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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 (Hn) and ionospheric peak electron density (NmM2) and height (hmM2) 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 Hn and NmM2 are nearly in anti-phase and percentage fluctuation amplitudes of Hn are nearly twice as large as those of NmM2, which indicate the non-migrating tide forced coupling between the ionosphere and thermosphere conforms to the Chapman theory, and suggests longitude variation of NmM2 can be used as a quantitative indicator for that of the thermal structure in the lower thermosphere. Longitude variation phases of Hn and hmM2 are also discrepant. That is due to tide vertical propagation since Hn and hmM2 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 Ne is electron density, h is height, NmM2 is the peak electron density of the M2 layer, hmM2 is the peak height of the M2 layer, and Hn is the scale height of CO2. That is to say, the shape of the electron density profile strongly depends on Hn. The key parameters of the M2 peak, NmM2 and hmM2, 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 Hn to best fit those profiles using the Chapman-α function.

Fig. 1
figure 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 NmM2, hmM2, and Hn

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 Hn to best fit the electron density profile. In view of the uncertainties of the MGS measurements, the fitted NmM2 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. Hn 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
figure 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 hmM2, NmM2, and Hn. 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 hmM2, NmM2, and Hn, respectively. hmM2 decreases while NmM2 increases with increasing latitude owing to the solar zenith angle decreases with increasing latitude (see Fig. 1). Similar to hmM2, Hn 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 hmM2 and Hn. 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 hmM2 can reach ~ 7 km, while the standard deviation of the gridded hmM2 is generally lower than ~ 4 km. The longitude fluctuation of NmM2 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 hmM2, NmM2, and Hn can reach the orders of ~ 2%, ~ 8%, and ~ 20%, respectively.

Fig. 3
figure 3

Longitude and latitude variations of hmM2, NmM2, and Hn. ac present the gridded mean hmM2, NmM2, and Hn, respectively; df are standard deviations of the gridded hmM2, NmM2, and Hn, respectively; gi show the residual hmM2, NmM2, and Hn, respectively, after removing zonal averages; jl are percentage longitude variations of hmM2, NmM2, and Hn, 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, Pl is parameter's longitude fluctuation (Fig. 3g–i), and An and ψn are the amplitude and phase of wave-n component, respectively. Figure 4a shows the longitude variations of the hmM2 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 hmM2, NmM2, and Hn, 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 NmM2 and Hn, which also can cause the uneven amplitudes of the peaks.

Fig. 4
figure 4

Analysis for the longitude wave components of hmM2, NmM2, and Hn. a shows longitude variation of the hmM2 at 64°N. The gray dots are gridded hmM2; 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 hmM2, NmM2, and Hn fittings. c is latitudinally averaged amplitudes of the longitude wave − 1 to − 6 in hmM2, NmM2, and Hn

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 Hn 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 Hn longitude variations. Zou et al. (2011) also estimated Hn 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 Hn. As shown in Fig. 3, the gridded mean Hn 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, Hn 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 hmM2, NmM2, and Hn (Fig. 4), which mainly manifests as that a dominant longitude variation component in the topography, the wave − 1, is not prominent in hmM2, NmM2, and Hn. 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 hmM2, NmM2, and Hn 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 Hn 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
figure 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. (eg) are latitude variations of the longitude wave − 3 in hmM2, NmM2, and Hn, 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 NmM2 are significantly asynchronous with those of hmM2 and Hn. 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 NmM2, hmM2, and Hn for comparison. Differences between the phases are evident. Taking NmM2 for reference, the phase difference between hmM2 and NmM2 is ~ 40°, and that between Hn and NmM2 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, NmM2 primarily depends on the CO2 density at hmM2 and Hn corresponds to the averaged neutral temperature in the vicinity of hmM2, 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, Tn 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, NmM2 variation should be negatively correlated with Hn variation in view of that NmM2 is positively correlated with n. That means longitude variations of NmM2 and Hn should be in anti-phase, just as presented in Fig. 6a. This result indicates that longitude variations of Hn driven by non-migrating tides modulate the concurrent longitude variations of NmM2 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
figure 6

Latitude variations of a the wave − 3 phases and b percentage amplitudes. The blue, red, and gray lines are for NmM2, hmM2, and Hn, respectively

hmM2 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 Hn, then longitude variations of hmM2 should be in-phase with those of Hn. 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, hmM2 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, hmM2 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 hmM2, 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 hmM2 variations. That means the height level of the atmospheric temperature determining hmM2 is lower than the height level of Hn. Thus, the difference of the wave − 3 phase between hmM2 and Hn 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 hmM2 should be in-phase with that of Hn 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 NmM2, hmM2, and Hn for comparison. The percentage amplitudes of Hn are nearly twice as large as those of NmM2. The latitudinally averaged ratio of Hn amplitudes to NmM2 amplitudes is ~ 2.3, similar to the ratio of their total longitude variation magnitudes (Fig. 3). For a Chapman-α layer NmM2 is proportional to Hn−1/2, which means a change of the neutral scale height ΔHn/Hn will cause a smaller change of the electron density ΔNmM2/ NmM2 with a magnitude of half that of ΔHn/Hn. Thus, the wave-3 amplitude ratio of Hn to NmM2 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 hmM2) used for fitting Hn is higher than hmM2. The percentage amplitudes of the longitude variations of hmM2 are much smaller than those of Hn. hmM2 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, Hn’ is the effective neutral scale height of the atmosphere below the M2 peak. Since the value of hmM2 is dominated by the base value of χ = 0 (e.g., Morgan et al. 2008), the percentage variation of hmM2 caused by the change of the neutral scale height is much smaller than that of the neutral scale height.

The observed wave phases of Hn and hmM2 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 (TECp, in units of TECu, 1TECu = 1016 electrons/m2) to investigate its longitude variations. In view of hmM2 varies with longitude and latitude under the selected condition (see Fig. 3), for each electron density profile a TECp 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. TECp data were also gridded according to the operation used in Fig. 3. Figure 7a shows longitude and latitude variations of the gridded mean TECp and Fig. 7b presents the corresponding standard deviations of the gridded TECp. TECp varies primarily with latitude due to the change of the solar zenith angle, which is similar to NmM2 (see Fig. 3), while its longitude variation appears to be not as evident as that in NmM2. Figure 7c presents the longitude variation using the residual TECp after removing zonal averages (TECp). As expected, the aforementioned wave − 3 and − 2 are not evident in TECp, and the longitude variation of TECp is basically equivalent to the standard deviation of the gridded TECp in amplitude. Figure 7d further shows the amplitudes of the longitude wave − 1 to − 6 of TECp. 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 TECp further supports that ionospheric longitude variations are related to upward propagating non-migrating tides.

Fig. 7
figure 7

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

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 NmM2 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, Hn 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 hmM2, NmM2, and Hn. 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 Hn, NmM2 and hmM2 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 hmM2, NmM2, and Hn are different from each other. The phase difference between Hn and NmM2 is about a half of a wave cycle, and the amplitudes of Hn are nearly twice as large as those of NmM2. Both are consistent with the Chapman theory. The much smaller amplitudes of hmM2 than those of Hn are also in line with the Chapman theory. Moreover, the phase difference between Hn and hmM2 can be attributed to the vertical propagation of atmospheric thermal tides, since Hn and hmM2 depend on the neutral temperatures at different height levels.

Availability of data and materials

The MGS electron density profiles are available at https://pds-ppi.igpp.ucla.edu/search/?sc=Mars Global Surveyor&t=Mars&i=RSS; the Martian topography data can be obtained from https://pds-geosciences.wustl.edu/missions/mgs/mola.html.

Abbreviations

H n :

Neutral scale height

N m M 2 :

Peak electron density of the M2 layer

h m M 2 :

Peak height of the M2 layer

MGS:

Mars Global Surveyor

SPW:

Stationary Planetary Wave

LST:

Local Solar Time

Ls:

Solar longitude of Mars

TEC p :

Total Electron Content of partial M2 layer

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Acknowledgements

The authors thank the MGS Radio Science Team for making the ionospheric electron density profile data and the MGS MOLA Science Team for producing the Martian topography data.

Funding

This research was supported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB 41000000), National Natural Science Foundation of China (41922029, 42030202), and Youth Innovation Promotion Association, CAS (Grant No. Y202021).

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YC performed the data analyses and wrote the manuscript. LL, HL, HZ and RZ participated in the discussion for the results and revised the manuscript. All authors read and approved the final manuscript.

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Correspondence to Yiding Chen.

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Chen, Y., Liu, L., Le, H. et al. Concurrent effects of Martian topography on the thermosphere and ionosphere at high northern latitudes. Earth Planets Space 74, 26 (2022). https://doi.org/10.1186/s40623-022-01582-w

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Keywords

  • Martian ionosphere
  • Neutral scale height
  • Longitude variation