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Corresponding author: A. Kleinböhl, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr., Pasadena, CA 91109, USA. (Armin.Kleinboehl@jpl.nasa.gov)
 Atmospheric thermal tides are global oscillations in atmospheric fields that are subharmonics of a solar day. While atmospheric tides on Earth are mainly relevant in the upper atmosphere, on Mars, they dominate temperature variations and winds throughout the atmosphere. Observations and model simulations to date have suggested that the migrating diurnal tide is the predominant mode in the Martian atmosphere, and that the semidiurnal tide is only relevant in the tropical middle atmosphere during conditions of high dust loading. New comprehensive observations by the Mars Climate Sounder in a geometry that allows coverage of multiple local times show that the semidiurnal tide is a dominant response of the Martian atmosphere throughout the Martian year. The maximum semidiurnal amplitude of ~ 16 K is found at southern winter high latitudes, which makes it the largest tidal amplitude observed in the Martian middle atmosphere outside of dust storm conditions. The semidiurnal tide can be successfully modeled due to recent advances of Mars General Circulation Models (MGCMs) that include the radiatively active treatment of water ice clouds. Tidal forcing occurs through absorption of radiation by aerosols and points to the vertical structure of dust and clouds and their radiative effects as being essential for our understanding of the thermal structure and the general circulation of the Martian atmosphere. As with terrestrial GCMs trying to quantify mechanisms affecting climate, future Mars modeling efforts will require microphysical schemes to control aerosol distributions, and vertically and temporally resolved measurements of temperature and aerosols will be essential for their validation.
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 In the context of a planetary atmosphere, tides are global oscillations in atmospheric fields like pressure, temperature, and wind that are subharmonics of a solar day. They are caused by changes in thermal forcing, driven by the migration of the subsolar longitude due to the rotation of the planet. Tides have the character of gravity waves that propagate vertically into the middle and upper atmosphere with their amplitude increasing with decreasing density. While atmospheric tides on Earth are mainly relevant in the upper atmosphere [Hagan, 2000; Hagan and Roble, 2001], on Mars, they dominate temperature variations and winds throughout the atmosphere [Zurek, 1976; Wilson and Hamilton, 1996; Banfield et al., 2000; Lee et al., 2009], and they can have a significant influence on the general atmospheric circulation [Hamilton, 1982; Zurek and Haberle, 1988; Lewis and Read, 2003]. In this work, we focus on the migrating thermal tide, which is zonally symmetric in a fixed local time reference frame [Forbes, 2004], in contrast to nonmigrating tide components, which occur through interaction with the zonal structure of planetary topography, thermal inertia, and albedo [Forbes and Hagan, 2000; Wilson, 2000; Wilson, 2002; Guzewich et al., 2012].
 In the following, we provide a brief review of the available observations of migrating tides in the middle atmosphere of Mars and their basic interpretation using models. We then use data from the Mars Climate Sounder (MCS) on the Mars Reconnaissance Orbiter (MRO) to show that, in contrast to our previous understanding, the semidiurnal tide is a dominant feature in the middle atmosphere of Mars throughout the Martian year. We compare the observed semidiurnal tidal structure to simulations by a Mars General Circulation Model (MGCM) and show that radiatively active water ice clouds (RAC) provide the most plausible explanation for the observed tidal structure. The connection between the semidiurnal tide and radiatively active water ice clouds points to profound implications concerning the influence of the vertical structure of aerosols and their radiative effects for our understanding and future modeling efforts of the Martian atmosphere. We discuss these implications.
2 Review of Observations of Migrating Tides
 On Mars, due to its comparatively thin atmosphere, most of the solar radiation reaches the surface, where it causes strong differences in temperature between day and night. Surface temperature maxima are typically reached at local noon or slightly later, while surface temperature minima are reached in the early morning between about 3 A.M. and 5 A.M. local time [Smith et al., 2004], depending on the thermal inertia of the surface. The heat flux from the surface causes changes in temperature and pressure in the lowermost atmosphere. The propagation of these changes gives rise to global oscillations in atmospheric pressure, temperature, and wind called atmospheric tides. Due to the nature of the forcing, the most prominent mode is the diurnal tide, although higher-order modes are also excited. Distributing the heating over a larger part of the atmosphere, e.g., due to suspended aerosol, strengthens contributions of the semidiurnal tide, which has a period of half a solar day. Due to its long vertical wavelength, it responds well to forcing that extends over a large altitude range [Wilson and Hamilton, 1996].
 Observations of the diurnal variations of the Martian atmospheric temperature that were recognized as signatures of the westward migrating diurnal tide go back to the infrared remote sensing measurements of the Mariner 9 and Viking missions [Hanel et al., 1973; Martin and Kieffer, 1979; Martin, 1981; Wilson and Richardson, 2000]. In addition, vertical oscillations observed in temperature profiles derived from the atmospheric entry of landers were attributed to the influence of the diurnal tide [Magalhães et al., 1999; Withers and Catling, 2010].
 Comprehensive measurements of diurnal temperature variations were made by the Thermal Emission Spectrometer (TES) on Mars Global Surveyor (MGS). The most valuable information concerning thermal tides stems from the aerobraking and science phasing period of observations. During this period, the orbit drifted with respect to local time, which allowed good sampling of the diurnally varying temperature structure. The diurnal thermal tide was quantified from these measurements to have a typical amplitude of order 4 K at altitudes up to 3–4 scale heights [Banfield et al., 2000]. During large dust storms, the amplitude was observed to exceed 8 K. The diurnal tide was also identified using the data obtained during the MGS mapping period, although only two local times were sampled due to the sun-synchronous orbit, which causes aliasing of higher-order modes into the diurnal response [Banfield et al., 2003].
 Recently, new studies of the diurnal tide have been enabled by MCS onboard MRO due to MCS' extended vertical range and improved vertical resolution. Using the output of the model by Richardson et al.  to expand the available MCS data, Lee et al.  found that the diurnal tide had an amplitude of 8.5 K at a pressure level of 2 Pa in the season around Ls = 150°, and that the highest amplitudes can reach up to 12 K in the equinoctial seasons. The diurnal tide in the Martian atmosphere has been shown to be well modeled by both classical tidal theory [Lindzen, 1970; Zurek, 1976] and Mars General Circulation Models (MGCMs) [Wilson and Hamilton, 1996; Wilson and Richardson, 2000; Lee et al., 2009].
 The observation of semidiurnal tides also goes back to the Viking era [Martin and Kieffer, 1979; Martin, 1981]. Wilson and Richardson  performed a reanalysis of Viking data in which they suggested a spectral leak in the 15 µm channel of the Infrared Thermal Mapper and showed that the observations were consistent with a semidiurnal tide in the tropical middle atmosphere if this effect was taken into account. While in a clear atmosphere, the diurnal tide was found to be dominant in the Martian tropics, the amplitude of the semidiurnal tide increased with increasing dust loading as solar heating is not confined to the surface anymore but becomes distributed over a larger part of the atmosphere. Based on a linear tidal model, Wilson and Richardson  suggested that the semidiurnal tide becomes the dominant component above moderate dust loadings (τ > 1). Components of the semidiurnal tide were also derived from TES data during aerobraking and science phasing [Banfield et al., 2000]; however, data are limited to the southern hemisphere, typically poleward of 20°S. A single fit suggested a maximum amplitude of the order of 8 K at low latitudes during the dusty season (Ls = 255–270°) at an altitude of 3–4 scale heights. In other regions and seasons, the semidiurnal component tended to be much smaller, typically around 1 K. The semidiurnal tide has also been modeled [Zurek and Haberle, 1988; Wilson and Richardson, 2000; Forbes and Miyahara, 2006]; however, significant contributions to the temperature structure of the middle atmosphere have always been associated with enhanced dust conditions.
3 Mars Climate Sounder Measurements
 Atmospheric temperature profiles were derived from observations made by MCS [McCleese et al., 2007], an infrared thermal emission radiometer on board MRO [Zurek and Smrekar, 2007]. MCS observes the Martian surface and atmosphere with eight infrared spectral channels and one visible/near-infrared channel. Each channel has a 21-element linear detector array. When pointed at the Mars limb, radiance profiles are measured simultaneously, from which vertical profiles of atmospheric temperature, dust, and water ice opacity are retrieved [Kleinböhl et al., 2009; Kleinböhl et al., 2011]. The retrievals give profile information up to ~ 80 km altitude with a vertical resolution of ~ 5 km.
 MCS typically views the forward limb in the direction of MRO's orbital movement (“in-track”), which leads to aliasing of higher-order tidal modes as MRO is in a sun-synchronous orbit. For this study, the observation strategy was modified to acquire coverage at additional local times. MCS uses its azimuth actuator to view the limb 90° “cross track” to the left and to the right with respect to the orbital movement or to view the limb “off-track” anywhere between 0° and 90°. For each additional azimuth angle, MCS observes one additional local time in the morning as well as in the afternoon part of the orbit. The cross-track measurement sequence alternates in-track and cross-track measurements in the following way:
 The local time pattern obtained by this sequence is shown in Figure 1. It results in six local time bins at low latitudes and mid-latitudes. At high latitudes, the observation sequence is modified to perform off-track measurements which provide coverage poleward of the cross-track direction as well as additional local times, typically yielding a total of seven or eight bins of local time.
 The observations were performed in campaigns of about 4 weeks duration, interspersed with periods of regular in-track scanning. Between September 2010 and May 2012, 11 campaigns were executed, covering one Mars year. Their time periods are given in Table 1.
Table 1. Cross-Track Observational Sequences Performed by the Mars Climate Sounder Between 2010 and 2012
Sequences 1–6 were performed in Mars year 30, while sequences 7–11 were performed in Mars year 31. Mars year is defined after Clancy et al. , with MY 1 beginning on 11 April 1955. Ls between 0° and 360° denotes the season on Mars with Ls = 0° being the beginning of northern spring/southern fall.
13 Sep 2010
11 Oct 2010
22 Nov 2010
20 Dec 2010
19 Jan 2011
28 Feb 2011
29 Mar 2011
25 Apr 2011
23 May 2011
20 Jun 2011
18 Jul 2011
16 Aug 2011
13 Sep 2011
10 Oct 2011
9 Nov 2011
6 Dec 2011
3 Jan 2012
30 Jan 2012
27 Feb 2012
26 Mar 2012
23 Apr 2012
21 May 2012
 To obtain zonal averages of temperature, measurements were separated by latitude. Data availability suggested that latitude bands of 5° width for latitudes poleward of 50°, 10° width for latitudes between 20° and 50°, and an equatorial band between 20°S and 20°N. Measurements in each latitude band were further separated by their local time. Measurements of the individual latitude bands and local time bins were averaged in bins of 30° longitude. Zonal averages were created for each latitude band at each local time by averaging the longitude bins at latitudes with no more than two unpopulated, nonadjacent longitude bins. This ensures an even longitudinal weight of the zonal average, which is important because of significant longitudinal variations in temperature due to nonmigrating tides [Wilson, 2000]. Temperature profiles were averaged on the pressure levels defined by the MCS retrieval, which have a spacing of one eight of a scale height [Kleinböhl et al., 2009].
 Figure 2 shows zonal mean atmospheric temperature and its deviation from the mean for the available local times in the latitude bands of 65°S–60°S and 20°S–20°N. Temperature deviation was calculated by subtracting a diurnally averaged temperature profile. Due to the gaps between morning and afternoon local times and the possibility of a different number of local time bins in the morning and the afternoon, this profile was created by first averaging the available morning and afternoon local time bins separately and then creating a diurnal average from the average morning and afternoon profiles. As the measurements in Figure 2 were taken during the southern winter season, a dynamically induced temperature maximum is found in the middle atmosphere in the southern high latitudes [McCleese et al., 2008; McCleese et al., 2010]. A strong semidiurnal signature can be seen between 5 and 0.1 Pa in southern high latitudes, characterized by temperature maxima around local midnight and local noon at higher altitudes, and somewhat later at lower altitudes. Equatorial latitudes exhibit a diurnal tide with a vertical shift in the phase that is consistent with a vertically propagating gravity wave, as suggested by theory [Zurek, 1976; Wilson and Richardson, 2000]. A temperature maximum around 0.65 sols (~3:30 P.M. local time) between 20 and 2 Pa, which is surrounded by lower temperatures toward local noon and later in the afternoon, also suggests a semidiurnal contribution in this altitude range. The longitudinal structure of the temperature fields (Figures 1 and 2 in supplementary materials) is dominated by a stationary wave at mid-latitudes [Banfield et al., 2003; Hinson et al., 2003; Guzewich et al., 2012].
 Harmonic contributions are analyzed by fitting the expression
to the local time dependence of the zonally averaged temperatures using a nonlinear least squares fit. Here T is the temperature, t is the local time, A0 corresponds to the diurnal temperature average, A1 and A2 are the amplitudes, and φ1 and φ2 are the phases of the wave 1 and wave 2 components, respectively. Note that with this definition, the phase corresponds to the first temperature maximum in local time for the considered wave. Fits were performed independently for each latitude band and each pressure level between 50 and 0.05 Pa (~ 25–75 km), when data of at least six local times were available. Examples of the temperature deviation calculated from these fits are given in the bottom panel of Figure 2.
 To estimate the error in the fit on each pressure level, fits to the local time dependence of temperature were performed with each zonal mean temperature perturbed by its standard error. The distribution of positive and negative perturbations was based on a power set. With typically six local time bins for each fit, 26 combinations of perturbations were investigated. The maximum deviation of any fitted quantity from the fit without perturbation is reported as error; hence, it has the character of a maximum error rather than a propagated standard deviation.
 Figure 3 shows the distribution of the analyzed tidal components for the observation sequence from Ls = 101°–114°. The diurnal tide is prominent in the tropics with amplitudes of 6–8 K, as has been inferred previously from MCS data [Lee et al., 2009]. It is vertically propagating as indicated by the phase variation, consistent with theory and modeling. There is a reversal in the phase variation with height between 0.5 and 0.2 Pa. Around 20°N–30°N, the diurnal tide in the middle atmosphere changes phase, as expected for this season, and shows the typical growth of the amplitude with height [Lee et al., 2009]. The amplitude of the semidiurnal component is fitted with a magnitude comparable to the diurnal component. The slow variation of the phase with altitude suggests a long vertical wavelength, consistent with classical tidal theory, which indicates that the migrating semidiurnal tide is dominated by a single Hough mode H2,2 with a broad meridional distribution and a long vertical wavelength [Wilson and Richardson, 2000; Forbes and Miyahara, 2006]. However, due to the uneven coverage in local time at low latitudes, an uncertainty of up to 5 K is estimated for the semidiurnal component in these regions (Figure 3 in supplementary materials). In the southern winter season, the semidiurnal tide is strong at pressures below 1 Pa south of ~50°S. The maximum tidal amplitude is hence located at a lower pressure than the temperature maximum in the polar winter region. The phase moves through about a third of a day between ~ 2 and 0.1 Pa, corresponding to a vertical wavelength of about 70 km.
 Figure 4 shows the results of the fits of the semidiurnal component for all seasons for latitudes of 65°S–60°S, 20°S–20°N, and 55°N–60°N. The semidiurnal tide at southern high latitudes is present between about 0° and 180° Ls. Maximum amplitudes of up to ~ 16 K are reached around Ls = 60°–90° at pressure levels between 0.5 and 0.2 Pa, with a maximum error of 1–2 K (Figure 4 in supplementary materials).
 At northern high latitudes, the semidiurnal tide is present during the other half of the Martian year (Ls≈ 180°–360°). The maximum amplitude of about 13 K is observed around Ls = 300°, with a maximum error around 2 K. However, higher amplitudes could occur closer to the pole, where steep horizontal gradients often prevent reliable retrievals [McCleese et al., 2010]. The tidal maximum seems to occur at slightly lower pressures than in the south. The phase of the tide is comparable to its southern counterpart.
 In the equatorial region, semidiurnal amplitudes consistently reach 6–8 K in the lower middle atmosphere between 10 and 1 Pa. The error in these amplitudes can reach 4–5 K due to the sparse local time coverage of the observations. However, the presence of the semidiurnal component is persistent throughout the Martian year.
4 Model Comparisons
 Mars General Circulation Model (MGCM) results published in literature do not suggest a significant semidiurnal tidal component outside of dust storm conditions [Wilson and Richardson, 2000; Lee et al., 2009]. To investigate its source, we employ the Geophysical Fluid Dynamics Laboratory (GFDL) MGCM, which has been extensively used to examine tides and planetary waves [Wilson and Hamilton, 1996; Wilson, 2000, 2002; Hinson et al., 2003] and cloud radiative effects [Hinson and Wilson, 2004; Wilson et al., 2008]. The model is run with a horizontal resolution of 2.8° × 2.8°. The vertical dimension is represented by a hybrid sigma/pressure grid with 36 vertical layers extending to 0.004 Pa (~95 km). The model includes surface and subsurface physics which allow the calculation of realistic surface temperatures; a budget for gaseous and condensed CO2 which yields a realistic annual cycle of global atmospheric mass, solar, and infrared radiative transfer for gaseous CO2 and atmospheric aerosols; and aerosol transport which allows for a self-consistent simulation of the aerosol distribution [Greybush et al., 2012].
 The model employs a water ice cloud microphysical scheme [Montmessin et al., 2004], which transports cloud ice mass and predicts a spatially varying mean cloud particle size. In order to explore the radiative impact of the clouds, we have included a scaling constant (CR) that determines the cloud opacity seen by the radiation code, and so it is straightforward to switch between simulations with radiatively passive (CR = 0) and radiatively active clouds (CR > 0). We have considered two key simulations to aid in the interpretation of the MCS observations. For the baseline model configuration, the vertical distribution of dust varies spatially and temporally due to advection in the model, but the column amount is tied to a column dust opacity corresponding to that observed by MGS TES between Ls = 150° in MY 24 and Ls = 150° in MY 25 [Greybush et al., 2012, scenario “TES dust” and Figure 9]. In the baseline simulation, clouds are radiatively passive. The other simulation differs only by the presence of radiatively active clouds (RAC). The model tends to overpredict water ice cloud opacity, so we have reduced the cloud opacity in the radiation code by setting CR = 0.5. This strategy of adjusting the radiative impact of the simulated clouds is adequate to explore the impact of radiative forcing on middle atmospheric temperatures.
 Figure 5 shows simulations of the local time variation of temperature anomaly in the two latitude bands shown in Figure 2. Temperature anomaly was calculated by subtracting a diurnally averaged profile created from the evenly spaced model output in local time. In the case where RAC is turned off and tidal forcing is mostly caused by solar heating of the surface and by direct solar heating of dust suspended in the atmosphere, no significant tidal activity is present at high latitudes. In the tropics, the temperature field is dominated by the diurnal tide. In the case with RAC, water ice clouds that form above dust (between ~ 300 and 10 Pa, Figure 5 in supplementary materials) are treated as radiatively active, hence they provide additional forcing within the atmosphere principally by absorbing upwelling longwave radiation emitted from the surface. At high latitudes in the winter hemisphere, there is a prominent semidiurnal tide with a strong phase advance with height above 10 Pa, in general correspondence with the observations. This is not a direct response to radiative forcing, which maximizes in the tropics of the summer hemisphere. The hemispheric asymmetry is much more pronounced than suggested by Forbes and Miyahara  and is likely related to the effect of background zonal mean winds. The simulated tropical response shows a significant semidiurnal tide, though the amplitude of the semidiurnal component in the lower atmosphere (50–10 Pa) is weaker than suggested in Figures 2 and 3 (see Figure 6 in supplementary materials). However, the model semidiurnal tide of ~4 K is consistent with the measured amplitude of 6–8 K after taking the measurement uncertainty of 4–5 K into account. By contrast, the baseline simulation yields a tropical semidiurnal amplitude of 1–2 K.
 The identification of a relatively strong tropical semidiurnal response is a surprise and can only be understood in the context of revising our understanding of the distribution of radiatively active aerosols in the tropics. MGCM modeling is very consistent in that vertically well-mixed dust cannot produce a tropical tide amplitude above 2 K, except for very dusty conditions [Wilson et al., 2008], which were not observed during the time period studied here and which would be particularly untypical for the southern winter season [McCleese et al., 2010]. To investigate the influence of isolated dust layers, as suggested by recent MCS observations [Heavens et al., 2011], sensitivity studies were carried out without RAC but with a parameterization of an equatorial dust layer centered around 30–50 Pa. Simulations with dust layer opacities sufficient to force a semidiurnal tide response comparable to the one observed tended to yield unrealistically warm temperatures around 10–50 Pa (not shown). In contrast, water ice clouds with a large vertical extent in the middle atmosphere have been recently observed by MCS [Heavens et al., 2010] and provide a viable source for the tidal forcing. Although dust layers could provide an additional contribution to the forcing, our sensitivity studies suggest that water ice clouds are more effective in producing the observed semidiurnal tide. The modeled semidiurnal tidal amplitudes are largely consistent with the tidal fits performed by Banfield et al. , which were not understood at the time, and were significantly larger than could be accounted for by dust forcing.
 The thermal influence of radiatively active water ice clouds causes various phenomena, among them, nighttime anomalies in tropical surface temperatures [Wilson et al., 2007]. RAC has been shown to improve modeling of the vertical temperature structure of the atmosphere [Madeleine et al., 2012; Greybush et al., 2012], in particular in the equatorial region during the aphelion season [Hinson and Wilson, 2004; Wilson et al., 2008]. Wilson  shows that RAC improves the simulation of the tropical temperature structure seen in MCS data.
 This work shows that the semidiurnal tidal forcing of radiatively active water ice clouds affects the temperature structure of the Martian atmosphere globally. Due to its long vertical wavelength, the semidiurnal tide not only influences the temperature in the middle atmosphere but is also expected to influence the density of the upper atmosphere [Bougher et al., 1993], a region soon to be investigated by the Mars Atmosphere and Volatile Evolution mission [Mitchell, 2010]. As cloud distribution in the Martian atmosphere is modulated by tides [Hinson and Wilson, 2004; Lee et al., 2009; Benson et al., 2010; Wilson, 2011], this leads to a feedback loop between clouds and tidal response. Atmospheric tides and their forcing have a significant influence on the atmospheric circulation [Hamilton, 1982; Zurek and Haberle, 1988; Lewis and Read, 2003]. Including RAC into the model strengthens the overturning meridional circulation and raises the temperature maximum in the polar winter middle atmosphere (Figure 6 in supplementary materials), which addresses a deficit in MGCMs pointed out by MCS observations [McCleese et al., 2008]. Future modeling efforts will require the distributions of cloud and dust to be controlled with detailed microphysical schemes for accurately modeling the tidal field and hence the global temperature structure and general circulation of the Martian atmosphere. This is comparable to the current challenges faced by terrestrial GCMs, which require modeling of cloud and aerosol microphysics to quantify effects on climate [Bollasina et al., 2011; Booth et al., 2012].
 In turn, the tide is a sensitive measure of the vertical distribution and temporal variation of aerosol forcing on Mars, with zonal wind fields also playing a role in influencing the global tidal response, as suggested by Wilson and Hamilton  and Takahashi et al. . Future measurements of the tidal structure by MCS in Mars years with different aerosol loadings are expected to give more detailed insight into the interactions between the vertical structure of aerosols and the atmospheric temperature field and will provide valuable information for improving MGCMs. Future missions with instrumentation for atmospheric investigations of the red planet should consider orbit geometries that allow coverage of multiple times of day to enable more comprehensive studies of the diurnal variations of the atmospheric temperature field and the distribution of cloud and dust aerosols.
 We are grateful to the MRO spacecraft team for keeping the MRO spacecraft alive and healthy and to the MCS instrument operations team for implementing and executing the MCS cross-track measurements. The contribution of R. J. W. was funded by the NASA Planetary Atmospheres Program. Work at the Jet Propulsion Laboratory, California Institute of Technology was performed under a contract with the National Aeronautics and Space Administration. The Editor thanks Jim Murphy and an anonymous reviewer for their assistance in evaluating this paper.