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\begin{document}

\title{Thermal Structure of the Middle and Upper Atmosphere of Mars from
ACS/TGO CO2 Spectroscopy}



\author[1,1]{Denis A. Belyaev}%
\author[1,1]{Anna A. Fedorova}%
\author[1,1]{Alexander Trokhimovskiy}%
\author[2,2]{Juan Alday}%
\author[1,1]{Oleg I Korablev}%
\author[3,3]{Franck Montmessin}%
\author[1,1]{Ekaterina Starichenko}%
\author[4,4]{Kevin Sutherland Olsen}%
\author[1,1]{Andrey Patrakeev}%
\affil[1]{Space Research Institute (IKI)}%
\affil[2]{Open University}%
\affil[3]{LATMOS CNRS/UVSQ/IPSL}%
\affil[4]{University of Oxford}%


\vspace{-1em}



  
  \date{June 14, 2024}


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\selectlanguage{english}
\begin{abstract}
Temperature and density in the upper Martian atmosphere, above
\textasciitilde{}100 km, are key diagnostic parameters to study
processes of the species' escape, investigate the impact of solar
activity, model the atmospheric circulation, and plan spacecraft descent
or aerobraking maneuvers. In this paper, we report vertical profiling of
carbon dioxide (CO2) density and temperature from the Atmospheric
Chemistry Suite (ACS) solar occultations onboard the ExoMars Trace Gas
Orbiter (TGO). A strong CO2 absorption band near 2.7 \selectlanguage{greek}μ\selectlanguage{english}m observed by the
middle infrared spectrometric channel (ACS MIR) allows the retrieval of
the atmospheric thermal structure in a large altitude range, from 20 to
180 km. We present the latitudinal and seasonal climatology of the
thermal structure for 1.5 Martian years (MYs), from the middle of MY 34
to the end of MY 35. The results show the variability of distinct
atmospheric layers, such as a mesopause (derived from 70 to 150 km) and
homopause, changing from 80-90 km at aphelion to 100-110 km at
perihelion. Some short-term homopause fluctuations are also observed
depending on the dust activity.%
\end{abstract}%



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\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\emph{Journal of Geophysical Research: Planets}

Supporting Information for

\textbf{Thermal Structure of the Middle and Upper Atmosphere of Mars
from ACS/TGO CO\textsubscript{2} Spectroscopy}

D. A. Belyaev\textsuperscript{1}, A. A. Fedorova\textsuperscript{1}, A.
Trokhimovskiy\textsuperscript{1}, J. Alday\textsuperscript{2}, O. I.
Korablev\textsuperscript{1}, F. Montmessin\textsuperscript{3}, E. D.
Starichenko\textsuperscript{1}, K. S. Olsen\textsuperscript{4}, and A.
S. Patrakeev\textsuperscript{3}

\textsuperscript{1}Space Research Institute (IKI), Moscow, Russia.

\textsuperscript{2}School of Physical Sciences, The Open University, UK.

\textsuperscript{3}LATMOS/CNRS, Paris, France.

\textsuperscript{4}Department of Physics, University of Oxford, UK.

Corresponding author: Denis Belyaev (dbelyaev@iki.rssi.ru)

\textbf{Contents of this file}

Text S1: Page 2 Figure S1: Page 3 Figure S2: Page 4 Figure S3: Page 5
Figure S4: Page 6

\textbf{Introduction}

The present Supporting Information describes details of the retrieval
concept for the temperature, density and pressure altitude profiles from
the transmission spectra measured by ACS MIR. Figure S1 demonstrates a
validation of the ACS MIR temperature profiles with the analogous
profiles of ACS NIR. We compare all individual profiles point-by-point,
derived from simultaneous and collocated MIR and NIR observations. The
ACS NIR data are taken from Fedorova et al. (2022). Figure S2 shows the
six temperature profiles containing CO\textsubscript{2} subfreezing
points. Figure S3 shows the latitudinal cross-sections of
CO\textsubscript{2} density profiles observed by ACS MIR in both equinox
seasons. Figure S4 shows sets of the temperature profiles containing a
warm layer at 60-90 km in the morning relative to the evening
terminators.

\textbf{Text S1. Details of the retrieval concept}

The transmission spectrum is calculated using well-known Beer-Lambert
law, taking into account all altitude layers above the considered one.
Free parameters of the fitting are temperature, concentrations of
CO\textsubscript{2} and H\textsubscript{2}O, and the aerosol slant
opacity. We do not consider any atmospheric scattering effect, neither
Rayleigh one, which is negligible in the middle IR range, nor the
aerosol one, which is rather weak relative to the directly incoming
solar flux. In the fitting procedure, an optimal search is based on
partial derivatives of the transmission on each of the free parameters.
Here, the key contribution comes from the cross section derivative with
respect to temperature: \emph{[?]σ/[?]T}\selectlanguage{english} (Fig. 3b). The first guess (a
priori) values for the considered atmospheric parameters are taken from
the Mars Climate Database (MCD 5.3; Millour et al., 2018) adapted for
the ACS occultation climatology in MY 34 and 35.

Since the altitude, \emph{z} , profiles of temperature \emph{T}
(\emph{z} ) and CO\textsubscript{2} density \emph{N}
\textsubscript{CO2}(\emph{z} ) are simultaneously fitted, the pressure
\emph{p} (\emph{z} ) is calculated by integrating \emph{T} (\emph{z} )
using the equation of hydrostatic equilibrium:\(p\left(z\right)=p_{o}\exp\left[-\int_{z_{o}}^{z}\frac{g\left(h\right)M(h)}{k_{B}T(h)}dh\right]\). Here,
\emph{k\textsubscript{B}} -- Boltzmann constant, \emph{g(z)} is the
gravity acceleration, and \emph{M(z)} is the atmospheric molecular
weight (taken from MCD). A reference pressure
\emph{p\textsubscript{o}}is calculated for a specified altitude
\emph{z\textsubscript{o}} from the ideal gas law:\(p_{o}=p\left(z_{o}\right)=\left(\frac{N_{\text{CO}2}\left(z_{o}\right)}{f_{\text{CO}2}\left(z_{o}\right)}\right)k_{B}T(z_{o})\). The
CO\textsubscript{2} volume mixing ratio \(f_{CO2}(z_{o})\) is also
derived from MCD. In all occultations, \emph{z\textsubscript{o}} is
selected between 20 and 60 km (Fig. 1d), where the retrieval
uncertainties are minimal. Once the hydrostatic pressure profile is
derived, we keep it fixed when a new temperature and
CO\textsubscript{2}density are retrieved on the next iteration. We
repeat this procedure about 5-6 iterations while the profiles reach a
convergence. Here, the values on an (\emph{i} -1)\textsuperscript{th}
step are used as a priori for the \emph{i} \textsuperscript{th} one.
When sounding the CO\textsubscript{2}-rich atmosphere by
CO\textsubscript{2} spectroscopy, the fitting of \emph{N}
\textsubscript{CO2} with the hydrostatic pressure assumption is
physically reasonable, rather than using the directly fitted pressure
while keeping \emph{N} \textsubscript{CO2} fixed.

Supplementing Figures:\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Figure S1. Validation of the temperature vertical profiles from ACS MIR
(\emph{T} \textsubscript{MIR}) and ACS NIR (\emph{T}
\textsubscript{NIR}; Fedorova et al., 2022) retrieved over 1.5
considered Martian years. a: differences (\emph{T}
\textsubscript{MIR}-\emph{T} \textsubscript{NIR}) as a function of
altitude for all the simultaneous observations (green points) made
during MY 34 and MY 35. Black curve is the average for points grouped in
the altitude interval of 2 km, error bars are corresponding standard
deviations. b: \emph{T} \textsubscript{MIR} as a function of\emph{T}
\textsubscript{NIR}. The gray dashed lines in these panels indicate the
expected trend if \emph{T} \textsubscript{MIR} =\emph{T}
\textsubscript{NIR}.

{\label{figure-s1.-validation-of-the-temperature-vertical-profiles-from-acs-mir-tmir-and-acs-nir-tnir-fedorova-et-al.-2022-retrieved-over-1.5-considered-martian-years.-a-differences-tmir-tnir-as-a-function-of-altitude-for-all-the-simultaneous-observations-green-points-made-during-my-34-and-my-35.-black-curve-is-the-average-for-points-grouped-in-the-altitude-interval-of-2-km-error-bars-are-corresponding-standard-deviations.-b-tmir-as-a-function-of-tnir.-the-gray-dashed-lines-in-these-panels-indicate-the-expected-trend-if-tmir-tnir.}}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

Figure S2. The six temperature profiles (black dots with error bars)
with the ``coldest'' mesopause points observed by ACS MIR, exhibiting
temperature below the CO2 condensation (blues dashed line). Geography
and time of observations are shown in each panel. See details in Section
4.1.

{\label{figure-s2.-the-six-temperature-profiles-black-dots-with-error-bars-with-the-coldest-mesopause-points-observed-by-acs-mir-exhibiting-temperature-below-the-co2-condensation-blues-dashed-line.-geography-and-time-of-observations-are-shown-in-each-panel.-see-details-in-section-4.1.}}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure S3. Latitude cross-sections of ACS MIR CO\textsubscript{2}
density profiles, grouped in 5\selectlanguage{ngerman}° bins corresponding to equinox seasons:
northern spring (a; L\textsubscript{S} = 330°-30° of MY 34\&35) and
northern autumn (b; L\textsubscript{S} = 160°-220° of MY 35). The color
code indicates different orders of magnitude of CO\textsubscript{2}
density in the logarithmic scale. Panels c, d show corresponding data
from MCD (Millour et al., 2018) adopted for geography of the considered
MIR occultations. The latitude cross-sections look a bit nonsmooth (c,
d), since each latitude bit correspond to different longitude and local
time.

{\label{figure-s3.-latitude-cross-sections-of-acs-mir-co2-density-profiles-grouped-in-5-bins-corresponding-to-equinox-seasons-northern-spring-a-ls-330-30-of-my-3435-and-northern-autumn-b-ls-160-220-of-my-35.-the-color-code-indicates-different-orders-of-magnitude-of-co2-density-in-the-logarithmic-scale.-panels-c-d-show-corresponding-data-from-mcd-millour-et-al.-2018-adopted-for-geography-of-the-considered-mir-occultations.-the-latitude-cross-sections-look-a-bit-nonsmooth-c-d-since-each-latitude-bit-correspond-to-different-longitude-and-local-time.}}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Figure S4.} Temperature profiles observed by ACS MIR
(\textbf{a-c} ) with an explicit warm layer at 60-90 km in the morning
terminator (in red) relative to the evening one (in blue). Seasonal and
latitudinal ranges are shown on the top of panels. Panels
\textbf{d-f}show corresponding profiles from MCD (Millour et al., 2018)
adopted for geography of the considered MIR occultations. See details in
Section 4.4.

\selectlanguage{english}
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