# Martian Dust Storms and Gravity Waves: Disentangling Water Transport to the
Upper Atmosphere

###### Abstract

Simulations with the Max Planck Institute Martian general circulation model
for Martian years 28 and 34 reveal details of the water “pump” mechanism and
the role of gravity wave (GW) forcing. Water is advected to the upper
atmosphere mainly by upward branches of the meridional circulation: in low
latitudes during equinoxes and over the south pole during solstices. Molecular
diffusion plays little role in water transport in the middle atmosphere and
across the mesopause. GWs modulate the circulation and temperature during
global dust storms, thus changing the timing and intensity of the transport.
At equinoxes, they facilitate water accumulation in the polar warming regions
in the middle atmosphere followed by stronger upwelling over the equator. As
equinoctial storms decay, GWs tend to accelerate the reduction of water in the
thermosphere. GWs delay the onset of the transport during solstitial storms
and change the globally averaged amount of water in the upper atmosphere by
10-25%.

Journal of Geophysical Research: Planets

Moscow Institute of Physics and Technology, Moscow, Russia Max Planck
Institute for Solar System Research, Göttingen, Germany Space Research
Institute, Moscow, Russia George Mason University, Fairfax, VA, USA

D. S<EMAIL_ADDRESS>
The impact of gravity waves and planet-encircling dust storms on the
hydrological cycle is explored with a global circulation model

Water enters the upper atmosphere mainly along upward branches of the
circulation, while molecular diffusion plays little role

Gravity waves modulate the onset and strength of upward water “pump” channels
during equinoctial and solstitial dust storms differently

## Plain Language Summary

Transport of water to the Martian upper atmosphere with subsequent
photodissociation and escape of hydrogen into space occurs near perihelion and
amplifies during global dust storms. One explanation is the so-called water
“pump” due to the seasonally varying global meridional circulation. Forcing by
atmospheric gravity waves is a major mechanism that drives this circulation in
the middle and upper atmosphere. The interplay between gravity waves, dust
storms and transport of water from the lower atmosphere to the thermosphere
has been explored with a Martian general circulation model. When dust storms
take place at equinoxes, gravity waves enhance warming in polar regions and
accumulation of vapor there. They also strengthen the uplift in low latitudes
leading to a significant increase of water in the thermosphere. When global
dust storms start to decay, wave forcing helps to remove water from upper
layers of the atmosphere more abruptly. When storms onset near the perihelion
solstice (southern hemisphere summer), gravity waves delay the upward
transport of water over the south pole first, but then intensify it and the
redistribution across the globe. Thus, more water is delivered to the
thermosphere during dust storms and, potentially, can escape to space as
atomic hydrogen.

##  1 Introduction

Gravity waves (GWs) are omnipresent in the atmosphere of Mars and continuously
disturb it at all heights. Recent observations not only provided ample
evidence for their existence, but also determined their seasonal and spatial
climatology in the lower [Heavens . (2020)] and upper atmosphere [Jesch .
(2019), Siddle . (2019), Vals . (2019), Leelavathi . (2020), Nakagawa .
(2020), Li . (2021), Starichenko . (2021), Yiğit . (2021a), Yiğit . (2021b)].
The main dynamical role of GWs in planetary atmospheres is to re-distribute
momentum and energy between atmospheric layers, thus providing a vertical
coupling between the lower and the upper atmosphere [Yiğit Medvedev (2015),
Yiğit Medvedev (2019)]. On Mars, various phenomena associated with GWs have
been studied over the recent decade [<]e.g., see the review
by¿[]medvedev2019gravity, however among the least explored remains the aspect
of how GWs influence the transport of minor species.

Water is an extremely important minor constituent in the Martian atmosphere.
Although the abundance of water vapor in the atmosphere is very small (of the
order of a few hundredths of a percent), it is the main source of hydrogen in
the thermosphere [Hunten McElroy (1970), Stone . (2020)]. Hydrogen is produced
by photodissociation of H2O molecules delivered to the upper atmosphere (above
$\sim$80 km) from below and, due to its low molecular mass, has the largest
probability of escaping into space compared to other species. It was suggested
that hydrogen escape was the main channel of atmospheric loss and dehydration
of Mars in the past [McElroy (1972), Parkinson Hunten (1972)]. There is
plentiful observational evidence that the amount of hydrogen atoms near the
exobase varies with seasons by an order of magnitude with the maximum near
perihelion (solar longitude $L_{s}\approx 270^{\circ}$) [Bhattacharyya .
(2017), Chaufray . (2021), Halekas (2017)]. Seasonal variations have been
found for water in the lower atmosphere [Smith (2002), Smith . (2009),
Maltagliati . (2011), Maltagliati . (2013), Fedorova . (2021)]. Both hydrogen
in the exosphere and water in the upper atmosphere increase significantly
during major dust storms [<]e.g.,¿[]bhattacharyya2015strong,
chaffin2014unexpected, clarke2014rapid, chaffin2017elevated,
fedorova2018water, fedorova2020stormy, heavens2018hydrogen, aoki2019water. The
observed seasonal behavior and the dependence on atmospheric dust has been
explained by the water “pump” mechanism [Shaposhnikov . (2019)], according to
which water is transported from the lower to upper atmosphere by the
meridional circulation. Similar results for the dust storm of MY34 have been
produced in the simulation study of neary2020explanation, which showed that
the water vapor distribution at higher altitudes is sensitive to the
distribution of dust. These authors emphasized the role of direct heating by
airborne aerosol and resulting inhibition of ice cloud formation in increasing
the amount of water in the middle atmosphere.

Our study examines the water transport mechanism further by including into
consideration the forcing provided by the subgrid-scale GWs, a mechanism that
has not been explored in the context of water transport so far. This is done
using simulations with our recently developed hydrological scheme
[Shaposhnikov . (2018), Shaposhnikov . (2019)] and the whole atmosphere GW
parameterization [Yiğit . (2008)] implemented in the Max Planck Institute
Martian general circulation model (MPI–MGCM). Since high-altitude water
abundances increase during dust storms, we selected Martian years 28 (MY28)
and 34, when major planet-encircling dust events have occurred near the
solstice and equinox, correspondingly. The main focus of the study is on MY34,
because simulations for MY28 have been already described in some detail
[Shaposhnikov . (2019)].

In section 2, we outline the model and setup of numerical experiments. Then,
in section 3, we discuss the impact produced by the MY34 dust storm on the
water cycle, and briefly compare model temperatures with the measurements of
the Mars Climate Sounder instrument onboard Mars Reconnaissance Orbiter
(MCS–MRO). The relative roles of advection and molecular diffusion are
explored in section 4. Differences introduced by GWs are described in section
5. In section 6, we zoom out and consider the temporal evolution of water and
its transport as well as the influence of GWs during the MY34 and MY28 dust
storms. The results for the MY34 simulations are compared with observations by
the Atmospheric Chemistry Suite (ACS) instrument onboard the ExoMars Trace Gas
Orbiter spacecraft in section 7.

##  2 Martian General Circulation Model and Design of Simulations

The MPI–MGCM is based on a spectral dynamical core, which solves the three-
dimensional nonlinear primitive equations of hydrodynamics on a globe.
Physical parameterization suitable for the Martian atmosphere are described in
detail in the papers of hartogh2005description, hartogh2007middle,
medvedev2007winter. The vertical grid is represented by 67 hybrid
$\eta$-levels extending from the surface to the pressure level $3.6\times
10^{-6}$ Pa ($\sim$160 km) in the thermosphere. All simulations were performed
at the T21 horizontal resolution, which corresponds to $\approx
5.6^{\circ}\times 5.6^{\circ}$ horizontal grid. The subgrid-scale GW spectral
parameterization was described in the work of medvedev2011influence, and its
recent application to studying global effects of GWs is given in the work by
yiugit2018influence. Other model parameters are the same as in the study of
medvedev2016comparison.

The water cycle of the model includes a semi-Lagrangian transport of water
vapor and ice [Shaposhnikov . (2016)] and accounts for the microphysics of
conversions between vapor and ice [Shaposhnikov . (2018)]. Condensation occurs
on cloud condensation nuclei (CCN), whose sizes are represented by four
characteristic bins. A bimodal log-normal dust size distribution is assumed in
each spatial bin following the observations of fedorova2014evidence. The loss
of vapor in the upper atmosphere is accounted for through photodissociation at
the Lyman-$\alpha$ wavelength as well as by applying open boundary conditions
at the model top.

Two predetermined dust scenarios for MY28 (2006–2007) [Medvedev . (2013)] and
MY34 (2017–2019) [Montabone . (2020)] were utilized in the simulations. The
scenarios are based on the observed total dust optical depth in IR. Vertical
distributions of the dust mixing ratio were calculated following the work by
conrath1975thermal with modifications as described in the paper of [formulae
(1)–(2)]medvedev2013general. Note a typo in (2) there: the expressions for
$\tau\geq 2$ and $\tau<2$ in (2) should be switched.

##  3 Influence of the MY34 Dust Storm

We start with an overall assessment of the impact of the MY34 dust storm on
the circulation and hydrological cycle. We selected a 10-day period at the
beginning of the storm ($L_{s}=194^{\circ}-200^{\circ}$), when changes in the
atmospheric fields were most rapid. For comparison, we use the same dates from
the simulation for MY28, when the storm has not started yet (see section 6)
and, thus, can be considered as a characteristic for dustless conditions. Note
that the MY34 and MY28 runs include parameterized effects of subgrid-scale GWs
as a standard model setup. Figure 1 presents the temperature and water vapor
abundance for MY34 (contours) and the associated differences between the
simulations for MY34 and MY28 (shaded). Figures 1a,c,e demonstrate the
atmospheric warming between 10 and 80 km by up to 30 K caused by the increased
absorption of the solar radiation by airborne aerosol, especially in low
latitudes. Dust particles block the radiation from reaching the surface, thus
cooling down the lowermost layers. Changes in the meridional circulation lead
to an adiabatic cooling in the upper atmosphere and heating in high latitudes
(the so-called middle atmosphere polar warmings), as was discussed in the
paper of [Sect. 5]medvedev2013general. The dust-induced changes in the water
vapor distribution are plotted in Figure 1b, while the net budget of water is
presented in Figures 1d,f. It shows that the amount of vapor in the lower
atmosphere significantly drops in response to stronger condensation at colder
air temperature as well as due to a weaker sublimation from the surface.
Contrary to that, higher temperature in the middle atmosphere leads to an
enhanced saturation and increase of vapor at 40–80 km, especially in low
latitudes. Finally, the comparison shows that the dust storm produces strong
water pumping into the upper atmosphere, similar to that during the solstitial
dust storm of MY28 [Shaposhnikov . (2019)]. However, the main transmission
channel in this case is over the equator, unlike over the polar region at
perihelion (see the paper of neary2020explanation and section 5 for more
discussion). Note that water is not lifted up above 40 km under the dustless
scenario. Once vapor reaches the middle and upper atmosphere during the
equinoctial MY34 storm, it is rapidly transported over all latitudes by the
two-cell meridional circulation.

A brief comparison of the simulated temperature with available measurements by
MCS–MRO is given in Figures 1c,e. The contours present the data from NASA’s
Planetary Data System [MCS Data Archive (2021)]. We find that the simulated
temperatures are 5 to 10 K smaller than the retrieved ones, which may result
in an underestimation by the model of the strength of the meridional cell in
the middle atmosphere in the northern hemisphere and of the intensity of
downwelling near the north pole, in particular.

##  4 Roles of Advection and Molecular Diffusion in the Upward Water Transport

In order to further investigate pathways by which water is transported
vertically we assess the relative roles of vertical advection and molecular
diffusion. For that, we selected a day before the onset of the MY34 dust storm
($L_{s}\approx 180^{\circ}$) and at its midst ($L_{s}\approx 200^{\circ}$),
and calculated the corresponding terms from the conservation equation for
vapor: $wdq/dz$ and $\rho^{-1}d/dz(\mu dq/dz)$, where $w$ is the vertical
velocity, $q$ is the water vapor mixing ratio, $\rho$ is the air density and
$\mu$ is molecular dynamic viscosity. They characterize the rate of change
$\partial q/\partial t$ by both processes, and are plotted in Figure 2 with
color shades. Division of these quantities by $q$ yields inverse
characteristic time scales, which are also shown with contours. It is seen
that advection dominates the transport in the lower and middle atmosphere,
while the role of molecular diffusion is appreciable above the mesopause and
increases with height. Next, both the advective and diffusive vertical
transport enhance by approximately an order of magnitude during the storm, as
depicted by the scales of color bars in the upper and lower rows. With and
without dust storms, advective time scales are much shorter than the diffusive
ones (weeks and months vs years) below $\sim$100 km. Between $\sim$100 and 120
km, the time scales are of the same order, thus signifying the importance of
both transport mechanisms. Above 120 km, molecular diffusion takes over
vertical advection. The most important inference in the context of this study
is that water is transported across the “bottleneck” (60-80 km) to the
mesopause region ($\sim$110 km) by advection, while molecular diffusion plays
virtually no role. Note that this conclusion does not concern horizontal
transport, whose characteristic time scales between 60 and 120 km are much
shorter (weeks and days), and which is solely responsible for latitudinal re-
distribution of vapor.

##  5 Effects of Gravity Waves on Water Transport During the MY34 Dust Storm

Figuring out the primary role of the global circulation (advection), we next
consider how GWs affect it and water transport during the equinoctial MY34
dust storm. This is done by comparing two simulations with the enabled and
disabled GW parameterization (“GW on and off”) for the same as in section 3
period, i.e., the beginning of the storm ($L_{s}=194^{\circ}-200^{\circ}$).
The meridional circulation in these two cases is visualized with stream
functions in the latitude-altitude plane in Figures 3a (“GW on”) and 3b (“GW
off”). The arrows show the direction of the zonal mean Eulerian transport of
air and water vapor parcels, and the red and blue contours indicate the
clockwise and anti-clockwise circulation cells, respectively. It is seen that
close to the equinox, the two cells are almost symmetric (with respect to the
equator) in the lower and middle atmosphere. The major differences caused by
GWs occur near and above the mesopause ($\sim$100-120 km, depending on the
latitude). Momentum forcing by breaking/dissipating GWs a) intensifies the
upper portions of both cells (the meridional velocity is proportional to the
vertical distance between the streamlines), and b) reverses the meridional
circulation inducing the one-cell south-to-north transport. The consequences
for the water flux are shown in the same panels. Red and blue shades present
the differences between the scenarios with and without GWs for the upward
(Figure 3a) and downward (Figure 3b) fluxes. It is seen that the enhancement
of the two-cell circulation increases the upward flux of water in low- to
middle latitudes between $\sim$50 and 100 km (reddish shades in panel a) and
the downward fluxes in the polar regions of both hemispheres at approximately
the same heights (red shades in panel b). In the thermosphere above 110-120
km, the GW-induced pole-to-pole cell reduces the vertical water flux in low
latitudes (blue shades in panel a), but speeds up the meridional transport.

The most discussed, and thus recognizable, effect of GWs is
acceleration/deceleration of the mean zonal wind, the latitude-altitude cross-
sections of which are plotted in Figures 3c and 3d for the simulations with
and without the subgrid-scale GWs, correspondingly. The equinoctial
circulation is represented by two eastward (prograde) midlatitude jets, with
the one in the northern hemisphere being stronger due to the seasonal
transition to the northern hemisphere fall. Both jets extend much higher, if
the GW momentum forcing, or GW drag, $a_{x}$ (shown with contours in Figure
3c) is not taken into account. Overall, the mean GW drag is directed against
the mean wind. It affects mainly the upper parts of the jets, reduces their
strength and even reverses the direction of the flow in the mesosphere and
lower thermosphere. The other dynamically important effect of the GW drag is
maintaining the meridional circulation. Outside the equatorial region, the
mean meridional transport velocity is
$\bar{v}^{*}\approx-(2\Omega\sin\varphi)^{-1}a_{x}$, where $\Omega$ is the
rotational rate of the planet and $\varphi$ is the latitude [<]e.g., see the
discussion around Eqn. (5) in¿[]medvedev2007winter. The additional dynamical
forcing by the small-scale GWs of hundreds m s-1 sol-1 accelerates the
meridional flow in the northern hemisphere and reverses it in the southern
hemisphere above the mesopause, according to the formula and as depicted by
streamlines in Figure 3a. This has important consequences for water entering
this region: the meridional transport rapidly re-distributes it over the
globe.

The latter is illustrated in Figure 3e, which shows the increased (by 40 to 60
ppm) water vapor mixing ratio in the thermosphere and its spread across
latitudes, if GW forcing is taken into account. Due to continuity, the
enhancement of the horizontal flow is accompanied by an intensification of the
downward motions over the poles, especially in the northern hemisphere. The
associated adiabatic heating affects temperature and produces the so-called
polar warmings, with the northern one being stronger and more extensive
(Figure 3f). Warmer air and the influx of water support more vapor in polar
regions, again more in the northern hemisphere. In turn, the intensified lower
atmospheric branches of the circulation transport more water equatorward and
facilitate its vertical pump in low latitudes. The colder air at low and
middle latitudes above $\sim$70 km is the result of the enhanced vertical
motions and the associated adiabatic cooling. This explains more water ice
(shown with gray contours in Figures 3a,b) in the simulation with GWs.
Finally, the drop of the water vapor abundance just below is also the result
of its intense upward transport.

Considering only the beginning of the MY34 dust storm may create an impression
that the impact of GWs on water vapor is characterized exclusively by an
increase in water concentration in the upper atmosphere. In the next section
we explore the seasonal evolution of the vapor flux to show the complexity of
GW effects on the distribution of water.

##  6 Influence of Gravity Waves on the Seasonal Behavior of Water During Dust
Storms

We compare temporal variations of water vapor during two major dust storms of
MY34 and MY28. The former took place close to the equinox, the latter has
developed near the solstice, hence, we call them the equinoctial and
solstitial storms, respectively. The corresponding observed total dust optical
depth in IR is shown in Figures 4a and 4b with contours. Since our focus is on
the penetration of water into the upper atmosphere taking into account GW
effects, we plotted with shades the vertical flux of water vapor at 80 km in
the same panels. Water usually does not rise that high throughout the year,
therefore, this altitude can be regarded as a bottleneck. Positive (red) and
negative (blue) values indicate the upward and downward fluxes. It is seen
that, in both cases, a rapid increase of vertical fluxes of H2O coincides with
the onsets of the dust storms, with maxima collocated approximately with those
of airborne dust at low-latitudes. The fluxes decline when the dust events
settle down. The differences in latitudinal distributions between the two
cases reflect the types of the meridional circulation. During the equinoctial
MY34 storm, the upward branch of the circulation cell is in low latitudes, and
most of water enters the upper atmosphere near the equator. Rapidly increased
downward water fluxes in middle to high latitudes in both hemispheres (dark
blue shades) are due to the intensified returning branches of the two-cell
circulation. Both upward and downward fluxes gradually diminish, as the storm
declines. A similar but weaker pattern repeats later this year (around
$L_{s}=330^{\circ}$) during the minor equinoctial storm.

The development of the global MY28 storm was less rapid than the one in MY34,
and consisted of a series of minor storms, during which the meridional
circulation itself seasonally transited from the equinoctial two-cell to the
one-cell pole-to-pole type. It was initiated at $L_{s}=261.7^{\circ}$,
probably driven by a Chryse storm track flushing storm [Wang Richardson
(2015)]. The transition to solstitial circulation was accelerated by a
regional dust storm occurred around $L_{s}=220^{\circ}$ followed by another
one at $L_{s}=235^{\circ}$. Between $L_{s}=240-260^{\circ}$, Mars was free of
regional dust storm activity. The peak of the planet-encircling storm occurred
around the solstice ($L_{s}\approx 270^{\circ}$). The MY28 and 34 storms do
contrast somewhat, with lifting centered near 50∘S during MY28 compared to
MY34, where lifting centers were largely equatorial [Heavens, Kass Shirley
(2019), Heavens, Kass, Shirley, Piqueux Cantor (2019)].

Again, the distribution of vertical water fluxes reflects that of the
meridional circulation with the maximum of the updraft in high latitudes of
the southern (summer) hemisphere. The amount of water is usually much lower in
the winter hemisphere. However, Figure 4b shows very large downward water
fluxes there. They are the result of the combination of a) the dust storm-
enhanced downward motions and b) the increased concentration of vapor
transported from the southern hemisphere. Thus, the main channels, through
which water is delivered from the lower to the upper atmosphere coincides with
the location of the upward branch of the meridional circulation: in low
latitudes during equinoxes (MY34) and in high latitudes of the summer
hemisphere (MY28). A certain amount of water is returned back to the middle
and lower atmosphere by the global circulation cells, thus decreasing the
total amount of vapor in the upper atmosphere.

Having considered the general patterns of water transport during dust storms,
we now turn attention to the influence of GWs in this process. For that, we
examine the globally averaged differences in water vapor content from
simulations with and without GWs, which are shown with shades in Figures 4c
and 4d for MY34 and MY28, correspondingly. The net budget of water abundances
in these simulations is also shown in Figure 4. It is seen that the account of
GWs leads to up to 50 ppmv (in the global-mean sense) increase of water above
100 km during the initial phase (up to $L_{s}\approx 220^{\circ}$) of the MY34
dust storm. This represents up to 15% change of the total amount (Figure
4e,g). After that and up to the end of the storm, the decrease of a similar
magnitude (15-20% ) is seen above $\sim$120 km. The analysis shows that such
behavior is caused by water flux differences in low and middle latitudes, in
the first hand. During the initial phase of the storm, they are up to 15 ppmv
m s-1 larger, if the GW forcing is included. We also note the increase of
global water content between 40 and 70 km. Comparison with Figure 3e shows
that it occurs due to accumulation of vapor in the high-latitude regions.
Similarly, the globally averaged temperature differences (contours in Figure
4c) are the result of the GW-induced polar warming at these altitudes (see
also Figure 3f). Higher temperatures facilitate the vapor build-up by
preventing condensation. Contrary to that, the GW-induced cooling above 80 km
does not affect vapor directly due to the lack of nuclei and condensation.

Later in the season of MY34 (between $L_{s}\approx 220^{\circ}$ and 270∘), the
meridional circulation cell becomes flatter, and the influx of water from
below in low latitudes stops. This occurs first in the upper portion of the
model domain (above 120 km) and then spreads downward. The GW-enhanced
returning branch of the circulation cell in high latitudes of the northern
hemisphere facilitates the removal of water from the atmosphere above 120 km,
but this process affects the total amount to a lesser degree.

A sudden drop of water (compared to the run without GWs) above 100 km during
the gradual development of the MY28 dust storm precedes the rapid rise
afterwards (Figures 4f). This difference represents up to 25% change, which
can be clearly seen in Figure 4f,h. The reason for this GW-induced drop can be
found from analyzing the vertical fluxes in Figure 4b. Before approximately
$L_{s}=260^{\circ}$, the meridional circulation transitioned from the
equinoctial type to the global one-cell solstitial one. GW forcing enhanced
the downward part of the cell, thereby limiting the flow of water upward. With
the onset of the global storm around $L_{s}=270^{\circ}$, the circulation
reversed, and GWs enhanced the vertical water flux.

In summary, dust storm-induced changes in the meridional circulation are
primarily responsible for the enhanced upward water transport. GW forcing
plays a secondary but important dynamical role in modulating the circulation
and transport, thus affecting timing and leading up to 10-25% changes in terms
of the global water content in the upper atmosphere.

##  7 Comparison with ACS Observations

Simulations of water with the MPI–MGCM for MY28 have been previously validated
[Shaposhnikov . (2019)] by comparing with the data obtained from the Mars
Climate Sounder instrument onboard Mars Reconnaissance Orbiter (MCS–MRO)
[Heavens . (2018)]. In this section, we compare the simulations for MY34 with
observations performed by Atmospheric Chemistry Suite (ACS) onboard ExoMars
Trace Gas Orbiter. ACS is an assembly of three infrared spectrometers, two of
which - the near-infrared (NIR, 0.7 to 1.7 $\mu$m) and middle-infrared (MIR,
around 2.6 - 2.7 $\mu$m) channels were used for retrieving temperature and
water vapor [Fedorova . (2020), Belyaev . (2021)]. Figures 5a and 5c present
the latitude-altitude distributions of temperature and water vapor,
correspondingly, compiled from 638 measurements between $L_{s}=185^{\circ}$
and $267^{\circ}$. This interval covers the period of the MY34 major dust
storm. The MGCM data were selected in a similar manner to match the
spatiotemporal coverage of the ACS observations, and the averages are plotted
in Figures 5b and 5d. The individual profiles vary greatly over time in the
simulations, therefore we present also the plots composed of minimums (Figure
5e) and maximums (Figure 5f) from the selected bins.

It is seen that the model reproduces the observed temperature, generally,
well. This includes both values and latitude-altitude distribution.
Nevertheless, we note systematic temperature differences in the equatorial
atmosphere at $\sim$75 km. The local minimum in the data at $\sim$35 km at
30-45∘S and differences in the temperature structure near the north polar hood
can be caused by the small amount of ACS profiles on the observational
borders. Diagonal banding in the data and the model at mid-high altitudes
generally look similar.

The model also reproduces the observed large-scale latitudinal and vertical
structure of the water vapor, although the simulated abundances are larger
than the measurements. The agreement is much better for the lower water vapor
estimate (Figure 5e). Given the sensitivity of the hydrological model to
microphysics parameters, this can be related, in particular, to the prescribed
dust scenario. Both observations and simulations show less than 10 ppmv of
water between 20 and 30 km at polar regions. The maximum of abundances are
located around 50 km near the equator. Above that height (between 60 and 70
km), water vapor decreases in this region, but not at middle to high
latitudes, both in the observations and simulations. There are differences in
the vertical structure of temperature near the south pole, with distinct
diagonal pattern and a high altitude patch in the model that are present to a
lesser extent in the ACS data. Vertical bands of large water vapor abundances
in the model also are not present in the data, particularly at $\sim$60-80∘N.
Note, that these differences are located mostly on the observational borders.
The model predicts more vapor near the top of the domain. High volume mixing
ratios in the thin atmosphere still correspond to low concentration of
molecules. This is why the instrumental errors of ACS are large there. The
other potential source of differences can be the lack of a detailed water
photochemistry in the model, which is very complex in the upper atmosphere
[Stone . (2020)]. Inclusion of it in the MGCM would likely bring the simulated
water closer to the observations.

##  8 Summary and Conclusions

We have examined the hydrological cycle on Mars during two major dust storms
of MY28 and 34 using the MPI Martian general circulation model and
predetermined dust scenarios. A particular focus was on the impact of small-
scale gravity waves (GWs), which were accounted for in the model with the
nonlinear spectral parameterization [Yiğit . (2008), Medvedev . (2011)]. The
simulations further elucidated the mechanism of water transport to the upper
atmosphere by the meridional circulation - the so-called global water “pump”
[Shaposhnikov . (2019)]. Dust storms and GW forcing affect the circulation and
temperature and, thus, control the amount of water vapor in the thermosphere,
its subsequent photodissociation and escape of hydrogen to space. Although
changes in temperature and circulation are intertwined, their influence on
water is different in the lower and upper layers. In the lower atmosphere,
warmer air can sustain more vapor and facilitates its sublimation from the
reservoirs on the surface. In the upper atmosphere, the lack of nuclei
prevents condensation, and water can only be redistributed. The main findings
of this work concerning the impact of global dust storms and GWs on the water
cycle are summarized below.

  1. 1.

Water is transported above 80-100 km by the global circulation (advection),
with molecular diffusion playing virtually no role. The impact of the latter
grows with height, and can no longer be neglected above $\sim$120 km.

  2. 2.

The main channels, through which water enters the upper atmosphere, are
collocated with the regions of air updraft by the meridional circulation: in
low latitudes during the northern autumn equinox and in high southern
latitudes during perihelion.

  3. 3.

Dust storm-induced global circulation is the primary mechanism that enables
water penetration to the upper atmosphere.

  4. 4.

GW forcing plays an important role in shaping the distribution of water by
modulating the timing and intensity of the transport.

  5. 5.

Accounting for small-scale GWs contributes to changes in globally averaged
high-altitude water abundance of up to 10-25%.

  6. 6.

During the equinoctial dust storm (MY34), the GW forcing leads to a globally
averaged increase (by up to 50 ppmv) of water above 80 km in the beginning of
the storm, more rapid drop at the later stage, and accumulation of vapor in
polar regions of both hemispheres in the lower and middle atmosphere.

  7. 7.

During the solstitial major dust event (MY28), the impact of GWs intensifies
the effect of the storm by increasing the high-altitude water amount by more
than 50 ppmv (in the global mean sense). GWs can produce a similarly large
drop of water during the earlier stage of the storm.

The presented MGCM simulations and comparison with ACS solidify the concept of
the water “pump” mechanism of transporting vapor directly to the upper
atmosphere. Model simulations also provide finer details and predictions,
which can be later verified with observations, once more data become
available. Overall, our results highlight the wide-reaching implications of
the GW-induced large-scale circulation and its potential role in modulating
the distribution of water on Mars.

###### Acknowledgements.

The data supporting the MPI–MGCM simulations can be found at
https://zenodo.org/record/5749676 [Shaposhnikov . (2021)]. The most recent
model output can be accessed at https://mars.mipt.ru. The ACS MIR temperature
and water data are available at
http://exomars.cosmos.ru/ACS_Results_stormy_water_vREzUd4pxG/ [Fedorova .
(2020)] and https://data.mendeley.com/datasets/995y7ymdgm/1 [Belyaev .
(2021)], correspondingly. The MCS–MRO data are available at
https://atmos.nmsu.edu/PDS/data [MCS Data Archive (2021)]. The authors thank
Denis Belyaev of IKI for assistance with the observational data and helpful
discussions. The work was partially supported by the Russian Science
Foundation grant 20-72-00110.

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Figure 1: Latitude-altitude cross-sections of temperature and water vapor at
the beginning of the MY34 dust storm ($L_{s}=194^{\circ}-200^{\circ}$). (a, b)
Temperature (a) and water vapor (b) abundances simulated for the MY34 dust
scenario (contours) and differences between the MY34 and MY28 dust scenarios
(shaded). (c, d) Temperature (c) and water vapor (d) abundances simulated for
the MY34 dust scenario (shaded) and temperature measurements derived from the
Mars Climate Sounder (c, contours) [MCS Data Archive (2021)]. (e, f)
Temperature (e) and water vapor (f) abundances simulated for the MY28 dust
scenario (shaded) and temperature measurements derived from the Mars Climate
Sounder (e, contours). The simulation for MY28 corresponds to the low-dust
conditions, since the major storm has not started yet (see Figure 4).

Figure 2: The rate of change of water mixing ratio $\partial q/\partial t$ due
to advection (left column) and molecular diffusion (right column) based on the
corresponding terms from the continuity equation. The upper row is for a day
before the onset of the MY34 dust storm, and the lower one is for a day in its
midst. The contours show the characteristic time scales for advection and
diffusion. The units refer to Martian week/month/year. Note, that figures a, b
and c, d have different color scale.

Figure 3: Latitude-altitude cross-sections of the quantities simulated with
the MY34 dust scenario at the beginning of the storm
($L_{s}$=$194^{\circ}$–$200^{\circ}$). (a and b, color shades): Differences
between the runs with (“GW on”) and without (“GW off”) subgrid-scale gravity
waves for the simulated upward (a) and downward (b) water vapor fluxes. (a and
b, gray contours): Water ice (in ppmv) for the “GW on” and “GW off” runs,
correspondingly. (a and b, streamlines with arrows): The meridional stream
function for the “GW on” (a) and “GW off” (b) simulations. (c-d): Mean zonal
wind (m s-1, shaded) and GW drag (m s-1 sol-1, contours) for the “GW on” and
“GW off” scenarios, correspondingly. Differences between water vapor VMR (e)
and temperature (f) simulated in the “GW on” and “GW off” runs. All fields are
averaged zonally and over 10 sols.

Figure 4: (a, b) Latitude-seasonal cross-sections of the zonally averaged
vertical water vapor flux at 80 km (shaded) simulated with gravity waves (GW)
included and the IR optical dust opacity (black contours). (c \- h) Altitude-
seasonal cross-sections of the globally averaged differences (c, d) of water
vapor (shaded) and temperature (contours) between the simulations with (e, f)
and without (g, h) GWs. Left (a, c, e, g) and right (b, d, f, h) columns are
for the MY34 and MY28 dust scenarios, correspondingly (see section 2).

Figure 5: Latitude-altitude distributions of temperature (a) and water vapor
(c) derived from the Atmospheric Chemistry Suite (ACS) measurements [Fedorova
. (2020), Belyaev . (2021)]. The corresponding distributions derived from
simulations for the MY34 dust scenario (b, d, e, f). The ACS data and the
model output are averaged over available measurements between
$L_{s}=185^{\circ}-267^{\circ}$. The MGCM data are taken at the same
coordinates and local times as the measurements. The simulated water vapor
composed of diurnal minimums (e) and maximums (f) at the same locations as the
ACS data.