EFFECTS OF OROGRAPHIC GRAVITY WAVE DRAG IN THE
MARTIAN ATMOSPHERE BY PARAMETERIZATION AND
GRAVITY WAVE-RESOLVING SIMULATIONS
A. Kling , NASA Ames/BAERI (alexandre.m.kling@nasa.gov), R. J Wilson, A. Brecht, M. Kahre, NASA
Ames, J. Murphy, NMSU, New Mexico, USA

Introduction:
Gravity or inertia-gravity waves are ubiquitous in
the Martian atmosphere [1, 2]. Gravity waves (GWs)
are described as orographic when they are excited by
an isentropic displacement of low-level winds that
encounter an obstacle (topography) or nonorographic when the source of the perturbation is
dynamic (e.g., convection, jet/front systems). In the
mesosphere and in the thermosphere, GWs may
break and interact with planetary waves, triggering
secondary waves [3, 4, 5] and dynamically alter the
circulation and thermal structure.
In principle, the effects of GWs could be incorporated into Mars Global Climate Models (MGCMs)
by explicitly resolving them and validating the results against extant observations, as can be done with
Mars’s baroclinic waves and thermal tides. In that
respect, some numerical studies have involved explicitly-resolved GWs with mesoscale local-area
simulations [6, 7], and “high-resolution” global modeling [8]. Because of their non-linear nature, short
vertical wavelength and small horizontal scale (few
10s-100s of km) GWs have remained challenging to
resolve explicitly on a global scale. It is therefore
generally more practical to parameterize GWs as
sub-grid scale processes using either orographic [9,
10] or non-orographic [11, 12, 13] numerical
schemes. In this study, we bridge the two methods
used to represent GWs in MGCMs by comparing the
parameterized and explicitly-resolving approaches
against each other, focusing at first on the orographic
waves since the source of these waves (displacement
of air flow over topographic surfaces) is most readily
understood.
Simulation set-up:
Orographic gravity wave drag scheme. The orographic scheme from Palmer et al. (1986) [14] is
used for the treatment of unresolved mountain waves,
and we summarize here the basics of its implementation. The variance of the unresolved orography to
the mean elevation is multiplied by the low level
winds (among other terms) to obtain the surface base
flux for the gravity wave. Working upward through
the atmospheric column, the stability of the layers
compared to the gravity wave is evaluated. When

saturation is detected (wave breaking occurs), momentum is transferred to the atmosphere in the form
of a deceleration tendency (drag in [m/s/sol]) that is
applied to both the zonal and meridional winds. The
implementation includes the wavelength-dependent
thermal damping rates from [15].
Grid set-up and mesosphere-specific physics. For
this study, we tested a set of varying horizontal resolutions ranging from ~3.75° to 0.25° and constant
vertical resolutions in the mesosphere ranging from 3
km to 800 m (60-520 layers). Hereafter we refer to
“Gravity-Wave Resolving Simulations” (GWRS) as
any simulation of horizontal resolution ≤ 1° and vertical resolution < 3 km in the mesosphere, and therefore suitable for resolving some of the GWs’ spectrum. For reference, a baseline grid set-up for the
MGCM would typically use ~3.75° of horizontal
resolution and vertical layers of increasing thicknesses, with a top layer on the order of 10 km thickness
at ~100 km. The CO2 15 µm cooling parameterization is adapted from [16] and dependent on temperature, CO2 density, and atomic oxygen density which
are self-consistently computed. The simulations do
not include UV-heating and molecular diffusion, so
while we place the model top at ~150 km to mitigate
wave reflection, we only focus on the 0-120 km domain for our analysis.
Treatment of aerosols. In the MGCM, the microphysics is sensitive to the physical time step, which is
in turn connected to the dynamical timestep and
therefore adjusted as the horizontal and vertical resolutions change. In order to isolate the effects of varying spatial resolution on the dynamics from radiative
effects due to aerosols, we use a simple prescription
for the aerosols that do not include water-ice or CO2
microphysics, nor their respective radiative forcings.
For the dust, we use the analytically prescribed
‘MGS’ scenario that is independent of the resolution
[17].
Evidence for GWs activity at refined horizontal and vertical resolutions:
We show here qualitative examples of resolved
GW activity. Figure 1 shows daytime vertical winds
at 80 km (shaded colors) above the Tharsis plateau
from a 0.25°/90 layers simulation at Ls 110°. Concentric waves are localized above Olympus Mons

and the Tharsis volcanoes, demonstrating that orographic waves are explicitly resolved and propagate
well into the mesosphere.

Nature of the dominant gravity waves during the
southern winter:
In Figure 3, we show the zonally-averaged temperature and winds at Ls 90° for a simulation at 3.75°
horizontal resolution and without the GW-drag parameterization. This simulation is used as our baseline case. MGCM simulations at this season are
known to be susceptible to a cold bias in southern
polar temperatures. [9]

Figure 1: Vertical winds at 80 km altitude show
concentric orographic waves in the Tharsis region.
In Figure 2, we apply a standard technique to retrieve wave features from the global outputs of the
GWRS: Temperature variances are retrieved from
the model outputs by subtracting an individual temperature profile to its low-order polynomial fit. The
detrended perturbations on the native pressure layers
are re-sampled on a uniform grid and a Fourier analysis using the Welch method is used to extract vertical wavenumbers and associated power spectral densities (PSD). Finally, resulting PSDs from individual
profiles are binned by region and altitudes of interest
(lower half of the mesosphere 0-50 km and upper
half 50-100 km). This procedure has been used in
observational studies for GW retrieval (e.g. radiooccultation [18, 19]) which offer opportunities for
model validation. Several features are accurately
captured by the GWRS. First, we note that the slope
of the PSD decreases with increasing vertical wavenumber (decreasing wavelength), which is consistent
with waves of shorter wavelengths being dissipated.
Second, we note that the PSD for waves in the upper
mesosphere (solid lines) are one order of magnitude
higher than in the lower mesosphere (dashed lines),
which is consistent with the growth in amplitude of
orographic and non-orographic GWs as they propagate upward.

Figure 2: Vertical wave spectrum as observed
from GWRS.

Figure 3 Reference zonal winds (shaded contours) and temperature (solid contours) from the reference 3.75° simulation at Ls 90°.
We computed the range for phase speeds of gravity waves originating from the surface at this season
(either of orographic source or other dynamic processes localized immediately near the ground) and
organized those into different latitude bins. This calculation tests for filtering of gravity waves harmonics
by the mean winds as they propagate upward and
shows the range of allowed phase speeds at any given height. Given that orographic waves have low
phase speeds (the source for the waves is the orography and therefore static), this calculation highlights
what type of waves may be expected throughout the
atmosphere. In Figure 4, it is seen that in the southern latitudes (bottom three graphs in the first column), low phase speeds are able propagate to altitudes 80-100 km whereas at the equator (top graph in
the first column) or in the northern latitudes (second
column), low phase speeds are filtered well before
they reach any significant altitude. Orographic gravity waves are therefore expected to have an impact
only in the southern hemisphere at this season.

Figure 4: Allowed phase speeds as a function of
height at Ls 90° for different latitude bins. Black
shades show forbidden domain and white shades
show low phase speeds. The red vertical lines show
the +/- 10 m/s domain as a reference.
Comparison of resolved and parameterized
GW drag:
The Palmer (1986) parameterization implemented in the MGCM uses a coupling factor as a tuning
parameter, effectively controlling the surface base
flux. Since a main application of GW drag schemes
is to alleviate biases in atmospheric temperature due
to unresolved waves, one approach is to tune the
schemes against available temperature observations
(e.g., Mars Climate Sounder). This is an indirect
approach in the sense that the output of the scheme (a
GWs-induced deceleration tendency in [m/s/sol]) is
adjusted based on its dynamical effects on the overall
temperature structure. It therefore requires aerosols
forcings and other physics to be well-enough represented in the MGCM simulation to be consistent with
the reference observations. GWRS offer an additional, and more direct, comparison point as the resolved
zonal wave-mean flow forcing ax= 1/ρ d(ρ u'w')/dz
[m/s/sol] can be directly compared against the output
from the parameterization.
In Figure 5, we compare the GW drag and its effect on the temperature structure for a 3.75° simulation with GW drag parameterization (top row) and
for a 0.25° GWRS with no parameterization. Both
cases are compared against the reference simulation
(3.75° with no GW parameterization, as shown in
Figure 3).

Figure 5: GW forcings in [m/s/sol] (left column),
and temperature difference (right column) against the
baseline simulation with no GW parameterization.
Top row is with the parameterization and bottom row
is with the GWRS.
Figure 5 shows good agreement between the
wave-mean flow forcings produced by the parameterization and those calculated from the GWRS in the
southern hemisphere at the 1-0.1 Pa level. The forcing has a negative sign implying that the effect is to
decelerate the circulation. In the northern hemisphere, the GWRS shows positive forcing (acceleration) which is not present with the GW parameterization, implying the mechanism at play is not orographic in nature. The dynamical effects for both the parameterization and the GWRS are consistent and on
the order of +20 K warming at the 1Pa level for the
southern pole. Adjacent cooling in the column at the
0.01 Pa level and warming in the order of +5 K at the
0.1 Pa level in the southern tropics are also consistent between the GWRS and the parameterization.
The GWRS shows additional forcings near the top of
the model which is not present in the parameterization. This indicates that a much richer spectrum of
waves is represented in the GWRS than can be accounted for in the parameterization, which is based
on a single wavelength.

Effect of orographic GWS drag on the climatology:
The agreement in the amplitudes for the wavemean flow forcings and the resulting dynamical effects on the temperature structure between the
GWRS and the parameterization suggests that the

parameterization is performing as intended. It is
therefore a convenient way to investigate the season
and location where orographic GW are prominent.
The calculation of allowed phase speed at Ls
270° (not shown) suggests that the northern winter is
the other main season when orographic gravity waves
are allowed to propagate to the upper mesosphere.
Figure 6 shows the GW forcings resulting from the
tuned parameterization at the 0.1 Pa level for an annual cycle. GW drag (as a decelerating effect) is
prominent at Ls 30-170° in the southern latitudes (50
S to 75 S) and in the northern latitudes (80 N) at Ls
200-300°.

Figure 6: Wave mean flow forcings [m/s/sol] at the
0.1 Pa level from the orographic GW drag parameterization.
It was found that the surface base flux for the orographic GWs does not show a strong correlation with
the observed drag at higher altitude (e.g., at 0.1 Pa in
Figure 6). This explains why GWs forcing by orographic waves is also observed during the northern
winter, while the northern plains are comparatively
mostly absent of orography: suitable conditions allowing for the upward propagation of GWs are more
important to wave growth than the amplitude of the
initial perturbation.
Conclusions:
GWRSs at sub-degree (1/4°) horizontal resolution with fine vertical structure (~100 layers) provide
a direct method to tune and validate subgrid-scale
parameterizations of wave-mean flow forcings due to
unresolved GWs. In this study, the resulting effect of
GWs on the temperature structure, namely a +20 K
dynamical warming of the southern pole at the ~1Pa
level is attributed to orographic gravity waves and is
remarkably consistent between the two methods at Ls
90°. GWRS are a promising method to fill observational gaps in the GW climatology as they offer a
comparison point to GW observations, such as radiooccultations [18] or remote sensing observations [2].
We foresee GWRSs as being insightful for the tuning
of non-orographic GWS subgrid-scale parameteriza-

tions, for those little is known about the sources of
those waves.

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