The Mars Express Radio Science Experiment (MaRS) investigates the lower and middle atmosphere of Mars between the surface and about 40 km with a very high vertical resolution. More than 600 profiles of temperature, pressure, and neutral number density were retrieved between 2004 and 2011 covering four Martian years (MYs 27–30). Radio occultation experiments provide the unique possibility to retrieve geopotential height information to supplement temperature values. The temperature field in the northern winter hemisphere displays strong temperature inversions indicating a pronounced polar warming in the northern polar night (MY 27). The temperature and geopotential fields imply the presence of a strong zonal jet, with peak wind speeds of more than 170 m/s at an altitude of about 30 km (~15 Pa) and a latitude of 60–65°N. The longitudinal temperature and geopotential fields in the southern winter of Martian year 30 at latitudes between 49° and 69°S are dominated by a stationary zonal wave s = 1 structure in the lower atmosphere. Associated meridional wind fields retrieved by assuming geostrophic balance have amplitudes up to 12 m/s at the 200 Pa level. An investigation of small-scale atmospheric waves reveals enhanced gravity wave activity in the daytime atmosphere above elevated terrain and in the winter extratropics. Radio occultation experiments also provide unique insight into the structure of the planetary boundary layer. The deepest convective boundary layers, up to 10 km, are found over elevated terrain.
 The exploration of planets using radio occultation measurements began with the flyby of the Mariner 4 spacecraft in 1965 [Kliore et al., 1965]. This mission introduced the use of radio science observations to obtain highly accurate profiles of temperature, pressure, and number density in the neutral atmosphere and profiles of electron density in the ionosphere of other planets. The Mariner 5, 6, and 7 missions improved the capabilities of this method [Fjeldbo et al., 1971; Kliore et al., 1969; Anderson et al., 1970]. Since then, radio science observations have been viewed as an essential component of almost all planetary flyby and orbital missions.
 Important subsequent observations of the Mars atmosphere were conducted by the Mariner 9 spacecraft [Kliore et al., 1972, 1973] and the Viking orbiter [Lindal et al., 1979; Fjeldbo et al., 1977; Simpson and Tyler, 1981].
 The most comprehensive data set to date is that obtained by radio science observations with Mars Global Surveyor (MGS) which carried out more than 21,000 occultations of the neutral atmosphere [Tyler et al., 1992; Hinson et al., 1999; Tyler et al., 2001]. These observations contributed significantly to the investigation of planetary wave phenomena [e.g., Hinson, 2006; Hinson et al., 2001, 2003; Hinson and Wilson, 2004].
 The ESA Mars Express spacecraft (MEX) was launched on 2 June 2003 and has orbited Mars since December 2003. Mars Express is in a highly elliptical polar orbit of inclination 86° and an apoapsis altitude of more than 10,000 km. The orbital period of 7.5 h in the first 440 days was reduced to 6.7 h for the remainder of the mission.
 The Mars Express Radio Science Experiment (MaRS) uses the radio subsystem on the spacecraft along with terrestrial tracking antennas to conduct a variety of observations. Radio occultation experiments are performed in a “two-way” mode of communication. The transmitted uplink X-band signal (at 7.1 GHz) is received by the spacecraft, coherently converted to two frequencies at X-band (8.4 GHz) and S-band (2.3 GHz), and transmitted to Earth. A single hydrogen maser on the ground serves as the frequency reference for the signals sent to and received from the spacecraft. The received signals are recorded routinely at the ESA ground stations in New Norcia, Australia, and at the tracking complexes of the NASA Deep Space Network. A detailed description of the MaRS experiment can be found in Pätzold et al. .
 In the remainder of this paper, following an introduction to the method, section 2, and the data set, section 3, we provide specifics as follows:
Section 4 investigates the global structure of the lower and middle atmosphere, focusing on latitudinal (section 4.1) and longitudinal (section 4.2) atmospheric phenomena like zonal winds in the northern and southern hemispheres and stationary wave structures in the southern hemisphere.
Section 5 analyzes the vertical fine structure of the lower atmosphere focusing on the occurrence of gravity waves in the low-latitude range.
Section 6 provides new results of the convective boundary layer (CBL). Correlations between the topography and the depth and structure of the CBL are examined.
2 Radio Science Observation Method
 Radio occultation observations are obtained during those times when the MEX orbit carries the spacecraft behind the planet as seen from the Earth. During such events, radio signals traveling from MEX to ground tracking stations pass through the atmosphere twice, once as the spacecraft moves behind the planetary disc and again as the spacecraft reappears from behind the opposite limb. Radial variations in the refractivity of the atmosphere lead to changes in the path geometry of the radio link. The associated phase delays lead to a frequency shift of the radio carrier signal which is used to calculate the refractive bending angle and ray periapsis. These parameters are used to calculate the refractivity profile of the atmosphere and ionosphere via the Abel transform [Fjeldbo et al., 1971].
 The neutral number density n of the atmosphere is directly proportional to the refractivity profile μ(z):
with a constant factor, C1, depending on the atmospheric composition, the altitude, z, and the Boltzmann constant, k. The constant C1 has a value of 1.306 × 10−6 K·m2/N [Essen and Froome, 1951] assuming a well-mixed standard atmosphere with 95.3% CO2, 2.7% N2, and 1.6% Ar.
 Atmospheric pressure is inferred from the number density. Assuming hydrostatic equilibrium [Eshleman, 1973; Hinson et al., 1999; Ahmad and Tyler, 1998],
where is the mean molecular mass of the atmosphere (≈7.221 × 10−26 kg), and g(z′) is the gravitational acceleration. Boundary conditions, n0, T0, and z0, terminate the profile above the sensible atmosphere. The required upper boundary condition of the temperature profile, T0, is inserted at a pressure level of 5 Pa. The temperature profile follows from the ideal gas law,
 Figure 1 shows a typical temperature profile obtained in the high northern latitudes. Retrieved profiles cover the altitude range from a few hundred meters above the surface, where the profiles are diffraction limited, to about 40–50 km. The standard deviations of the temperature at the upper boundaries of the retrievals are in the range of ≤10%. The accuracy increases with decreasing altitude reaching uncertainty values near the surface of fractions of a Kelvin (~1 Pa). The vertical resolution of this profile, about 500 m, surpasses the performance of conventional atmospheric sounders by an order of magnitude [Smith et al., 2001a; McCleese et al., 2010].
3 The Data Set
 Figure 2 shows the spatial distribution of the occultation points—the projections of the closest approach of the radio link on the Martian surface at a geometrical occultation entry point—as a function of latitude and longitude. The dependence on the use of ground tracking stations to provide a stable signal limits the number of observations. The orbital geometry and the restriction of the observations to occultation ingress favor the accumulation of occultation measurements in the northern hemisphere of the planet. More than 600 atmospheric profiles were retrieved in the 12 occultation seasons between 2004 and August 2011. To date, the MaRS data set covers four Martian years (MYs) between April 2004 (MY 27) and August 2011 (MY 30). Martian time is commonly counted in MYs, where year 1 (MY 1) began at Ls = 0° on 11 April 1955 [Clancy et al., 2000].
 The local time dependency, latitudinal coverage, and seasonal distribution of the measurements are shown in Figure 3 as a function of the solar longitude. The solar longitude (Ls) is the adopted measure of the seasons on Mars. Ls = 0° corresponds to the northern hemispheric spring equinox, while Ls = 90° denotes the northern summer solstice. Ls = 180° and Ls = 270° correspond to the northern autumn equinox and the northern winter solstice, respectively. These observations cover a broader range of local time than the MGS radio occultation measurements, which sampled the tropics only at local times a few hours before sunrise.
 Seasonal coverage with MEX is nearly complete for both hemispheres. Currently, coverage gaps remain for the northern hemisphere in summer and for the southern hemisphere in spring, which will be filled in the upcoming occultation seasons with Mars Express.
4 The Global Temperature Structure of the Middle and Lower Mars Atmosphere
 Compared with other remote sensing techniques, radio occultation measurements are limited geometrically in their global coverage. Nevertheless, temperature data, together with simultaneous geopotential measurements with a good latitudinal/longitudinal coverage spanning several Martian years, can be used to gain valuable insight into global atmospheric structures and circulations.
4.1 Latitudinal Variations in the Mars Atmosphere
 The highly elliptical orbit of Mars Express favors the coverage of several latitudes and local times during one occultation season (v. Figure 3) in contrast to Mars Global Surveyor whose circular, sun-synchronous orbit provided extensive longitudinal coverage at a more restricted range of latitudes and local times.
 Figure 4 provides an example of the typical latitudinal temperature structure observed in the northern hemisphere during late autumn and early winter (northern winter solstice) (Ls = 253–274°, 2005, MY 27). This figure was constructed from 41 temperature profiles; their locations are indicated in Figure 2. The measurements began in the low-latitude range, in late morning (DOY 201, local time ≈10:30 h), and moved toward the high northern latitudes, up to DOY 234, local time ≈15:00 h. The observations are evenly distributed with respect to longitude, as shown in Figure 2. The atmospheric profiles are interpolated to a uniform geopotential altitude grid, and a second-order polynomial was fitted to the data points to approximate the zonal-mean temperature structure at each geopotential altitude level. The approximated temperature structure is shown in Figure 4. The temperature field contains a strong, low-altitude inversion at midlatitudes as well as sharp meridional gradients, with isotherms at 150–190 K sloping poleward with increasing altitude. The temperature near the pole reaches a minimum at roughly 100 Pa (~15 km), above which it increases steadily in the overlying atmosphere (e.g., Figure 1). This result is in good agreement with previous observations, for example, from the Thermal Emission Spectrometer (TES) on MGS [Smith et al., 2001a] and the Mars Climate Sounder (MCS) on the Mars Reconnaissance Orbiter [McCleese et al., 2008, 2010]. Adiabatic heating in the subsiding branch of the Hadley circulation leads to strong warming over the winter pole. The zonal-mean thermal structure in this region may also be influenced by the presence of (breaking) gravity waves, planetary waves, and/or thermal tides in the middle atmosphere [e.g., Barnes, 1990; Zurek and Haberle, 1988; Wilson, 1997; Medvedev and Hartogh, 2007].
 The strong temperature gradient associated with intense polar warming in the upper atmosphere and the very cold polar night temperatures in the lower polar atmosphere are associated with strong zonal jets in the Martian winter hemisphere. With a vertical resolution of <1 km and the capacity to measure not only temperature but also geopotential height on surfaces of constant pressure, radio occultation provides new insight into this zonal wind field, particularly in the lowest scale height above the surface. Other remote sensing techniques, e.g., spectrometers, measure temperature versus pressure, and the wind fields derived from this type of observation require a boundary condition at the surface. These passive atmospheric sounders are therefore generally restricted to the atmosphere above the lowest scale height (>5–10 km) due to their limited vertical resolution and the need of this lower boundary condition.
 The momentum balance in the region surrounding the winter polar vortex is influenced by centrifugal forces in addition to the Coriolis and pressure gradient forces [e.g., Smith et al., 2001a]. Zonal winds u can be deduced from the gradient wind equation [e.g., Holton, 2004],
where rM is the Martian radius, Ω the rotation rate of the planet, Φ the planetary latitude, ρ the atmospheric density, and z the geopotential height. The derivation of winds from radio occultation measurements is a valuable diagnostic tool, owing to the scarcity of direct wind measurements on Mars.
 Figure 5 shows samples of pressure versus latitude on a surface of constant geopotential. Before estimating the meridional gradient, the data are calibrated to account for seasonal variations arising from polar condensation of CO2. A solution for (∂p/∂Φ)z = const is then derived by fitting a polynomial to the calibrated samples of pressure, as shown in Figure 5, and computing the derivative analytically. Substitution into equation (4) yields a solution for u versus latitude. By smoothing the data, this fitting procedure suppresses the effects of atmospheric waves on the estimate of the zonal-mean zonal winds.
 Figure 6 shows the zonal-mean zonal wind field obtained by applying this procedure systematically to uniformly spaced surfaces of constant geopotential. Its most striking feature is a strong eastward jet centered at about 65°N near the top of the domain. Maximum wind velocities of about 170 m/s are found at 30 km (p ≈ 15 Pa), in good agreement with previous results [Smith et al., 2001a; McCleese et al., 2010]. According to previous observations [Smith et al., 2001a; Banfield et al., 2003; McCleese et al., 2010] as well as numerical simulations [e.g., Haberle et al., 1993; Wilson and Hamilton, 1996], the zonal wind field achieves its peak intensity near the winter solstice in the northern hemisphere, under the conditions depicted in Figure 6.
 The same method was applied to another data set in the southern hemisphere (MY 29, Ls = 342–353°). The results are shown in Figure 7. The zonal winds are much smaller than those observed in the northern hemisphere, in good agreement with results from McCleese et al. . The strongest winds (~70 m/s) are found at the upper boundary of the investigation range (~15 Pa, ~30 km).
4.2 Longitudinal Variations in the Mars Atmosphere
 Occultation season 11 (2010, MY 30) provided an opportunity to observe almost all longitudes in the southern hemisphere in the latitude range 49–69°S. The measurements are located around southern winter solstice (Ls = 61–110°) in the early afternoon (LT 13:07–14:02 h). The almost uniform longitudinal coverage of these measurements provides the opportunity to study stationary wave structures at almost constant local time. Traveling waves play only a minor role in the southern winter hemisphere at these latitudes [e.g., Barnes et al., 1993; Banfield et al., 2004].
 It is not possible to unambiguously differentiate between thermal tides and stationary waves with measurements at a single local time due to aliasing [Hinson et al., 2003; Banfield et al., 2003; Wilson, 2000, 2002]. When observed at fixed local time, sun-synchronous tides introduce a bias, while non-sun-synchronous tides, whose solar time dependence is modulated by topography or other influences, introduce zonal variations in temperature that appear to be stationary.
 Several model simulations predict the presence of stationary Rossby waves [Zurek et al., 1992; Hollingsworth and Barnes, 1996; Barnes et al., 1996; Forget et al., 1999], and unambiguous observations by several instruments confirmed their existence [Hinson et al., 2001, 2003; Hinson, 2006; Banfield et al., 2003; Cahoy et al., 2006]. These waves are excited by the interaction of strong zonal jets in the winter hemisphere with the topography. They play a major role in the redistribution of heat, momentum, and dust in the atmosphere.
Banfield et al.  have shown that thermal tides play an insignificant role at the latitudes and altitudes observed here; Hinson et al.  came to the same conclusion at slightly higher latitudes during southern midwinter (Ls = 134–160°). Non-sun-synchronous thermal tides are more strongly forced in the tropics, but their amplitudes at these latitudes are quite low [Banfield et al., 2003; Hinson et al., 2003]. Summer solstice investigations at the same latitudes in the northern hemisphere by Mars Global Surveyor support the hypothesis that stationary Rossby waves dominate the lower atmosphere [Cahoy et al., 2006]. Thermal tides become increasingly important in the upper atmosphere with a transition region between the predominance of stationary waves and thermal tides at ≈75 km [Cahoy et al., 2006]. Significant wave-2 structures caused by thermal tides are found in the Martian thermosphere [Cahoy et al., 2006; Withers et al., 2003, 2011].
 The unique ability of radio occultation measurements to investigate simultaneously the geopotential height and the temperature provides valuable insight into the structure of atmospheric waves.
 The quasi-stationary temperature and geopotential structures, 〈T〉 and 〈Z〉, respectively, can be separated into a zonal mean value and a zonally varying term A′(λ), which is a function of the planetary longitude λ. That is,
 where “A” denotes either the temperature T or the geopotential height Z [see Andrews et al., 1987, p. 220].
 The zonal mean value varies gradually with the solar longitude Ls. It is therefore approximated by a second-order polynomial to account for seasonal pressure changes caused by condensation or sublimation [Hinson et al., 2001, 2003]. The pressure changes are approximated with model simulations using the general circulation model (GCM) from the Laboratoire Météorologie Dynamique in Paris [Forget et al., 1999].
 Zonal variations A′(λ) of the temperature (A = T) or geopotential (A = Z) can be approximated by stationary harmonic functions of the form
where s is the zonal wave number, while As and αs are constant factors describing the amplitude and phase of the zonal variations.
 We obtained a least squares solution for 〈T〉 by fitting equations (5) and (6) to measurements at constant pressure. The procedure was repeated at uniformly spaced pressure levels, yielding the results in Figure 8. The zonal temperature variations in the upper pressure range are dominated by two temperature maxima at the upper boundary of the investigation range and some smaller maxima and minima near the surface. The atmosphere between these boundaries is dominated by a wave-1 structure with a pronounced temperature maximum at east longitudes of ≈60° and a temperature minimum located above east longitudes of ≈330° (~144 K). These results generally agree with the findings from Hinson et al.  during the southern hemispheric midwinter (Ls = 134–160°) and TES observations from MY 24/25 [Banfield et al., 2003], although the highest temperatures found here (~172 K at the upper end of the investigation range, 25 Pa) are somewhat larger than those reported by Hinson et al.  and Banfield et al. .
Banfield et al.  and Hinson et al.  have shown that stationary waves have substantial amplitudes at s = 1 and 2, while modes with larger values of s have much smaller amplitudes and are confined near the surface. The wave modes s = 3 and 4 are therefore not shown explicitly in this study.
 The differences between the zonal mean temperatures and the observed quasi-stationary temperature structure 〈T〉 are shown in Figure 9. Wave-1 features dominate the zonal variations above a pressure level of ≈250 Pa. The temperature structure below this level is more chaotic with the highest values located at ~60°E and the lowest values at ~330°E. Zonal variations of geopotential height show minima near the surface at east longitudes of ~60° and 330° (v. Figure 10). The observed temperature variation amplitudes (up to 10 K) are slightly higher than those reported by Hinson et al. , while the geopotential altitude variation amplitudes are comparable (up to ~700 m). The gradients of both T′ (Figure 9) and Z′ (Figure 10) are primarily horizontal.
 A separation of the wave field into individual zonal components provides deeper insight. Figure 11 shows the wave-1 component of the temperature and geopotential fields. This wave mode can propagate to high altitudes, as indicated by the progressive westward phase shift with increasing height, which implies a downward phase velocity, an upward group velocity, and forcing at the ground [s., e.g., Andrews et al., 1987, p. 179]. The same behavior is observed in the wave-1 geopotential field whose maxima show a phase shift of roughly ~60–90° relative to the s = 1 component of temperature (v. Figure 11). Eastward winds are conducive to the vertical propagation of Rossby waves. These waves are ducted by the winter polar jet but are evanescent outside this region [e.g., Nappo, 2002; Banfield et al., 2003]. The amplitude of the s = 1 mode generally increases with height, reaching values of 10 K and 600 m near the upper boundary of Figure 11.
 The wave-2 mode has an equivalent barotropic vertical structure, as shown in Figure 12. As in previous observations [Hinson et al., 2003; Banfield et al., 2003], the zonal variations of both temperature and geopotential have positive peaks near 60°E and 240°E, independent of altitude. The amplitude in temperature variations reaches 2.5 K at the 100 Pa pressure level, while the amplitude in geopotential height variations increases from 50 m near the ground to 300 m at the top of the panel (25 Pa).
 The observed longitudinal gradient of Z′, , evaluated on constant pressure surfaces, can be used to calculate the geostrophic meridional winds v′ [e.g., Holton, 2004]:
 Here f denotes the Coriolis parameter, rM is the Martian radius, g the gravitational acceleration, and Φ the latitude. The assumption of geostrophic balance requires that the Coriolis parameter f is much larger than the meridional gradient of the mean zonal wind; in other words, the Rossby number must be very small (Ro ≪ 1). This condition is violated at the equatorward and poleward flanks of the strong winter polar jets and close to the equator. Geostrophic balance also requires that
where denotes the zonal mean wind. Although this condition is violated near the core of the winter circumpolar jet, equation (7) remains accurate within the lowest scale height above the surface. For this reason we restrict our estimates of v′ to pressures exceeding 200 Pa, where the zonal wind speed is much smaller than its peak value.
 Equation (7) shows that the strongest meridional winds occur at Z′ = 0. Owing to the phase shift between temperature and geopotential in the s = 1 wave mode (Figure 11), the strongest meridional winds nearly coincide with the temperature maxima. This coalignment of the meridional wind and the temperature s = 1 mode produces an effective poleward heat transport. Figure 13 shows the estimated meridional wind field. The meridional wind reaches values of 12 m/s at the upper boundary of the investigation range (200 Pa). Meridional wind maxima are located at east longitudes of ~300°E.
 Figure 14 provides a comparison of the poleward meridional heat flux F of the s = 1 and 2 wave modes:
where is the zonal mean product of the meridional wind and temperature variations, v′ and T′, respectively, ρ is the mass density, and cp is the specific heat at constant pressure.
 The wave-1 coalignment of temperature and meridional wind is consistent with the poleward transport of warm air and a corresponding transport of cold air into the equatorial region. The wave-2 heat flux indicates a heat flux in the opposite direction, but the stationary wave-1 structure dominates the eddy meridional heat transport above a pressure level of ~300 Pa in these observations, therefore contributing significantly to the redistribution of heat in the southern winter hemisphere. This result is consistent with MGS radio science observations during southern midwinter [Hinson et al., 2003].
5 Gravity Wave Activity
 The high vertical resolution of the radio occultation temperature profiles provides a unique opportunity to study small-scale temperature disturbances with altitude not accessible by any other remote sensing measurement technique. These small-scale temperature perturbations are mainly caused by gravity waves, excited, for example, by the displacement of air masses flowing over elevated topographical features. Other important source mechanisms comprise convection, wind shear instabilities, and near-ground thermal contrasts; unbalanced flows close to jet streams and wave-wave interactions might also contribute to the temperature disturbances [e.g., Fritts and Alexander, 2003]. The restoring force of these waves is buoyancy. Strong diurnal changes in the boundary layer structure and dynamics lead to a significant variability of gravity wave activity with local time. The unique local time coverage of the MaRS measurements provides insight into the different types of gravity wave sources. Gravity waves are known to play an important role in the energy and momentum budget of the Earth [e.g., Fritts and Alexander, 2003]; atmospheric models also predict that gravity waves have a significant influence on the atmospheres of other terrestrial planets. Mesoscale models are able to predict gravity wave occurrences on Mars [Pickersgill and Hunt, 1981; Rafkin and Michaels, 2003; Spiga et al., 2012], while GCMs are only parameterizing the gravity wave activity [e.g., Barnes, 1990; Joshi et al., 1995; Forget et al., 1999]. Simulations show, for example, that breaking gravity waves could contribute to the observed strong polar warming on Mars [Barnes, 1990]. Gravity waves might also contribute to the formation of extremely cold temperatures in the mesosphere [Spiga et al., 2012].
 Observations of small-scale temperature perturbations with wavelengths less than 10 km provide us with a means to study the gravity wave activity at different locations and seasons. We selected this upper bound on wavelength to exclude the effects of thermal tides, whose typical vertical wavelengths are in the range of 20 km. The temperature fluctuations are extracted by low-pass filtering of the temperature profile and subtracting the smoothed profile from the original measurement (v. Figure 15). Temperature fluctuations in Figure 15b show a steady increase in wave amplitude with increasing altitude, consistent with the exponential growth expected for freely propagating waves in the absence of appreciable dissipation. Such waves can grow up to the level of atmospheric instability, at which point they saturate or break. Breaking gravity waves are expected to have a significant influence on the mean atmospheric circulation [e.g., Barnes, 1990; Medvedev et al., 2011]. Figure 15c shows that the static stability of the atmosphere, i.e., the difference between temperature lapse rate and dry adiabatic lapse rate, is significantly reduced in the upper atmosphere. The atmosphere appears to become unstable at an altitude of ≈33 km, at which level the exponential growth of the wave amplitude ceases, consistent with wave breaking. Other observations support this conclusion [Heavens et al., 2010].
 A widely used parameter for the evaluation of gravity wave activity in atmospheric studies is the wave potential energy per unit mass [Tsuda et al., 2000, 2004; Ratnam et al., 2004; Creasey et al., 2006]:
where g denotes the gravity acceleration, N is the Brunt-Väisälä (buoyancy) frequency, T′ is the temperature perturbation, and is the mean background temperature given by the low-pass filtered temperature profile.
 A subset of measurements located at low latitudes is chosen to investigate the topographical dependency of the gravity wave activity. All measurements were taken close to 17:00 h. Figure 16 shows the spatial distribution of the observations. The data were obtained during the northern spring season of 2004 (MY 27). The measurements covered the period from Ls = 44.5°, in the northern hemisphere, and continued until Ls = 73.8°, in the southern low latitudes.
 The color code of Figure 16 shows the integrated gravity wave potential energy in the altitude range of 15–35 km for each measurement. The lower boundary was chosen to avoid the transition region between the planetary boundary layer and the overlying free atmosphere, which is subject to strong diurnal temperature changes. A change in the temperature lapse rate caused by the development of thermal inversions during the night and the buildup of a convective boundary layer during the day might adversely affect the result.
 The strongest gravity wave activity is found in the elevated terrain around the Tharsis region, with the maxima located at the flanks of Arsia Mons (~10°S, ~270°E); the wave activity in the northern lowlands is comparatively low (v. Figure 16). Several possible source phenomena might contribute to this topographical dependency. Two of them shall be investigated in more detail: Direct topographical forcing by wind flow over elevated orographic features and convection in the planetary boundary layer.
 Topographical forcing can lead to vertical displacement of air parcels inducing gravity waves in the lee of these obstacles. General circulation models invoke surface stress forcing mechanisms for gravity wave simulations [e.g., Collins et al., 1997; Forget et al., 1999]. The highest gravity wave activity in GCMs is therefore found over topographically elevated terrain. The linking of gravity wave detection and generation might be complicated by two factors: Gravity waves are influenced by the static stability of the background atmosphere and by wind shear, which can modulate or eliminate some gravity wave modes. Moreover, gravity waves can propagate over long distances, so that the source might be far removed from the location of the observation.
 Convection in the planetary boundary layer is a possible second source mechanism for the observed gravity wave activity. Strong solar forcing during daytime leads to the formation of a CBL in the lowest few kilometers above the surface. The CBL is particularly deep over elevated terrain (up to ~10 km [Hinson et al., 2008], v. next section) due to the low surface pressure and the concomitant atmospheric density at these altitudes [Hinson et al., 2008]. An increase of the depth of the boundary layer is associated with an intensification of the convective motions. Convection in the regions above the daytime surface might therefore contribute to the excitation of gravity waves over elevated terrain. Convectively generated gravity waves are a well-known phenomenon in the Earth atmosphere. Their occurrence is especially pronounced over convectively active boundary layers in the presence of vertical wind shear [Kuettner et al., 1987].
 As in previous measurements by MGS [Creasey et al., 2006], the observed correlation between topography and gravity wave activity is weaker than in simulations by GCMs. This effect might arise in part from the inability of this study to completely exclude the effects of temperature inversions. Model simulations have shown that temperature inversions in the low-latitude range can be caused by two different mechanisms: (i) by zonally modulated thermal tides [e.g., Hinson and Wilson, 2004] or (ii) by a water ice cloud layer [e.g., Colaprete and Toon, 2000]. Hinson and Wilson  have shown that the tropical temperature inversions can arise at this season from zonally modulated thermal tides and that the temperature inversions are enhanced by the radiative effects of water ice clouds. Thermal tides are especially prominent in this low-latitude range during summer, at which time they are strongly correlated with low-lying water ice clouds [Hinson and Wilson, 2004]. Our observations cannot discriminate unambiguously between thermal tides forced by thermal radiation and topographically forced small-scale gravity waves. Wilson et al.  found a strong diurnal variability of tropical water ice clouds with the most extensive cloud layers located over the elevated terrain during nighttime. Temperature inversions induced by water ice clouds are therefore a less serious concern for daytime observations in the low-latitude range.
 Figure 17 shows the vertical structure of the temperature fluctuations in two selected areas (indicated by white ovals in Figure 16). The two measurements in the northern lowlands (v. Figures 17a and 17b) reveal only moderate wave activity with amplitudes barely exceeding 1 K. The wave activity above the Tharsis ridge (Figures 17c and 17d), on the other hand, is much more vigorous. Wave amplitudes reach values of ≈6 K at the upper boundary of the investigation range (≈30–40 km). All four wave amplitudes grow with altitude, indicating freely propagating waves with low wave damping in this altitude range. The large amplitudes found over the elevated terrain might lead to atmospheric instabilities in the overlying atmosphere.
 The effect of breaking gravity waves is expected to be especially pronounced in the polar regions of the winter hemispheres [Barnes, 1990]. Figure 18 shows the seasonal dependence of gravity wave activity using four typical temperature profiles located in the northern hemisphere at latitudes between 52°N and 64°N (longitude 239–272°E). The typical daytime atmosphere in the northern spring season, with its monotonically decreasing temperatures, shows only moderate wave activity (v. Figure 18a). The atmosphere above the CBL is stable with no significant growth in wave amplitude. On the other hand, strong atmospheric dynamics during autumn and winter lead to large gravity wave amplitudes (v. Figures 18b to 18d). Strong temperature inversions accompany the strong zonal winter jets and enhance the growth of wave amplitude in the winter hemisphere. The highest gravity wave amplitudes, concomitant with the lowest static stability of the atmosphere, are found in the late autumn season where significant regions of atmospheric instability are seen in several profiles (v. Figure 18c). Convective instabilities in the winter extratropics observed with MCS have been interpreted as resulting from gravity wave saturation in regions of low static stability created by thermal tides [Heavens et al., 2010].
 The observed strong seasonal dependency is in good agreement with previous measurements [e.g., Creasey et al., 2006] and model predictions [Barnes, 1990]. Strong zonal jets amplify the topographical forcing during the winter season and support the vertical propagation of gravity waves via wave ducting [Barnes, 1990].
6 The Convective Boundary Layer
 At the base of the atmosphere lies a region known as the planetary boundary layer where the thermal structure and atmospheric dynamics are strongly influenced by interactions with the surface. Surface heating during daytime leads to the formation of a CBL where a variety of complex processes occur. For example, small-scale eddies caused by wind shear and convection effectively transport momentum toward the surface and heat away from it [e.g., Holton, 2004]. Many characteristics of the CBL are still poorly understood owing to its intricacy, the scarcity of in situ observations, and the difficulty of sounding this atmospheric region from the orbit.
 The near-surface environment was investigated through in situ measurements by the two Viking landers [Hess et al., 1977] and Mars Pathfinder [Schofield et al., 1997], while observations of the Miniature Thermal Emission Spectrometers (Mini-TES) on the Mars Exploration Rovers, Spirit and Opportunity, examined the lowest ~2000 m of the atmosphere [Smith et al., 2004, 2006]. The coldest temperatures were found in the early morning at sunrise, while the warmest temperatures occurred in late afternoon. The largest diurnal variations occur within a shallow layer adjacent to the surface, with superadiabatic lapse rates during daytime and strong temperature inversions at night.
 The presence of a CBL and the location of its upper boundary are revealed most clearly in profiles of potential temperature θ, defined as
where θ is the temperature that a parcel of dry air at temperature T and pressure p would reach if it were brought adiabatically to the standard pressure p0 [e.g., Holton, 2004]. R denotes the gas constant, while cp is the specific heat at constant pressure. The standard pressure p0 is set to 610 Pa in this investigation.
 Radio occultation measurements are the only remote sensing technique able to identify the depth of the convective boundary layer. Hinson et al.  mapped the depth of the CBL and its variations across the tropics through analysis of MaRS radio occultation measurements from the northern spring of MY 27. No previous atmospheric sounder had the necessary combination of vertical resolution and coverage in local time to achieve this objective. The depth of the CBL at a fixed local time varied between 3 and 10 km, showing a strong correlation with surface elevation. The deepest CBL (8–10 km) was found above elevated terrain, where the effect of surface heating is enhanced by the low surface pressure and atmospheric density, while the CBL is comparatively shallow (4–6 km) above low-lying terrain [Hinson et al., 2008].
 Figure 19 shows four atmospheric profiles in the northern tropics of MY 28 (2006). The season was early northern spring (Ls = 23–27°), and the local time was late afternoon (15.6 h). Each profile extends downward to within about 1 km of the surface. The thermal structure is highly repeatable in each pair of measurements (profiles a and c and profiles b and d), with only slight changes over the span of a few days. Each profile contains a well-defined CBL where the temperature lapse rate is nearly adiabatic and the potential temperature is nearly constant. At higher altitudes, θ increases steadily with height and the atmosphere is stably stratified. The boundary between the mixed layer and the overlying free air is quite distinct.
 The depth of the CBL increases with surface elevation, from about 5 km in Amazonis Planitia (profiles a and c in Figure 19) to about 8 km in the Tharsis region (profiles b and d in Figure 19). The increase in the depth of the boundary layer is comparable to the increase in surface elevation, about 5 km, so that the altitude at the top of the boundary layer differs by about 8 km at the two locations.
 The new results in Figure 19 illustrate the strong influence of Martian topography on the characteristics of the lower atmosphere. Our conclusions are consistent with MaRS observations from the preceding year [Hinson et al., 2008] and provide a foundation for additional large-eddy simulations of the structure and dynamics of the mixed layer [Spiga et al., 2010].
7 Summary and Conclusions
 The Mars Express Radio Science Experiment (MaRS) conducted more than 600 atmospheric measurements between 2004 and 2011, spanning four Martian years (MYs 27–30) at a wide range of local times, latitudes, and seasons.
 The extensive data set allows investigation of global atmospheric structures with a series of localized, nearly radial observations. The radio occultation experiments provide measurements of both temperature and geopotential height at high vertical resolution, enabling detailed investigation of planetary-scale atmospheric waves. For example, stationary Rossby waves in the southern hemisphere (MY 30) show a strong wave-1 characteristic transporting effectively heat and momentum to higher altitudes. The deduced meridional wind speeds indicate a pronounced meridional heat and momentum transport between the polar region and the low-latitude range.
 The zonal-mean thermal structure in the northern winter of MY 27 includes a strong temperature inversion, with peak temperatures of more than 210 K near 15 km altitude at 45°N. The corresponding zonal wind field contains a strong zonal jet with wind speeds reaching 170 m/s.
 The exceptionally high vertical resolution of radio occultation experiments provides the opportunity to investigate small-scale vertical temperature structures between the surface and ≈40 km. Gravity waves with short vertical wavelengths (λ < 10 km) can be investigated to understand their topographical dependency, vertical structure, and seasonal variability. The highest wave activity in the late afternoon during northern spring (MY 27) is found over elevated terrain. The observed topographical dependency suggests that the waves are either induced by direct topographical forcing or by convective penetration at the top of the CBL. The exponential growth of gravity wave amplitudes with height displays a weak wave damping, perhaps the result of saturation, in the lower atmosphere. Regions of atmospheric instability are observed in several profiles, especially in the late autumn season above strong thermal inversions. Autumnal breaking of gravity waves is expected to have a significant influence on the atmospheric polar structure amplifying the polar warming observed in the upper atmosphere [Barnes, 1990].
 Radio occultation is the only remote sensing instrument currently able to resolve the depth of the convective boundary layer. A strong topographical dependency is found with the deepest CBL (~10 km) over elevated terrain, where the effect of surface heating is accentuated by the low surface pressure and atmospheric density.
 This paper presents results of a research project funded by the Deutsches Zentrum für Luft- und Raumfahrt (DLR) under contract 50 QM 1004 and a contract with NASA. Our investigation could not have been successful without the efforts of the ESA Mars Express Science and Mission Operations teams, the MEX Flight Control Team, and the ESA ESTRACK ground station crews. We particularly appreciate the support of the MEX Project Scientist O. Witasse (ESTEC) and MEX Mission Operations Manager F. Jansen (ESOC). The MaRS experiment has benefited greatly from the continued support of the NASA Deep Space Network. In this respect, it is a pleasure to thank T. W. Thompson, S. W. Asmar, P. Varanasi, and D. P. Holmes (JPL) for their efforts. We also like to thank P. Withers (Boston University) for the valuable and fruitful discussions.