# Study of gravity waves distribution and propagation in the thermosphere of
Mars based on MGS, ODY, MRO and MAVEN density measurements

###### Abstract

_By measuring the regular oscillations of the density of CO 2 in the upper
atmosphere (between 120 and 190 km), the mass spectrometer MAVEN/NGIMS
(Atmosphere and Volatile EvolutioN/Neutral Gas Ion Mass Spectrometer) reveals
the local impact of gravity waves. This yields precious information on the
activity of gravity waves and the atmospheric conditions in which they
propagate and break. The intensity of gravity waves measured by MAVEN in the
upper atmosphere has been shown to be dictated by saturation processes in
isothermal conditions. As a result, gravity waves activity is correlated to
the evolution of the inverse of the background temperature. Previous data
gathered at lower altitudes ($\sim$95 to $\sim$150 km) during aerobraking by
the accelerometers on board MGS (Mars Global Surveyor), ODY (Mars Odyssey) and
MRO (Mars Reconnaissance Orbiter) are analyzed in the light of those recent
findings with MAVEN. The anti-correlation between GW-induced density
perturbations and background temperature is plausibly found in the ODY data
acquired in the polar regions, but not in the MGS and MRO data. MRO data in
polar regions exhibit a correlation between the density perturbations and the
Brunt-Väisälä frequency (or, equivalently, static stability), obtained from
Global Climate Modeling compiled in the Mars Climate Database. At lower
altitude levels (between 100 and 120 km), although wave saturation might still
be dominant, isothermal conditions are no longer verified. In this case,
theory predicts that the intensity of gravity waves is no more correlated to
background temperature, but to static stability. At other latitudes in the
three aerobraking datasets, the GW-induced relative density perturbations are
correlated with neither inverse temperature nor static stability; in this
particular case, this means that the observed activity of gravity waves is not
only controlled by saturation, but also by the effects of gravity-wave sources
and wind filtering through critical levels. This result highlights the
exceptional nature of MAVEN/NGIMS observations which combine both isothermal
and saturated conditions contrary to aerobraking measurements._

Planetary and Space Science

Laboratoire de Météorologie Dynamique (LMD/IPSL), Sorbonne Université, Centre
National de la Recherche Scientifique, École Normale Supérieure, École
Polytechnique, Paris, France Institut Universitaire de France, Paris, France
Space Science Institute, Greenbelt, MD, USA

M<EMAIL_ADDRESS>
Gravity wave activity causes density perturbations in the Martian
thermosphere.

MAVEN found a correlation between gravity wave activity and inverse background
temperature.

Lower-altitude aerobraking measurements do not show this correlation, except
for Mars Odyssey.

Aerobraking data and climate models suggest instead wave activity correlated
with static stability.

No such correlation in low latitudes points to a mix of saturation, critical
levels and sources.

##  1 Introduction

Gravity waves propagate as perturbations of the stratified atmospheric fluid
(Gossard and Hooke, 1975), with the buoyancy force being the restoring
mechanism giving rise to the waves (cf Fritts and Alexander, 2003; Alexander
et al., 2010, for a review). While being essentially regional-scale phenomena,
gravity waves can be responsible for significant dynamical and thermal forcing
of the global atmospheric state, as they transfer their momentum and energy
upon their saturation and breaking in the upper atmosphere (Lindzen, 1981;
Palmer et al., 1986; McFarlane, 1987).

Gravity waves are ubiquitous in the Martian atmosphere and were actually one
of the first atmospheric phenomenon to be witnessed by orbiting spacecraft
(Briggs and Leovy, 1974). As is the case on Earth (O’sullivan and Dunkerton,
1995; Vincent and Alexander, 2000; Plougonven et al., 2003; Spiga et al.,
2008), those waves may be triggered in the Martian lower atmosphere by
different sources: topography (Pickersgill and Hunt, 1979, 1981), convection
(Spiga et al., 2013; Imamura et al., 2016), or jet-streams and fronts in
ageostrophic evolution. Amongst all those sources, only the impact of the
topographic source on the global circulation is accounted for in all Martian
Global Climate Models (GCM, e.g. Barnes, 1990; Collins et al., 1997; Forget et
al., 1999; Hartogh et al., 2005), although the exploration of the impact of an
additional non-orographic source is a topic of current active research
(Medvedev et al., 2015; Gilli et al., 2018).

The upward propagation of gravity waves from their tropospheric sources to the
upper atmosphere leads to large departures of density, temperature and winds
in the thermosphere, owing to the exponential increase of gravity wave
amplitude with height (Fritts and Alexander, 2003; Parish et al., 2009).
Measurements of CO2 density through accelerometers, gathered during the
aerobraking of Mars Global Surveyor (MGS), Mars Odyssey (ODY) and Mars
Reconnaissance Orbiter (MRO) observed the sustained gravity wave activity in
the Martian thermosphere between 90 and 130 km (Fritts et al., 2006; Creasey
et al., 2006; Tolson et al., 2007b). Those measurements also demonstrated the
large variability of the gravity-wave amplitudes with season, local time,
latitude and longitude.

The Mars Atmosphere and Volatile Evolution (MAVEN) mission to Mars (Jakosky et
al., 2015), operating since 2014, is dedicated to studying the upper
atmosphere of Mars and, as such, is a unique opportunity to broaden the
knowledge of gravity wave activity on Mars. The mass spectrometer NGIMS
(Neutral Gas Ion Mass Spectrometer) on board MAVEN (Mahaffy et al., 2015)
recently delivered new and more accurate measurements of density fluctuations
at upper altitudes between 120 and 300 km, identified as typical gravity-wave
signatures (Yiğit et al., 2015; England et al., 2017).

Based on those MAVEN/NGIMS measurements, Terada et al. (2017) observed that
gravity-wave amplitudes derived from Ar density with wavelengths between
$\sim$100 and $\sim$500 km near the exobase in the Martian thermosphere are
anti-correlated with the background temperature. The authors demonstrated this
anti-correlation by considering gravity waves saturation caused by convective
instability in the upper thermosphere. These observations were further
discussed in a recent study focusing on Ar density between 120 and 200 km by
Siddle et al. (2019), who observed that gravity waves amplitudes also increase
with increasing solar zenith angle.

The goal of this paper is to build on those recent findings by MAVEN and to
expand this analysis by comparing all available aerobraking data from other
orbiting spacecraft. In particular, we explore the saturation conditions of
gravity waves in a lower part of the thermosphere (between 90 and 130 km) than
the one observed by MAVEN (between 120 and 300 km). Thus, we obtain a broader
dataset of the variability of gravity wave activity with altitude, latitude
and season. This allows us to compare the available measurements with
diagnostics obtained by GCM through the Mars Climate Database (MCD Lewis et
al., 1999; Forget et al., 1999; Millour et al., 2015)

This paper is organized as follows. In section 2, we provide information on
the datasets. Section 3 features a discussion of the MAVEN/NGIMS measurements,
while section 4 features a comparative discussion of the aerobraking datasets.
We conclude in section 5.

##  2 Data and Method

###  2.1 Datasets used in this study

During aerobraking operations in the Martian thermosphere, the accelerometers
of MGS, ODY and MRO (Lyons et al., 1999; Smith and Bell, 2005; Tolson et al.,
2008) acquired data during 850 passes for MRO (since September 1997, Martian
Year [MY] 23) (Keating et al., 2002), 320 passes for ODY (since October 2001,
MY 25) (Tolson et al., 2007a), and 430 passes for MGS (from April to August
2006, MY 28) (Tolson, 2007), covering latitude ranges from 60∘N to 90∘S for
MGS, 30∘N to 90∘N for ODY, and 0∘ to 90∘S for MRO. Periapsis altitudes varied
from about 95 km to 150 km (see Figures 1 and 2).

In addition to those aerobraking datasets, the CO2 density variations from
3124 orbits are available from MAVEN/NGIMS mass spectrometer data reported in
the NASA Planetary Data System from October 2014 (MY32) to February 2017
(MY33) (Benna and Lyness, 2014). Considering the NGIMS settings were changed
to a new operating mode starting from February 2015, as mentioned in England
et al. (2017) and Terada et al. (2017), we chose to focus on datasets from
February 2015 to February 2017. The instrument is still in operation at the
time of writing and the present study can be complemented in the future by an
analysis of the interannual variability. The MAVEN observations cover (high
periapsis) altitude ranges between $\sim$120 km and $\sim$190 km, and have
large latitudinal coverage, as shown in Figure 1 and Figure 2.

Figure 1: Vertical (km) and seasonal (Solar Longitude in degrees) coverage of
Mars Global Surveyor (MGS), Mars Odyssey (ODY), Mars Reconnaissance Orbiter
(MRO) and MAVEN (MVN) spacecrafts, each dot corresponds to the periapsis
location of one orbit Figure 2: Latitudinal (degrees) and seasonal (Solar
Longitude in degrees) coverage of Mars Global Surveyor (MGS), Mars Odyssey
(ODY), Mars Reconnaissance Orbiter (MRO) and MAVEN (MVN) spacecrafts, each dot
corresponds to the periapsis location of one orbit

###  2.2 Computing the amplitude of gravity wave perturbations

Along each orbit trajectory, we extract the longitudes, latitudes, solar
longitudes (Ls, which is the position of the planet on its orbit, defined as
an angle from a reference position, corresponding by convention to the
northern spring equinox), local times, altitudes, CO2 density measurements, as
well as the elapsed time from the periapsis. The geodesic distance from the
periapsis is calculated from the latitude and longitude displacements. A
relative density perturbation $\delta\rho_{r}$ is obtained by subtracting the
mean density $\rho_{m}$ (considered here to be a 40-second rolling averaged
density, as in Tolson et al., 1999, 2005, 2007b, 2008; Creasey et al., 2006)
from the instantaneous density $\rho_{i}$ , and by normalizing with the mean
density

$\delta\rho_{r}=\frac{\rho_{i}-\rho_{m}}{\rho_{m}}$ (1)

Typical examples of orbit trajectory, absolute and relative density
variations, obtained for the MGS orbit 1046 and for the MAVEN orbit 3641 are
shown in Figure 3. Considering the relative density perturbations, rather than
the absolute value, enables a direct diagnostic of the effect of gravity
waves, with the underlying assumption that the 40-second average provides an
acceptable estimate of the “background” atmospheric state upon which the
gravity waves propagate.

---
Figure 3: Left: example of orbit 1046 from MGS, Right: example of orbit 3641
from MAVEN. From Left to Right: orbit’s trajectory characterized by the
displacement in altitude along the distance from periapsis in km; Density
variations in kg km-3 in function of the distance from periapsis in km ;
Relative density variation in function of the distance from periapsis in km.

In order to quantify the amplitude (i.e. the intensity) of the observed
gravity waves on a single orbit, and to assess the spatial and seasonal
variability of the gravity wave activity, we calculate for each orbit the Root
Mean Square (RMS) of the fluctuations of relative densities $\delta\rho_{r}$
along the trajectory.

Figure 4 (MAVEN/NGIMS data) and Figure 5 (aerobraking data) show the seasonal
variations of the GW activity as quantified by this RMS quantity, i.e. the RMS
as a function of the Ls, all other parameters (longitudes, latitudes, local
times, altitudes) confounded. A distinctive pattern of amplitude fluctuations
with season is found in the MAVEN data in Figure 4, in agreement with the
tendencies discussed in Terada et al. (2017).

Figure 4: Seasonal variability of GWs amplitudes measured by MAVEN/NGIMS. Each
point corresponds to the RMS of the relative densities calculated over each
orbit. In this figure the RMS has been calculated on the points around the
periapsis, where the trajectory is close to be horizontal, at distances from
the periapsis comprised between -700 and 700 km. This restriction reduces the
altitude range to around 15 km above the periapsis. Data gathered from Martian
Year (MY) 32 are in red, and data from MY33 in blue. Figure 5: Seasonal
variability of GWs amplitudes measured by aerobraking instruments MGS, ODY and
MRO. Each point corresponds to the RMS of the relative densities calculated
over each orbit. In this figure the RMS has been calculated on the points
around the periapsis, where the trajectory is close to be horizontal, at
distances from the periapsis comprised between -400 and 400 km. Beyond these
distances the aerobraking data become very noisy. This restriction reduces the
altitude range to around 10 km above the periapsis.

###  2.3 Temperature estimates

The background temperature $T$ is estimated at each point of each orbit with
the ideal gas law and the hydrostatic equilibrium, as a function of the mean
density of CO2 $\rho$ and the altitude $z$ as follows:

${\int{\frac{\partial\rho}{\rho}}}=-\frac{g}{R_{CO_{2}}T}\int\partial z$ (2)

with $g$ the gravitational acceleration and $R_{CO_{2}}$ the ideal gas
constant of CO2.

We split the orbit in three parts.

  1. 1.

The middle leg is the part of the orbit track close to the periapsis, where
the displacement is almost horizontal, the density almost constant, and,
consequently, where the temperature can no longer be deduced from equation 2.
We arbitrarily define this middle leg as containing the points for which the
ratio between the mean density and the maximal density is greater than 10%.

  2. 2.

The inbound leg corresponds to the points located ”before” the perapsis not
included in the middle leg.

  3. 3.

The outbound leg refers to the points located ”after” the periapsis not
included in the middle leg.

Thus the middle leg of the measurements is excluded from the comparative
analysis, and we only keep the inbound and outbound profiles for all
aerobrakings and MAVEN/NGIMS measurements.

We found that in the inbound and outbound legs, the temperature profiles
follow a similar vertical gradient. We thus study the variability of
temperature from one orbit to another with a single representative value for
both the inbound and outbound legs, chosen as the average value on each leg.
Those temperatures estimated from aerobraking and MAVEN/NGIMS measurements are
compared in Figure 6 and Figure 7 with the temperature in the Mars Climate
Database (built from Global Climate Model (GCM) simulations Millour et al.,
2015) for the same spatio-temporal coordinates (Ls, longitude, latitude,
altitude, local time). Only the comparisons of temperatures measured on
outbound legs versus temperature modeled in the MCD are displayed for the sake
of brevity; the analysis for inbound legs is similar. The MCD temperatures are
systematically lower than those observed by MAVEN and aerobraking, and there
is also much more variability in the observation data points; however, the
overall seasonal variability is well reproduced, except the
$L_{s}=290^{\circ}$ maximum observed by ODY. This gives us confidence that
using a value of background temperature averaged over the inbound and outbound
legs is suitable to carry out an analysis of the seasonal (climatological)
trends.

---
Figure 6: Mean background temperature estimated over the outbound leg and
calculated from the CO2 density observations (blue dots) and estimated with
the MCD (red dots) as a function of Solar Longitude; from the upper to the
lower : MGS, ODY and MRO Figure 7: Mean background temperature estimated over
the outbound leg and calculated from the CO2 density observations of NGIMS
instrument (blue dots) and estimated with the MCD (red dots) as a function of
Solar Longitude

##  3 Vertical Propagation of Gravity Waves: analysis of the MAVEN
observations in the thermosphere

In the absence of additional wave sources and dissipation processes (e.g.,
radiative damping Eckermann et al., 2011), the amplitude of gravity waves is
expected to grow exponentially with altitude as the atmospheric density
decreases. Conversely, the amplitudes of gravity waves appear to anti-
correlate with altitude, according to the altitudes of the MAVEN measurements
shown in Figure 1 and the amplitudes $\delta\rho$ of the perturbations shown
in Figure 4. In other words, in the MAVEN observations, gravity-wave amplitude
seems to correlate with density, as opposed to an anti-correlation expected if
the amplification of gravity-wave amplitude with altitude (and reduced
density) was the only controlling factor. This is confirmed by considering the
seasonal variations of density perturbations $\delta\rho$ at a constant
pressure level, e.g. at pressures $4\times 10^{-8}<P<6\times 10^{-8}$ Pa
(corresponding to altitudes between $\sim$160 and $\sim$240 km) in Figure 8.
The observed variability in gravity-wave amplitude must be controlled by
either the sources of those waves and/or the impact of saturation and critical
levels.

Figure 8: Upper: Vertical (km) and seasonal (Solar Longitude in degrees)
coverage of MAVEN (MVN) spacecraft, each dot corresponds to the periapsis
location of one orbit. Down: Seasonal variability of GWs amplitudes measured
by MAVEN/NGIMS at a constant pressure level P such as $4\times
10^{-8}<P<6\times 10^{-8}$Pa. Each point corresponds to the RMS of the
relative densities calculated over each orbit. Data gathered from Martian Year
(MY) 32 are in red, and data from MY33 in blue.

In the MAVEN measurements, gravity wave activity in the thermosphere is
randomly distributed with longitude and latitude (figures not shown). No
correlation appears to exist between this gravity wave activity and either the
position of topographical highs and lows (mountains and craters), or the
position of mesospheric jet-streams. This suggests that the regional
distribution of the intensity of gravity waves is more controlled by
propagation effects (e.g., filtering by saturation or critical levels, Fritts
and Alexander, 2003) than by the distribution of the sources triggering those
waves.

The background horizontal wind plays a particularly crucial role in impacting
the conditions for the upward propagation of gravity waves emitted in the
troposphere. A critical level occurs when and where the background horizontal
wind velocity ${\bar{u}}$ almost equals the gravity wave phase speed $c$
(first Eliassen-Palm theorem, Lindzen, 1981). A gravity wave that reaches a
critical level can no longer propagate towards the thermosphere: hence
horizontal circulations may filter out gravity waves emitted in the
troposphere from the mesosphere and the thermosphere.

Considering, for the sake of simplicity, a gravity-wave phase speed $c=0$
(typical of orographic gravity waves), we explored the regional and seasonal
variability of background horizontal winds ${\bar{u}}$ simulated in the MCD
from the troposphere to the lower mesosphere (since no measurements of such
winds are available). We found no correlation between this variability, and
the regional and seasonal variability of the gravity wave amplitudes observed
by MAVEN (not shown). While the modeled winds have not been validated and may
differ from reality, there is no reason to explain the variability of the
observed gravity wave amplitudes solely with the occurrence of critical
levels.

It follows from the above discussions that the most likely possibility to
explain the observed variability of gravity wave amplitude in the MAVEN
observations is the breaking/saturation due to convective instability. This
shall lead to, according to Terada et al. (2017), the gravity wave amplitudes
to be inversely proportional to the background temperature. Let us propose an
alternate, yet equivalent, derivation of the theoretical arguments in Terada
et al. (2017) that we will use in section 4.

The saturation of a gravity wave occurs as soon as it encounters convective
instability (Lindzen, 1981; Hauchecorne et al., 1987; Terada et al., 2017).
Local mixing occurs as the gravity wave breaks, inducing an adiabatic
(neutral) temperature lapse rate. We consider the case of a medium-frequency
gravity wave ${f}\ll{\omega}\ll{N}$, where ${f}$, ${\omega}$ and ${N}$ are
respectively the Coriolis, the gravity-wave and the Brunt-Väisälä frequencies,
with $N$ such that

$N^{2}=\frac{g}{T}\left[\frac{\partial T}{\partial z}+\frac{g}{C_{p}}\right]$

assuming the short-wavelength approximation ${2\,H\,k_{z}}\gg{1}$, where
${k_{z}}$ is the vertical wave number. Which are reasonable assumptions for
most gravity waves observed in planetary upper atmospheres (Fritts and
Alexander, 2003). In those conditions, according to Hauchecorne et al. (1987),
the saturated conditions lead to

${k_{z}}{\theta^{\prime}_{s}}=\frac{N^{2}\bar{\theta}}{g}\qquad\Rightarrow\qquad{\frac{\theta^{\prime}_{s}}{\theta}}=\frac{N^{2}}{gk_{z}}$
(3)

where ${\theta^{\prime}_{s}}$ is the amplitude of the wave at saturation
(expressed in perturbations of potential temperature), $\bar{\theta}$ the
background potential temperature and $g$ the acceleration of gravity. Besides,
the linearized fluid equations applied to the propagation of gravity waves
(Fritts and Alexander, 2003) lead to:

$\frac{\theta^{\prime}}{\bar{\theta}}=\frac{1}{c_{s}^{2}}\frac{P^{\prime}}{\bar{\rho}}-\frac{\rho^{\prime}}{\bar{\rho}}$
(4)

where $\rho$ is the density, $P^{\prime}$ and $\rho^{\prime}$ the pressure and
density perturbations, and ${c_{s}}$ the sound speed. We can neglect the
compressibility term related to the background density gradient, which is
equivalent to filter out acoustic gravity waves (${c_{s}}\rightarrow\infty$).
This entails:

${\left|\frac{\rho^{\prime}}{\bar{\rho}}\right|}={\left|\frac{\theta^{\prime}}{\bar{\theta}}\right|}$
(5)

Combining equations 3 and 5, we obtain the equation expressing the relative
density perturbations by gravity waves:

$\boxed{\delta\rho=\frac{|\rho^{\prime}|}{\bar{\rho}}=\frac{N^{2}}{k_{z}g}}$
(6)

which corresponds to the observed diagnostic described in equation 1.
Isothermal background profiles $T=T_{0}$ are often observed in the Martian
thermosphere, where EUV heating is offset by molecular conduction (Bougher et
al., 1990). In the specific case of isothermal profiles, ${N^{2}}$ can be
reduced to:

$N^{2}=\frac{g}{\bar{\theta}}\frac{\textrm{d}\bar{\theta}}{\textrm{d}z}=\frac{g^{2}}{C_{p}T_{0}}$
(7)

which yields the “inverse temperature” dependency (Terada et al., 2017) in the
case of isothermal profiles at saturation:

$\boxed{\delta\rho=\frac{|\rho^{\prime}|}{\bar{\rho}}=\frac{g}{k_{z}\,C_{p}}\frac{1}{T_{0}}}$
(8)

MAVEN data are acquired high in the Martian thermosphere (above 150 km) even
for deep dip acquisitions: hence the temperature profiles retrieved by MAVEN
are approximately isothermal (England et al., 2017; Terada et al., 2017). The
temperature profiles modeled and compiled in the MCD also indicate widespread
isothermal profiles at the altitudes probed by MAVEN. Comparing Figures 4 and
9 confirms qualitatively equation 8, i.e. the correlation between the
amplitude of gravity wave perturbations and the inverse background
temperature. Quantitatively, in the case of the inbound leg of each orbit, a
correlation coefficient $R\simeq 0.70$ between the average of the relative
density and the calculated temperature is found (see Figure 10). Our analysis
of the MAVEN is thus compliant with the one conducted by Terada et al. (2017),
and we now turn to the analysis of aerobraking data in the lower thermosphere.

Figure 9: Seasonal variability of the background temperature estimated from
MAVEN/NGIMS density measurements (ideal gas law and hydrostatic equilibrium).
Each point corresponds to the inverse of the mean background temperature
calculated over the outbound leg of each orbit. Data gathered from Martian
Year (MY) 32 are in red, and data from MY33 in blue. Figure 10: Correlation
between the average of the absolute relative density and the average of the
background temperature calculated for MAVEN/NGIMS data over the inbound leg of
each orbit. Temperature is obtained from the density observations by means of
the ideal gas law and the hydrostatic equilibrium

##  4 Gravity Waves in the Lower Thermosphere: Aerobraking Data

###  4.1 Analysis

Aerobraking data have been studied in the past to observe the activity of
gravity waves in the lower thermosphere, either to discuss the variability of
potential sources (Creasey et al., 2006) or to assess wave filtering by zonal
jets and how large-amplitude GWs could penetrate to high altitudes (Fritts et
al., 2006). Here we assess if the “inverse temperature” correlation inferred
from the MAVEN/NGIMS data (Terada et al., 2017, and section 3 of this paper)
can be extended to those lower-thermosphere aerobraking observations obtained
by the three accelerometers of MGS, ODY and MRO.

In the aerobraking observations, as is emphasized by Tolson et al. (2005) and
Tolson et al. (2008), the intensity of density perturbations are
systematically lower when the spacecraft enters the polar vortex (e.g. MRO
during the southern hemisphere winter and ODY during the northern hemisphere
winter). Figure 11 shows two examples: ODY orbit 155, which goes through the
northern hemisphere winter vortex at $Ls=298.30^{\circ}$ and latitude 82.43∘N,
and MRO orbit 250, going through the southern hemisphere winter vortex at
$Ls=90.01^{\circ}$ and latitude=69.50∘S. These variations of density
perturbations within the same orbital track could be explained by the anti-
correlation between temperature and gravity wave activity explained above (an
explanation that was not provided in Tolson et al., 2008). Polar warming at
thermospheric altitudes (first observed by ODY during aerobraking, Keating et
al., 2003) results from the adiabatic heating generated by the subsidence of
air over the winter pole produced by strong interhemispheric transport
(González-Galindo et al., 2009). The entry of the spacecraft inside the polar
vortex is then expected to be associated with an increase of temperature,
leading to a decrease of gravity wave activity according to equation 8.

|
---|---
Figure 11: Examples of orbit 155 of ODY and orbit 250 of MRO. Density
variations in kg km-3 in function of the distance from periapsis in km

In Figures 12 and 13, the observed RMS of the relative density variations is
compared to the inverse of the background temperature, calculated for each
orbit of each instrument over the outbound leg (for the sake of brevity,
similar results over the inbound leg are not shown). Latitudinal and seasonal
variability are displayed respectively in Figures 12 and 13.

The amplitude of gravity waves present similar features with the inverse of
temperature in the MGS observations, with an amplitude increase at latitudes
60∘S, 50∘N and particularly at 20∘S, where inverse temperature is higher in
Figure 12, corresponding to L${}_{s}\sim 70^{\circ}$ in Figure 13. The anti-
correlation seems easier to identify in ODY data, in particular at polar
latitudes around 80∘N, where a clear decrease of GWs amplitude is correlated
with the polar warming (see previous paragraph). Conversely, no obvious
correlation between density perturbations and inverse temperature is found in
the MRO aerobraking data: there is an increase in gravity waves activity from
latitude -90∘ to -70∘, while the tendency for inverse temperature is unclear,
corresponding to L${}_{s}\sim 35^{\circ}$ in Figure 13. Furthermore, the
gravity waves activity decreases at L${}_{s}\sim 95^{\circ}$, corresponding to
a latitude of -20∘, whereas it is not the case for inverse temperature.
Correlations have been calculated for the three instruments between the
gravity waves amplitude and inverse temperature as done for MAVEN in Figure
10, but for all of them the correlation coefficient $R$ remains below $0.5$.
The largest correlation coefficient is obtained for ODY ($R=0.48$), whereas it
is around $0.2$ for the two other datasets.

---
Figure 12: From the upper to the lower: MGS, ODY, MRO. From the left to the
right: RMS of the relative density calculated over the outbound leg according
to the latitude of the orbit’s periapsis, inverse of the mean background
temperature calculated from the observations over the outbound leg according
to the latitude of the orbit’s periapsis
---
Figure 13: From the upper to the lower: MGS, ODY, MRO. From the left to the
right: RMS of the relative density calculated over the outbound leg according
to Ls, inverse of the mean background temperature calculated from the
observations over the outbound leg according to Ls

###  4.2 Discussion

The correlation between density perturbations, caused by gravity waves, and
the inverse background temperature, suggested by equation 8, appears to be
observed by MAVEN/NGIMS. A similar correlation, albeit less clear-cut than
with the MAVEN/NGIMS dataset, is also noticed during ODY aerobraking phases at
high latitudes. This correlation seems to be observed at certain locations for
MGS, as seen in the previous section, and also in particular cases for MRO, as
seen in the previous section for the orbits located in the polar warming.
However, for those two spacecrafts, the correlation is not clear at all in the
global analysis of the complete datasets.

The aerobraking density measurements correspond to periapsis conditions at
lower altitudes than the MAVEN/NGIMS measurements (cf. Figure 1). There, the
assumption of isothermal profiles could not be valid. Indeed, in Figure 14 we
compare the temperature gradients calculated with the MCD for the three
aerobraking missions along with MAVEN/NGIMS. The Figure shows that MAVEN/NGIMS
data mainly correspond to isothermal profiles, whereas the three other
instruments present larger temperature gradients. Yet, equation 8 is only
effective in isothermal conditions. As a matter of fact, we observe in the ODY
data that a potential correlation between gravity wave activity and inverse
temperature only appears where the temperature gradient is the lowest, at
higher latitudes. This is also possibly the case for MGS at the points located
around latitudes -60∘ and -20∘. However, MRO, which presents the lowest
temperature gradient, presents no clear correlation with the inverse
temperature. There could be an explanation for the temperature gradient being
lower for ODY and MRO, despite the fact they are lower in altitude: at polar
latitudes, the polar warming shifts the threshold for isothermal conditions to
lower altitudes in the mesosphere. Furthermore, when the temperature gradient
is significant, the more general equation 6 shall prevail instead of equation
8, which means that the amplitude of gravity waves is proportional to the
static stability $N^{2}$ rather than the inverse background temperature.

---
Figure 14: Upper: Absolute value of the mean temperature gradient along the
latitude calculated with the MCD over the outbound leg of each orbit of the
different aerobraking instruments and MAVEN/NGIMS. Down: Absolute value of the
mean temperature gradient along the Ls calculated with the MCD over the
outbound leg of each orbit of the different aerobraking instruments and
MAVEN/NGIMS.

The possible correlation with static stability $N^{2}$ can be tested with the
MCD in the conditions that were met by the aerobraking measurements. Figure 15
displays the comparison between the RMS of the relative density acquired at
the different aerobraking orbits and the static stability calculated from the
MCD (for the corresponding orbital spatio-temporal coordinates). We observe
the same peak of gravity waves activity and static stability for MGS at
latitude -20∘ and in the North pole, but not for the other latitudes. A good
correlation between the GWs activity and the static stability, as with the
inverse temperature, can be found for ODY. Regarding MRO, the static stability
$N^{2}$ correlates well to the observed amplitude of gravity waves in high-
latitude regions (latitudes above $-50^{\circ}$S), but such a correlation is
not found at lower latitudes.

|
---|---
|
|
Figure 15: From the upper to the lower: MGS, ODY, MRO. Left : RMS of the
relative density calculated over the outbound leg of each orbit of aerobraking
data according to the latitude of the orbit’s periapsis ; Right : Mean static
stability $N^{2}$ calculated over the outbound leg of each orbit of
aerobraking data according to the latitude of the orbit’s periapsis, $N^{2}$
has been calculated by means of the Mars Climate Database (MCD) at the
different orbital characteristics and with the corresponding dedicated MCD
dust scenarios of Mars Year (MY) 25 (MCD detailed document, Montabone et al.
(2015))

There might be multiple reasons for aerobraking measurements not following
equation 6 in the low and mid latitudes. Firstly, while no correlation was
found with potential sources of gravity wave, it is still possible that
outside the polar regions, propagation effects would compete with the regional
variability of gravity-wave sources. Secondly, following a similar argument,
the filtering by critical levels was ruled out for a lack of clear tendency,
but might be of peculiar importance for specific regions (see Spiga et al.,
2012). Thirdly, the regional variability of vertical wavelength $k_{z}$, a
parameter found in equations 6 and 8, in principle could impact density
perturbations (Smith et al., 1987), which then would be less clearly
correlated to static stability $N^{2}$.

##  5 Conclusion

We have studied the seasonal and regional variability of density
perturbations, putatively caused by the propagation of gravity waves in the
thermosphere, in different sets of data issued from the aerobraking phases of
MGS, ODY and MRO (accelerometers) and the observations of the NGIMS instrument
on board MAVEN. The modeling compiled in the Mars Climate Database has been
used to complement background atmospheric conditions obtained by observations.
Our conclusions are as follows:

  1. 1.

The correlation found in the MAVEN observations by Terada et al. (2017)
between the inverse background temperature and the density perturbations
reasonably extends to the ODY aerobraking measurements, but not to the MGS and
MRO aerobraking measurements. This result emphasizes the exceptional nature of
MAVEN datasets, which combine both isothermal and saturated conditions
(equation 8). The seasonal variability of inverse background temperature
measured by MAVEN is reproduced in the Mars Climate Database.

  2. 2.

In comparison to MAVEN/NGIMS measurements, MGS, ODY and MRO aerobraking data
cover a lower layer in the thermosphere, where the Mars Climate Database
predicts non-isothermal conditions. In these conditions, and under the
hypothesis of saturation, a correlation between the gravity waves perturbation
with the static stability is expected (equation 6). A correlation of density
perturbations monitored both by ODY and MRO during aerobraking in polar
regions with static stability $N^{2}$ is observed and indicates that wave
saturation might be still dominant, but the isothermal conditions are no
longer verified (equation 6).

  3. 3.

The spatial variability of gravity-wave-induced density perturbations are
difficult to explain for the global MGS dataset and in lower latitudes for ODY
and MRO aerobraking, where no clear correlation with neither inverse
temperature nor static stability is found. The effects of gravity-wave
sources, or wind filtering effects through critical levels, were ruled out as
explanations for most of the measured variability, yet might play a stronger
role in the low-to-mid latitudes.

Future studies will employ measurements during the aerobraking phase of the
ExoMars Trace Gas Orbiter, as well as new measurements by MAVEN, to confirm
the conclusions drawn in this study and the existing literature. Broadening
the knowledge of gravity wave activity in the mesosphere and thermosphere is
crucial to understand the large-scale heat and momentum budget of this part of
the Martian atmosphere.

###### Acknowledgements.

The authors acknowledge Centre National d’Études Spatiale (CNES) and European
Space Agency (ESA) for financial support. We thank two reviewers for thorough
and constructive comments that helped us to improve this paper.

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