmission values below 220 nm, where there is greater noise in the spectra and straylight contamination represented by a growth in relative errors. This optimal wavelength range over which to perform the O3 fit coincides with the magnesium II h and k doublet solar emission at 280 nm, which is often used as a diagnostic of solar activity (e.g. Snow et al. 2019). As the determination of the Hartley band depth in any given spectrum may be influenced by the residual presence of this feature as the LoS moves across the solar disk, the values at 280 nm are discarded and an interpolation is performed either side of this wavelength.
Examples of the fitting procedure results on two example occultations are shown in Figure  5 where the overall composite fit has been combined to construct the final modelled transmission. The O3 model sometimes deviates from the observation below 255 nm primarily due to known straylight within the system causing a non-real excess in the recorded transmission values below this threshold. In general, the results <220 nm are not considered here due to the loss in responsivity of the CCD at these wavelengths . A lower altitude cut-off is applied to all profiles at the 1% transmission level at a wavelength of 255 nm, below which the signal on the CCD detector becomes comparable to the noise. Using the total abundance extracted from the O3 fit of the modelled spectra coupled with the cross-section values the total integrated number density (slant density) is then calculated by applying the Beer-Lambert law defined in section 2.3. Note that the 220-230 nm fitting region is also shown in this plot, but it is not used in the fitting process due to the poor data quality at these wavelengths in this occultation.

Vertical Inversion
The slant density of an absorbing species gives a measure of the total integrated number of molecules per unit area along the LoS of each measurement. To convert this slant density profile into an associated set of local densities, or a true vertical profile, a vertical inversion of the slant densities is performed.
To achieve this inversion a standard onion peeling process is used (Auvinen 2002, Quemerais 2006, Rodgers 2000, a procedure that requires the observed two-dimensional atmospheric slice be split into concentric layers. This structure, illustrated in Figure 4, is provided by the observational data, each layer being defined by the tangent altitude of the LoS in successive measurements above the same areoid surface defined in section 3.1. This results in a single measured transmission spectrum corresponding to each atmospheric layer. A spherically symmetric atmosphere is assumed in the plane defined by the observed lines of sight. It should be noted that O3 is unlikely to be distributed in a spherically symmetric manner along the line of sight along the terminator (see e.g., Piccialli et al., 2021 for a discussion of this issue), and therefore this assumption will have some associated (unavoidable) error, that cannot be quantified in a meaningful way at this time. The separate path lengths that every measurement's LoS takes through each of the atmospheric layers are then calculated geometrically In combination with an interpolation between the layers, an Abel integral provides the coefficients of the individual elements of the weighting function matrix, , which defines all combinations of path lengths per layer in the two-dimensional observational grid

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Where f(z) is the interpolated pressure as a function of altitude z, , and , are the altitude limits covered by the ℎ layer. All (virtual) path lengths constructed via this method that are external to the atmosphere will not contribute to the total observed abundance in any given atmospheric line-of-sight and therefore are given a zero weighting in the final matrix.
With the weighted path lengths encoded in the matrix the local densities, , forming the vertical profile can be calculated from the known slant densities, , and their associated uncertainties, , by a matrix inversion of the form = ⋅ − + This then provides a final vertical profile from the observed slant densities. An example of a calculated O3 vertical profile obtained through this method and its associated slant density profile are shown in Figure 6. Measured O3 number densities range from ~10 10 in the lower altitudes down to ~10 7 below which the noise floor inherent in the retrieved slant densities is reached, demonstrated here by the shaded envelope in Figure 6. Since in the present study only upper limits can be defined above ~60 km, the results presented here will focus on the detections confirmed below this altitude.

Uncertainties on the vertical profile
The main source of uncertainty in the occultation data arises from instrumental noiseeach spectrum has an associated instrumental error value, with the median value of this error within each occultation being less than 1%.

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To determine the associated uncertainty in the retrieval, the 1-experimental uncertainty from the random instrumental noise associated with every observed transmission, , is used in order to calculate a weighted deviation (W) between the model, as evaluated from the Beer-Lambert equation (section 2.3), the fitted model data ( ), and the observation data ( ).

= ( ) − ( )
The square of these weighted residuals are the 2 values that, through successive iterations, are minimized in order to arrive at a final best fit solution to the modelled data, the associated cost function can be expressed as The covariance matrix, , in this process describes the covariance of every combination of pairs of measurements, the diagonal elements therefore represent the self-covariance (the variance) of each observation with itself, the individual errors on the obtained slant density measurements are thus obtained from the square-root of the diagonal of the covariance matrix. An averaging kernel, K, is constructed from the weighting function and covariance matrices, whose i ℎ row describes the weighting influence of each atmospheric layer on the i ℎ LoS derived number density: Where the matrix L, whose contribution is governed by the smoothness coefficient λ , is given by: This kernel represents the quality of the retrieval per retrieved number density value in the final vertical profile.
The uncertainty in the number densities of the final vertical profile is derived in an analogous way to the number densities themselves, as shown below. In an iterative procedure, the respective errors of each observed slant density are combined in quadrature with the sum of the previously calculated errors on all higher layers, weighted by the proportional path length that those layers represent in the current line of sight column.
This quantity is then scaled based on the path length of the layer in question (the lowest layer) in the current column to obtain a final error on the number density in that layer of the vertical profile. Median errors on the calculated number density are found to be up to 7% between an altitude range of 20-50 km.

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This article is protected by copyright. All rights reserved. Figure 7 shows the seasonal variation of the O3 vertical profiles from the NOMAD-UVIS retrievals for observations made in the northern hemisphere and the southern hemisphere. Generally, retrieved NOMAD O3 profiles extend to 50-70 km altitudes, based on NOMAD O3 sensitivity limits and Mars upper level O3 abundances (previous section, e.g., Figure 6). It should also be noted that these plots show the vertical profile over varying latitudesin some cases, moving from the polar regions to equator in a small LS period. Thus, care must be taken in interpreting these plots, as latitudinal gradients can appear mapped into temporal (LS) changes.

O3 vertical distribution
Given the strong photochemical anticorrelation of O3 with H2O, we also present the water profiles simultaneously retrieved with the IR channel of NOMAD , providing the first direct comparison of contemporaneous and co-located O3 and H2O vertical profiles. Unfortunately, at the time of writing NOMAD water profiles retrievals are only publicly available up to LS = 345° in MY34 (Feb 2019), and therefore the water profiles shown in Figure 7 only contain NOMAD water retrievals to LS = 345°.
To provide a comparative water vapour dataset for the remaining period through to LS = 320° in MY35 (November 2020), we performed an assimilation of MCS v5.3.2 temperature profiles and column dust retrievals (Kleinböhl et al. 2017) using the OU modelling group Mars GCM described in section 3.1.1. An ensemble of assimilation runs was conducted over the whole time period, in which the parameters of albedo and thermal inertia of perennial surface ice were varied to select an optimum water vapour simulation. Navarro et al. (2014) adopted this approach in a forward GCM study, to model Mars atmospheric water column variations. The selected assimilation run was chosen to optimize water vapour comparisons with respect to NOMAD water vapour retrievals towards the end of the period for which they are available (late 2018, when the MY34 dust storm effects have largely abated). Comparison with as yet unpublished NOMAD water profile observations for this period show the modelled water to be qualitatively consistent with the observed water profiles.
The bottom panels of Figure 7 present this NOMAD-model composite description of water profiles corresponding (in position and LS) to retrieved NOMAD O3 profiles in the top panels. It should be noted that the average difference in time between the model output time and each specific observation time is 12 minutes. This provides a partial comparison of NOMAD water vapour and O3 profile measurements, for the published dust storm period of NOMAD observations (LS = 190-345° in MY34). It also allows a predictive (model) description of the very distinct behaviour of Mars water vapour centred on the aphelion climate of Mars (LS ~0-180°) in MY35.
NOMAD-retrieved O3 profiles are presented in the top panels of Figure 7 and compared to simulated O3 profiles in the middle panels. These simulated O3 profiles are strictly based on the MCS temperature and dust assimilation modelling described above. Consequently, they correspond to modelled, not observed, atmospheric water vapour distributions for the entire presented LS range in Figure 7. These simulated water vapour profiles are constrained by assimilated MCS temperature and dust profiles, as described above, such that they more closely correspond to contemporaneous water vapour saturation conditions, including the MY34 dust storm, high latitudes, and the aphelion period.

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This article is protected by copyright. All rights reserved. Nevertheless, the model-NOMAD comparisons for O3 profiles in the top two panels of Figure 7 still retain significant uncertainties associated with GCM simulations of Mars water vapor (Navarro et al., 2014;Daerden et al., 2019). Direct assimilation of NOMAD retrieved H2O profiles should allow much more quantitatively direct (and photochemically diagnostic) comparisons of model and observed O3 profiles. For current purposes, these model/data O3 comparisons allow a preliminary assessment of the detailed seasonal and spatial variations of the vertical distribution of Mars O3 from NOMAD, in the context of a best-effort approach for modelling Mars atmospheric water profile behaviour based on assimilated dust and temperature profiles.

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This article is protected by copyright. All rights reserved. represent the timing of the MY34 global dust storm and regional storm respectively. Altitude values are with reference to the Mars areoid, and the latitude that each profile is taken at is indicated by the top plot.
The effect of the MY34 global dust storm (approximately LS = 190 -250°) on the O3 retrievals, through reduced limb transmission, is most noticeable in the increasing lower altitude cut-off due to the sharp increases in dust loading (e.g. Smith 2019; Liuzzi et al. 2020;Montabone et al. 2020). In the equatorial and mid-latitudes, retrievals are only possible down to ~30 km, allowing only mid-to-upper level regions of atmospheric O3 to be detected. At higher latitudes, where lower dust content is present, O3 retrievals are possible to altitudes below 10-20 km. Elevated water abundances at high altitudes (>30-50 km) are observed in both northern and southern hemispheres during the MY34 (2018) global dust storm after LS = 190-200° , similar to behaviour observed and modelled during the MY28 (2007) global dust storm (Heavens et al. 2018). This leads to correspondingly reduced O3 abundances above 20-30 km between LS -200-300° in both hemispheres, in both MYs, associated with the strong photochemical anti-correlation between O3 and water. As noted previously, the highaltitude enhancements of O3 observed in the southern hemisphere (and to a lesser extent the northern hemisphere) from spring equinox are covered in detail in the companion paper to this study (Khayat et al. 2021) and are not discussed here. A comparison of the difference in MY34/35 O3 distribution during the global dust storm period is given in section 4.3; however, care must be taken when comparing periods in Figure 7, since the latitude of the observations vary significantly and will be different between Mars years.
Altitude-resolved NOMAD O3 abundances below 15 km altitudes represent new measurements and will prove significant in assessing previous column (nadir) measurements of Mars ozone (e.g., Perrier et al., 2006). Such column measurements are often dominated by maximum lower atmospheric O3 abundances, particularly at high latitudes, that may contribute disproportionately to existing model-data disagreements for column O3 comparisons (Clancy et al., 2016). Peak near-surface O3 densities (and mixing ratios) are generally observed to be present throughout the Mars year and occur, in part, due to reduced HOx production from H2O UV photolysis (associated with increasing CO2 extinction of UV radiation, e.g., Montmessin and Lefèvre, 2013).
This near-surface O3 layer is particularly evident at southern winter latitudes, when cold aphelion temperatures lead to the aphelion cloud belt (ACB) and much reduced transport of water vapor into the southern winter hemisphere , and thus minimum HOx loss rates for O3 at all altitudes (Lefèvre et al., 2004;Daerden et al., 2019). Figure 7 demonstrates this behaviour in, respectively, NOMAD retrievals and assimilation modelling of O3 and H2O abundances in the southern hemisphere lower atmosphere (LS = ~0-180°). The northern hemisphere winter is generally obscured due to the presence of dust from the MY34 global dust storm. Increasing O3 abundances below ~15 km altitudes are retrieved between LS = 190 -250°, associated with northern winter. But overall, reduced O3 and increased H2O abundances (both, in this case, from NOMAD retrievals) are present relative to the aphelion, southern winter period. Figure 8 shows the ratio of the O3 abundance observed by NOMAD, to that simulated by the GCM following assimilation of MCS dust and temperature observations. Overall, there are periods/altitudes of both good and poor agreement between observation and model. The period LS = 200-300° in general shows a good agreement in modelled O3, compared to observation, when little O3 is present. For example, at LS = 210-240° in the northern hemisphere (i.e. during the global

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This article is protected by copyright. All rights reserved. dust storm) there is an approximate unity observation/model ratio over most altitudes. A similar situation occurs at LS = 180-200° in the southern hemisphere, with approximate unity observationmodel ratio above ~35 km. Around aphelion in the northern hemisphere there are generally low observation/model O3 ratio values over all altitudes. In the southern hemisphere during this period, there are higher observation/model ratio values above and below the 25-35 km altitude range, with a sharp increase in ratio value around 35-40 km at the base of the enhanced O3 layer. Figure 7 showed that the qualitative distribution of O3, including the structure and timing of the high latitude, high altitude peaks, is represented well by the GCM. However, Figure 8 shows that, in general, while there can be good agreement with the absolute abundances simulated in the GCM, there are also periods and altitudes when the GCM values are over a factor of ten lower than that observed by NOMAD. This is most likely due to the fact that the water saturation conditions are only partially constrained by the temperature and dust assimilation, such that water abundances are not adequately represented in the model simulations (early on, water abundances from the assimilation of temperature and dust from MCS are approximately a factor of 2 higher than those observed by NOMAD). It is also likely that there are deficiencies in our understanding of the HOx processes in the atmosphere of Mars (see e.g., Lefèvre et al., 2021), which could contribute to such a discrepancy in O3 abundance. Model assimilation of the observed NOMAD water profiles, once publicly available, will address this modelled O3 abundance deficiency.

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This article is protected by copyright. All rights reserved. Figure 9 shows the NOMAD ozone profile retrievals, plotted as a function of latitude for LS periods of 20°. Towards perihelion (LS = 251°) in northern winter, O3 is generally present at low altitudes at mid/high latitudes. A comparison of the northern autumnal equinox periods for  indicates that observed O3 abundances extend to higher altitudes in the non-global dust storm year (MY35). Mid/high-latitude O3 abundances above ~20 km are reduced during the MY34 global dust storm, due to the elevated water abundance above these altitudes associated with this storm (e.g., Aoki et al., 2019;Fedorova et al. 2020). The period LS = 180-200° presents an especially high number of observations in both years, and thus is most appropriate for this comparison. In MY34 during this period, O3 reaches an altitude of 20-30 km in the southern polar regions, at the onset of the global dust storm. In the MY35 equivalent period, O3 reaches an altitude of 30-40 km, highlighting the reduction of O3 abundances in this region in MY34 associated with dust-driven increases in water vapour at higher altitudes. Northern mid-latitudes (~30-45°N) also exhibit higher O3 abundances in the LS = 180-200° period in MY35 with respect to MY34, but limited observations during the MY34 period make it difficult to compare this latitude region further. Following cessation of the regular period of dust activity centred near LS = 330° in MY34 (e.g., Smith, 2004;Kass et al., 2016), the development of increased O3 abundances to altitudes of ~35 km is observed in the southern polar regions in MY34 at LS = 340 -0°).

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The notable low-to-mid latitude increases in 20-50 km altitude O3 over the extended northern summer season (LS = 40-120°) reflect the aphelion saturation conditions for water vapor above ~20 km altitudes. This orbitally-driven cooling of the global Mars atmosphere leads to the formation of the ACB Smith et al., 2004;Montmessin et al., 2004) and sharp increases in O3 abundances above 20 km (Clancy and Nair, 1996;Lefèvre et al., 2004) at this time. These vertically extended increases in aphelion O3 abundances continue until LS ~120°, after which O3 abundances above 20-30 km begin to decrease with increasing atmospheric temperatures and water vapor. The ACB similarly declines over this period (Smith et al., 2004).
At LS = 40-60° in Figure 9, meridional circulation during the transition from equinoctial to solstitial circulation is evident in the latitudinal O3 distribution, where O3 formation along the flow path of O atoms highlights the meridional circulation. The downwelling branch of the main Hadley cell typical of this time of year (e.g. Montmessin and Lefèvre, 2013;Barnes et al. 2017) shapes the O3 distribution in the southern hemisphere and manifests as a latitudinal contour of O3 abundance beginning at a latitude of ~30°S and altitude of ~45 km down to a latitude of ~55°S and altitude of 20 km. There is evidence of a thermally indirect (Ferrel) cell at high northern latitudes at altitude, manifesting as an O3 abundance contour extending from a latitude of ~50°N and 30 km down to a latitude of ~70°N and ~20 km. Progressing towards solstitial circulation, in the LS = 60-80° period there is a possible signature of the elevation of the thermally indirect (Ferrel) cell flow path, being elevated by approximately 10-15 km, with the O3 contour highlighting the circulation flow path spanning from a latitude of ~35°N at 45 km down to ~65°N at ~30 km. It should be noted that the meridional circulations highlighted here do not represent the strength or extent of the circulation nor the transport of O3, but serve only to highlight the (possibly weak) circulation paths where the formation of sufficient O3 is permitted and thus made observable.

O3 distribution compared to H2O
O3 and H2O are always photochemically anti-correlated in terms of HOx chemistry. Care must be taken when using the terms "correlated" and "anti-correlated" in studies such as presented here, to avoid misunderstanding regarding the relationship between O3 and H2O. While these two species are fundamentally anticorrelated from a chemical reaction perspective, the variation of these species over altitude is not necessarily constrained in the same manner. For example, it is possible for both O3 and H2O to follow the same decrease in relative abundance over altitude, while remaining photochemically anti-correlated. Competing photochemical processes will dominate at different altitudes (e.g., solar UV at high altitudes enhancing destruction pathways and reducing in effectiveness towards the surface). A common assumption that follows the statement of anti-correlation between the two species is that their profile shapes will also be anticorrelatedthis is not necessarily always the case. NOMAD is capable of measuring simultaneously O3 and H2O vapour profiles to demonstrate this through observations; here we discuss the relationship of the two species regarding their relative vertical distribution. Figure 10 presents the comparison of O3 and H2O as a function of altitude and latitude. Figure 10 shows the distribution of NOMAD O3 and H2O retrievals from LS = 163° onwards for the remainder of MY34, and also the NOMAD O3 compared to the modelled O3 (following MCS dust and temperature assimilation) for MY35 up to LS = 280°.

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At perihelion in MY34 between LS = 200-320° there is a greater relative density of NOMAD-retrieved H2O, particularly at high altitudes (> 30 km) in both hemispheres, due to the ~20 K increase in average atmospheric temperatures associated with the ~40% increase in solar flux , and due to the related intense dust activity during the global and regional storms Liuzzi et al., 2020). During this period, O3 is confined to lower altitudes, with the altitude of peak O3 values in general being coincident with peak H2O values. O3 and H2O show a similar overall trend in increasing relative abundance with decreasing altitude. Either side of this period (i.e. LS = 160-200° and 320-0°), water abundance is generally lower, and distinct increased O3 abundance is observed at high latitudes in both hemispheres, coincident with latitudes where H2O abundances are decreased. This anti-correlation in distribution continues into MY35, with the latitudinal anti-correlation immediately evident in the LS = 0-40° period, and continuing albeit to a lesser degree throughout the rest of the year.
Towards aphelion in MY35 during the northern summer there is an overall lower density of modelled H2O, and a higher density of O3, consistent with the generally colder aphelion season due to decreased solar insolation and dust loading. In MY35, O3 retrievals were possible to lower altitudes than in MY34 due to the absence of storm-related high dust loading. From LS = 0-160°, H2O is confined below 40 km in both hemispheres, showing dry south polar regions to the minimum altitudes observed by NOMAD (~5-10 km). From LS = 40-120°, O3 density is consistently high across all latitudes up to altitudes of ~50 km, consistent with the generally low H2O densities in these regions. At LS = 120-160° H2O abundances increase across all latitudes, shifting the abundances upwards by ~5 km in altitude. This general increase in H2O at high altitudes results in a corresponding decrease in O3, showing an anti-correlation with the H2O distribution across latitudes and above 30 km. With the reappearance of the high latitude, high altitude O3 enhancement >40 km, no corresponding H2O peak is seen below the O3 enhancement, as observed during vernal equinox. In MY34 through perihelion, the relative abundance of both O3 and H2O increases coherently towards the surface with peak values of both species occurring at the lowest altitudes, consistent with the build-up of O3 at lower altitudes attributed to the reduced H2O photolysis rates arising from the overlying CO2 atmosphere and the increase in efficiency of the three-body ozone forming reaction at lower altitudes (higher pressures) . In MY35 through aphelion, H2O profiles show an inflection around 20-30 km, resulting in maximum H2O abundances occurring at higher altitudes than during perihelion. O3 profiles show a sharp drop at the point of the H2O maxima. While the photochemical anti-correlation of O3 and H2O remains valid throughout the martian year, there is a clear difference in the shape of the H2O profiles between the warmer, wetter perihelion season and the colder, drier aphelion season (Clancy et al. 1997). The top row in Figure 11 shows the O3 and H2O vertical profile shapes at high latitudes in the southern summer, whereas the bottom row demonstrates the equivalent profiles for similar latitudes located in the southern polar vortex. For the latter, the higher altitude O3 enhancements are created through the descent of O atoms via Hadley circulation , altering the shape of the profile with respect to the southern summer period. Direct NOMAD O3-H2O comparisons in MY35 should confirm these observations in detail. Furthermore, assimilating retrieved NOMAD H2O profiles are expected to lead to much better O3 absolute abundance simulations, which often appear lower than NOMAD measurements (Figure 8).

Night-to-day and day-to-night terminator perspectives
A key feature of the non-Sun-synchronous orbit of TGO is that it allows NOMAD to observe different local times of day on Mars. This benefit is key to NOMAD nadir observations, which enable total column measurements at varying local times across the planet. Whilst occultation observations are also made at differing local times as a function of latitude and season, by definition an occultation observation always occurs at local sunrise/sunset, at the terminator. Interpreting fine-scale diurnal variations in NOMAD occultation data should be done with care, since occultation measurements will always be performed with the observation tangent point at the day/night boundary, and do not represent the diurnal mean ozone profile.
It is valid, however, to draw conclusions on the difference between sunrise and sunset occultations. From the perspective of viewing geometry, the TGO spacecraft is in eclipse behind Mars prior to a sunrise occultation; the NOMAD-Sun LoS therefore transects the atmosphere that is emerging from the nightside conditions of Mars for a sunrise occultation. For a sunset occultation, the opposite is true, where TGO points towards the Sun after passing over the dayside of Mars. For a sunset occultation, the NOMAD-Sun LoS therefore transects the atmosphere that has been subjected to the dayside conditions of Mars (high temperatures, solar UV). Both cases will consist of observations with part-night/part-day optical paths, with the difference being the exposure period of each optical path to day/night conditions. Figure 12 shows the vertical profiles for a group of observations between LS = 42-54°, and latitude range 30-50°S. Whilst local time is plotted, this serves primarily to discriminate between sunrise and sunset occultations, to discern the differences between the nightside and dayside atmospheric 'context' of the occultations. In Figure 12a, the sunrise occultations show an O3 number density at approximately 10 9 cm -3 up to an altitude of ~35 km. This is in stark contrast to the equivalent sunset occultations, where the equivalent number density only reaches an altitude of ~20 km. Figure 12b shows this striking distinction, with the profile averages for sunset and sunrise during this period at similar values above ~45 km and below ~15 km but showing vastly different abundances between these altitudes. The relative shape of the distribution between 20 and 40 km is similar, but the abundance of O3 is an order of magnitude higher at sunrise than at sunset. Figure 12 thus shows a clear bias towards higher O3 abundances at sunrise for altitudes between 15 and 45 km than for equivalent sunset occultations within the same period. This difference could arise from diurnal partitioning between O3 and O, which leads to nighttime conversion of O to O3 when O3 photolysis is inactive, resulting in significant O3 increases above 20-30 km altitudes associated with altitude increasing O densities (e.g., Nair et al., 1994). Day-time photolysis of O3 to O leads to reduced O3 densities above 20-30 km. Consequently, the photolysis-driven diurnal partitioning of O3 and O can plausibly create the observed sunrise and sunset O3 profile variations indicated in Figure 12a.

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This article is protected by copyright. All rights reserved. However, the occultation atmospheric paths transect day and night illuminated regions at both terminators, and diurnal O3 variations associated with O3 partitioning are not instantaneous at the terminators. Previous studies have investigated diurnal changes in O3 from a model perspective (e.g., Holmes et al., 2018), however a photochemistry model investigation of the diurnal variation of ozone is beyond the scope of this paper. Additionally, it should be noted that the measurements shown in Figure 12 are not made at precisely the same local time and LS, and there is a possibility that the water vapour profile abundance has changed over the short period of ~3 weeks for the observations in Figure 12, and the difference could therefore be driven by differences in the water profile between sunrise and sunset. Comparison to NOMAD water profile observations is unfortunately not possible at the present time, but once available, detailed photochemical modelling is planned to assess these NOMAD sunrise-sunset distinctions which should yield new constraints on Mars photochemistry.

Conclusions
We have analysed the first martian year of occultation observations from the NOMAD instrument on ExoMars TGO and presented a new climatology of the vertical distribution of O3 for the period LS = 163° in MY34 to LS = 320° in MY35. The vertical, latitudinal, and seasonal (LS) variations of these retrieved NOMAD O3 profiles are compared with coincident NOMAD H2O profiles obtained during the MY34 global dust storm , and to Open University data assimilation modelling of O3 and H2O profiles, in which MCS temperature and dust profiles are assimilated to constrain water vapor saturation conditions. These NOMAD O3 profile retrievals present the first detailed, global description of Mars O3 vertical distributions as a function of season and latitude, and with accurate sensitivity from below 10 km (depending on variable atmospheric aerosol extinction) to above 50 km (depending on variable O3 abundance) altitudes. Key global-scale variations in Mars atmospheric O3 are well characterized in their vertical extents, including: large aphelion (LS = 40-120°) increases in lowto-mid latitude O3 abundances over 20-50 km altitudes, distinct high latitude (> ±55°), high altitude (40-55 km) enhancements in O3 abundances during equinoctial seasons (centred on LS = 0,180°), and very large perihelion O3 decreases over the extended atmosphere. The aphelion increases and perihelion decreases are generally consistent with model predictions of global variation in water vapor saturation altitudes (hygropause) as driven by the elliptical Mars orbit and accentuated by perihelion dust storm heating of the extended atmosphere. During perihelion, the relative vertical abundances of O3 and H2O increases below ~40 km towards the surface, with both species having peak abundances at similar altitudes close to the surface; during aphelion, the same general trend applies, but with well-defined decreases in O3 abundances present in the profiles at altitudes of 20-30 km, coincident with local peaks in H2O. Between LS 40 -50° in MY35, the difference in O3 abundance between 20 and 40 km was found to be on average an order of magnitude higher at the sunrise terminator, compared to the sunset terminator.
In general, modelled O3 densities are either in agreement with or lower than NOMAD observed O3 densities, most likely due to H2O abundance conditions being inadequately constrained in the model without significant tuning. An in-progress objective of assimilating NOMAD water profile measurements should provide the most diagnostic photochemical analysis of martian O3, necessary to accurately represent the formation and distribution of O3 on Mars.