Concurrent effects of Martian topography on the thermosphere and ionosphere at high northern latitudes

Abstract

Martian topography modulated non-migrating tides play important roles in the upper atmosphere and thus in the ionosphere through their coupling, especially in their longitude variations. In this study, the neutral scale height (H_n) and ionospheric peak electron density (N_mM₂) and height (h_mM₂) retrieved from the MGS radio occultation measurements were used to investigate the coupling between the Martian thermosphere and ionosphere under the forcing of topography modulated tides by investigating their concurrent longitude variations. A segment of the measurements with fixed local time was selected to analyze the relationships between the longitude variations of the parameters in detail. Longitude variations of the thermosphere and ionosphere are significant though topographic fluctuations are not very prominent at high northern latitudes. Longitude fluctuations of H_n and N_mM₂ are nearly in anti-phase and percentage fluctuation amplitudes of H_n are nearly twice as large as those of N_mM₂, which indicate the non-migrating tide forced coupling between the ionosphere and thermosphere conforms to the Chapman theory, and suggests longitude variation of N_mM₂ can be used as a quantitative indicator for that of the thermal structure in the lower thermosphere. Longitude variation phases of H_n and h_mM₂ are also discrepant. That is due to tide vertical propagation since H_n and h_mM₂ depend on the atmospheric thermal structures at different height levels. The thermosphere and ionosphere show longitude variations due to the topography; however, they are dominated by inconsistent longitude components. This implies discrepant exciting and propagating efficiencies of various topography modulated tides.

Graphical Abstract

Introduction

The solar-driven thermal tides play important roles in the variability and dynamics of the upper atmosphere of rapidly rotating planets such as the Earth and Mars; they transmit energy and momentum from the lower atmosphere to higher altitudes (e.g., Forbes et al. 2020; Moudden and Forbes 2008a). The thermal tides are westward propagating sun-synchronous waves when they are forced by zonally symmetrical solar heating (Chapman and Lindzen 1970), namely, migrating tides. Meanwhile, sun-asynchronous non-migrating tides are excited owing to the nonlinear modulation of zonal inhomogeneities near atmospheric lower boundary, such as topography, surface albedo, thermal inertia and so on (e.g., Withers et al. 2003), to the solar forcing. These non-migrating tides zonally propagate eastwards or westwards. Non-migrating tides were thought to be more important on Mars than on the Earth owing to the thinner atmosphere and much larger topographic fluctuations on Mars (e.g., Wang et al. 2006; Withers et al. 2003). They can significantly modulate Martian aerobraking region, and even may affect Martian atmosphere loss, known as the Jeans escape (e.g., Jakosky et al. 2015), if they propagate through the thermosphere to the exobase (Forbes et al. 2020). As the ionized part of the upper atmosphere, the ionosphere closely couples with the neutral atmosphere. Thus, non-migrating tides also can significantly modulate the Martian ionosphere (e.g., Bougher et al. 2001; Cahoy et al. 2007; Fang et al. 2021; Haider et al. 2011; Krymskii et al. 2003, 2004; Mahajan et al. 2007; Thaller et al. 2020; Wang and Nielsen 2004; Withers 2009) through the coupling between the ionosphere and the upper atmosphere.

The influence of non-migrating tides on the Martian atmosphere manifests as planetary-scale longitude variations as seen from sun-synchronous orbits (fixed local times), where the influence of migrating tides is zonally symmetrical. The earlier knowledge on the longitude structures of the Martian upper atmosphere mainly came from accelerometer measurements. Keating et al. (1998) found a persistent zonal wave-2 structure in Martian atmospheric density based on the Mars Global Surveyor (MGS) accelerometer measurements; they suggested that the structure may be caused by a stationary planetary wave (SPW) associated with Martian topography. Subsequent analyses (e.g., Forbes and Zhang 2018; Wang et al. 2006; Wilson 2002) indicated there were significant differences in the longitude wave phase between different local solar times (LST), suggesting that upward propagating non-migrating tides are responsible for the wave structure. The in situ neutral density measurements from the recent Mars Atmosphere and Volatile Evolution (MAVEN) mission were also used to reveal the longitudinal wave structures associated with non-migrating tides in the upper atmosphere and their latitudinal and seasonal variations (e.g., England et al. 2016; Liu et al. 2017). Non-migrating tide propagation from the lower atmosphere into the thermosphere of Mars has been investigated by some simulations (e.g., Forbes et al. 2002; Moudden and Forbes 2008b; Wilson 2002); whereas, vertical phase changes of the longitude structure were not clear in neutral density observations (e.g., Wang et al. 2006; Withers et al. 2003). Wave–wave interactions make tide propagation more complicated. Although SPWs excited in the lower atmosphere were generally not thought to be capable of propagating into the thermosphere, they can be generated by nonlinear wave–wave interactions in the upper atmosphere (e.g., Forbes et al. 2020).

Longitude variations of the Martian atmosphere were also revealed in its thermal structure that controls the variability of the upper atmosphere. Banfield et al. (2000) investigated the longitude waves in the thermal structure of the Martian atmosphere using the neutral temperature profiles retrieved from the thermal emission spectrometer on board the MGS. They extracted various migrating tides, non-migrating tides, and SPWs from the observations. Their results were mainly for the region below the thermosphere, the amplitudes of non-migrating tides were only on the order of ~ 1 K (the percentage with respect to zonal mean was ~ 1%). Withers et al. (2011) showed the presence of atmospheric temperature longitude variations up to 110 km altitude using the measurements of the Spectroscopy for the Investigation of the Characteristics of the Atmosphere of Mars aboard Mars Express. In their results, the zonal temperature variations can reach the order of 10 K and wave − 2 and wave − 3 components are dominant. Recently, England et al. (2019) presented the longitude wave − 3 variations of neutral temperature in the upper thermosphere using the remote observations of the Imaging Ultraviolet Spectrograph aboard the MAVEN mission. Combining with the temperature measurements at lower altitudes by the Mars Reconnaissance Orbiter, they showed a phase shift with altitude in the wave − 3 component, indicating vertical wave propagation form the lower atmosphere to the upper atmosphere. Stevens et al. (2017) presented different longitude wave phases of atmospheric thermal structure between the mesosphere and the thermosphere.

Longitude variations associated with the non-migrating tides were also found in the Martian ionosphere. Bougher et al. (2001, 2004) showed a similar longitude variation profile of Martian dayside ionospheric peak height with that of the neutral density at 130 km height measured by the MGS. They suggested that ionospheric peak height can be used as a proxy of atmospheric longitude variations. Unlike ionospheric peak height, longitude variations of ionospheric peak electron density were not thought to be a primary effect of non-migrating tides since the electron density peaks occur near constant pressure levels (e.g., Mendillo et al. 2003; Rishbeth and Mendillo 2004); whereas, evident longitude variations were also observed in the electron density (e.g., Cahoy et al. 2006, 2007; Haider et al. 2006; Krymskii et al. 2003; Mahajan et al. 2007). Cahoy et al. (2007) investigated longitude variations of ionospheric electron densities at different altitudes; they showed vertical phase change of the electron density longitude variations. Mahajan et al. (2007) showed that longitude variations of the height and density of the ionospheric peak are anticorrelated, which they characterized as an anomalous feature.

Therefore, although longitude variations of the thermosphere and the ionosphere have been presented, they are still deserving of further investigations, especially the relationship between them and how they couple under the forcing of non-migrating tides. This is the objective of this study. In “Data processing and results” section, data processing method of the MGS radio occultation electron density profiles is introduced and concurrent longitude variations of the thermosphere and ionosphere are presented. In “Discussion” section, the relationship between the observed thermospheric and ionospheric longitude variations and the topography is discussed, and the coupled responses of the thermosphere and ionosphere to the forcing of non-migrating tides are analyzed in terms of the Chapman theory. Finally, a summary is presented in “Summary” section.

Data processing and results

The MGS spacecraft launched in November 1996 arrived at Mars in September 1997. The spacecraft carried a radio occultation instrument that can measure Martian ionospheric electron density profiles. 5600 electron density profiles were obtained in total from the measurements during the MGS mission. This dataset has been well used to investigate Martian ionospheric variations (e.g., Bougher et al. 2001; Breus et al. 2004; Fox and Yeager 2009; Krymskii et al. 2003, 2004; Mahajan et al. 2007; Martinis et al. 2003; Mendillo et al. 2003; Rishbeth and Mendillo 2004; Zou et al. 2006, 2011).

Figure 1 shows a typical electron density profile of the Martian ionosphere measured by the MGS radio occultation as an example. The principal characteristic of the profile is the primary layer peaked at ~ 135 km, the M₂ layer. Below the M₂ layer there is a secondary layer peaked at ~ 110 km, the M₁ layer. The M₂ peak is always conspicuous in Martian dayside electron density profiles, while the M₁ peak is usually not obvious, instead often appearing as a shoulder (e.g., Fox and Yeager 2009). The M₂ peak is produced from the photoionization of CO₂ by solar extreme ultraviolet irradiance, in which the Helium-II 30.4 nm line is a major ionization source (e.g., Rishbeth and Mendillo 2004). The ionized CO₂⁺ reacts with atomic oxygen so that the final dominant ion is the molecular ion O₂⁺ in the vicinity of the M₂ peak. As a result, variations of the electron density around the M₂ peak agree with those of a Chapman-α layer for which the neutral scale height is a crucial parameter (e.g., Fox and Yeager 2009; Mendillo et al. 2015; Rishbeth and Mendillo 2004; Sánchez-Cano et al. 2016). For a Chapman-α layer the altitudinal profile of the electron density can be described by the following Chapman-α function (for the M₂ layer):

$${N}_{e}\left(h\right)={N}_{m}{M}_{2}\bullet exp\left[0.5\bullet \left(1-\frac{h-{h}_{m}{M}_{2}}{{H}_{n}}-{e}^{-\frac{h-{h}_{m}{M}_{2}}{{H}_{n}}}\right)\right],$$

(1)

where N_e is electron density, h is height, N_mM₂ is the peak electron density of the M₂ layer, h_mM₂ is the peak height of the M₂ layer, and H_n is the scale height of CO₂. That is to say, the shape of the electron density profile strongly depends on H_n. The key parameters of the M₂ peak, N_mM₂ and h_mM₂, can be reliably identified from the electron density profiles recorded by the MGS radio occultation instrument, and the neutral scale height can be estimated by adjusting H_n to best fit those profiles using the Chapman-α function.

Fig. 1

A MGS electron density profile as an example illustrating Chapman-α fitting. The gray dots are MGS electron density measurements; the blue solid line is the Chapman-α fitting for the height range of – 10 km to 20 km around the M₂ peak. The fitting parameters are labeled, including N_mM₂, h_mM₂, and H_n

The ionization of atomic oxygen becomes important with increasing altitudes above the M₂ peak, and the ionization of CO₂ by solar X-ray gradually dominates the ionization rate with decreasing altitudes below the M₂ peak so that the M₁ layer forms. Thus, the Chapman-α function can only well describe the partial electron density profile in the vicinity of the M₂ peak. In this study, we used the Chapman-α function to fit the electron density profile within the altitudinal range of − 10 km to + 20 km around the M₂ peak. This can avoid the lower M₁ layer and the higher M₂ topside. A 5-point running average was first applied to each electron density profile and the M₂ peak was identified from the profile to determine the fitting range. Then we applied the Chapman-α function to each profile to estimate the neutral scale height by adjusting H_n to best fit the electron density profile. In view of the uncertainties of the MGS measurements, the fitted N_mM₂ was also slightly adjusted (not exceed ± 2%) from the maximum electron density point recorded in the profile to achieve a best fitting. The typical uncertainty level of the MGS electron density is ~ 3 × 10⁹ m⁻³ as compared with a characteristic peak density of ~ 80 × 10⁹ m⁻³ observed at a solar zenith angle of 80° (Tyler et al. 2001), i.e., ~ 3.8%. This adjustment does not exceed that uncertainty level. In Fig. 1, the blue solid line shows a Chapman-α fitting as an example. The fitting can well capture the partial electron density profile around the M₂ peak. H_n was determined by the fitting. The vast majority of the electron density profiles were well fitted. The fitting errors are well within the uncertainty level of the MGS electron density; the mean error is 1.70 × 10⁹ m⁻³ and the standard deviation is 0.74 × 10⁹ m⁻³.

The objective of this study is to investigate the effects of Martian topography modulated tides on longitude variations of the ionosphere and thermosphere. The longitude difference of solar forcing to the ionosphere, which can be estimated by the solar zenith angle and solar irradiance flux, should be excluded for investigating ionospheric longitude variations. Moreover, the LST of the measurements should be fixed as possible owing to the propagating nature of non-migrating tides. Figure 2 shows solar longitude of Mars (Ls), solar 10.7 cm radio flux on Mars as well as latitude, longitude, the solar zenith angle, and LST of the MGS radio occultation measurements. All measurements occurred under the Martian seasonal condition of Ls is ~ 70° to ~ 220°. The measurements were mainly confined to high northern latitudes and high solar zenith angles. Although the solar zenith angle changed with latitude, the measurements repeatedly covered the whole longitude range at different latitudes to ensure longitude variations of the parameters can be investigated. However, the measurements covered more than a half of the Solar Cycle 23 so that the solar flux changed significantly between different occultation seasons, and the LST of the measurements significantly changed during each occultation season. Thus, we selected an episode of the occultation season 2 in order to reduce the effect of solar flux change and confine the LST range of the measurements. As indicated by the red box in Fig. 2, the measurements repeatedly covered different longitudes when the solar zenith angle decreased with increasing latitude, while the changes of solar flux and LST (confided to LST ≤ 04:00) were smaller. That is to say, the solar forcing and the LST over different longitudes are basically equivalent at fixed latitudes so that the longitude variations associated with non-migrating tides can be retrieved.

Fig. 2

Various parameters associated with the MGS radio occultation measurements. a Solar longitude of Mars Ls; b solar 10.7 cm radio flux on Mars; c latitude, d longitude, e the solar zenith angle, and f local solar time LST of the MGS radio occultation measurements. The red dashed box indicates the selected time segment used for this study

We binned the data using a moving window of longitude 30° × latitude 4° with a step length of longitude 15° × latitude 2° to obtain gridded h_mM₂, N_mM₂, and H_n. The gridded data were further averaged to obtain mean longitude and latitude variations of the parameters, as shown in Fig. 3a–c. This is a smoothing operation combining measurements from different orbits to obtain average longitude variations of the parameters. Figure 3d–f shows the corresponding standard deviations of the gridded h_mM₂, N_mM₂, and H_n, respectively. h_mM₂ decreases while N_mM₂ increases with increasing latitude owing to the solar zenith angle decreases with increasing latitude (see Fig. 1). Similar to h_mM₂, H_n tends to decrease with increasing latitude although the solar zenith angle decreases. This may be the manifestation of that neutral temperature decreases with decreasing altitude in the lower thermosphere. There are evident longitude fluctuations in the parameters, especially in h_mM₂ and H_n. The dominant longitude variation pattern is the 3-peak structure. In view of the background latitude variations of the parameters, we removed their longitudinal averages to more clearly present the longitude fluctuations, as shown in Fig. 3g–i. The mean longitude variations dominate over the standard deviations of the gridded data (Fig. 3d–f), indicating the significance of the mean longitude variations. For example, the mean longitude variation of h_mM₂ can reach ~ 7 km, while the standard deviation of the gridded h_mM₂ is generally lower than ~ 4 km. The longitude fluctuation of N_mM₂ becomes clearer after removing the longitudinal averages. All parameters show significant 3-peak longitude structure. It is notable that the longitude variation phases of the parameters are inconsistent with each other and the amplitudes of the peaks are somewhat uneven. The percentage longitude variations of the parameters with respect to their zonal means were calculated, as shown in Fig. 3j–l. The percentage longitude variations of h_mM₂, N_mM₂, and H_n can reach the orders of ~ 2%, ~ 8%, and ~ 20%, respectively.

Fig. 3

Longitude and latitude variations of h_mM₂, N_mM₂, and H_n. a–c present the gridded mean h_mM₂, N_mM₂, and H_n, respectively; d–f are standard deviations of the gridded h_mM₂, N_mM₂, and H_n, respectively; g–i show the residual h_mM₂, N_mM₂, and H_n, respectively, after removing zonal averages; j–l are percentage longitude variations of h_mM₂, N_mM₂, and H_n, respectively, with respect to zonal averages

A sixth-order Fourier decomposition was applied to the parameters' longitude fluctuations to further estimate the relative importance of various longitude variation components in more detail:

$${P}_{l}\left(\lambda \right)=\sum_{n=1}^{6}{A}_{n}cos\left[\frac{2\pi n\bullet \left(\lambda {-\psi }_{n}\right)}{360}\right],$$

(2)

where λ is longitude, P_l is parameter's longitude fluctuation (Fig. 3g–i), and A_n and ψ_n are the amplitude and phase of wave-n component, respectively. Figure 4a shows the longitude variations of the △h_mM₂ at 64°N and its Fourier fitting to illustrate the decomposition. The solid line is the Fourier fitting; the dashed lines indicate the fitting error estimated by the standard deviation of the difference between the fitting and the observation. The fitting can well capture the longitude variations, which significantly dominate over the fitting error. Thus, various wave amplitudes can be calculated from the fitting to estimate the relative importance of different wave components. Figure 4b presents the fitting errors of △h_mM₂, △N_mM₂, and △H_n, and Fig. 4c shows the latitudinally averaged amplitudes of the longitude wave-1 to -6 for the three parameters. The wave-2 and -3 are dominant longitude components; their amplitudes are significantly larger than the fitting errors. The wave-3 is somewhat higher in amplitude. The wave-3 corresponds to the conspicuous 3-peak structure in Fig. 3g–i, and the wave-2 can be used to explain the uneven amplitudes of the peaks. Moreover, the wave-1 is also important to some extent for N_mM₂ and H_n, which also can cause the uneven amplitudes of the peaks.

Fig. 4

Analysis for the longitude wave components of h_mM₂, N_mM₂, and H_n. a shows longitude variation of the △h_mM₂ at 64°N. The gray dots are gridded △h_mM₂; the solid line is the Fourier fitting; the dashed lines indicate the corresponding 1-σ error. b presents latitude variations of the 1-σ errors of △h_mM₂, △N_mM₂, and △H_n fittings. c is latitudinally averaged amplitudes of the longitude wave − 1 to − 6 in △h_mM₂, △N_mM₂, and △H_n

Discussion

The electron density profiles of the Martian dayside M₂ layer can be used to investigate the thermal structure of the lower thermosphere since they are dominated by photochemical processes. Krymskii et al. (2003, 2004) retrieved H_n from the MGS electron density profiles by assuming a parabolic electron density distribution in the vicinity of the M₂ peak; they showed the presence of H_n longitude variations. Zou et al. (2011) also estimated H_n from the MGS electron density profiles using the Taylor decomposition of the electron density with respect to altitudes to analyze seasonal variations of the neutral atmosphere. In this study, we used a Chapman-α function that can well describe the electron density profiles of a photochemical equilibrium layer to estimate H_n. As shown in Fig. 3, the gridded mean H_n varies from ~ 9 km to ~ 14 km under the selected condition, basically consistent with the previous results (e.g., Krymskii et al. 2003, 2004; Zou et al. 2011).

The amplitudes of thermal tides should increase with increasing altitudes according to the classical tidal theory (Chapman and Lindzen 1970); in contrast, the actual condition is that thermal tides undergo dissipation when propagating upwards (e.g., Withers et al. 2003). As shown in Fig. 3l, H_n longitude variations can reach ~ 20% in the lower thermosphere, which is much higher than the longitude variations of the neutral temperature at lower altitudes (e.g., Banfield et al. 2000). That is to say, tide wave amplitudes increase when propagating upwards into the lower thermosphere. For the ionosphere, Fang et al. (2021) recently analyzed longitude variations of the ionospheric electron densities above the M₂ peak measured by the MAVEN mission. Their results indicated that longitude variation amplitudes of ionospheric electron density also trend to increase with increasing altitude; the longitude variations can reach ~ 15% near 200 km, significantly larger than the ~ 8% longitude variation of the electron density at the M₂ peak presented in this study. It is notable that Fang et al. (2021) showed that the amplitude of the wave-1 is comparable to those of the wave-2 and -3, which are two dominant longitude components in this study. This is possibly due to the different observational conditions and sampling modes of the two types of measurements, especially Fang et al. (2021) used the MAVEN measurements near 20°S while in this study we used the MGS measurements at high northern latitudes.

Topographic fluctuations are generally prominent on Mars, which were suggested to be the primary reason for atmospheric longitude variations (e.g., Forbes et al. 2002; Moudden and Forbes 2008b). Figure 5a shows Martian topography changes. The topography changes are much more significant at mid- and low-latitudes than at high latitudes; the most notable changes are two asymmetrical plateaus. Withers et al. (2003) and Moudden and Forbes (2008b) performed Fourier decompositions to the Martian topography and compared the decomposed zonal components with those of the MGS neutral density to relate atmospheric longitude variations to the topography. Their comparisons were for large latitudinal scales and indicated relevance between atmospheric longitude variations and the topography, with emphasis on low- and mid-latitudes. This study is confined to the longitude variations at high northern latitudes. The Fourier decomposition was also applied to the topography. As shown in Fig. 5b, the Fourier amplitudes of the longitude variations are significantly larger at low- and mid-latitudes than at high latitudes. The dominant longitude components include the wave − 1, − 2, and − 3, and the wave − 2 is more prominent in the northern hemisphere. The selected MGS radio occultation measurements are located at higher northern latitudes, as indicated by the red dashed box in Fig. 2. Figure 5c shows that the wave − 1, − 2, and − 3 are also dominant components at middle to high northern latitudes, and the mean amplitude of wave − 3 is somewhat lower than those of wave − 1 and − 2. Nonlinear modulation of topographic longitude wave-n to the solar forcing should induce apparent longitude wave-n variation in the atmosphere as seen at a fixed LST (e.g., Forbes et al. 2002). That is to say, the topographic longitude components are not fully consistent with those of h_mM₂, N_mM₂, and H_n (Fig. 4), which mainly manifests as that a dominant longitude variation component in the topography, the wave − 1, is not prominent in h_mM₂, N_mM₂, and H_n. Then, what is the manifestation of the relevance between the ionospheric and thermospheric longitude structures and the topography in the selected data set? We took the dominant wave − 3 in the ionosphere and thermosphere to further analyze. A notable feature of the topographic wave− 3 is that the wave − 3 phase changes with latitude; it shifts westwards with increasing latitude in the latitudinal range of ~ 50°N to ~ 80°N and turns to shift eastwards beyond ~ 80°N. Figure 5d presents the topographic wave − 3 in the latitudinal range of the MGS measurements to show these phase shifts. Latitude variations of the wave-3 in h_mM₂, N_mM₂, and H_n are presented in Fig. 5e–g, respectively, for comparison; where the data are extended to a larger LST range (LST < 6.7) to include those MGS measurements at higher latitudes to investigate the effect of the topographic wave − 3 phase turning at 80°N. It is interesting that similar phase shifts and turning appear in the three parameters, consistent with the topography. It is notable that the LST of the MGS measurements significantly increases with increasing latitude beyond ~ 80°N in the extended date set, which also contributes to the eastward wave − 3 phase shift in the MGS measurements at higher latitudes. The DE2 and SE1 tide components were suggested to be primarily responsible for the wave-3 longitude variations, and SE1 was thought to be more important at high latitudes (e.g., Cahoy et al. 2007; Forbes et al. 2002; Moudden and Forbes 2008b; Withers et al. 2003). Taking H_n for example, the wave-3 phase shifts eastwards ~ 48° form 80°N grid to 86°N grid. The calculated mean LST of the gridded data changes ~ 2.1 h from 80°N grid to 86°N grid, which corresponds to a wave-3 phase eastward shift of 10.5° (21°) for DE2 (SE1), significantly lower than the observed 48° phase shift. Thus, the observed turning of the phase shift at 80°N should be related to the topography. Based on simulations, Wilson (2002) also indicated westward phase shift of the wave-3 in neutral density with increasing latitude at high northern latitudes. The similar phase shifts in ionospheric and thermospheric longitude variations and in the topography indicate a commonality between them. Exciting and upward propagating efficiency may be different for various tide wave modes (e.g., Wang et al. 2006). Thus, the difference in the dominant longitude components between the three parameters and the topography is possibly due to that various topography modulated wave modes have discrepant exciting and propagating efficiencies.

Fig. 5

Comparison between Martian topography and ionospheric and thermospheric longitude variations. a Shows Martian topographic fluctuations; b presents latitude variations of the amplitudes of topographic longitude wave − 1 to − 6; c is averaged amplitudes of topographic longitude wave − 1 to − 6 over the latitude range of 30–90°N; d shows topographic longitude wave − 3. (e–g) are latitude variations of the longitude wave − 3 in h_mM₂, N_mM₂, and H_n, respectively

It is noticeable from Fig. 5e–g that the longitude variation phases of the three parameters are different from each other; especially the wave − 3 peaks of N_mM₂ are significantly asynchronous with those of h_mM₂ and H_n. Then, how do the ionosphere and thermosphere couple under the forcing of the topography modulated non-migrating tides? Fig. 6a further presents the wave-3 phases (ψ₃ in Eq. (2)) of N_mM₂, h_mM₂, and H_n for comparison. Differences between the phases are evident. Taking N_mM₂ for reference, the phase difference between h_mM₂ and N_mM₂ is ~ 40°, and that between H_n and N_mM₂ is ~ 60°, just a half of a wave-3 cycle (120° in longitude). Previous studies presented the phase discrepancies between the longitude variations of different neutral parameters. Withers et al. (2011) developed a formalism to explain the phase difference between neutral temperature and atmospheric pressure, where the phase difference was attributed to the vertical change of the longitude variation amplitude of atmospheric pressure. England et al. (2019) presented the phase difference between the longitude variations of neutral temperature and atmospheric density. In this study, N_mM₂ primarily depends on the CO₂ density at h_mM₂ and H_n corresponds to the averaged neutral temperature in the vicinity of h_mM₂, they are related to the state of the lower thermosphere at similar height levels. The ionization peak forms at the height where atmospheric optical depth [Eq. (3)] reaches one according to the Chapman theory that assumes the atmosphere is isothermal and horizontally stratified (Rishbeth and Garriott 1969):

$$\tau =\sigma n{H}_{n}\bullet \mathrm{sec}\chi ,$$

(3)

where σ is absorption cross section, n is neutral density, and χ is the solar zenith angle. That means the ionization peak occurs at a constant atmospheric pressure level (Eq. (4)) for a fixed solar zenith angle:

$$P=nk{T}_{n}=n{H}_{n}mg,$$

(4)

where k is the Boltzmann constant, T_n is neutral temperature, m is molecular mass, and g is the gravity acceleration. Simulations (González-Galindo et al. 2013) showed that the Martian M₂ peak at the subsolar point is nearly located at the same atmospheric pressure level through a Martian year. Thus, N_mM₂ variation should be negatively correlated with H_n variation in view of that N_mM₂ is positively correlated with n. That means longitude variations of N_mM₂ and H_n should be in anti-phase, just as presented in Fig. 6a. This result indicates that longitude variations of H_n driven by non-migrating tides modulate the concurrent longitude variations of N_mM₂ according to the Chapman theory, although the Martian atmosphere is longitudinally varying and is not strictly isothermal (the neutral temperature in the lower thermosphere can increase by tens of Kelvin from ~ 120 km to ~ 160 km, e.g., Cui et al. 2018; Fox et al. 1996; Mendillo et al. 2011).

Fig. 6

Latitude variations of a the wave − 3 phases and b percentage amplitudes. The blue, red, and gray lines are for N_mM₂, h_mM₂, and H_n, respectively

h_mM₂ is positively correlated with the neutral scale height according to the Chapman theory (Rishbeth and Garriott 1969). Longitude variations of the ionosphere can be attributed to those of H_n, then longitude variations of h_mM₂ should be in-phase with those of H_n. However, they are also not in-phase in observations (see Figs. 3 and 6a). The atmospheric optical depth increases with decreasing altitude, and for an ionization layer dominated by photochemical processes, h_mM₂ corresponds to the height where the atmospheric optical depth equal to one. The atmospheric optical depth is related to the column content of ionized neutral composition downward from atmospheric top. The atmospheric column content depends on the underlying atmospheric temperature, which determines the expansion or contraction of the overlying atmosphere (e.g., Bougher et al. 2001; Zou et al. 2011; González-Galindo et al. 2013). Thus, h_mM₂ mainly depends on the neutral temperature below the M₂ peak, which controls the atmospheric column content above the M₂ peak. For the actual Martian atmosphere (in which neutral temperature changes with increasing altitudes), this neutral temperature should be the effective one of the underlying atmosphere mostly lower than h_mM₂, as revealed by Zou et al. (2011) that the effective neutral scale height between the lower atmosphere and the ionospheric peak is the primary driver for h_mM₂ variations. That means the height level of the atmospheric temperature determining h_mM₂ is lower than the height level of H_n. Thus, the difference of the wave − 3 phase between h_mM₂ and H_n indicates vertical change of the longitude variation phase of neutral temperature. Although both SPWs, which can be generated from nonlinear atmospheric wave–wave interactions (e.g., Forbes et al. 2020), and non-migrating tides can cause atmospheric longitude variations, the observed wave phases of the thermosphere and ionosphere under the selected condition is consistent with vertical non-migrating tide propagation, since the wave − 3 of h_mM₂ should be in-phase with that of H_n if the longitude variations are caused by SPWs (their phases keep constant with varying altitude).

The percentage magnitudes of the longitude variations of the parameters also differ from each other, as presented in Fig. 3j–l. Figure 6b further shows the wave-3 percentage amplitudes [A₃ in Eq. (2)] of N_mM₂, h_mM₂, and H_n for comparison. The percentage amplitudes of H_n are nearly twice as large as those of N_mM₂. The latitudinally averaged ratio of H_n amplitudes to N_mM₂ amplitudes is ~ 2.3, similar to the ratio of their total longitude variation magnitudes (Fig. 3). For a Chapman-α layer N_mM₂ is proportional to H_n^−1/2, which means a change of the neutral scale height ΔH_n/H_n will cause a smaller change of the electron density ΔN_mM₂/ N_mM₂ with a magnitude of half that of ΔH_n/H_n. Thus, the wave-3 amplitude ratio of H_n to N_mM₂ is basically consistent with the Chapman-α layer. A possible reason for the smaller difference is that the mean height of the altitudinal range (− 10 km to 20 km around h_mM₂) used for fitting H_n is higher than h_mM₂. The percentage amplitudes of the longitude variations of h_mM₂ are much smaller than those of H_n. h_mM₂ linearly depends on the neutral scale height according to the Chapman theory:

$${h}_{m}{M}_{2}\left(\chi \right)={h}_{m}{M}_{2}\left(\chi =0\right)+{H}_{n}^{^{\prime}}\bullet \mathrm{ln}\left(\mathrm{sec}\chi \right),$$

(5)

where χ is the solar zenith angle; in view of the vertical changes of neutral temperature, H_n’ is the effective neutral scale height of the atmosphere below the M₂ peak. Since the value of h_mM₂ is dominated by the base value of χ = 0 (e.g., Morgan et al. 2008), the percentage variation of h_mM₂ caused by the change of the neutral scale height is much smaller than that of the neutral scale height.

The observed wave phases of H_n and h_mM₂ indicate the presence of the effect of upward propagating non-migrating tides, which is consistent with Cahoy et al. (2007), who presented vertical phase shifts of ionospheric longitude waves using the MGS electron density profiles. Owing to the vertical change of wave phase associated with tides, the dominant longitude variations should be weakened when integrating the electron densities with respect to altitudes, since out-of-phase longitude variations of the electron densities at different altitudes counteract partially. Thus, we calculated the total electron content of partial M₂ layer (TEC_p, in units of TECu, 1TECu = 10¹⁶ electrons/m²) to investigate its longitude variations. In view of h_mM₂ varies with longitude and latitude under the selected condition (see Fig. 3), for each electron density profile a TEC_p value was obtained by integrating the electron densities in the altitudinal range of − 15 km to 25 km around the M₂ peak, where a main portion of the M₂ layer locates. TEC_p data were also gridded according to the operation used in Fig. 3. Figure 7a shows longitude and latitude variations of the gridded mean TEC_p and Fig. 7b presents the corresponding standard deviations of the gridded TEC_p. TEC_p varies primarily with latitude due to the change of the solar zenith angle, which is similar to N_mM₂ (see Fig. 3), while its longitude variation appears to be not as evident as that in N_mM₂. Figure 7c presents the longitude variation using the residual TEC_p after removing zonal averages (△TEC_p). As expected, the aforementioned wave − 3 and − 2 are not evident in △TEC_p, and the longitude variation of △TEC_p is basically equivalent to the standard deviation of the gridded TEC_p in amplitude. Figure 7d further shows the amplitudes of the longitude wave − 1 to − 6 of △TEC_p. There is seems no a wave component that can be dominant at different latitudes. The amplitudes of others wave components can be comparable to those of wave − 3 and − 2. Thus, the analysis for △TEC_p further supports that ionospheric longitude variations are related to upward propagating non-migrating tides.

Fig. 7

Longitude and latitude variations and amplitudes of longitude wave components of TEC_p. a Presents the gridded mean TEC_p; b is the standard deviation of the gridded TEC_p; c shows the residual TEC_p after removing zonal averages; d presents the amplitudes of the longitude wave − 1 to − 6 of the residual TEC_p

The above analyses indicate that the observed ionospheric longitude variations are the results of the coupling between the ionosphere and thermosphere through photochemical processes under the forcing of topography modulated thermal tides. For this coupling, the neutral scale height is the key atmospheric parameter determining ionospheric longitude variations. The relationship between ionospheric and thermospheric longitude variations conforms to the Chapman theory and vertical propagation of non-migrating thermal tides. The results suggest that longitude variation of N_mM₂ can be used as a quantitative indicator for that of the thermal structure in the lower thermosphere (for both amplitude and phase).

Summary

In this study, H_n of the Martian lower thermosphere was retrieved from the MGS electron density profiles, then concurrent longitude variations in the Martian ionosphere and lower thermosphere at high northern latitudes were investigated using h_mM₂, N_mM₂, and H_n. The data during a period with small LST changes were used such that longitude variations associated with topography modulated non-migrating tides can be analyzed in detail. Longitude variations of H_n, N_mM₂ and h_mM₂ can reach ~ 20%, ~ 8% and ~ 2%, respectively. The thermosphere and the ionosphere have similar longitude components dominated by the wave − 3 and − 2; however, these components are not fully consistent with those of the topography, in which the wave − 1 is also dominant. Moreover, longitude variations of the three parameters are different from each other.

The dominant wave − 3 was further analyzed in detail. Longitude variations of the ionosphere and thermosphere show evident relevance to the topography. With increasing latitudes, the wave phases of the thermosphere and ionosphere show similar westward shifts with that of the topography. Thus, the different longitude components of the ionosphere and thermosphere from those of the topography imply discrepant exciting and propagating efficiencies of various topography modulated waves. Ionospheric longitude variations form as the result of the coupling between the ionosphere and the thermosphere; for this coupling the neutral scale height is the key atmospheric parameter determining ionospheric longitude variations. Both the wave-3 phases and percentage amplitudes of h_mM₂, N_mM₂, and H_n are different from each other. The phase difference between H_n and N_mM₂ is about a half of a wave cycle, and the amplitudes of H_n are nearly twice as large as those of N_mM₂. Both are consistent with the Chapman theory. The much smaller amplitudes of h_mM₂ than those of H_n are also in line with the Chapman theory. Moreover, the phase difference between H_n and h_mM₂ can be attributed to the vertical propagation of atmospheric thermal tides, since H_n and h_mM₂ depend on the neutral temperatures at different height levels.