Aerosols and tides in the martian tropics during southern

hemisphere spring equinox from Mars Climate Sounder data

L. J. Steele, A. Kleinböhl, D. M. Kass and R. W. Zurek

Jet Propulsion Laboratory, California Institute of Technology, Pasadena,
California, USA.

Corresponding author: Liam Steele<EMAIL_ADDRESS>
## Key points

  * $\bullet$

Mars year 29 has large amplitude thermal tides in the tropics during southern
hemisphere spring equinox that are not seen in other years.

  * $\bullet$

Data in other years suggests there was a shift in the phase of the diurnal
tide to an earlier local time in MY29, due to early dust activity.

  * $\bullet$

Radiative cooling from water ice clouds at night causes increased downwelling
and stronger temperature inversions due to adiabatic warming.

## Abstract

We analyze Mars Climate Sounder temperature and aerosol data in the tropics to
study atmospheric tides and their relation to the dust and water ice
distributions. Our results from data covering Mars years (MY) 29–35 reveal
that MY29 has large amplitude non-migrating thermal tides during southern
hemisphere spring equinox that are not observed at the same local time in any
other year. It is the nighttime temperatures that are most perturbed compared
to other years, with strong temperature inversions at 35–55 km altitude.
Analysis of data at different local times reveals that the temperatures and
water ice clouds at 03:45 am in MY29 more closely resemble those at 05:00 am
in other years, suggesting there was a shift in the phase of the diurnal tide
to an earlier local time. This phase shift, and the large amplitude non-
migrating thermal tides, appear to be related to early dust activity. Two
early dust storms occurred in MY29 around the time there was upwelling over
the tropics, associated with the Hadley circulation, enabling the dust to be
transported to higher altitudes where it has a larger radiative influence. As
well as dust, water ice clouds are also found to influence the tidal
structure. Due to the interaction of non-migrating tides, water ice clouds
occur in two discrete longitudinal regions at night. The increased radiative
cooling results in increased downwelling above the clouds, leading to
increased adiabatic warming and a strengthening the temperature inversions.

## Plain Language Summary

Tides can cause oscillations in Mars’ atmosphere, just like they can cause
oscillations in the Earth’s oceans. The tides on Mars are caused by variations
in the heating of the atmosphere by the sun, and they can affect temperatures,
wind, pressure, and the transport of aerosols. We investigate these tides
using data from the Mars Climate Sounder instrument onboard the Mars
Reconnaissance Orbiter spacecraft. We find that while the daytime atmosphere
in different years is similar, the nighttime atmosphere in one particular year
- Mars year 29 - has a noticeably different structure. We determine that this
difference is due to a combination of the effects of both dust and water ice.
These aerosols cause regions of localized heating and cooling, which affects
the structure of the tides, and the circulation of the atmosphere.

##  1 Introduction

Thermal tides are global-scale oscillations of atmospheric temperature,
pressure and wind, which are sub-harmonics of a solar day. They are driven by
solar heating of the atmosphere and surface, and due to Mars’ thinner
atmosphere they play a much more significant role than on Earth. They can
influence surface pressure and wind, affect the transport of aerosols, and
propagate into the upper atmosphere (Zurek,, 1976; Wilson and Hamilton,, 1996;
Forbes,, 2002). Observations of thermal tides on Mars date back to the 1970s,
when data from Mariner 9 and the Viking landers and orbiters were analyzed
(e.g. Leovy et al.,, 1973; Zurek,, 1976, 1988; Conrath,, 1976; Leovy and
Zurek,, 1979; Leovy,, 1981; Wilson and Richardson,, 2000). Since this time,
orbiters and surface instruments have provided a wealth of data about the
tides.

Data from the Rover Environmental Monitoring Station (REMS) on board the Mars
Science Laboratory (MSL) are the most complete set of surface data since the
Viking landers. MSL is located near the equator within Gale crater, and the
tropics are a region with weather dominated by tides (Wilson and Hamilton,,
1996; Hinson and Wilson,, 2004; Hinson et al.,, 2008). REMS measurements show
that diurnal and semidiurnal tides in Gale Crater are highly correlated with
atmospheric opacity, with enhanced tidal amplitudes observed during the Mars
Year (MY) 34 dust storm (Guzewich et al.,, 2016, 2019; Viúdez-Moreiras et
al.,, 2019).

Vertical profiles of global atmospheric temperatures in the lower and middle
atmosphere (at altitudes below $\sim$80 km), particularly from the Thermal
Emission Spectrometer (TES) and Mars Climate Sounder (MCS) instruments,
provide a rich data set with which to analyze thermal tides. Such data,
covering multiple Mars years, have revealed the presence of migrating (sun-
synchronous) tides, as well as non-migrating tides that can move westward or
eastward, with zonal wavenumbers of 1–4 being most prominent (Banfield et
al.,, 2000, 2003; Lee et al.,, 2009; Guzewich et al.,, 2012; Kleinböhl et
al.,, 2013; Guzewich et al.,, 2014; Wu et al.,, 2015, 2017). Thermal tides
have also been detected in the thermosphere, with analysis of accelerometer
data from the aerobraking phases of Mars Global Surveyor and Mars Odyssey
revealing zonal wavenumber 2–3 patterns in density at altitudes of 100–160 km
(Keating et al.,, 1998; Withers et al.,, 2003; Wang et al.,, 2006). More
recently, Mars Atmosphere and Volatile EvolutioN (MAVEN) measurements have
been used to detect zonal wavenumber 1–3 structures at altitudes of up to 190
km (Lo et al.,, 2015; England et al.,, 2016; Stevens et al.,, 2017; Jiang et
al.,, 2019). MGS Radio Science measurements have revealed tidal effects up to
altitudes of 200 km (Bougher et al.,, 2004; Cahoy et al.,, 2006), while Mars
Reconnaissance Orbiter (MRO) radio tracking data have revealed zonal
wavenumber 1–2 patterns in density in the exosphere, at $\sim$250 km (Mazarico
et al.,, 2008).

Numerical simulations and classical tidal theory suggest that the zonal
patterns observed in the atmosphere are the result of thermal tides
propagating from at or near the surface. These tides are modulated by
variations in Mars’ surface properties (topography, thermal inertia and
albedo), the atmospheric dust loading, water ice clouds, and interactions
between planetary waves and tides (Zurek,, 1976; Conrath,, 1976; Joshi et
al.,, 2000; Forbes and Hagan,, 2000; Wilson,, 2002; Hinson and Wilson,, 2004;
Forbes and Miyahara,, 2006; Moudden and Forbes, 2008a, ; Moudden and Forbes,
2008b, ; Moudden and Forbes,, 2010, 2011). Eastward-propagating Kelvin waves
are found to be the dominant component for zonal wavenumbers $>1$ (Wilson,,
2000; Banfield et al.,, 2003; Withers et al.,, 2011; Guzewich et al.,, 2012),
as these are close to resonance in the martian atmosphere (Zurek,, 1988;
Wilson and Hamilton,, 1996).

For global temperature data from low polar orbiters, available at two local
times 12 hours apart ($\sim$2 am/pm for TES data and $\sim$3 am/pm for MCS in-
track data), the standard tidal analysis technique is to perform Fourier
analysis of the average and difference fields of the two local times (e.g.
Banfield et al.,, 2003; Lee et al.,, 2009; Guzewich et al.,, 2012). To date,
studies utilizing MCS data have only performed Fourier analysis on the in-
track measurements, observed in the direction of MRO’s orbital movement. MCS
also performed cross-track scanning, viewing the limb at 90° to the left and
right of the orbit trajectory, obtaining measurements between 1.5–3 hours
earlier and later in local time than the in-track measurements, depending on
latitude. Kleinböhl et al., (2013) used the cross-track data to study tides by
applying nonlinear least-squares fits to the time series data, but Fourier
analysis of the data, and investigations of the aerosol behavior, have not
been performed. We perform this additional analysis here, in order to
investigate the temporal behavior of thermal tides and their relation to
aerosols. In particular, we focus our attention on the tropics, as this region
was not analyzed in earlier studies.

##  2 Data and analysis method

MCS is a nine-channel limb radiometer on board MRO, with 8 mid- and far-
infrared (IR) channels and one visible/near-IR channel. Each channel consists
of 21 detectors, providing a radiance profile from the surface to $\sim$90 km,
with $\sim$5 km resolution (McCleese et al.,, 2007). The retrieval algorithm
inverts the radiance profiles to produce geophysical quantities, including
vertical profiles of temperature, dust and water ice extinction (Kleinböhl et
al.,, 2009, 2011, 2017). MCS typically observes the limb in the direction of
MRO’s orbital movement, producing in-track measurements. However, beginning in
MY30, and continuing through MY35, the observation strategy was modified to
also view the limb at 90° to the orbit trajectory, producing cross-track
measurements (Kleinböhl et al.,, 2013). Figure 1 shows how the local times of
the measurements vary with latitude. As the orbit moves from the equator to
$\pm$60° latitude, the time spanned by the earlier (blue) and later (red)
cross-track measurements increases from $\sim$2.7 hours to $\sim$6.2 hours.
For simplicity, and due to focusing on the tropics, when referring to local
times we will reference the equator-crossing local time.

Figure 1: Local time coverage of MCS in-track (green) and cross-track (blue,
red) measurements. Data are from MY30, LS = 185–190°.

In order to perform Fourier analysis on the MCS temperature retrievals, we
first binned the data spatially and temporally on the MCS retrieval pressure
levels. We binned the data by 15° in longitude, 5° in latitude and 5° in LS.
These values were chosen to ensure the majority of bins were filled with data,
but that bins were not too large that potentially interesting spatial and
temporal structures were missed. As Fourier analysis requires all longitudinal
bins at a given latitude and pressure level to be populated, bins with missing
data were filled using cubic spline interpolation. Interpolation was not
performed if two consecutive longitudes bins had missing data, or if more than
25% of the longitudinal bins had missing data. For the period we are
interested in (LS $\approx$ 180–360°) there are typically one or two
longitudinal bins in the tropics during the daytime that require
interpolation. Away from the tropics, and at most locations during the night,
interpolation is typically not required.

For the in-track data (green symbols in Figure 1), and the cross-track data at
earlier and later local times (blue and red symbols in Figure 1), binning
produced morning (am) and afternoon (pm) temperature fields, from which
averages and differences were created via:

$\displaystyle T_{\mathrm{ave}}$
$\displaystyle=(T_{\mathrm{pm}}+T_{\mathrm{am}})/2,$ (1) $\displaystyle
T_{\mathrm{diff}}$ $\displaystyle=(T_{\mathrm{pm}}-T_{\mathrm{am}})/2.$ (2)

For periods with only in-track data this resulted in one $T_{\mathrm{ave}}$
and one $T_{\mathrm{diff}}$ field, while for periods with in-track and cross-
track data there were three $T_{\mathrm{ave}}$ and three $T_{\mathrm{diff}}$
fields. Fourier analysis was then performed, in order to obtain the amplitudes
and phases of the tides. This assumes that at a given latitude and pressure
level, the temperature variation with longitude, $\lambda$, and local time,
$t_{\mathrm{LT}}$, can be expressed as

$\displaystyle T(\lambda,t_{\mathrm{LT}})$
$\displaystyle={\sum}_{s,\sigma}T_{s,\sigma}\cos[(s-\sigma)\lambda+\sigma
t_{\mathrm{LT}}-\delta_{s,\sigma}]$
$\displaystyle={\sum}_{s,\sigma}T_{s,\sigma}\cos(m\lambda+\sigma
t_{\mathrm{LT}}-\delta_{s,\sigma}),$ (3)

where $s=0,\pm 1,\pm 2...$ is the zonal wavenumber (with positive and negative
values denoting westward and eastward propagation respectively),
$\sigma=0,1,2...$ is the frequency, $m=|s-\sigma|$ is the satellite-relative
wavenumber, $T_{s,\sigma}$ is the amplitude of the tide and
$\delta_{s,\sigma}$ is the phase. A stationary wave has $\sigma=0$, while
diurnal and semidiurnal tides have $\sigma=1$ and $\sigma=2$, respectively.
Fourier analysis of $T_{\mathrm{ave}}$ and $T_{\mathrm{diff}}$ provides
different information on the tides present. For example, only even (odd)
values of $\sigma$ appear in the $T_{\mathrm{ave}}$ ($T_{\mathrm{diff}}$)
fields. Some thermal tides can propagate vertically in the atmosphere, while
others are trapped in the region of excitation. Additionally, thermal tides
can be decomposed into components which are symmetric or anti-symmetric about
the equator. (Forbes,, 1995; Banfield et al.,, 2003; Lee et al.,, 2009;
Guzewich et al.,, 2012, 2014, For more details see.)

When discussing various tidal components we will use ‘D’ and ‘S’ to denote
diurnal and semidiurnal tides, and ‘E’ and ‘W’ to denote eastward and westward
propagation, with the number following denoting the zonal wavenumber $s$. For
example, DE1 represents an eastward-propagating diurnal wavenumber 1 tide,
while SW2 denotes a westward-propagating semidiurnal wavenumber 2 tide.
Zonally-symmetric tides, which do not propagate eastward or westward and have
no zonal wavenumber, are represented by D0 or S0. Tides which propagate
westward with the apparent phase speed of the Sun (e.g. DW1 and SW2) are
called migrating tides, while the others are called non-migrating.

##  3 Results

###  3.1 Tide amplitudes

We first look at the amplitudes from the Fourier analysis of the
$T_{\mathrm{ave}}$ and $T_{\mathrm{diff}}$ fields. We focus on satellite-
relative wavenumbers m = 1–3, as these have the largest amplitudes in the MCS
data. After analyzing tides from different Mars years, it is clear that the
behavior in the tropics in MY29 around southern hemisphere spring equinox (LS
$\approx$ 160–200°) is different to other years, and is noticeable for the
appearance of tides with amplitudes $>5$ K. The atmosphere around this time in
MY29 was dustier than in other years observed by MCS due to two early local
dust storms (Wang and Richardson,, 2015). One storm originated in the northern
hemisphere at LS $\approx$ 143°, while another originated in the southern
hemisphere at LS $\approx$ 152°.

Figure 2 shows the m = 1–3 components of the $T_{\mathrm{ave}}$ and
$T_{\mathrm{diff}}$ fields for MY29, with the data averaged over LS =
180–200°, which is when the amplitudes in the tropics are at their largest.
The black contours overlain on the $T_{\mathrm{ave}}$ and $T_{\mathrm{diff}}$
fields show the m = 0 components. For $T_{\mathrm{ave}}$ this component is
mostly dominated by the time- and zonal-mean temperature (for which
$s=\sigma=0$), but will also have contributions from the sun-synchronous
semidiurnal tide, SW2, and possibly higher even-harmonic sun-synchronous
tides. For $T_{\mathrm{diff}}$ this component is mostly dominated by the sun-
synchronous diurnal tide, DW1, with additional contributions from higher odd-
harmonic sun-synchronous tides (Zurek,, 1976; Banfield et al.,, 2003; Lee et
al.,, 2009; Guzewich et al.,, 2012; Kleinböhl et al.,, 2013).

Figure 2: Amplitudes of the m = 1–3 components of the (a–c)
$T_{\mathrm{ave}}$, and (d–f) $T_{\mathrm{diff}}$ fields, averaged over LS =
180–200°, MY29. Black contours show the m = 0 component (10 K intervals for
$T_{\mathrm{ave}}$ and 2.5 K intervals for $T_{\mathrm{diff}}$), with dashed
lines representing negative values. Data are from in-track measurements at a
local time of 3:45 am/pm.

The tidal features in the mid- to high- latitudes have been discussed in
detail previously (Wilson and Hamilton,, 1996; Banfield et al.,, 2000, 2003;
Lee et al.,, 2009; Guzewich et al.,, 2012) so are not considered further here.
Instead we focus on tides in the tropics. In the $T_{\mathrm{ave}}$ fields
(Figure 2a–c), the regions of large amplitude tropical tides are located
between $\sim$1–5 Pa. As m progresses from 1–3, the vertical extents of these
regions increase, and they shift southwards in latitude, becoming centered on
the equator. In the $T_{\mathrm{diff}}$ fields (Figure 2d–f) the large
amplitudes all occur at a similar height, centered at $\sim$3 Pa, which
corresponds to a region of strong gradients in the diurnal tide (black
contours). They are offset north of the equator with relatively small vertical
extents, and the amplitudes decrease with increasing $m$. For m = 2 and m = 3
in both the $T_{\mathrm{ave}}$ and $T_{\mathrm{diff}}$ fields there are two
weaker tidal signatures below the main ones identified, at $\sim$25 Pa and
$\sim$300 Pa, which are centered more on the equator.

Figure 3: As Figure 2, but from MY30 cross-track measurements at a local time
of 5:00 am/pm.

Such large-amplitude tropical tides are not seen in the in-track measurements
in other Mars years (see Figure S1), but some similar tidal features do appear
when looking at cross-track measurements taken $\sim$1.5 hours later in local
time. Figure 3 shows the m = 1–3 components of the $T_{\mathrm{ave}}$ and
$T_{\mathrm{diff}}$ fields from MY30 cross-track measurements at local times
$\sim$5:00 am/pm. MY30 was chosen for comparison as it is representative of
the behavior seen in MY31–33 and MY35 in this LS period (MY34 experienced a
global dust storm around this time, so cannot be compared, Kass et al.,, 2019;
Kleinböhl et al.,, 2020, e.g.). Large amplitude tropical tides of 4–6 K appear
at this later local time in the m = 2 and m = 3 components of
$T_{\mathrm{ave}}$ (Figure 3b,c), and a smaller amplitude tide of 2–3 K
appears in the m = 1 component of $T_{\mathrm{diff}}$ (Figure 3d). These tides
appear in similar locations to those seen in the MY29 in-track measurements,
with again the $T_{\mathrm{ave}}$ amplitudes more vertically-extensive, and
the $T_{\mathrm{diff}}$ amplitude located in the region of strong gradients in
the diurnal tide.

As the tide amplitudes in the Fourier analysis are derived from daytime and
nighttime temperature measurements, we can also look at these two times of day
individually. The temperature distributions in the daytime are broadly similar
in MY29 and MY30 (see Figure S2), but the nighttime temperature distributions
are markedly different in MY29 compared to MY30. Thus, it is the nighttime
temperature structure which is responsible for the large amplitude tides seen
in the MY29 in-track data, and not in the MY30 in-track data. Figure 4 shows
the temperature and water ice cloud distributions, as a function of longitude
and altitude, from MY29 data at a local time of 03:45 am, and MY30 data at
three different local times (02:20 am, 03:35 am and 05:00 am). Data are
averaged between 0–10°N, as this latitude range contains large amplitudes for
all tidal components in MY29. Comparing the in-track data in both years, it is
clear that MY29 has prominent temperature inversions at 03:45 am between
$\sim$3–20 Pa (Figure 4d) which are not seen at 03:35 am in MY30 (Figure 4b).
The inversions are located between 15–90°W and 75–110°E, with the inversions
being strongest in the western hemisphere, where temperatures at 4 Pa are
$\sim$30 K warmer than in MY30. However, when looking at a later local time of
05:00 am in MY30 (Figure 4c), temperature inversions can be seen, and this
results in the appearance of the tropical tide signals seen in Figure 3. As
the temperature inversions in MY30 are not as strong as in MY29, and the
tropical tide amplitudes are weaker.

Figure 4: Temperatures (shaded) and the log of the water ice opacity per km
(contours) from (a–c) MY30 in-track and cross-track data at different local
times, and (d) MY29 in-track data. Ice opacity contours range from $-$3.6 to
$-$2.4, in steps of 0.3. Data are averaged between 0–10°N and LS = 180–200°.
(See Figure S3 for a similar plot of the shaded water ice cloud distribution.)

###  3.2 Tide structure

####  3.2.1 MY30 in-track data

To further investigate the differences between the tides in MY29 and MY30, and
the changes to the tides with local time in MY30, we look at the longitudinal
structure of the tides, in terms of their amplitudes and phases. We begin with
the tide structure from the MY30 in-track measurements, as this is similar to
all years other than MY29, and so is representative of the general behavior.
Figure 5 shows the m = 1–3 components of the amplitudes and phases of the
$T_{\mathrm{ave}}$ and $T_{\mathrm{diff}}$ fields, averaged between 0–10°N and
LS = 180–200°. Corresponding nighttime temperature and water ice distributions
are shown in Figure 4b. Stationary waves and semidiurnal tides are the most
likely contributers to the $T_{\mathrm{ave}}$ field, while diurnal tides are
the most likely contributers to the $T_{\mathrm{diff}}$ field. Higher
frequency tides (e.g. terdiurnal and quadiurnal) can also potentially
contribute, though these generally have smaller amplitudes and a less
significant impact on the observed tidal structure (Lee et al.,, 2009; Moudden
and Forbes,, 2014; Guzewich et al.,, 2016).

Figure 5: Amplitude and phase of the m = 1–3 components of the (a–c)
$T_{\mathrm{ave}}$, and (d–f) $T_{\mathrm{diff}}$ fields. Data are from MY30
in-track measurements at a local time of 3:30 am/pm, averaged between 0–10°N
and LS = 180–200°.

In terms of the $T_{\mathrm{diff}}$ field, the structure of the m = 1
component (Figure 5d) shows evidence for the zonally-symmetric diurnal tide,
D0, caused by the higher altitude topography of the Tharsis region. The weak
amplitudes and phase shift between $\sim$4–50 Pa are due to the effects of the
diurnal tide. This can be seen in Figure S1d, where the m = 0 component of
$T_{\mathrm{diff}}$ changes sign, signifying warmer temperatures at 3:30 am
compared to 3:30 pm. Outside of the tropics, where the diurnal tide behavior
changes and the amplitude of the s = 1 component of topography increases, the
D0 tide becomes stronger and extends up to $\sim$10 Pa. There is also evidence
of a westward-tilted tide, which is most likely DW2. This becomes more
prominent at latitudes polewards of $\sim$30°N (not shown), in tandem with the
increasing amplitude of the s = 1 component of topography.

The m = 2 component of $T_{\mathrm{diff}}$ (Figure 5e) shows evidence of a
tide with a long vertical wavelength that is tilted slightly eastward with
height, which is suggestive of the DE1 tide forced by the interaction of the
diurnal tide with the $s=2$ component of topography. (This tide is most clear
in MY33; see Figure S4e.) The DE1 tide has been studied extensively from the
surface to the upper atmosphere, with the earliest observations revealing its
presence during the 1971 global dust storm (Conrath,, 1976), and an
enhancement in the surface pressure signal in the Viking lander data during
the 1977 global dust storms (Leovy,, 1981; Zurek and Leovy,, 1981; Zurek,,
1988; Wilson and Hamilton,, 1996; Bridger and Murphy,, 1998). Analysis of
orbiter data and computer simulations have also revealed the presence of DE1
in the lower and middle atmosphere (Wilson and Hamilton,, 1996; Wilson,, 2000;
Banfield et al.,, 2000, 2003; Hinson et al.,, 2008; Guzewich et al.,, 2012,
2014) as well as its dominance high in the atmosphere (Wilson,, 2002; Wang et
al.,, 2006; Withers et al.,, 2011; Lo et al.,, 2015).

The m = 3 component of $T_{\mathrm{diff}}$ (Figure 5f) shows evidence for an
eastward propagating tide with a long vertical wavelength, which is most
likely DE2. There have been numerous studies of DE2, from the lower atmosphere
up to aerobraking altitudes where it is found to play a prominent role in the
density structure (Wilson,, 2000, 2002; Banfield et al.,, 2003; Wang et al.,,
2006; Withers et al.,, 2011; Guzewich et al.,, 2012; Moudden and Forbes,,
2014; Lo et al.,, 2015; Holstein-Rathlou et al.,, 2016). Superimposed on the
DE2 tide’s structure are regions of increasing and decreasing amplitudes,
which may be the result of the constructive and destructive interference
between DE2 and DW4, which is the most likely westward propagating tide. (This
DE2 and DW4 interaction is also clear in MY33; see Figure S4.) Analysis of the
phase tilts with height in Figure 5f, as well as in other years, suggests
vertical wavelengths of $\sim$3H for the westward-traveling wave and $\sim$9H
for the eastward-traveling wave (where H is the atmospheric scale height, with
each decade of pressure $\sim$2.3H), which are in agreement with the expected
wavelengths for the DE2 and DW4 tides (Wilson,, 2000; Hinson and Wilson,,
2004; Moudden and Forbes,, 2014; Guzewich et al.,, 2012). See Forbes et al.,
(2020) for typical vertical wavelengths of tides based on classical theory.
The phase structure near the surface is in agreement with the phase of the
$s=3$ component of topography.

The two eastward-propagating tides, DE1 and DE2, play a large role in shaping
the nighttime cloud distribution seen in Figure 4b. At 3:35 am there is a
region of clouds centered at $\sim$90°W, which extends from the surface to
$\sim$1 Pa and is tilted slightly eastward with height. There is a similar
region in the eastern hemisphere, though cloud opacities are slightly lower
here. These cloud regions occur at longitudes where the DE1 and DE2 tides
constructively interfere to decrease nighttime temperatures. Elsewhere,
temperatures remain too warm, resulting in the cloud-free regions. Where
clouds form, local radiative cooling will lead to further decreases in
temperature, and possibly further cloud formation, resulting in a positive
feedback. This increased nighttime cooling due to clouds is partly responsible
for the phase shift between 1–50 Pa in Figure 5e, which does not correlate
with the expected vertical propagation of the surface-forced DE1 tide. Another
factor contributing to the phase shift is the anti-symmetric component of the
tide (not shown) which tilts eastward with height and has a vertical
wavelength of $\sim$6.5H, corresponding to the first anti-symmetric component
of DE1 (Forbes et al.,, 2020). The anti-symmetric component is weaker than the
symmetric component, but its phase is shifted $\sim$60° to the east compared
to the symmetric component.

The nighttime clouds located at $\sim$90°W have larger opacities than those at
$\sim$90°E. One reason for this is likely due to the global atmospheric
circulation. Stationary waves play a large role in the transport of water away
from the subliming north polar ice cap, and the stationary waves over the
Tharsis region around southern hemisphere spring equinox tend to transport
humid air southwards, while those in the Arabia Terra/Isidis region tend to
transport drier air northwards (Steele et al.,, 2014). As such, the Tharsis
region generally has larger water vapor abundances (Smith,, 2002, 2004;
Maltagliati et al.,, 2011; Wolkenberg et al.,, 2011; Trokhimovskiy et al.,,
2015), and hence clouds are likely to be more abundant. Another factor may be
the effects of the D0 tide, which results in cooler nighttime temperatures due
to the higher topography of the Tharsis region (Banfield et al.,, 2003;
Guzewich et al.,, 2012).

In terms of the $T_{\mathrm{ave}}$ field, the phase structure of the m = 1
component suggests the presence of a tide with a westward phase tilt with
height (Figure 5a), with a vertical wavelength of $\sim$7H, possibly SW3. The
m = 2 component of $T_{\mathrm{ave}}$ (Figure 5b) is less organized, and the
changing amplitudes and phases with height suggest interference between
eastward and westward propagating tides. Analysis of the phase tilts with
height in other years, and at other latitudes in the tropics, suggests the
westward- and eastward-propagating tides have vertical wavelengths of
$\sim$2.5H and $\sim$4H respectively. It is not possible to identify the exact
tides present, but the most likely are S0 and SW4. Lo et al., (2015)
previously found evidence for S0 in upper-atmosphere MAVEN observations in mid
latitudes. The larger amplitudes between 10–30 Pa may be the result of the
radiative cooling associated with the nighttime clouds seen in Figure 4b. The
m = 3 component of $T_{\mathrm{ave}}$ (Figure 5c) shows a barotropic structure
above $\sim$10 Pa. This is likely the SE1 tide, which has previously been
observed in both the middle atmosphere (Guzewich et al.,, 2012) and upper
atmosphere (Wilson,, 2002; Wang et al.,, 2006; Lo et al.,, 2015).

####  3.2.2 MY30 cross-track data

Figure 6: As Figure 5, but for MY30 cross-track data at a local time of 5:00
am/pm.

Figure 6 shows tide amplitudes and phases in the same format as Figure 5, but
for MY30 cross-track measurements at a local time of $\sim$5:00 am/pm. As
noted earlier, the amplitudes of the m = 2 and m = 3 components of
$T_{\mathrm{ave}}$ (Figure 6b,c), and the m = 1 component of
$T_{\mathrm{diff}}$ (Figure 6d) increase when moving from 03:35 am to 05:00
am, and resemble those in MY29. The corresponding nighttime temperature and
water ice distributions are shown in Figure 4c.

At altitudes below 10 Pa, the m = 2 component of $T_{\mathrm{ave}}$ shows a
slight amplification of the tide structure that was present in the in-track
data (compare Figures 5b and 6b). This may be from sampling the same tide at a
different phase (due to the $\sim$1.5 hour time difference), but the increased
amplitudes also correlate with the regions of increased nighttime cloud
abundance in Figure 4c. Thus, there may also be a contribution from local
radiative cooling. Between $\sim$1–10 Pa, there is a region of large
amplitudes that appear in the cross-track data, but are absent in the in-track
data (peak amplitudes are $\sim$5 K at $\sim$4 Pa). This region shows a
$\sim$90° phase shift compared to the tide structure below. Comparing with
Figure 4c, this region of increased amplitudes corresponds to the appearance
of nighttime temperature inversions below $\sim$5 Pa.

The vertical structure of the temperature inversions is shown in Figure 7,
where temperature profiles from three different longitude regions between LS =
185–190° are plotted. (Figure S5 shows the locations of all detected tropical
temperature inversions.) Figure 7a shows profiles from a region where there
are no large temperature inversions below $\sim$1 Pa, and there is little
change in the temperature structure between 03:35 am and 05:00 am. In the
80–90°W and 60–70°E regions (Figure 7b,c), temperatures below $\sim$10 Pa
($\sim$40 km) have cooled between 03:35 am and 05:00 am, likely due to cloud
radiative effects (Hinson et al.,, 2014), with greater cooling at 80–90°W
where clouds are thicker. Above the tops of the inversions (above $\sim$5 Pa),
the temperatures can be seen to closely follow the adiabatic lapse rate,
whereas this is not the case at 160–170°W, where no inversions occur. The
local cooling by clouds, with associated warming above, suggests the increased
temperatures are the result of adiabatic warming due to downwelling, with
stronger downwelling and increased warming in regions with thicker clouds.
This was confirmed via analysis of Ensemble Mars Atmosphere Reanalysis System
data (see Appendix A). This area of adiabatic warming above the cooling cloud
region is the reason for the 90° phase shift at $\sim$10 Pa seen in Figures 6b
and 6e.

Figure 7: MY30 temperature profiles at 03:35 am (blue) and 05:00 am (red),
from three different longitude regions. Data are averaged between 0–10°N and
LS = 185–190°. The dashed black lines show the adiabatic temperature gradient
$g/c_{p}=4.5$ K km-1.

In terms of the m = 3 component of $T_{\mathrm{ave}}$, the phases are
essentially the same in the in-track and cross-track measurements (compare
Figures 5c and 6c), but the peak amplitude has increased from $\sim$3 K to
$\sim$6 K between 3:35 am and 05:00 am. This suggests the presence of the same
tide as before, SE1, with the larger amplitude the result of sampling the tide
at a different phase. The m = 1 component of $T_{\mathrm{diff}}$ (Figure 6d)
shows increased amplitudes between $\sim$3–8 Pa that appear associated with a
westward-tilted tide, with a vertical wavelength of $\sim$3.5H. This is in
agreement with the expected structure of the DW2 tide (Guzewich et al.,,
2012). The increased amplitudes correspond to a region of increasing cloud
abundance, so there is again likely a contribution from cloud radiative
effects. The remaining fields (the m = 1 component of $T_{\mathrm{ave}}$ and
the m = 3 component of $T_{\mathrm{diff}}$) do show changes to the tide
structure between the in-track and cross-track data, but no large amplitude
tides appear, and as such we do not discuss these components further.

####  3.2.3 MY29 in-track data

Comparing Figures 4b–d, the MY29 nighttime temperature and water ice
distributions at 03:45 am more closely resemble the MY30 05:00 am data, as
opposed to the MY30 03:35 data, despite the latter being closer in local time.
As the temperature and ice distributions are largely influenced by diurnal
tides, this suggests the early dust activity in MY29 has shifted the phase of
the diurnal tide to an earlier local time. Such a shift, as a response to
increased dustiness during global dust storms, has been noted previously in
modeling and observations (e.g. Wilson and Richardson,, 2000; Guzewich et
al.,, 2016). However, the early dust activity in MY29 did not produce large
dust optical depths like those experienced in global dust storms.

Figure 8: As Figure 5, but for MY29 in-track data at a local time of 3:45
am/pm.

The amplitudes and phases of the tides in MY29 between LS = 180–200° are shown
in Figure 8. There is a general eastwards shift in the m = 2 and m = 3 tide
phases compared to MY30 (Figure 5), which results in the clouds in Figure 4d
being located further east than in MY30 (Figure 4b,c). This phase shift
corresponds to an increase in the dust abundance of the low-lying planitias,
which shifts the largest column dust opacities eastward between LS = 150–170°.
The dust distribution then remains steady until LS = 200°, and correspondingly
the tide phases show little change during this time. There is also an increase
in the amplitudes of the westward-propagating tide components. These were most
prominent after the onset of the early dust activity, but began to decrease in
amplitude between LS = 150–170° as the dust lofted by the storm began
decreasing in altitude. Despite this eastward shift, the tide structure in
MY29 below $\sim$10 Pa generally resembles that in the MY30 in-track data
(Figure 5).

Figure 9: Temperature profiles from MY30 nighttime (green), MY29 nighttime
(blue), and MY29 daytime (red) in-track measurements. Data are shown for three
different longitude regions, and are averaged between 0–10°N and LS =
190–195°. The dashed black lines show the adiabatic temperature gradient.

As in the MY30 cross-track data, nighttime temperature inversions occur in
MY29, but these are much stronger than those in MY30, particularly in the
western hemisphere. Figure 9 shows individual temperature profiles from three
different longitude regions between LS = 190–195°, when the inversions are
strongest. (Figure S6 shows the locations of all detected tropical temperature
inversions.) Data are shown from 03:35 am in MY30, and 03:45 am/pm in MY29.
The daytime temperatures are similar in all three regions, as are the
nighttime temperatures above $\sim$1 Pa. In Figure 9a, where no large
temperature inversions occur below $\sim$1 Pa, the nighttime temperatures in
MY29 and MY30 are generally similar. In the 60–70°W region, which has the
strongest inversions (Figure 9b), the nighttime temperatures increase by
$\sim$25 K while ascending from 35–50 km. The coolest temperatures at the base
of the inversions at 35 km are $\sim$20 K cooler compared to the 150–160°W
region, and the warmest temperatures at 50 km are $\sim$25 K warmer. The
80–90°E region has weaker temperature inversions (Figure 9b), with peak
temperatures occurring at $\sim$45 km, compared to $\sim$50 km at 60–70°W.

As in the MY30 cross-track data at 05:00 am (Figure 7), temperatures closely
follow the adiabatic lapse rate above the tops of the inversions, suggesting
adiabatic warming due to downwelling. However, the temperature inversions are
much stronger in MY29 than in MY30, which suggests the diurnal and semidiurnal
tides have been strengthened in the regions with inversions. The diurnal and
semidiurnal tides have been observed to strengthen during global dust storms
(Leovy and Zurek,, 1979; Zurek,, 1980; Bridger and Murphy,, 1998; Guzewich et
al.,, 2016, 2019; Viúdez-Moreiras et al.,, 2019), while more recent studies
have revealed the semidiurnal tide is prominent all year, and is influenced by
the distribution of water ice clouds as well as dust (Kleinböhl et al.,, 2013;
Guzewich et al.,, 2016; Haberle et al.,, 2019). Due to the increased coverage
to lower altitudes compared to MY30 cross-track measurements, the temperatures
below the bases of the inversions in MY29 can also be seen to follow the
adiabatic temperature gradient (Figure 9b,c), showing that this is a region of
convective instability (Hinson et al.,, 2014). This instability may cause
water vapor (as well as dust and any other constituents present) from lower in
the atmosphere to be transported upwards, increasing the cloud opacity and
further strengthening the local cooling, leading to a positive feedback.

The nighttime temperature inversions in MY29 begin to appear at LS $\approx$
145°, and they strengthen and expand longitudinally until LS $\approx$ 200°
(see Figure S6), in tandem with a general warming of the atmosphere. The
increasing temperatures and longitudinal spreading of the regions with
temperature inversions suggest that dust is playing a role in their formation.
The dust abundance rapidly increases after the onset of the early dust
activity, but then the height of the dust top falls between LS $\approx$
150–170°, before slowly rising again after LS $\approx$ 170°. This more slow
rising is likely due to upwelling in the Hadley cells, as the twin Hadley cell
structure moves equatorward from the onset of the dust activity at LS
$\approx$ 143° to LS $\approx$ 200° (Steele et al.,, 2014). The increase in
dust height and opacity will lead to a strengthening of the diurnal and
semidiurnal tides, which can in turn impact the non-migrating thermal tides.
The inversions begin to decline between LS $\approx$ 200–210°, during which
time the circulation changes from a twin Hadley cell structure with upwelling
in the tropics to an equator-crossing Hadley cell.

As seen in Figure 2, apart from the m = 3 component of $T_{\mathrm{ave}}$, the
large amplitude tides in the tropics in MY29 are focused in the 2–5 Pa region,
and biased to the northern tropics, suggesting the tides are linked to a
similar forcing mechanism. Also, from the analysis of MY30 cross-track data at
local times of 05:00 am/pm, when the ice cloud distribution is a good match
for that in MY29, only the m = 2 and m = 3 components of $T_{\mathrm{diff}}$
show a large amplitude increase (Figure 3). This suggests that the dust
distribution in MY29 is playing an important role in strengthening the tides.
Indeed, water ice clouds have been shown to influence the semidiurnal tide
(Kleinböhl et al.,, 2013), which plays a key role in the structure of the
$T_{\mathrm{ave}}$ field. This is likely why the tides in the
$T_{\mathrm{ave}}$ field show an increase with local time in MY30, as the ice
cloud distribution changes over the $\sim$1.5 hour period, whereas the dust
does not. However, the $T_{\mathrm{diff}}$ field is affected mainly by the
diurnal tide, which is known to be sensitive to local dust loading (Leovy and
Zurek,, 1979; Bridger and Murphy,, 1998; Guzewich et al.,, 2016). This is
likely why the $T_{\mathrm{diff}}$ field shows stronger tides in MY29 compared
to MY30, as the atmospheric dust content was larger.

The m = 1 components of both $T_{\mathrm{ave}}$ and $T_{\mathrm{diff}}$ have
peak amplitudes at $\sim$30–40°W. This corresponds to a region of low-lying
topography to the east of the Tharsis plateau and south of Acidalia Planita,
but does not correlate to a region of high or low amplitudes in the s = 1
component of topography, ruling out surface forcing of the tides. However,
this region is a favored location for equator-crossing dust storms (Cantor,,
2007; Wang and Richardson,, 2015; Shirley et al.,, 2020), and the early dust
activity in MY29 occurred in this region. Due to the low-lying topography, the
column dust abundances here are larger, resulting in a stronger forcing of the
m = 1 components of the tide. The phase change at $\sim$3 Pa is related to the
nighttime warming associated with the stronger downwelling.

The tide structures in the m = 2 components of $T_{\mathrm{ave}}$ are similar
to those in the MY30 cross-track data (Figure 6b,e). The eastward tilt in the
$T_{\mathrm{diff}}$ field is from an anti-symmetric tidal mode (not shown),
with a wavelength of $\sim$6H. This is comparable to the first anti-symmetric
component of DE1 (Forbes et al.,, 2020). This anti-symmetric component exists
with a similar amplitude in all years, but in MY29 it constructively
interferes with the symmetric component, causing an amplification of the tide
above 10 Pa. The large-amplitude tide in the m = 3 component of
$T_{\mathrm{ave}}$ shows a westward phase tilt compared to MY30. The lower
atmosphere shows evidence for a westward-propagating wave with a vertical
wavelength of $\sim$3H, possibly SW5, which may be interacting with SE1 and
causing the observed tilt. The region of large amplitudes in the m = 3
component of $T_{\mathrm{diff}}$, centered at $\sim$3 Pa, appears to result
from an amplification of the westward-propagating DW4 tide, a weakening of the
eastward-propagating DE2 tide, or both.

##  4 Conclusions

The results of the Fourier analysis of MY29 in-track temperatures, at a local
time of $\sim$03:45 am/pm around southern hemisphere spring equinox, reveal
large amplitude non-migrating tides in the tropics that are not present in any
other Mars year observed by MCS. MY29 experienced early dust activity,
beginning at LS $\approx$ 143°, and the observed tides began to strengthen
after this dust activity, reaching their largest amplitudes at LS $\approx$
190°. Comparisons between daytime and nighttime temperatures show that it is
the nighttime temperature distribution that is most perturbed in MY29, with
strong temperature inversions located at $\sim$35–55 km in the 15–90°W and
75–110°E regions, though these regions expand eastward with time between LS =
185–200°. Due to this observed longitudinal spreading with LS, the temperature
inversions in MY29 appear to be related not only to the topography, but also
to the aerosol distribution.

While the temperature inversions and tides continue to strengthen until LS
$\approx$ 190° in MY29, the early dust storm activity ceased at LS $\approx$
157° (Wang and Richardson,, 2015). The continued strengthening of the tropical
tides, and the longitudinal expansion of the regions displaying temperature
inversions, suggests that dust continued to be transported equatorward and
vertically. This is plausible, as the twin Hadley cell circulation has its
upwelling branch over the tropics during southern hemisphere spring equinox.
Transport by the Hadley cell circulation, aided by thermal tides, has been
suggested as a mechanism for dust entering the northern jet and encircling
Mars during the MY34 global dust storm, which also occurred during southern
hemisphere spring equinox (Gillespie et al.,, 2020).

When analyzing MCS cross-track data in other years, taken at later local times
of $\sim$05:00 am/pm, some stronger tides do appear, notably in the m = 2 and
m = 3 components of $T_{\mathrm{ave}}$, where the tide structures resemble
those in MY29. The $T_{\mathrm{ave}}$ field can have contributions from
stationary waves, but the phases and inferred vertical wavelengths seem to
suggest that it is the semidiurnal non-migrating tides that are amplified at
later local times. In the case of the m = 3 component of $T_{\mathrm{ave}}$,
the amplification is likely due to sampling the eastward-propagating SE1 tide
at a different local time, with aerosols having little impact. For the m = 2
component of $T_{\mathrm{ave}}$, the tide amplification appears to be related
to the water ice cloud distribution. The radiative cooling associated with
regions of higher-opacity nighttime clouds causes stronger downwelling of the
air aloft, and increased adiabatic warming. The local cooling at cloud level
and warming above results in the appearance of nighttime temperature
inversions.

The nighttime cloud structure, which results in the strengthening of the
semidiurnal tide, is itself strongly influenced by the diurnal non-migrating
tides, particularly the combination of the eastward-propagating DE1 and DE2
tides. Where these tides constructively interfere to decrease nighttime
temperatures, clouds preferentially form, leading to increased radiative
cooling. Due to this cooling, the bases of the temperature inversions are
regions of convective instability, which could result in water vapor (as well
as dust and any other constituents present) from lower in the atmosphere being
transported upwards, increasing the cloud opacity and further strengthening
the local cooling, leading to a positive feedback.

Comparing different Mars years and different local times, it appears as though
the radiative influence of water ice clouds is impacting the semidiurnal non-
migrating tides in MY29 (and other years), while the large-amplitude diurnal
non-migrating tides in MY29 are influenced by the early dust activity. The
dust in MY29 was concentrated mostly in the northern tropics, which explains
why the large tide amplitudes are biased towards this region. The fact that
nighttime temperature inversions occur at earlier local times in MY29 (03:45
am) compared to other years (05:00 am) suggests there was a shift in the phase
of the diurnal tide to an earlier local time. Such a shift, as a response to
increased dustiness during global dust storms, has been noted previously in
modeling and observations (e.g. Wilson and Richardson,, 2000; Guzewich et
al.,, 2016).

While the early dust activity in MY29 did not produce large dust optical
depths like those experienced in global dust storms, the dust activity
occurred at a time when there was upwelling over the tropics, associated with
the Hadley circulation, enabling the dust to be transported to higher
altitudes where it has a larger radiative influence. The warmer tropical
temperatures associated with the dust led to a strengthening of the Hadley
circulation (as determined from the increased temperatures in the polar
warmings above both polar vortices), resulting in a positive feedback.
Combined with this increased vertical transport of dust, southern hemisphere
spring equinox is when the water vapor column abundances in the tropics reach
their largest value over the year (Smith,, 2004; Heavens et al.,, 2011;
Wolkenberg et al.,, 2011; Steele et al.,, 2014; Trokhimovskiy et al.,, 2015).
As such, water vapor is also available for transport, which can result in
increased cloud formation, which in turn can impact the tidal structure
through local radiative heating and cooling. The tide amplitudes and
temperature inversion strengths in MY29 begin to decrease after LS $\approx$
190°, in combination with a decrease in the dustiness of the tropics, a change
in the overturning circulation to an equator-crossing Hadley cell, and a
decrease in the water vapor abundance.

##  Appendix A Temperature inversions in EMARS data

In order to test the hypothesis that downwelling associated with the diurnal
tide can cause the temperature inversions observed in the MCS measurements, we
use Ensemble Mars Atmosphere Reanalysis System (EMARS) version 1.0 data
(Greybush et al.,, 2019) for MY29. This dataset results from the assimilation
of MCS in-track temperature profiles using a Local Ensemble Transform Kalman
Filter (LETKF; see Hoffman et al.,, 2010; Greybush et al.,, 2012; Zhao et
al.,, 2015), and is freely available at
https://www.datacommons.psu.edu/commonswizard/MetadataDisplay.aspx?Dataset=6171.
Dust and water ice tracers are advected by the model winds, and are
radiatively active. However, for dust there is a source/sink term in the
boundary layer that relaxes the model column opacities towards the dust maps
of Montabone et al., (2015). We use the ‘background’ files, which result from
1-hour forecasts initiated from the LETKF analyses, as the analysis files only
contain state variables and hence provide no information on the aerosol
distributions. We temporally interpolate the hourly data in each grid box to
obtain values at the same local time at each longitude.

Figure A1: EMARS MY29 simulation results of (a,d) temperature, (b,e) radiative
heating rate, and (c,f) vertical wind speed at 11:00 pm and 1:00 am. Data are
averaged between 0–10°N over LS = 180–200°. Black contours show water ice
opacity per km in log units, in steps of 0.5.

Nighttime temperature inversions exist in the EMARS dataset in the LS =
180–200° period, but they occur earlier in the night and lower in the
atmosphere compared to the MCS data. The inversions begin forming at around
$\sim$9:00 pm, strengthen the most between 11:00 pm and 1:00 am, and disappear
just after 3:00 am. The maximum temperature in the inversion over the Tharsis
region increases by $\sim$20 K between 11:00 pm and 1:00 am, while the
temperature minima below the inversion increases by $\sim$15 K. Figure A1
shows temperatures, radiative heating rates and vertical winds at 11:00 pm and
1:00 am. The heating rate is due to all gases and aerosols combined, as EMARS
does not split the contributions from different species. It is clear that
heating rates are negative everywhere below $\sim$1 Pa, resulting in a cooling
of the atmosphere. Thus, some other process must be responsible for the
increased temperatures in the inversions. At this time the vertical wind
speed, w, has negative values around the altitude of the inversions. This
indicates downwelling in the atmosphere, and is strongest in regions with
larger ice opacities. (Vertical winds were calculated from
$\omega=\mathrm{d}p/\mathrm{d}t$, as output by EMARS, by assuming hydrostatic
equilibrium.) The overall downward progression with time is associated with
the diurnal tide, which is amplified by the radiative influence of clouds
(Wilson and Richardson,, 2000; Wilson and Guzewich,, 2014). Due to compression
of the air as it moves downwards, its temperature increases due to adiabatic
warming (Hinson and Wilson,, 2004; Wilson and Guzewich,, 2014).

Figure A2: (a) Temperature change between 23:00 and 01:00 from EMARS MY29
simulation results, averaged between 0–10°N over LS = 180–200°. (b)
Temperature change obtained by taking the 23:00 temperature and applying only
the adiabatic dynamical heating from the vertical velocity. Black contours
show the change in water ice opacity, in units of 10-3 km-1

To investigate the potential warming caused by downwelling, we take the 11:00
pm temperatures, and using only the adiabatic temperature changes caused by
the vertical wind field (ignoring radiative heating or cooling) we calculate
new temperatures in 5 minute intervals until 01:00 am. We do this at each grid
point by using the vertical wind to determine the altitude of an air parcel 5
minutes earlier. We then interpolate the temperature profile to find the
temperature at this location, $T_{\mathrm{init}}$. Over the time interval
$\Delta t$ we then calculate the temperature change as $\Delta T=-w\Delta
tg/c_{p}$, assuming a dry adiabatic lapse rate of $g/c_{p}=4.5$ K km-1. The
new temperature at the grid point is then
$T_{\mathrm{new}}=T_{\mathrm{init}}+\Delta T$. The results, after two hours of
iteration, are shown in Figure A2. As can be seen, most of the temperature
changes that occur away from the surface between 11:00 pm and 1:00 am in the
EMARS data can be attributed to the adiabatic heating or cooling of the air in
response to the vertical winds. The temperature changes are slightly too large
in the Tharsis region as radiative cooling is not taken into account. Between
3:00–5:00 am the vertical wind around the cloud layer becomes positive, and
adiabatic heating ceases. Thus, it is likely that the large temperatures seen
in the inversions in the MCS data are the result of increased downwelling due
to stronger tides forced by cloud radiative effects.

## Acknowledgements

The authors are grateful to Jeffrey Forbes for fruitful discussions about
thermal tides, and to Sylvain Piqueux and Nicholas Heavens for helpful
comments on the manuscript. The data used here are freely available from
NASA’s Planetary Data System at
https://atmos.nmsu.edu/data_and_services/atmospheres_data/MARS/mcs.html. This
work was performed at the Jet Propulsion Laboratory, California Institute of
Technology, under a contract with NASA. Copyright 2020, California Institute
of Technology. Government sponsorship acknowledged.

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