# Water Vapor Vertical Distribution on Mars after Six Years of TGO/NOMAD Solar Occultations. Part II: Cross-validation within TGO and comparison with models

Adrian Brines, Miguel Ángel López-Valverde, Francisco Gonzalez Galindo, Shohei Aoki, Anna A. Fedorova, Denis A. Belyaev, François Forget, Eran Vos, Franck Montmessin, Bernd Funke, et al.

► To cite this version:

Adrian Brines, Miguel Ángel López-Valverde, Francisco Gonzalez Galindo, Shohei Aoki, Anna A. Fedorova, et al. Water Vapor Vertical Distribution on Mars after Six Years of TGO/NOMAD Solar Occultations. Part II: Cross-validation within TGO and comparison with models. 2025. [hal-05237196]

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Water Vapor Vertical Distribution on Mars after Six Years of
TGO/NOMAD Solar Occultations. Part II: Cross-validation within
TGO and comparison with models

Adrian Brines¹, Miguel Ángel López-Valverde², Francisco Gonzalez Galindo¹, Shohei AOKI³, Anna A. Fedorova⁴, Denis A. Belyaev⁵, François Forget⁶, Eran Vos⁷, Franck Montmessin⁸, Bernd Funke¹, José Juan López-Moreno⁹, Julio Rodriguez-Gomez⁹, Frank W. Daerden¹⁰, Ian Richard Thomas¹¹, Loïc Trompet¹², Ashimananda Modak¹³, Geronimo Luis Villanueva¹⁴, Manish R Patel¹⁵, Giancarlo Bellucci¹⁶, and Ann Carine Vandaele¹⁷

¹Instituto de Astrofísica de Andalucía, CSIC

²Instituto de Astrofísica de Andalucía

³Graduate School of Frontier Sciences, The University of Tokyo

⁴Space Research Institute

⁵Space Research Institute (IKI)

⁶LMD

⁷Laboratoire de Météorologie Dynamique

⁸LATMOS CNRS/UVSQ/IPSL

⁹Instituto de Astrofísica de Andalucía, IAA-CSIC

¹⁰Royal Belgian Institute for Space Aeronomy BIRA-IASB

¹¹Belgian Institute for Space Aeronomy

¹²Royal Belgium Institute for Space Aeronomy

¹³Institute for Basic Science (IBS)

¹⁴NASA Goddard Space Flight Center

¹⁵The Open University

¹⁶Istituto Nazionale di Astrofisica

¹⁷Royal Belgian Institute for Space Aeronomy

May 23, 2025

Abstract

This is the second part of an investigation of water vapor in the Martian atmosphere using solar occultation observations by the spectrometer NOMAD on board the ExoMars Trace Gas Orbiter. Following the analysis performed in the first part, hereafter named as Paper I, a cross-validation exercise between NOMAD and ACS results is presented, showing global as well as profile-by-profile comparisons. The results reveal an overall good agreement between different teams and instruments, taking into account the different retrieval methodologies. In order to compare with model predictions, we perform an exhaustive analysis of the water vapor simulated by Mars Planetary Climate Model (MPCM). It shows that the MPCM reproduces most of the water vapor climatological features observed in the atmosphere. However, several discrepancies between model and observations are noticed. Some of these are possibly related to the vertical distribution of dust and its effect on the global circulation and on the water vapor vertical transport. Other data-model differences found at 60 km seem to be related to discrepancies on the
water ice cloud formation in the MPCM. In addition, we include a cluster analysis of Martian water vapor vertical profiles for the first time. This technique applied to MPCM and NOMAD water vapor retrievals reveal distinct groups of profiles being representative of specific seasons and latitudinal regions, similarly distributed in both model and observations. Moreover, it allows us to provide a simplified water vapor climatology, useful to detect out-of-season events and biases in the retrieval processes.

H₂O VMR (ppm) @ Northern hemisphere

<figure><img src="image_1.png" /></figure>

H₂O VMR (ppm) @ Southern hemisphere

<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>
<figure><img src="image_7.png" /><figcaption>H₂O VMR (ppm) @ Southern hemisphere</figcaption></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>
JOMAD-SO: 20210412_132501_1p0a_SO_A

a

ACS-NIR: orb015104_N2

<figure><img src="image_13.png" /></figure>

JOMAD-SO: 20201229_060923_1p0a_SO_A

b

ACS-NIR: orb013830_N1

<figure><img src="image_14.png" /></figure>

JOMAD-SO: 20200625_082114_1p0a_SO_A

c

ACS-NIR: orb011547_N1

<figure><img src="image_15.png" /></figure>

JOMAD-SO: 20180919_023512_1p0a_SO_A

d

ACS-NIR: orb003665_N2

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

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<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>
Morning

<figure><img src="image_23.png" /></figure>

Evening

<figure><img src="image_24.png" /></figure>
<figure><img src="image_25.png" /></figure>

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MY 34

<figure><img src="image_28.png" /></figure>

MY 35

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MY 36

<figure><img src="image_30.png" /></figure>

MY 37

<figure><img src="image_31.png" /></figure>

MY 34

<figure><img src="image_32.png" /></figure>

MY 35

<figure><img src="image_33.png" /></figure>

MY 36

<figure><img src="image_34.png" /></figure>

MY 37

<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>
<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /></figure>

<figure><img src="image_39.png" /></figure>

<figure><img src="image_40.png" /></figure>

<figure><img src="image_41.png" /></figure>

<figure><img src="image_42.png" /></figure>

<figure><img src="image_43.png" /></figure>
<figure><img src="image_44.png" /></figure>

<figure><img src="image_45.png" /></figure>

<figure><img src="image_46.png" /></figure>

<figure><img src="image_47.png" /></figure>

<figure><img src="image_48.png" /></figure>

<figure><img src="image_49.png" /></figure>
# Water Vapor Vertical Distribution on Mars after Six Years of TGO/NOMAD Solar Occultations. Part II: Cross-validation within TGO and comparison with models

A. Brines<fnref n="1" />, M. A. López-Valverde<fnref n="1" />, F. González-Galindo<fnref n="1" />, S. Aoki<fnref n="2" />,<fnref n="3" />,

A. Fedorova<fnref n="4" />, D. Belyaev<fnref n="4" />, F. Forget<fnref n="5" />, E. Vos<fnref n="5" />, F. Montmessin<fnref n="5" />, B. Funke<fnref n="1" />,

J. J. Lopez-Moreno<fnref n="1" />, J. Rodriguez-Gomez<fnref n="1" />, F. Daerden<fnref n="2" />, I. R. Thomas<fnref n="2" />,

L. Trompet<fnref n="2" />, A. Modak<fnref n="6" />, G. L. Villanueva<fnref n="7" />, M. R. Patel<fnref n="8" />, G. Bellucci<fnref n="9" />, and

A. C. Vandaele<fnref n="2" />

## Key Points:

* Cross-validation between NOMAD and ACS water vapor observations shows good agreement despite differing methods.

* The MPCM reproduces the observed NOMAD climatology but shows discrepancies likely due to modeled global circulation and water saturation.

* Cluster analysis applied to NOMAD vertical profiles identifies seasonal and latitudinal unique profiles, providing a simplified climatology.

<footnote n="1">¹Instituto de Astrofísica de Andalucía (IAA/CSIC), Spain</footnote>

<footnote n="2">²Royal Belgian Institute for Space Aeronomy, Belgium</footnote>

<footnote n="3">³Department of Complexity Science and Engineering, University of Tokyo, Japan</footnote>

<footnote n="4">⁴Space Research Institute, Russia</footnote>

<footnote n="5">⁵Laboratoire de Météorologie Dynamique, IPSL, Paris, France</footnote>

<footnote n="6">⁶Institute for Basic Science, South Korea</footnote>

<footnote n="7">⁷NASA Goddard Space Flight Center, USA</footnote>

<footnote n="8">⁸Open University, UK</footnote>

<footnote n="9">⁹Istituto di Astrofisica e Planetologia, Italy</footnote>
**Abstract**

This is the second part of an investigation of water vapor in the Martian atmosphere using solar occultation observations by the spectrometer NOMAD on board the ExoMars Trace Gas Orbiter. Following the analysis performed in the first part, hereafter named as Paper I, a cross-validation exercise between NOMAD and ACS results is presented, showing global as well as profile-by-profile comparisons. The results reveal an overall good agreement between different teams and instruments, taking into account the different retrieval methodologies. In order to compare with model predictions, we perform an exhaustive analysis of the water vapor simulated by Mars Planetary Climate Model (MPCM). It shows that the MPCM reproduces most of the water vapor climatological features observed in the atmosphere. However, several discrepancies between model and observations are noticed. Some of these are possibly related to the vertical distribution of dust and its effect on the global circulation and on the water vapor vertical transport. Other data-model differences found at 60 km seem to be related to discrepancies on the water ice cloud formation in the MPCM. In addition, we include a cluster analysis of Martian water vapor vertical profiles for the first time. This technique applied to MPCM and NOMAD water vapor retrievals reveal distinct groups of profiles being representative of specific seasons and latitudinal regions, similarly distributed in both model and observations. Moreover, it allows us to provide a simplified water vapor climatology, useful to detect out-of-season events and biases in the retrieval processes.

**Plain Language Summary**

This study is a follow-up to a previous paper focused on the analysis of Martian water vapor vertical profiles. We make profit of the large data set to compare water vapor measurements from two instruments, NOMAD and ACS, both onboard the ExoMars Trace Gas Orbiter (TGO). These comparisons show good agreement between the instruments, despite differences in how the data is processed by different teams. To further validate our findings, this study compares these measurements to simulated water vapor vertical profiles from the Mars Planetary Climate Model (MPCM). The model generally manages to predict the observed water vapor seasonal and latitudinal patterns on Mars, although there are some notable discrepancies. These differences between model and observations are linked to how the model handles the distribution of dust and its impact on the global circulation, as well as possible misinterpretations in simulating the formation of water ice clouds at high altitudes. Additionally, our study introduces a new post processing methodology on Mars water vertical profiles: cluster analysis. This approach simplifies the analysis of water vapor patterns and helps identify unusual events or potential issues with the data processing.

**1 Introduction**

Although water vapor is relatively scarce on Mars, it plays a key role in several surface and atmospheric interactions, including regolith-atmosphere exchange, chemical and photochemical reactions, nucleation, sublimation, and transport. Its distribution is influenced by these processes and temperature variations, making it a fundamental component of the planet's complex climate. Understanding the behavior, sources, and variability of water vapor on Mars, both today and in the past, is vital to reconstructing the planet's climatic and geological evolution, as Mars has transitioned from a warmer, wetter environment to the cold, dry conditions we observe today.

Knowledge about water vapor vertical distribution has been limited until recent years. Mars' thin atmosphere, with surface pressures only about 1% of Earth's, makes detecting and measuring trace gases challenging and most information so far came from nadir-looking orbital observations, which provided integrated column abundances (Smith, 2002), and global circulation models (Forget et al., 1999; Haberle et al., 2019). However,
the application of the solar occultation technique, widely used for atmospheric studies on Earth, has enabled an unprecedented sensitivity for detecting and profiling water vapor and other trace species at different altitudes in the Martian atmosphere.

This study, the second in a two-part series, presents the continuation of the analysis of water vapor in the Martian atmosphere presented in Part I (Brines et al., 2025a), using data from 7624 solar occultations by the Nadir and Occultation for MArS Discovery (NOMAD) instrument onboard the ExoMars Trace Gas Orbiter (TGO). The high sensitivity of the NOMAD instrument allowed us to obtain water vapor abundances from ~5 – 10 km up to ~110 – 120 km altitude.

The analysis in Part I revealed significant seasonal and latitudinal variations, with the most striking differences observed between perihelion and aphelion seasons. During perihelion, the southern hemisphere experiences much higher and more extended water vapor concentrations, particularly during its summer. These seasonal patterns are influenced by multiple factors, including Martian orbital eccentricity, dust storms, sublimation from polar ice caps, and the planet's topography (Montmessin et al., 2017). In part I it was reported enhanced vertical transport of water vapor at 60°S, where abundances reached about 50 ppm at 100 km altitude during specific solar longitude ($L_S$) periods close to the perihelion of Martian years (MYs) 35 and 36, confirming previous studies on this same feature (Brines et al., 2024; Belyaev et al., 2021). Additionally, the Global Dust Storm (GDS) in MY 34 injected significant amounts of water vapor into the upper atmosphere, with concentrations reaching 100 ppm at 80 km altitude after the northern autumn equinox as previously shown in Brines et al. (2023). The study presented in Part I, improving previous works on TGO data and extending the vertical coverage up to 120 km altitude, also revealed that water vapor profiles are consistently more vertically extended and abundant during the evenings than the mornings throughout all years, attributing this systematic effect to stronger vertical transport during daytime. In addition, an unusual enhancement in vertical transport was observed in MY 37 during the aphelion season in the northern hemisphere, at $L_S = 112°$, a phenomenon not seen in previous years.

Building on the Part I, which outlined the methodology and initial findings, this paper focuses into the detailed comparison, cross-validation and statistical analysis of water vapor vertical profiles from different instruments and research teams across MYs 34 to 37. The extensive data set used in this series of papers permits a robust comparison between other NOMAD and Atmospheric Chemistry Suite (ACS) results revealing overall a good agreement between different teams and instruments. In addition, a global comparison of water vapor vertical profiles measured by NOMAD and those simulated by the Mars Planetary Climate Model (MPCM) shows a systematic overestimation of water vapor abundances in the model under dusty atmospheric conditions. For the first time, an application of cluster analysis techniques to Martian water vapor vertical profiles is presented. The structure of this paper is as follows: In Section 2 we describe the details about the NOMAD instrument and the analysis of the absorption spectra. The comparison between NOMAD and ACS is presented in Section 3. The NOMAD-MPCM comparison is shown in Section 4. The cluster analysis applied to both NOMAD profiles and MPCM simulated profiles is presented in Section 5. The interpretation and discussion of the results is shown in Section 6. Finally, Section 7 summarizes the results highlighting the main conclusions of this work. A Supporting Information document is included, showing a detailed profile-by-profile comparison and additional insights for the NOMAD-GCM comparison and cluster analysis.

## 2 Data set and analysis

Since in Part I of this series of papers the data set and retrieval methodology are thoroughly described, here, we only briefly summarize that information. Hence, for a more detailed description, please refer to Part I (Brines et al., 2025a).
## 2.1 The NOMAD instrument and data analysis

The NOMAD instrument is a suit of three spectrometers able to sample the Mar-
tian atmosphere in different viewing geometries and at different spectral ranges operat-
ing between 0.2 to 4.3 µm covering the UV, visible and infrared (IR) regions of the spec-
trum (Vandaele et al., 2018). The Solar Occultation (SO) channel dedicated for solar oc-
cultation measurements in the IR (2.3-4.3 µm), was designed based upon the Solar Oc-
cultation in the Infrared (SOIR) instrument onboard Venus Express (Bertaux et al., 2007).
It has a spectral resolution of about λ/Δλ~17000 (Neefs et al., 2015) and during each
solar occultation, NOMAD is able to sample the atmosphere acquiring sets of spectra
at less than 1 km tangent height step. An Acousto Optical Tunable Filter (AOTF) is
used to select six diffraction orders measured quasi-simultaneously at every altitude. A
detailed description of the NOMAD instrument was presented by Neefs et al. (2015) and
its most recent instrumental characterization is summarized in Villanueva et al. (2022).

The data processing and analysis performed at IAA-CSIC with NOMAD SO mea-
surements have been extensively described in previous works (López-Valverde et al., 2023).
The work presented here is focused on the cross-validation and statistical analysis of wa-
ter vapor profiles, being the extension of the Part I (Brines et al., 2025a) devoted to the
study of the water vapor climatology during 3 complete MYs. For that reason, for this
work we used the same data set as in Part I, a sample of 7624 NOMAD solar occulta-
tions taken during MYs 34, 35, 36 and 37. These observations cover a Solar Longitude
range from Ls ~ 160° of MY 34 to Ls ~ 160° of MY 37. These two papers build
upon two previous studies of water vapor (Brines et al., 2023, 2024), but extending the
data set and improving the data processing, retrieval scheme and vertical extension of
the water vapor vertical profiles.

As described in Part I, we used Level 1 calibrated transmittances (Trompet et al., 2023) from the latest pipeline processing at the Belgian Institute for Space Aeronomy (BIRA-IASB), available at ESA (2024b) and corrected from major systematics such as (i) a bending of the spectral continuum characterized with a fourth order polynomial, and (ii) a spectral shift. To perform this correction precisely, we used line-by-line forward model calculations carried out with the Karlsruhe OPtimized Radiative transfer Algorithm (KOPRA, Stiller (2000)). The cleaning of the NOMAD SO data has been extensively described in López-Valverde et al. (2023) and in Brines et al. (2023). The measurement noise provided by the official NOMAD calibration (Thomas et al., 2022) is improved by our in-house pre-processing pipeline by the characterization of covariance matrices (C-matrix). The diagonals of these matrices provide an estimation of the random component of the measurement noise, being 2-4 times smaller than the nominal one and improving the sensitivity of our retrievals at the uppermost atmosphere. The water vapor vertical profiles were obtained using the Retrieval Control Program (RCP, von Clarmann et al. (2003)) incorporating KOPRA as its Forward Model and using a first order Tikhonov regularization optimized for each diffraction order, applying a strong regularization at low altitudes with high dust optical depth. Similarly to Brines et al. (2023, 2024), the full vertical profiles were retrieved using a combination of two diffraction orders, 134 (3011-3035 cm⁻¹) or 136 (3056-3081 cm⁻¹) for the lower atmosphere (typically below 60 km) and 168 (3775-3805 cm⁻¹) or 169 (3798-3828 cm⁻¹) for the middle/upper atmosphere (above 60 km). This strategy is needed in order to avoid using strong absorption lines in optically thick conditions (low altitudes), where they saturate. We estimated the optimal transition altitude between orders for each occultation using the curve of growth of the strongest lines in orders 168 and 169 computed with KOPRA simulations. For a primary atmosphere considered during the inversions, we used pressure and temperature profiles extracted from specific runs of MPCM (Forget et al., 1999) at the exact time and location of each solar occultation.

The PCM includes the key parameterizations that control the water cycle, as described in Navarro et al. (2014) (see also Montmessin et al. (2004)): condensation on and
sublimation from the surface, transport and mixing in the boundary layer and by the general circulation, cloud microphysics (nucleation on dust grains, ice particle growth, sedimentation, scavenging of dust particles due to the condensation of ice) and transport. The radiative effect of clouds is taken into account (Madeleine et al., 2012). Compared to the model version described in Navarro et al. (2014), the version used here (version 6.1) notably includes an improved parameterization of the dust vertical distribution (Millour et al., 2024) to account for sub-grid scale processes such as “rocket dust storms” (Wang et al., 2018) and the re-injection in altitude of near-surface dust by anabatic winds along the flanks of large volcanoes. Combined with the effect of an improved parameterization of effect of gravity waves, this allow for an improved prediction of the temperature fields relevant here, as reported in Liu et al. (2023).

The MPCM runs were performed taking into account the best estimate of the dust optical depths from Montabone et al. (2020) for each MY, including the GDS in MY 34. Due to the lack of measured data by the time the retrievals were performed, for MY 37 we used the same dust climatology than for MY 36. Since only the aphelion season of MY 37 is analyzed here, known to typically being clear from dust, we considered this approach to be appropriate.

## 3 NOMAD and ACS comparisons

Several teams within the TGO consortium are studying water vapor with different instruments onboard the spacecraft, characterizing topics such as the water at high altitudes (Belyaev et al., 2021; Brines et al., 2024), isotopic fractionation (Alday et al., 2021; Villanueva et al., 2022), water vapor saturation ratios (Fedorova et al., 2023) or water vapor seasonal variability (Aoki et al., 2022; Brines et al., 2023). In this Section we show a comparison of the results presented in Part I of this paper, referred to as SO-Brines25 within this section of the paper, with the results obtained from three of the most recent and extensive studies on water vapor performed with NOMAD (Aoki et al., 2022), hereafter referred to as SO-Aoki22, and ACS (Belyaev et al., 2021; Fedorova et al., 2023), hereafter referred to as MIR-Belyaev21 and NIR-Fedorova23 respectively. ACS, also onboard TGO, is a suite of three high resolution spectrometers: (i) the near-infrared channel (NIR), (ii) the middle-infrared channel (MIR) and (iii) the thermal infra-red channel in honor of Professor Vassily Ivanovich Moroz (TIRVIM). This instrument operates in the spectral range from 0.65 to 17 µm (Korablev et al., 2018) and like NOMAD, was designed to observe the atmosphere in solar occultation, nadir and limb geometries. The NIR channel, operating in the spectral range 0.73-1.6 µm, follows the design of the SPICAM-IR instrument, this is, based on an AOTF filter and an echelle-grating, entirely similar to the NOMAD SO channel.

In the case of SO and NIR channels, the pointing of both instrument is extremely similar during most of the atmospheric scans, making observations from both channels mostly collocated, besides some latitude-longitude variation at decimal precision. For this comparison analysis, we used those collocated scans, comparing only ACS NIR and NOMAD SO occultations within a latitude-longitude boxes of 5° × 5°. With this, we selected a subset of measurements during MYs 34, 35 and 36 resulting in a total of 936 vertical profiles common between SO-Brines25 and NIR-Fedorova23, making a total of 36416 coincident water vapor measurements. On the other hand, the profiles presented in Belyaev et al. (2021) measured with ACS MIR were obtained at totally different locations and times from those taken with NOMAD SO. Because of this limitation, we performed the comparison between NOMAD SO and ACS MIR by averaging all profiles from MIR-Belyaev21 and SO-Brines25 measured within boxes of 10° latitude × 30° longitude × 30° in solar longitude. In addition, we imposed the criterion of comparing only profiles obtained at the same terminator, morning (from 1 am to 12 pm) or evening (from 12 pm to 12 am). With these restrictions we were able to obtain a total of 221 averaged profiles to compare. In the case of the data set from (Aoki et al., 2022), all water vapor
<figure><img src="image_50.png" /></figure>

Figure 1: Comparison of water vapor abundances presented in (Brines et al., 2025a) (this work, y-axis) with those obtained by (Fedorova et al., 2023) (x-axis). Colors indicate point density (a1, a2), Solar Longitude (b1, b2) and altitude (c1, c2) of the observations for the northern (left) and southern hemispheres (right). Red dashed line in top panels shows the linear fitting. Gray dashed line indicates $y = x$. Note that top panels are shown in linear scale.

vertical profiles were obtained with NOMAD SO, so the co-location criterion with SO-Brines25 is granted. The number of common occultations available for the comparison between the work presented here with SO-Aoki22 during MYs 34, 35 and 36 is 4197, making a total of 89901 coincident water vapor measurements.

Typically, the volume mixing ratios (VMR) used in studies of water vapor vertical profiles in Mars are expressed for a given reference atmosphere. So, in order to eliminate the effect of using different atmospheric densities in different retrieval schemes (GEM-Mars in the case of SO-Aoki22, and the MPCM in our inversion), the VMR from SO-Aoki22 and NIR-Fedorova23 data sets were scaled computing new VMRs using the total atmospheric density from SO-Brines25 as reference. Hence, the scaled VMRs used for these comparisons are defined as $VMR^A = \rho_{H_2O}^A/\rho_{TOT}^B$ and $VMR^F = \rho_{H_2O}^F/\rho_{TOT}^B$, where $\rho_{TOT}^B$ is the total atmospheric density from SO-Brines25 and $\rho_{H_2O}^A$, $\rho_{H_2O}^F$ are the retrieved water vapor number density from SO-Aoki22 and NIR-Fedorova23 respectively. For the comparison with MIR-Belyaev21 we focused the analysis on absolute water vapor number density instead of VMR.
<figure><img src="image_51.png" /></figure>

Figure 2: Comparison of water vapor abundances presented in (Brines et al., 2025a) (this work, y-axis) with those obtained by (Aoki et al., 2022) (x-axis). Colors indicate point density (a1, a2), Solar Longitude (b1, b2) and altitude (c1, c2) of the observations for the northern (left) and southern hemispheres (right). Red dashed line in top panels shows the linear fitting. Gray dashed line indicates $y = x$. Note that top panels are shown in linear scale.

The procedures and retrieval methodology used in SO-Brines25 and those used in the rest of data sets are all different, each one of them requiring specific assumptions to consider during the inversions. Our retrievals rely on a global fit (this is, spectra at all altitudes are taken into account during the data-model fitting) and a priori profiles from the MPCM. However, in the case of SO-Aoki22, the a priori information used during the inversion comes from simulations of the GEM-Mars and the water vapor density is retrieved using the optimal estimation method Rodgers (2000), processing the spectrum at each altitude as an independent measurement assuming a constant volume mixing ratio along the line of sight (LOS). In the case of MIR-Belyaev21 and NIR-Fedorova23, water vapor vertical profiles were obtained using a global fit method, similar to what it is done in this study, where the spectra at all altitudes are processed simultaneously Fedorova et al. (2020). Additionally, it should be noted that for each H₂O density retrieved from ACS they derived a reference temperature using rotational CO₂ lines in the assumption of hydrostatic pressure. It may result in discrepancies between ACS and NOMAD-SO profiles in a case of water saturation. Therefore, the comparisons presented here must be taken with caution. The data analysis and inversion methods performed by each team
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are described in Aoki et al. (2022); Belyaev et al. (2021) and Fedorova et al. (2023) for SO-Aoki22, MIR-Belyaev21 and NIR-Fedorova23 retrievals respectively.

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In Figures 1 and 2 we show correlograms with the comparison between the results obtained in SO-Brines25 (this work, y-axis) and those from NIR-Fedorova23 and SO-Aoki22 respectively (x-axis). Left and right panels indicate measurements from the northern and southern hemispheres respectively. For both Figures, colors in top panels show the point density distribution (the more yellowish, the larger number of points) whereas the colors in the middle and bottom panels represent the solar longitude and the altitude of the observations respectively. Overall the agreement is good in both comparisons, with mean correlation factors of 0.92 for the comparison with NIR-Fedorova23 and 0.83 in the case of SO-Aoki22. A linear fit of the comparison also shows an excellent agreement between the three sets of retrievals, considering the large differences in the retrieval approaches. Nevertheless, we notice that the results presented in this work are globally about ~7.5% larger than SO-Aoki22 and about ~11% systematically smaller than NIR-Fedorova23, values which fall within the retrieval's uncertainties of both NOMAD and ACS.

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Despite the overall good agreement, Figures 1 and 2 show some profiles with systematic bias. The comparison with NIR-Fedorova23 reveals a diverging branch toward higher abundances retrieved from ACS NIR during the aphelion season in the southern hemisphere, as shown in Figure 1-b2. In addition, this bias seems to appear systematically at altitudes about 50-60 km, which for this season and hemisphere, might correspond with the top most retrieved altitude suggesting border effects during the inversion being a possible reason of this discrepancy. The comparison with SO-Aoki22, on the other hand, reveals a diverging branch towards higher water abundances in SO-Brines25 results in the northern hemisphere and another towards higher VMR values in SO-Aoki22 results in the southern hemisphere. As shown in Figure 2-b1, this first branch corresponds with profiles measured during the aphelion season at low altitudes below 20-30 km as shown in Figure 2-c1. Similarly, in the southern hemisphere the observed bias also occurs at low altitudes during the aphelion, but in this case showing a deficit in SO-Brines25 abundances. One possible reason for these discrepancies could be in the retrieval method itself. In the case of SO-Aoki22, the assumption of a constant VMR along the LOS and not considering the contribution of the spectra from the layers above the observation shall introduce biases under conditions of strong vertical gradients, which are common at low altitudes during the northern summer. This discrepancy was previously noticed and discussed in Brines et al. (2024) (see their Supporting Information document).

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In order to complement this comparison, a selection of 32 sets of profiles, 16 for each hemisphere at a wide variety of latitudes and measured during different seasons are presented in Figures S1 and S2 on the SI document for the northern and southern hemispheres respectively. A smaller sample of four sets of profiles is shown in Figure 3. This set was selected because it captures an assortment of representative features observed in the water vapor profiles, covering different atmospheric conditions, from low to high water vapor abundance. Each panel shows the retrieved profiles from SO-Brines25 (blue, this work), SO-Aoki22 (green) and NIR-Fedorova23 (red). Overall, as discussed above in this Section, the agreement between the three retrievals is good, with all three profiles capturing the same vertical structures. However, some discrepancies arise regarding the amplitude of those structures, with more pronounced features appearing in SO-Brines25 as illustrated in Figures 3-b and 3-d. The reason of these differences might be due to the different vertical resolution obtained during the inversions, i.e. the width of the averaging kernels, which are directly related with the altitudes that are being mixed to obtain the information from each tangent altitude. This is affected by the regularization imposed during the inversions and by the uncertainties on the measurements. Our retrievals seem optimal in terms of vertical resolution, and as discussed in Part I, since the objective of our study was to provide a global water vapor climatology, our regularization common
<figure><img src="image_52.png" /></figure>

Figure 3: Comparison of water vapor volume mixing ratio vertical profiles retrieved from NOMAD (blue, green) and ACS (red) observations. The locations (longitude, latitude) of NOMAD and ACS observations are indicated in blue and red respectively. Season ($L_s$) and local time (LST) of indicated in black. Dashed line shows the water vapor volume mixing ratio extracted from the MPCM at the NOMAD locations.

for all the retrievals was fine tuned to provide reliable results on a wide variety of atmospheric scenarios.

As described at the beginning of this section, unlike NOMAD-SO and ACS-NIR, which both point in nearly the same direction, the ACS-MIR pointing differs from that of NOMAD-SO, resulting in the observations of these two instruments not being collocated. Hence, in order to compare with this instrument we decided to perform averages with the water vapor vertical profiles retrieved at specific boxes of latitude, longitude and solar longitude. Then, we computed the ratio between those averages. A selection of four cases is shown in Figure 4. Since variations on the location and timing of the observations imply possible variations on the thermal structure of the atmosphere and on the water vertical distribution, some vertical features on the water vapor profile are observed by one instrument but not by the other, revealing "spikes" on the ratio profiles. These "spikes" are observed at a wide variety of altitudes and did not reveal systematic biases at any specific atmospheric layer, as shown in Figure 5 when all ratios are put together. This is true for MYs 35, 36 and MY 34 below 90 km ($>10^{-3}$ mbar) which shows larger ACS water vapor abundances than NOMAD at high altitudes (Figure 5-a). Al-
<figure><img src="image_53.png" /></figure>

Figure 4: Comparison of water vapor number density vertical profiles retrieved from ACS MIR and NOMAD SO at four longitude-latitude-$L_s$ windows. For each set of three panels, left panel shows the water vapor vertical profiles from NOMAD (blue) and ACS (red). When more than one observation falls within the window, thin lines show the individual profiles while thick line shows the averaged profile. Middle panel shows the ratio between the averaged NOMAD and ACS profiles, and right panel shows the geographic location of the NOMAD (blue) and ACS (red) observations. Thin dots show the location of all observations while thick dots show the location of the observations within the window. Vertical and horizontal gray lines indicate the limits of the longitude-latitude window.

though perhaps this discrepancy could be due to boundary constraints during the retrievals, this feature is different to that observed in the comparison with ACS NIR which showed a similar bias at the top most altitudes during the aphelion season, not the perihelion season as observed in the comparison with ACS MIR. Nevertheless, besides this discrepancy in MY 34 and taking into account that a profile-by-profile comparison is not possible between these two instruments due to non collocated measurements, both datasets show qualitatively a global good agreement, both capturing the same water vapor seasonal trends.

# 4 NOMAD and MPCM comparisons

## 4.1 Seasonal variability

Global circulation models (GCMs) are essential tools to provide a complete and detailed understanding of the atmospheric dynamics and climate. Although physics are the core of these models, real observations are required in order to improve, fine tune and validate the picture drawn by the pure theoretical assumptions made during the elaboration of the GCMs. For that purpose, here we provide a first comparison of the NOMAD SO dataset presented in Part I (Brines et al., 2025b) with the Laboratoire de Météorologie Dynamique (LMD) Mars Planetary Climate Model (MPCM, Forget et al. (1999)).

In Figure 6 we show the absolute difference $\Delta\mu_{H_2O} = \mu_{\text{NOMAD}} - \mu_{\text{M-PCM}}$ between the NOMAD SO ($\mu_{\text{NOMAD}}$) and the M-PCM ($\mu_{\text{M-PCM}}$) water vapor volume mixing ratio from the second half of MY 34 to the first half of MY 37. In order to provide a meaningful analysis, the water vapor vertical profiles from the MPCM have been produced for the exact location and time as those obtained from the NOMAD SO observa-
<figure><img src="image_54.png" /><figcaption>Figure 5: Ratios of averaged SO-Brines25 vertical profiles with averaged MIR-Belyaev21 profiles within boxes of 10° latitude × 30° longitude × 30° in solar longitude, computed for MYs 34 (a), MY 35 (b) and MY 36 (c). Thin blue and red lines indicate the ratio during morning and evening observations respectively. Thick lines show the mean ratio. Vertical black dashed line indicates ratio equal 1. Gray shaded area indicates the dispersion of the average of all profiles.</figcaption></figure>

tions. Top panels (a) and (b) show the latitude and differences averaged in altitude windows of 5 km centered at 30 and 80 km respectively, in both cases within boxes of 5° in latitude and 5° in solar longitude. In panels (c) and (d), the differences between measured and simulated vertical profiles are shown in bins of 1° in solar longitude. In all these panels from Figure 6, reddish colors indicate larger values of water vapor abundance (VMR) observed with NOMAD whereas blueish hues indicate larger values in the MPCM. The color scheme of this figure has been defined in order to emphasize differences at least larger than | $\Delta\mu_{H_2O}$ | = 10 ppm and by making this map showing absolute differences we are highlighting the observed-modeled discrepancies during periods of large water vapor abundance, this is, perihelion season and low altitudes during northern summer season. An additional figure showing relative differences defined as $\delta\mu_{H_2O} = (\mu_{H_2O}^{\text{NOMAD}} - \mu_{H_2O}^{\text{M-PCM}})/\mu_{H_2O}^{\text{M-PCM}}$ is shown in Figure S3 of SI document.

From Figures 6-a and 6-b, and focusing the analysis on MYs 35 and 36 (two complete MYs), the MPCM seems to underestimate water vapor abundances at low altitudes, particularly during $L_s=240°-360°$ in the southern hemisphere. This effect is also noticeable in Figure S3-a of SI, where larger NOMAD water vapor abundances are observed at 30 km in the aphelion season during $L_s=0°-150°$ at both hemispheres. In contrast, at high altitudes, the MPCM systematically overestimates water vapor abundances during almost the whole year with some exceptions at $L_s \sim 120°$ in both hemispheres as shown in Figure S3-b, and during $L_s=260°-300°$, shown in Figure 6-b. The first could be due to an underestimation of the modeled global circulation, which seems to be actually more intense according to the larger water vapor abundances observed by NOMAD at all latitudes. This underestimation of the model, however, only appears above 30 km altitude. Below this altitude the model is overestimated, a feature observed during the whole apohe-
<figure><img src="image_55.png" /></figure>

Figure 6: Absolute difference of water vapor volume mixing ratio $\Delta\mu_{H_2O}$ between NOMAD SO and the MPCM over Solar Longitude during MYs 34, 35, 36 and 37 for the Northern (c) and Southern (d) hemispheres. Top two panels show the $\Delta\mu_{H_2O}$ at 30 km (a) and 80 (b) as a function of latitude and Solar Longitude. All panels use the same color scheme. Blue colors indicate MPCM abundances larger than NOMAD.

tion season in the northern hemisphere. The second exception mentioned above corresponds to the perihelion water vapor pumping in the southern hemisphere analyzed by Brines et al. (2024) and could be due again to a deficient vertical transport of water vapor in the model at high southern latitudes.

Looking at the left hand side of Figure 6 (all panels), the presence of blue hues during almost the whole My 34 in both hemispheres is evident, suggesting that the MPCM overestimates water vapor abundance during MY 34's GDS and its decay phase. This overestimation is observed throughout the whole vertical range analyzed here, with the exception of a short period of underestimated abundances below 40 km during $L_S \sim 260^\circ$ in the northern hemisphere. Looking at the aphelion season ($L_S=0^\circ-180^\circ$) of MYs 35, 36 and 37, particularly at mid-low northern latitudes and at low altitudes below 30 km (Figure 6-c), water vapor abundances are systematically larger in the MPCM. Besides this low altitude aphelion overestimation, interestingly only a short period during MY 37 ($L_S \sim 120^\circ$) shows a strong underestimation of water vapor VMR with the model, suggesting and observed rare water vapor injection up to 50 km altitude at latitudes $50^\circ$N-$60^\circ$N not simulated in the MPCM.
In contrast to the aphelion, the perihelion season shows a different pattern in the seasonal and vertical distribution of the differences between model and NOMAD SO measurements. In this case, during the period $L_S = 240°-300°$, the overestimation in the model appears at 40-80 km altitude in the northern hemisphere whereas the opposite (NOMAD water vapor larger than MPCM) occurs below 40 km altitude in the northern hemisphere and systematically at almost the whole vertical range in the southern hemisphere, evidencing difficulties in the model to reproduce the southern's summer water enhancement. In addition, at $L_S \sim 270°$ MPCM underestimates water vapor abundance at 100 km altitude in the northern hemisphere. This water vapor enhancement observed by NOMAD and not reproduced in the model, as mentioned above, could be related with the plumes observed in the southern hemisphere (Brines et al., 2024). This pattern, similarly observed in both MYs 35 and 36, suggests not only a more efficient vertical transport of water vapor in the southern hemisphere than the model predicts but also that the meridional transport in the MPCM could be overestimated at 40-80 km while underestimated at altitudes as high as 100 km. This difficulty in reproducing the distinct water vapor increase in the southern hemisphere during the perihelion was also reported by (Vals et al., 2022), who attributed the issue to the difficulty of the model to reproduce the true dust vertical distribution.

## 4.2 Latitudinal variability

In addition to the seasonal variability study discussed above, we performed a latitudinal variability analysis with MPCM simulations, similar to that presented in Part I with NOMAD SO observations. The differences on the latitudinal distribution between observations and simulations are shown in Figures 7 and 8 for temporal windows of 30° $L_S$ during the aphelion (from $L_S = 0°$ to $L_S = 180°$) and perihelion (from $L_S = 180°$ to $L_S = 360°$) seasons respectively. For a given latitude, in order to avoid mixing different local times, we distinguish occultations from the morning terminator (top two rows) to the evening ones (bottom two rows). For representing the maps in Figures 7 and 8, all vertical profiles within 5° latitude bins were averaged. For each $L_S$ window, observations and simulations from MYs 35, 36 were used to compute the latitudinal distribution. Additionally, a selection of maps showing the absolute water vapor volume mixing ratio (VMR) from NOMAD and the MPCM used to compute the differences during solstices and equinoxes are shown in Figure 9.

During the beginning of the MY from $L_S = 0°$ to $L_S = 30°$, as shown in Figure 9-a1, 9-a2, 9-a3, and 9-a4, the model succeeds in predicting the overall latitudinal distribution. Nevertheless, when looking at the relative differences between the model and the observations, different behaviors are noticed at both terminators. In Figure 7-a1 for the morning observations, the model shows a region of excess of water vapor below 20 km altitude at both hemispheres followed by a layer with deficit of water at 20-40 km. In contrast, during the evening and shown in Figure 7-b1, the region showing lower abundances in the model than in the NOMAD observations extends from 5 to 60 km. However, in both cases, water vapor is systematically overestimated in the MPCM above 60 km altitude, pattern which repeats itself until $L_S = 90°$.

As the northern spring advances a clear interhemispheric asymmetry arises below 40 km, with MPCM highly overestimating water vapor abundance at low altitudes in the northern hemisphere as shown in Figures 7-a2, 7-a3, 7-b1. This feature remains constant for the rest of the season, being the region between 40-60 km the one presenting more variability. Besides this discrepancy, once again the MPCM provides overall a good prediction of the wtaer vapor distribution as shown in Figures 9-b1, 9-b2, 9-b3, and 9-b4.

Another interesting discrepancy between model and NOMAD measurements can be observed by the end of the aphelion season during $L_S = 120°$ to $L_S = 180°$, pe-
<figure><img src="image_56.png" /></figure>

Figure 7: Multi-annual average of the latitudinal distribution of the relative differences $\delta\mu_{H_2O}$ between NOMAD SO and MPCM water vapor volume mixing ratio (VMR) during the aphelion season from observations at the morning terminator (top two rows from a1 to a6) and evening terminator (bottom two rows from b1 to b6). Blue colors indicate larger MPCM abundances than NOMAD.

riod when the northern hemisphere above 20 km seems to be more humid than the MPCM predicts, as illustrated in Figures 7-a5, 7-a6, 7-b5 and 7-b6. As shown in Figures 8-a1 this same situation is maintained until $L_s = 180^\circ-210^\circ$. At this moment, the model clearly overestimates the water vapor abundances above 60 km systematically at all latitudes, as shown in Figures 9-c1, 9-c2, 9-c3, and 9-c4.

However, as the southern summer approaches, the picture changes and the differences NOMAD-MPCM reveal a strong deficit in the water vapor abundance simulated in the southern hemisphere. By $L_s = 240^\circ-270^\circ$, although the agreement between model and observations is good below 60 km at mid latitudes as shown in Figures 8-a3 and 8-b3, the model underestimation at high southern latitudes becomes progressively more relevant as shown in Figures 8-a4 and 8-b4. During $L_s = 270^\circ - 300^\circ$, larger water va-
<figure><img src="image_57.png" /></figure>

Figure 8: Multi-annual average of the latitudinal distribution of the relative differences $\delta\mu_{H_2O}$ between NOMAD SO and MPCM water vapor volume mixing ratio (VMR) during the perihelion season from observations at the morning terminator (top two rows from a1 to a6) and evening terminator (bottom two rows from b1 to b6). Blue colors indicate larger MPCM abundances than NOMAD.

por abundances reaching altitudes as high as 100 km are observed in NOMAD profiles. This structures, or plumes, were known to not be properly reproduced in the MPCM, as previously discussed in Brines et al. (2024) and illustrated here in Figures 9-d1, 9-d2, 9-d3, and 9-d4. Interestingly, they report an interannual variability of this feature, revealing a weaker and delayed appearance of the plume during the MY 34, suggesting a larger dust deposition over the southern polar cap during the GDS, leading to a reduced and delayed sublimation after the storm. However estimations of the diffusion of water through a dust layer indicate that such a layer needs to be as thick as several millimeters to produce the desired effect. We performed a calculation using a novel approach that includes subsurface ice in the MPCM and estimates the loss rate (Vos et al., 2024). This is shown in Figure S8 in the SI document. Such a thick layer has never been observed

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<figure><img src="image_58.png" /></figure>

Figure 9: Multi-annual average of the latitudinal distribution of the NOMAD SO (from a1 to d1 and from a3 to d3) and MPCM (from a2 to d2 and from a4 to d4) water vapor volume mixing ratio (VMR) during equinoxes ($L_s = 0°$ and $L_s = 180°$) and solstices ($L_s = 90°$ and $L_s = 270°$). The two columns on the left (right) show observations at the morning (evening) terminator. MPCM altitudes are masked in the same manner as the NOMAD observations to ease visual comparison.

in polar regions therefore we consider that the transport and deposition of dust in MY 34 may not be directly affecting this water vapor injection. Let us notice that the reason for the low water vapor abundance at high latitudes following a GDS, which has also been observed by (Pankine et al., 2023), is still a mystery.

Back to the NOMAD-MPCM comparisons, in Figure 8-a4 it is clear the connection of the strong water vapor injection in the southern hemisphere with the layer of underestimated water vapor in the model at 100 km altitude in the northern hemisphere. It is also interesting to highlight the differences observed during this period at ~60 km in the northern hemisphere, clearly visible in Figures 8-a4 and 8-b4 and being particularly more intense at the morning.

## 4.3 Statistical comparison

Besides the analysis focused on the seasonal and latitudinal variability, it is convenient to study the global correlation between both the model and the observations in order to provide a general view of the agreement/discrepancies. For that reason, in Figure 10 we show a series of correlograms of the water vapor VMR as observed by NOMAD ($\mu_{\text{NOMAD}}$) in the x-axis and that modeled by the MPCM ($\mu_{\text{MPCM}}$) in the y-axis. For each
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MY and in order to provide a meaningful picture of the comparison, we repeated the scat-
ter plot coloring different magnitudes such as the density of points (panels a), the solar
longitude (panel b), the latitude and longitude of the measurements (panels c and d),
the local solar time (panel e) and the altitudes (panel f). In order to highlight the region
of 0-100 ppm, a set of figures showing these same panels but in logarithmic scale is pre-
sented in the SI document.

MY 34

<figure><img src="image_59.png" /></figure>

MY 35

<figure><img src="image_60.png" /><figcaption>Figure 10: Comparison of NOMAD SO water vapor abundances (x-axis) with those simulated by the MPCM (y-axis) for MYs 34 (panels a1 to f1), 35 (panels a2 to f2), 36 (panels a3 to f3) and 37 (panels a4 to f4). For each MY, colors in panels a to f indicate the density of measurements (panel a), solar longitude (panel b), latitude and longitude (panels c and d), local solar time (panel e) and altitude (panel f). Gray dashed line indicates y = x.</figcaption></figure>

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From Figure 10-a1 to 10-f1 for MY 34, we observe water vapor abundances system-
atically larger in the MPCM. In particular, abundances at high altitudes between 100-
<figure><img src="image_61.png" /><figcaption>MY 37</figcaption></figure>

<figure><img src="image_62.png" /><figcaption>Figure 10: (continued)</figcaption></figure>
120 km are highly overestimated in the MPCM, observed in the form of reddish branches in Figure 10-f1. During MY 34, unlike the following years, a clear structure with higher density of points can be observed around $\mu_{MPCM}=100-150$ ppm (Figure 10-a1) corresponding mostly to observations in the southern hemisphere at mid-low altitudes between 30-50 km during the decay phase of the GDS ($L_S=220°-260°$). Corresponding with the peak of the GDS during $L_S=180°-200°$, another structure can be observed at $\mu_{MPCM} \sim 200$ ppm. Interestingly, its horizontal shape and color gradient shown in Figures 10-f1 and S4-f1 suggests more vertical variability in NOMAD than in the MPCM, the later producing similarly large water vapor abundances at every altitude.

For MYs 35 and 36 the situation is slightly different. As previously discussed, although there are some discrepancies between model and observations during specific periods and altitude regions, in this case the overall agreement seems qualitatively better than in MY 34. During these two MYs showing similar structures are noticeable (Figures 10-a2 to 10-f2 for MY 35 and 10-a3 to 10-f3 for MY 36). As shown in these figures and clearly visible in log-scale (Figures S4 and S5 from SI), multiple horizontal branches are observed during the whole year with no clear correlation with the latitude or local time of the observations. In contrast, when looking at the altitude distribution of these structures (Figures S4-f2 and S5-f3) and similarly to what is observed during MY 34, it is evident the tendency of the MPCM on sustaining higher water vapor abundances at higher altitudes.

At last, for the MY 37 (Figure 10-a4 to 10-f4), systematically higher abundances are observed in MPCM during $L_S=150°-180°$ at both hemispheres. In contrast and unlike previous years, a population of larger NOMAD abundances is observed around $L_S \sim 120°$ in the northern hemisphere (Figures 10-b4, 10-c4, S5-b4 and S5-c4) mostly below 50 km altitude (Figures 10-f4 and S5-f4). Finally, and common in the four MYs analyzed here, we do not observe any correlation of excess/defect of water vapor abundance in the model with the longitude of the observations (Figure 10-d1, 10-d2, 10-d3 and 10-d4), suggesting the zonal distribution of water being properly predicted by the model.

Besides this analysis, it is important to note the coupling of solar longitude, latitude and local time of the NOMAD observations due the orbital geometry of TGO. This imposes a strong restriction on the location and time of the observations, forcing some latitudes to be sampled only during specific times and seasons. Nevertheless, this potential observational bias is overcome by the large amount of measurements during different years analyzed here, successfully filling the gaps left by the orbital geometry during individual years.

# 5 Cluster analysis

The water vapor distribution on Mars exhibits a strong variability with season and latitude, although it follows repeated patterns and similar vertical structures every MY. Therefore, a characterization by means of a small set of representative profiles could be very useful to characterize the water vapor climatology. In this Section we present the results obtained after the application of cluster analysis techniques to our retrieved data set of profiles in order to identify the most relevant vertical structures associated to different seasons and locations. Cluster analysis is a statistical method used to categorize similar objects into groups, or "clusters," ensuring that objects within the same cluster are more similar to each other than to those in different groups. The main objective of cluster analysis is to reveal the inherent groupings in a data set without any prior knowledge about the subsets. There are several techniques for clustering, each with distinct advantages and limitations. For this work, and based on previous similar studies on Martian temperature vertical profiles (Cala Hurtado, 2016), we used the K-means algorithm (Pedregosa et al., 2011). This is an iterative method which clusters data minimizing the distance between data points within a given cluster while maximizing the mean distance
between clusters. First, a number of clusters is provided. Then, a representative vertical profile for each cluster is randomly defined, i.e. centroid, and the retrieved NOMAD profiles are assigned to each one of those clusters in a way that the mean euclidean distance between each profile and the cluster's centroid is minimum. After that, the centroids are recalculated for the new clusters and the assignation process is done again. These two steps are repeated until convergence, that is, until the difference between the new centroids and the previous one is less than a certain value. Here we explored different initial configurations and several numbers of clusters, from 2 to 20, in order to evaluate the impact of the random initialization of centroids and the sensitivity to different levels of clustering. We studied several quality metrics commonly used in this kind of studies such as the Silhouette coefficient Rousseeuw (1987), the Davies-Bouldin index Davies and Bouldin (1979) or the Calinski-Harabasz index Calinski and Harabasz (1974). All these metrics try to evaluate and compare the between-cluster separation with the within-cluster dispersion, where the larger the first and the smaller the second, the better. After these tests and based on visual inspections, we decided to use $K = 6$ clusters to provide a simplified view of the water vapor climatology, describing the seasonal and latitudinal inter-annual variability with 6 distinct representative profiles. We applied the clustering to the whole data set at once, including the four MYs and both southern and northern hemisphere measurements during the cluster assignation.

<figure><img src="image_63.png" /><figcaption>Figure 11: Left panels show the seasonal-latitudinal distribution of the retrieved NOMAD SO water vapor vertical profiles for MYs 34, 35, 36 and 37 (from top to bottom respectively). Colors indicate the clusters where profiles were assigned. Right panel shows the representative water vapor VMR vertical profile of each cluster.</figcaption></figure>

In Figure 11, we show the results of the clustering for MYs 34, 35, 36 and 37. Left panels indicate the latitude and solar longitude of each identified group, labeled with a different color for each MY. The representative profiles of each cluster are presented in the right hand side panel. From Figure 11 we can identify different features represented by distinct groups.

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• First, Group 0 is observed during $L_S \sim 0^\circ - 180^\circ$ and $L_S \sim 340^\circ - 360^\circ$ and includes all the profiles representative for the aphelion season and the northern spring equinox. It shows low and nearly constant water vapor abundance at all altitudes and is common during this period in all MYs. On the other hand, groups 1 to 5 are used to describe the variability during the perihelion season.

• Group 1, characterized by abundances about 100 ppm below 50 km, appears scattered during the second half of the year, although seems to be more common in the southern hemisphere. It is particularly frequent during $L_S \sim 200^\circ - 250^\circ$ in MY 34, period which coincides with the decay phase of the GDS. It is also common around $L_S \sim 320^\circ$ in MYs 34, 35, 36 coinciding with the appearance of C-storms at the end of each MY.

• Group 2, with abundances between 50 to 100 ppm below 40 km, is common at mid-high northern latitudes below $70^\circ$. Unlike any other year, this profile appears also during the aphelion of MY 37 at $L_S \sim 110^\circ - 120^\circ$.

• Group 3 shows abundances ranging between 100 to 200 ppm below 50 km and about 50 ppm above 80 km. It appears only in the southern hemisphere (mid latitudes) and is common during $L_S \sim 250^\circ - 280^\circ$ in MYs 34,35,36. This period corresponds with the perihelion and its time and location of appearance coincides with the detection of high water vapor abundance in the upper atmosphere, as discussed by (Belyaev et al., 2021), and more recently by (Brines et al., 2024).

• Group 4, with abundances above 100 ppm below 45 km and with a sharp decrease above, appears scattered in both hemispheres, usually acting as a transition between groups 1, 2 and 3.

• Finally, Group 5 represents water vapor profiles with abundances of about 200 ppm below 60 km and about 50 ppm at 80 km, decreasing with altitude. This type of profiles appears at $L_S \sim 180^\circ - 210^\circ$ in MY 34 and are representative of the peak activity of the GDS during that year. This group is also briefly observed during the perihelion at $L_S \sim 260^\circ$ in MYs 35 and 36 and $L_S \sim 280^\circ$ in MY 34, between observations of the Group 3.

These results show that seasonal variability is overall more relevant than the latitudinal or local time variations. However, some groups may have a preference to appear in the northern or southern hemispheres, and similarly, a few groups were observed more frequently during specific local times.

<figure><img src="image_64.png" /><figcaption>Figure 12: Left panel shows the number of profiles measured at the northern (red) and southern (blue) hemisphere for each group. Right panel shows the same but for profiles measured during mornings (blue) and evenings (red).</figcaption></figure>
In Figure 12 we show the number of NOMAD SO observations grouped in each cluster, indicating if the profiles within the group correspond to measurements taken at the northern or southern hemisphere (left panel) and if the observations correspond to the morning or evening terminators (right panel). Although some of these groups were observed with a slightly larger frequency in one hemisphere than in the other, only Groups 1 and 3 stand out clearly to be representative for the southern hemisphere. While the first corresponds to the observations during the decay phase of the GDS, the second represents profiles showing the largest abundance of water vapor at high altitudes. On the other hand, Group 2 seems to be more frequent in the northern hemisphere during the winter solstice. Regarding the local time, profiles from Groups 3 and 4 appear more repeatedly during evening observations. However, the larger amount of evening profiles in Group 5, which contains mostly profiles observed during the GDS, is due to the fact that this event was observed only during evenings indicating a bias in the sample rather than a true feature.

<figure><img src="image_65.png" /><figcaption>Figure 13: Left panels show the seasonal-latitudinal distribution of the Mars-PCM water vapor vertical profiles for MYs 34, 35, 36 and 37 (from top to bottom respectively). Colors indicate the clusters where profiles were assigned. Right panel shows the representative water vapor VMR vertical profile of each cluster.</figcaption></figure>

For completion, in Figure 13 we show the result of repeating the clustering exercise with water vapor vertical profiles extracted from the MPCM. Here we observe a similar seasonal pattern as that obtained with NOMAD observations, with a Group 0 characterized by low water vapor abundances dominating the aphelion season, a specific Group 5 representative for the MY 34 GDS and a wide variety of profiles during the second half of each MY. In this case, in contrast with the clustering from NOMAD, the latitudinal and seasonal correlations with the different groups seem more evident due to the less variability produced by the model.
• Group 1, similarly to the NOMAD clustering, is particularly frequent in the south-ern hemisphere during $L_S \sim 200^\circ - 250^\circ$ in MY 34, corresponding with the decay phase of the GDS. Then, it has a repeated appearance at $50^\circ S - 60^\circ S$ at $L_S = 240^\circ$

• Group 2 is mainly observed at mid-high latitudes, typically above $50^\circ$ in both hemi-spheres during $L_S \sim 200^\circ - 330^\circ$ with some excursions to low southern latitudes at the end of MYs 35 and 36.

• Group 3 is dominant at the perihelion, around $L_S \sim 240^\circ$ mainly in the southern hemisphere, although during MY 34 is also abundant in the northern one.

• Group 4, in this case, is more abundant at latitudes below $50^\circ$ in both hemispheres, being particularly frequent during $L_S=180^\circ-210^\circ$ and $L_S=270^\circ-300^\circ$ for MYs 35 and 36 and during $L_S=300^\circ-360^\circ$ for MY 34

What is also interesting from this analysis, with both NOMAD and MPCM clustering, is the extremely similar climatology observed during the perihelion of MYs 35 and 36 and the strong contrast with the same season in MY 34. This evidences once again the impact of global dust storms on the water vapor global distribution (Aoki et al., 2019; Brines et al., 2023; Fedorova et al., 2020). In addition, it is worth noting the strong difference of the clusters obtained from the MPCM with those obtained from NOMAD at high altitudes. Above 60 km, the gradient observed in the clusters from NOMAD is noticeably larger than those observed in the MPCM clusters. This fact highlights once again the systematically wetter atmosphere produced by the model particularly during and after the GDS and during the perihelion the northern hemisphere.

In order to extend the cluster analysis further, we performed two additional tests. First, as illustrated in Figures 11 and 13, applying the clustering algorithm to the water vapor VMR profiles directly in ppm units provides a climatology more sensitive to the perihelion season. In contrast the aphelion season is characterized basically by one common profile of low abundances. To address that complication, we applied the clustering not to the VMR profiles but to their logarithm. This way the grouping was more sensitive to profiles of low water vapor abundance. The results of this additional test are shown in Figures S6 and S7 of SI. Although some sensitivity was lost at the perihelion, more groups were assigned to the aphelion season revealing distinct groups representative of specific latitudes during the first half of the MYs that were missing with the clustering previously discussed. Secondly, in order to look for possible anomalies or issues during the retrieval process, we run the clustering assignation with 20 clusters. After doing this exercise we did not find any cluster to be representative of potentially wrong or anomalous profiles.

# 6 Discussion

## 6.1 Cross-validation within TGO

Cross-validation is an essential task in remote sensing measurements, such as those made by TGO, to verify the robustness and reliability of the results. The comparison presented in this work, taking into account instrumental uncertainties and differences in data processing, retrieval methods, and vertical resolution/information content, revealed an overall good agreement between teams and instruments. This is illustrated and quantified with the good correlation factors obtained in the two comparisons SO-Brines25 - SO-Aoki22 and SO-Brines25 - NIR-Fedorova23, of 0.83 and 0.91 respectively. Nevertheless, some discrepancies in the SO-Brines25 - SO-Aoki22 comparison are observed, mostly during the aphelion season, which correspond to biases on the high water vapor abundances at low altitudes. This is a well known discrepancy to the two teams involved in this comparison and has been already discussed in Brines et al. (2024) attributing the observed differences to the very different retrieval approaches. First, our SO-Brines25 inversion follows a global fit approach and is therefore more sensitive to the vertical gra-
dients expected at those altitudes during this season providing a more accurate descrip-
tion of the vertical structure. Second, the retrieval method of SO-Aoki22 does not require
any regularization while our inversion does. On the other hand, the comparison with NIR-
Fedorova23 revealed some biases also during the aphelion season but only at the top-most
altitude of the water vapor profiles in the southern hemisphere. A similar bias is observed
in the comparison with ACS MIR during the perihelion season of MY 34, with system-
atically lower water vapor abundances in our dataset above 90-100 km. In addition, in
the case of MIR we observed discrepancies for some specific occultations in the form of
sudden changes in the water vapor density at certain altitudes. It is important to remind
here that, in contrast to NIR, observations from MIR and NOMAD SO are not exactly
coincident. Hence, this differences in the vertical structure observed in some water va-
por profiles are possibly due to differences on the thermal vertical structure leading to
supersaturation and condensation processes. These features, captured by one instrument
but not by the other, suggest the aforementioned processes to be extremely local and dif-
ferences in timing/location of the observations are relevant to properly detect these events.
Nevertheless, besides these discrepancies at specific altitudes due to the different loca-
tions and local times of the compared profiles, globally both datasets show similar sea-
sonal trends on the water vapor vertical distribution.

## 6.2 Comparison with the MPCM

Modeling the Martian water cycle is complex, with many atmospheric variables and
processes directly or indirectly affecting it. The sensitivity of the modeled water vapor
integrated column to poorly known parameters such as the thermal inertia and albedo
of surface ice, the effective variance of the ice particle size distribution (which influences
their sedimentation) and the dust-water "contact parameter" (which control the nucle-
ation of ice) is described in details in Navarro et al. (2014). With realistic values of these
parameters and a good representation of the permanent water ice surface reservoir, the
MPCM can predict the column water vapor with an error of 10 to 20 percents. The ver-
tical distribution of water vapor that we can now explore with TGO is locally controlled
by processes that are even more model-sensitive and poorly constrained. Three key pro-
cesses dominate in theory: 1) the vertical transport by the general circulation, driven
by the large scale temperature contrast and wave-mean flow interaction, 2) the thermal
structure (and thus the airborne dust distribution), that controls the hygropause and
to which the condensation of ice and the water vapor vertical distribution is extremely
sensitive because non-linear behavior of the Clausius-Clapeyron water vapor-pressure equa-
tion and 3) above the hygropause, the degree to which the model microphysics can al-
low water supersaturation (Montmessin et al., 2017; Urata et al., 2025). These are the
three processes that we can evaluate and constrain in our comparison between the model
and our observations.

The differences analyzed here are considered relevant and non dependent on the
specific run of the MPCM used in this work (SVN3323, config. MCD6) and may there-
fore be taken into account for future improvements of the water cycle modeling. One of
the most striking discrepancies between the model and the NOMAD measurements is
observed during MY 34. As a result of the MY 34's Global Dust Storm (GDS) and the
enhanced dust abundances and temperatures, large water vapor abundances are observed
as high as 80 km (Aoki et al., 2019; Brines et al., 2023; Fedorova et al., 2020). Although
the MPCM effectively produces an enhancement during MY 34, its intensity and dura-
tion are way larger than what it is observed, producing a systematic overestimation of
the water abundances at almost all altitudes and during the whole year. This may be
due to not only a not well reproduced dust vertical distribution, but also to the warmer
temperatures observed in the model (Vals et al., 2022). Besides these differences due to
the uniqueness of the GDS event, other discrepancies seem to be repeated every season.
During the aphelion season, i.e. the first half of the MY, the excess of water vapor ob-
served in the model at low altitudes, where the bulk of water vapor is located during this
<figure><img src="image_66.png" /><figcaption>Figure 14: (a) Water vapor total integrated column computed from the MPCM by averaging MYs 35 and 36 and (b) from TES measurements averaging MYs from 24 to 27. (c) and (d) show the columns obtained from the MPCM from 0 to 120 km, and from 30 to 80 km respectively, both at the location of NOMAD observations during MYs 35 and 36. (e) shows the columns computed with the water vapor profiles retrieved from NOMAD from 30 to 80 km during MYs 35 and 36. (f) shows the relative difference between the columns from NOMAD and MPCM computed from 30 to 80 km. Blue colors in (f) indicate larger MPCM abundances than NOMAD. Note that the 0 km level in (a) refers to the surface while in (c) refers to the areoid.</figcaption></figure>

season, suggests the MPCM to have a more efficient water vapor release and transport from the polar regions to lower latitudes. This same feature was also noticed by Rossi et al. (2022) (see their Figure 6), who reported similar discrepancies between ACS and a previous version of the MPCM during MYs 34 and 35. In addition, although it was not discussed in their paper, their Figure 5 reveals also systematically higher temperatures at low altitudes during this same period, supporting the hypothesis of a more efficient water vapor release and transport. In contrast, during the perihelion, i.e. the second half of the MY, the differences between NOMAD and the MPCM are less dramatic in the northern hemisphere at low altitudes. In contrast, it is interesting to highlight the discrepancies observed during $L_s = 270°–330°$ at ~60 km in the northern hemisphere. Particularly in the morning, this region shows some overestimation in the model perhaps due to water ice clouds formation in the atmosphere not well reproduced in the MPCM.
This hypothesis is compatible with the results reported by Rossi et al. (2022), where they found that the water vapor condensation above 60 km is not correctly represented in the model during this period of the year. As an alternative or as an additional reason of this this discrepancy, the excess of water in the northern hemisphere at 60 km and the overall deficit of water in the southern one could suggest an excessive northward transport from the southern hemisphere at middle altitudes. In addition, a deficient modeling of the strong water vapor injection to high altitudes at high southern latitudes could also be related with the observation that around 100 km in the northern hemisphere, the MPCM abundances are deficient compared to NOMAD. Since the model is not able to reproduce the high altitude southern water injection, it is not able either to reproduce the strong meridional transport at high altitudes leading to a water vapor deficit at 100 km in the northern hemisphere. With all these evidences on the table, the two most potential candidates to explain the observed discrepancies between model and observations during the perihelion season are the atmospheric temperatures and the water vapor supersaturation.

For a better understanding of the NOMAD-MPCM discrepancies, one should not only look at the vertical distribution but also at the total water vapor column. We computed the water integrated columns from the MPCM profiles for the MYs 35 and 36 for both the whole latitudinal/seasonal grid (Figure 14-a) and at the location of NOMAD observations (Figure 14-c). We noticed that the total amount of water vapor from our simulations that is injected into the atmosphere (Figure 14-a) is qualitatively smaller than other previous simulations (Pottier et al. 2017), see their figure 9). This is particularly noticeable during the perihelion season in the southern polar region, where our simulated columns are about a factor 3 smaller. This feature of lower modeled water vapor column abundances during the southern summer is also noticeable when comparing with measurements from the Thermal Emission Spectrometer (TES). In Figure 14-b, the measured water vapor columns around the southern polar region (SPR) at $L_s$ 270° – 330° are slightly larger than those predicted by the MPCM. Although it is not possible to obtain analogous full integrated columns from NOMAD SO observations due to the lack of measurements at the lowermost altitudes where the aerosol opacity is large, we compared simulated (Figure 14-d) and measured (Figure 14-e) water vapor columns by vertical integration in the altitude range between 30 and 80 km, region where full vertical profiles can be retrieved from NOMAD for most of the Martian year. This comparison shown in Figure 14-f suggests that, at least above 30 km, the largest discrepancies occur during the aphelion season. Particularly for the southern hemisphere at latitudes between 30°-60°, the total amount of water observed with NOMAD is larger than the model’s prediction. During this season in the northern hemisphere this statement is not clear, with regions of both excess and deficit of water. For the perihelion season the relative differences are smaller in the northern hemisphere and low southern latitudes with values about 10-20%. Nevertheless, although less dramatic than that observed during the aphelion season, again a deficit of water in our model’s columns is observed mainly at the southern hemisphere supporting the aforementioned suggestion of a too small water injection in the southern hemisphere in our MPCM simulations. A summary highlighting the five most relevant discrepancies between NOMAD and MPCM is shown in 1.

## 6.3 Cluster analysis

Finally, being a purely statistical tool blind to physics, the cluster analysis performed in this work revealed meaningful water vapor latitudinal and seasonal distributions, providing a simplified water vapor climatology. The clustering successfully captured the water vapor strong seasonal variability and resulted to be more sensitive to it above other variations due to latitude or local time. Specific climatological events such as the peak of the MY 34 GDS or the water vapor pumping in the southern hemisphere during the perihelion were assigned to distinct groups standing out as separate vertical profiles. Improving the assignation method and focusing the analysis on specific periods could help
<table><caption>Table 1: Summary of the five most relevant discrepancies between NOMAD and MPCM found in this work (left column) along with the most probable issues in the model causing them (right column)</caption><thead><tr><td>Discrepancies</td><td>Potential cause</td></tr></thead><tbody><tr><td>Low altitude overestimation in the model during the aphelion in the northern hemisphere (L<sub>S</sub> = 30° – 90°).</td><td>Too much water ice sublimation from the north polar cap.</td></tr><tr><td>MPCM underestimates abundances around L<sub>S</sub> = 120° in both hemispheres.</td><td>Global circulation too weak. Incorrect dust vertical distribution.</td></tr><tr><td>Southern hemisphere's perihelion seasonal enhancement not properly reproduced in the MPCM (L<sub>S</sub> = 240° – 300°).</td><td>Too little water ice sublimation from the southern polar region</td></tr><tr><td>MPCM overestimates abundance at 40-60 km during L<sub>S</sub> = 270° – 330° (northern hemisphere)</td><td>Too little water ice cloud formation in the model. Excess of northward transport at 50-80 km</td></tr><tr><td>MPCM overestimates water vapor abundance during MY 34 GDS.</td><td>Dust vertical distribution not properly modeled. Too much heating by dust.</td></tr></tbody></table>

to highlight some of the interhemispheric and local time variations discussed here and in Paper I. The goal of this analysis was to provide a first and simplified view of the water vapor latitudinal/seasonal distribution, settling the framework for future studies on clustering of Martian water vapor vertical profiles, possibly focused on more specific times and locations. In addition, we also applied the clustering to the MPCM water vapor profiles. This raveled similar seasonal patterns as those observed with NOMAD, highlighting the high capability of the MPCM on reproducing the water cycle on Mars. However, above 60 km the vertical structure of the group profiles obtained from the MPCM differ from those obtained from NOMAD observations, showing a systematic wetter atmosphere in the model at high altitudes.

## 7 Conclusions

For this work, we analyzed NOMAD SO spectra from 7624 occultations collected over MYs 34 to 37, covering four different spectral regions and combining them in the vertical in order to avoid optically thick absorption lines. Our pre-processing pipeline significantly improved the correction of systematic errors in the NOMAD SO data, particularly for high-altitude measurements where accurate baseline characterization is crucial. This permitted the retrieval of extended water vapor vertical profiles from approximately 5 km to 120 km altitude in a single consistent inversion. Our large data set allowed us to perform an exhaustive comparison not only with other teams and instruments but also with the Mars Planetary Climate Model (MPCM). In addition, a novel post-processing strategy based on the statistical technique of cluster analysis was applied for the first time to Martian water vapor vertical profiles. Our main conclusions can be summarized as follows:

* The results presented in this work extend and complement previous recent studies on water vapor vertical profiles. Here we presented a comparison with other three TGO teams retrieving water vapor from observations by NOMAD and ACS
and revealing overall good agreement between different teams and datasets, with
correlation factors of 0.8-0.9.

* The comparison between NOMAD SO and the MPCM revealed the model's capability to properly simulate the most relevant seasonal patterns of the water vapor climatology during different MYs. However, some notorious discrepancies arise. There is a systematic excess of the modeled water vapor abundances at both hemispheres during the whole second part of MY 34 (during and after the GDS), probably because the dust distribution is not properly modeled in the MPCM. During the aphelion season, an excess of water vapor is observed in the model at low altitudes below 30 km while a lack of it is present above. This may be the result of an overestimation of the water vapor release from the North polar cap and/or a deficient vertical transport in the model during this season. During the perihelion season (around $L_s = 240° - 300°$) of MYs 35 and 36, the vertical distribution of water vapor in the southern hemisphere is underestimated in the model, possibly as a result of an underestimation of the dust vertical transport during this season. In addition, a deficit in the simulation of water ice formation above 60 km seem to be responsible of a wetter atmosphere in the northern hemisphere at high altitudes above 50 km during the second half of the year. These differences are intriguing and modeling efforts are very needed in order to find out a solution.

* We presented for the first time an application of cluster analysis techniques to NOMAD SO water vapor vertical profiles. We identified at least 6 distinct type of profiles representative of different atmospheric conditions and proving this technique to be useful for providing a simplified view of the water vapor climatology. Some efforts are ongoing in order to evaluate some of the discrepancies observed between NOMAD and ACS dataset and more comparison exercises will be needed to improve the agreement and reliability of the results. Moreover, from a modeling point of view, more observations and studies of the vertical distribution of water vapor are needed to not only extend the comparisons presented here, but also to improve the physics involved in the global climate models and to cross validate future model predictions and measurements.

## Open Research Section

The NOMAD SO Level 1a calibrated data used in this work are available at the European Space Agency Planetary Science Archive (ESA, 2024b). More information about the data on the PSA can be found in the NOMAD Experiment-to-Archive Interface Control Document (ESA, 2024a). The results retrieved from the NOMAD SO measurements presented in this work are being archived and available at Brines et al. (2025b). The data generated for this publication is also available through the VESPA portal at https://vespa.obspm.fr/planetary/data/display/?&service_id=ivo://bira-iasb/nomad/q/epn_core.

## Acknowledgments

The IAA/CSIC team acknowledges financial support from the Severo Ochoa grant CEX2021-001131-S and by grants PID2022-137579NB-I00, RTI2018-100920-J-I00 and PID2022-141216NB-I00 all funded by MCIN/AEI/10.13039/501100011033. A. Brines acknowledges financial support from the grant PRE2019-088355 funded by MCIN/AEI/10.13039/501100011033 and by 'ESF Investing in your future'. ExoMars is a space mission of the European Space Agency (ESA) and Roscosmos. The NOMAD experiment is led by the Royal Belgian Institute for Space Aeronomy (IASB-BIRA), assisted by Co-PI teams from Spain (IAA-CSIC), Italy (INAF-IAPS), and the United Kingdom (Open University). This project acknowledges funding by the Belgian Science Policy Office (BELSPO), with the financial and contractual coordination by the ESA Prodex Office (PEA 4000103401, 4000121493), by Spanish Ministry of Science and Innovation (MCIU) and by European funds under
grants PGC2018-101836-B-I00 and ESP2017-87143-R (MINECO/FEDER), as well as by UK Space Agency through grants ST/V002295/1, ST/V005332/1, ST/Y000234/1 and ST/X006549/1 and Italian Space Agency through grant 2018-2-HH.0. This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 101004052. US investigators were supported by the National Aeronautics and Space Administration. Canadian investigators were supported by the Canadian Space Agency. This work was supported by the Institute for Basic Science (IBS-R035-C1). We want to thank M. Vals, F. Montmessin, F. Lefèvre and the broad team supporting the continuous development of the Mars PCM.

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Wang, C., Forget, F., Bertrand, T., Spiga, A., Millour, E., & Navarro, T. (2018). Parameterization of rocket dust storms on mars in the lmd martian gcm: Mod-
1030

eling details and validation. *Journal of Geophysical Research: Planets*, 123(4), 982-1000.

1031
<caption>Figure 1.</caption>
<figure><img src="image_67.png" /><figcaption>H₂O VMR (ppm) @ Southern hemisphere</figcaption></figure>

<figure><img src="image_68.png" /></figure>

<figure><img src="image_69.png" /></figure>

<figure><img src="image_70.png" /></figure>

<figure><img src="image_71.png" /></figure>

<figure><img src="image_72.png" /></figure>
<caption>Figure 2.</caption>
<figure><img src="image_73.png" /><figcaption>H₂O VMR (ppm) @ Southern hemisphere</figcaption></figure>

<figure><img src="image_74.png" /></figure>

<figure><img src="image_75.png" /></figure>

<figure><img src="image_76.png" /></figure>

<figure><img src="image_77.png" /></figure>

<figure><img src="image_78.png" /></figure>
<caption>Figure 3.</caption>
JOMAD-SO: 20210412_132501_1p0a_SO_A

a

<figure><img src="image_79.png" /></figure>

ACS-NIR: orb015104_N2

JOMAD-SO: 20201229_060923_1p0a_SO_A

b

<figure><img src="image_80.png" /></figure>

ACS-NIR: orb013830_N1

JOMAD-SO: 20200625_082114_1p0a_SO_A

c

<figure><img src="image_81.png" /></figure>

ACS-NIR: orb011547_N1

JOMAD-SO: 20180919_023512_1p0a_SO_A

d

<figure><img src="image_82.png" /></figure>

ACS-NIR: orb003665_N2
<caption>Figure 4.</caption>
Ls = 210° - 240° (morning)

<figure><img src="image_83.png" /></figure>

<figure><img src="image_84.png" /></figure>

Ls = 240° - 270° (morning)

<figure><img src="image_85.png" /></figure>

<figure><img src="image_86.png" /></figure>

Ls = 300° - 330° (evening)

<figure><img src="image_87.png" /></figure>

<figure><img src="image_88.png" /></figure>

Ls = 270° - 300° (evening)

<figure><img src="image_89.png" /></figure>

<figure><img src="image_90.png" /></figure>
<caption>Figure 5.</caption>
a MY 34

<figure><img src="image_91.png" /></figure>
<caption>Figure 6.</caption>
NOMAD-MPCM @ 30 km

<figure><img src="image_92.png" /></figure>

NOMAD-MPCM @ 80 km

<figure><img src="image_93.png" /></figure>

Northern hemisphere

<figure><img src="image_94.png" /></figure>

Southern hemisphere

<figure><img src="image_95.png" /></figure>
<caption>Figure 7.</caption>
Morning

<figure><img src="image_96.png" /></figure>

<figure><img src="image_97.png" /></figure>

<figure><img src="image_98.png" /></figure>

Relative difference (%)

<figure><img src="image_99.png" /></figure>

<figure><img src="image_100.png" /></figure>

<figure><img src="image_101.png" /></figure>

Evening

<figure><img src="image_102.png" /></figure>

<figure><img src="image_103.png" /></figure>

<figure><img src="image_104.png" /></figure>

Relative difference (%)

<figure><img src="image_105.png" /></figure>

<figure><img src="image_106.png" /></figure>

<figure><img src="image_107.png" /></figure>
<caption>Figure 8.</caption>
Morning

<figure><img src="image_108.png" /></figure>

Evening

<figure><img src="image_109.png" /></figure>
<caption>Figure 9.</caption>
Morning

NOMAD

<figure><img src="image_110.png" /></figure>

MPCM

<figure><img src="image_111.png" /></figure>

Evening

NOMAD

<figure><img src="image_112.png" /></figure>

MPCM

<figure><img src="image_113.png" /></figure>

L<sub>s</sub> = 90-120 (morning)

<figure><img src="image_114.png" /></figure>

L<sub>s</sub> = 90-120 (morning)

<figure><img src="image_115.png" /></figure>

L<sub>s</sub> = 90-120 (evening)

<figure><img src="image_116.png" /></figure>

L<sub>s</sub> = 90-120 (evening)

<figure><img src="image_117.png" /></figure>

L<sub>s</sub> = 180-210 (morning)

<figure><img src="image_118.png" /></figure>

L<sub>s</sub> = 180-210 (morning)

<figure><img src="image_119.png" /></figure>

L<sub>s</sub> = 180-210 (evening)

<figure><img src="image_120.png" /></figure>

L<sub>s</sub> = 180-210 (evening)

<figure><img src="image_121.png" /></figure>

L<sub>s</sub> = 270-300 (morning)

<figure><img src="image_122.png" /></figure>

L<sub>s</sub> = 270-300 (morning)

<figure><img src="image_123.png" /></figure>

L<sub>s</sub> = 270-300 (evening)

<figure><img src="image_124.png" /></figure>

L<sub>s</sub> = 270-300 (evening)

<figure><img src="image_125.png" /></figure>
<caption>Figure 10a.</caption>
<figure><img src="image_126.png" /><figcaption>MY 35</figcaption></figure>
Figure 10b.
<figure><img src="image_127.png" /><figcaption>MY 37</figcaption></figure>

<figure><img src="image_128.png" /></figure>
Figure 11.
<figure><img src="image_129.png" /></figure>

<figure><img src="image_130.png" /></figure>

<figure><img src="image_131.png" /></figure>

<figure><img src="image_132.png" /></figure>

<figure><img src="image_133.png" /></figure>
Figure 12.
<figure><img src="image_134.png" /></figure>

<figure><img src="image_135.png" /></figure>
Figure 13.
MY 34

<figure><img src="image_136.png" /></figure>

MY 35

<figure><img src="image_137.png" /></figure>

MY 36

<figure><img src="image_138.png" /></figure>

MY 37

<figure><img src="image_139.png" /></figure>

Altitude (km)

<figure><img src="image_140.png" /></figure>
Figure 14.
<figure><img src="image_141.png" /></figure>

<figure><img src="image_142.png" /></figure>

Latitude

<figure><img src="image_143.png" /></figure>

H₂O column @ av. MYs 24,25,26,27

<figure><img src="image_144.png" /></figure>

<figure><img src="image_145.png" /></figure>

<figure><img src="image_146.png" /></figure>

MPCM H₂O integrated column at 30-80 km

<figure><img src="image_147.png" /></figure>

<figure><img src="image_148.png" /></figure>

<figure><img src="image_149.png" /></figure>

NOMAD-MPCM H₂O integrated column at 30-80 km
AGU

PUBLICATIONS

*Journal of Geophysical Research: Planets*

Supporting Information for

**Water Vapor Vertical Distribution on Mars after Six Years of TGO/NOMAD Solar Occultations. Part II: Cross-validation within TGO and comparison with models.**

**A. Brines**<fnref n="1" />, M. A. López-Valverde<fnref n="1" />, F. González-Galindo<fnref n="1" />, S. Aoki<fnref n="2" />,<fnref n="3" />, A. Fedorova<fnref n="4" />, D. Belyaev<fnref n="4" />, F. Forget<fnref n="5" />, F. Montmessin<fnref n="5" />, E. Vos<fnref n="5" />, B. Funke<fnref n="1" />, J. J. Lopez-Moreno<fnref n="1" />, J. Rodriguez-Gomez<fnref n="1" />, F. Daerden<fnref n="2" />, I. R. Thomas<fnref n="2" />, L. Trompet<fnref n="2" />, A. Modak<fnref n="6" />, G. L. Villanueva<fnref n="7" />, M. R. Patel<fnref n="8" />, G. Bellucci<fnref n="9" />, and A. C. Vandaele<fnref n="2" />

**Contents of this file**

Figures S1 to S8

**Introduction**

The Supporting Information presented here contains figures showing a profile-by-profile comparison between profiles retrieved from Nadir and Occultation for MArS Discovery (NOMAD) Solar Occultations (Aoki et al. 2022 and Brines et al. 2025, this work) and from ACS-NIR (Fedorova et al. 2023) infrared spectra. In addition, complementary figures for the NOMAD comparisons with the Mars Planetary Climate Model (MPCM) are included, showing the seasonal-vertical distribution of the relative NOMAD-MPCM differences and log-scale correlogams with NOMAD and MPCM water vapor volume mixing ratios (VMRs). Figures on log-scale for the cluster analysis presented in the main paper are included, as well as a figure showing the relation between water ice sublimation flux with the thickness of dust coatings, as simulated by the MPCM.

<footnote n="1">¹Instituto de Astrofísica de Andalucía (IAA/CSIC), Spain</footnote>

<footnote n="2">²Royal Belgian Institute for Space Aeronomy, Belgium</footnote>

<footnote n="3">³Department of Complexity Science and Engineering, University of Tokyo, Japan</footnote>

<footnote n="4">⁴Space Research Institute, Russia</footnote>

<footnote n="5">⁵Laboratoire de M'et'eorologie Dynamique, IPSL, Paris, France</footnote>

<footnote n="6">⁶Institute for Basic Science, South Korea</footnote>

<footnote n="7">⁷NASA Goddard Space Flight Center, USA</footnote>

<footnote n="8">⁸Open University, UK</footnote>

<footnote n="9">⁹Istituto di Astrofisica e Planetologia, Italy</footnote>
<figure><img src="image_150.png" /></figure>

**Figure S1.** Comparison of water vapor vertical profiles at the northern hemisphere retrieved from NOMAD (blue, green) and ACS (red) observations.
<figure><img src="image_151.png" /></figure>

<figure><img src="image_152.png" /></figure>

<figure><img src="image_153.png" /></figure>

<figure><img src="image_154.png" /></figure>

<figure><img src="image_155.png" /></figure>

<figure><img src="image_156.png" /></figure>

<figure><img src="image_157.png" /></figure>

<figure><img src="image_158.png" /></figure>

<figure><img src="image_159.png" /></figure>

<figure><img src="image_160.png" /></figure>

<figure><img src="image_161.png" /></figure>

<figure><img src="image_162.png" /></figure>

<figure><img src="image_163.png" /></figure>

<figure><img src="image_164.png" /></figure>

<figure><img src="image_165.png" /></figure>

<figure><img src="image_166.png" /></figure>

**Figure S2.** Comparison of water vapor vertical profiles at the southern hemisphere retrieved from NOMAD (blue, green) and ACS (red) observations.
<figure><img src="image_167.png" /><figcaption>**Figure S3.** Relative difference of water vapor volume mixing ratio as measured by NOMAD SO and simulated with the MPCM over Solar Longitude during MYs 34, 35, 36 and 37 for the Northern (c) and Southern (d) hemispheres. Top panels indicate the Latitude and relative differences at 30 km (a) and 80 km (b) altitude. Blue colors indicate larger MPCM abundances than NOMAD.</figcaption></figure>
MY 34

<figure><img src="image_168.png" /></figure>

MY 35

<figure><img src="image_169.png" /></figure>

**Figure S4.** Comparison of NOMAD SO water vapor abundances (x-axis) with those simulated by the Mars-PCM (y-axis) for MYs 34 (panels a1 to f1) and 35 (panels a2 to f2). For each MY, colors in panels a to f indicate the density of measurements (panel a), solar longitude (panel b), latitude and longitude (panels c and d), local solar time (panel e) and altitude (panel f). Gray dashed line indicates y=x.
MY 34

<figure><img src="image_170.png" /></figure>

MY 35

<figure><img src="image_171.png" /></figure>

**Figure S5.** Comparison of NOMAD SO water vapor abundances (x-axis) with those simulated by the Mars-PCM (y-axis) for MYs 36 (panels a3 to f3) and 37 (panels a4 to f4). For each MY, colors in panels a to f indicate the density of measurements (panel a), solar longitude (panel b), latitude and longitude (panels c and d), local solar time (panel e) and altitude (panel f). Gray dashed line indicates y=x.
<figure><img src="image_172.png" /><figcaption>**Figure S6.** Clustering analysis applied to the logarithm of water vapor VMR vertical profiles extracted from the Mars-PCM. Left panels show the seasonal-latitudinal distribution of the vertical profiles for MYs 34, 35, 36 and 37 (from top to bottom respectively). Colors indicate the clusters where profiles were assigned. Right panel shows the representative vertical profile of each cluster.</figcaption></figure>
<figure><img src="image_173.png" /><figcaption>**Figure S7.** Clustering analysis applied to the logarithm of NOMAD SO water vapor VMR vertical profiles. Left panels show the seasonal-latitudinal distribution of the vertical profiles for MYs 34, 35, 36 and 37 (from top to bottom respectively). Colors indicate the clusters where profiles were assigned. Right panel shows the representative vertical profile of each cluster.</figcaption></figure>
<figure><img src="image_174.png" /></figure>

**Figure S8.** Simulation of the flux of water vapor released from the sublimation of a subsurface ice reservoir at latitude of 80° S under a layer of dust coating. Here we used a 1D version of the MPCM following a novel approach that includes subsurface ice and calculates the loss rate (Vos et al., 2024).