Carbon dioxide (

Mars is the second most studied terrestrial planet due to its similarity and
also differences to Earth. For example, Mars is half the size of Earth, has
two very exotic dwarf satellites, Phobos and Deimos, and has an orbital tilt
similar to Earth's, and it takes Mars nearly 1.9 Earth years to go around the
Sun, with a much larger eccentricity than Earth (Appendix

Because the mean Martian mesosphere is in general warmer than the
condensation threshold,

The next step in the attempt to explain the observations of high-altitude

Propagation of GWs into the thermosphere has been studied extensively for
Earth using idealized wave models

The structure of our paper is as follows: the next section describes the
methods utilized in this research, describing the MPI-MGCM, the whole
atmosphere GW parameterization, and the link between clouds and waves;
Sect.

We next describe the MGCM, outline the implemented whole atmosphere GW
parameterization, how it is linked to

The Max Planck Institute Martian General Circulation Model (MPI-MGCM)
calculates a three-dimensional time-dependent evolution of the horizontal and
vertical winds, temperature, and density of the neutral atmosphere by solving
the momentum, energy, and continuity equations on a globe. The present state
of the model is the result of incremental historical development. It contains
the physical parameterizations of the earlier versions

The simulations have been performed with the T21 horizontal spectral
truncation, which corresponds to

GCMs typically have resolutions insufficient for reproducing small-scale GWs.
Therefore, the influence of subgrid-scale GWs on the larger-scale atmospheric
circulation has to be parameterized. The parameterizations then estimate the
effects of unresolved GWs on the resolved, large-scale flow using first
principles. The vast majority of GW schemes have been designed for
terrestrial middle atmosphere GCMs

Physically based parameterizations usually rely on certain simplifications.
In the GW scheme applied here, information about wave phases is neglected,
while covariances, including the squared amplitude, are still evaluated. In
particular, the scheme calculates the vertical evolution of the vertical flux
of GW horizontal momentum,

Here overbars denote an appropriate averaging, the subscript

The available observational constraints on GW sources in the lower atmosphere
of Mars have been discussed in the work of

In the simulations to be presented, the vertical fluxes due to subgrid-scale
GWs (Eq.

As was described above, the GW parameterization calculates covariances of
wave field variables. Of particular interest is the amplitude of temperature
fluctuations

In the paper, we loosely call it the “probability of

To determine

After a multi-year spinup, the model was run for a full Martian year
(669 sols

Global annual mean temperature, and cooling by gravity waves and radiative
processes in carbon dioxide molecules.

Gravity waves can facilitate

Altitude–latitude distributions of the mean zonal mean fields
during vernal equinox
and northern summer solstice (aphelion):

Figure

Altitude–latitude distributions of mean zonal mean cloud
probability and gravity wave effects:

Figure

Seasonal variations of mean (i.e., daily and zonally averaged)
atmospheric fields.

Figure

Seasonal variations of cloud formation probability, GW drag, and
GW-induced temperature fluctuations:

Figure

We next investigate the seasonal variations of the simulated temperature and
wind in more detail by focusing on three representative altitudes in the
mesosphere and lower thermosphere: 80, 100, and 120 km. There are too few
observations at these altitudes to date to validate the simulations. The
exception is the temperature at

In the upper mesosphere (100 km, Fig.

Parameterized GW-induced temperature fluctuations (

In the upper mesosphere (100 km, middle row), GW-induced temperature
fluctuations increase, along with the GW drag imposed on the mean
circulation, and the cloud formation probability demonstrates a more
definitive correlation with the GW activity during all seasons. Cold pockets
occur more frequently at middle and high latitudes (

As mentioned in the description of the model, the

The vast majority of studies report on cloud observations in the Martian
mesosphere below

It is observationally challenging to determine the precise altitude of

There are certain disagreements between the modeled cloud formation
probabilities and existing observations at high altitudes (80 km and above).
In particular, the dayside observations of

One source of uncertainty in our simulations is the assumed degree of
supersaturation, which is currently

In all our simulations, only probabilities of GW-induced clouds were
calculated and, thus, no radiative effects of such clouds were taken into
account. Such radiative feedback has been considered, for example, in the
work by

An obvious candidate for explaining mismatches between the modeling and
observations is the specification of sources in the GW parameterization. In
the simulations, we assumed a globally uniform and constant-with-time
distribution of GW momentum fluxes. The magnitudes of the fluxes were chosen
from observations to capture the “background” effect of small-scale waves,
as described in detail in our earlier works

Finally, other limitations in the model can result in imperfections with the
simulated mean fields and, as a consequence, erroneous estimates of cloud
formation probability

We presented simulations with the Max Planck Institute Martian General
Circulation Model (MPI-MGCM)

Inclusion of effects of small-scale GWs facilitates

GWs lead to

Simulations reveal strong seasonal variations of GW effects in the upper mesosphere and lower
thermosphere with solstitial maxima: eastward GW drag peaks during the summer
solstices and westward GW
drag maximizes around the winter solstices with up to

Around the mesopause, GW-induced temperature fluctuations

Overall, GW temperature fluctuations substantially correlate with the cloud formation probability, in particular at middle and high latitudes in the upper mesosphere and mesopause region during all seasons.

Cloud formation exhibits strong seasonal variations larger than 30 %, with summer solstitial maxima at high latitudes in the mesosphere and around the mesopause.

The simulated seasonal variations of cloud probabilities in the mesosphere are in reasonable agreement with previous detections of two distinct mesospheric types of clouds, i.e., equatorial and mid-latitude clouds.

This study has shown that accounting for GW-induced temperature fluctuations
in the Martian GCM reproduces supersaturated cold temperatures in the upper
mesosphere throughout all seasons. GWs maintain globally cooler air, which is
necessary for ice cloud formation, and help to explain some features of the
observed seasonal behavior of high-altitude

This study also puts forward new questions. Are our results concerning
shaping the seasonal behavior of ice clouds model-specific? Can

Upon request, the data used for the publication of this research are available from Erdal Yiğit (eyigit@gmu.edu).

Mars demonstrates in terms of planetary parameters some similarities as well
as differences to Earth as summarized in Table

In planetary atmospheres, one “sol” refers to the duration of a solar day
on Mars. The length of a day is longer on Mars than on Earth. One Martian sol
is about 24 h and 39 min (i.e., 24.65 h), and thus slightly longer than an
Earth day. One Martian year is 687 days long or 669 Martian sols. Due to
different eccentricities of Mars and Earth, their distance can vary
significantly over the course of their orbital motion around the Sun. Martian
seasons are described by the solar longitude

Some key planetary parameters of Earth and Mars.

The solar distance designates the average distance from the Sun,
given in terms of AU

EY performed the simulations and wrote a substantial portion of the paper. ASM significantly contributed to writing and analysis of research results. PH contributed to the discussion of results.

The authors declare that they have no conflict of interest.

The modeling data supporting the figures presented in this paper can be obtained from EY (eyigit@gmu.edu). This work was partially supported by German Science Foundation (DFG) grant HA3261/8-1. EY was funded by National Science Foundation (NSF) grant AGS 1452137.Edited by: Petr Pisoft Reviewed by: two anonymous referees