Volume 130, Issue 6 e2024JE008854
Research Article
Open Access

Ionospheric Analysis With Martian Mutual Radio Occultation

Jacob Parrott

Corresponding Author

Jacob Parrott

Imperial College London, London, UK

Correspondence to:

J. Parrott,

[email protected]

Contribution: Conceptualization, Methodology, Software, Validation, Formal analysis, ​Investigation, Data curation, Writing - original draft, Writing - review & editing, Visualization

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Håkan Svedhem

Håkan Svedhem

TU Delft, Delft, The Netherlands

Contribution: Methodology, Validation, Writing - review & editing, Supervision

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Beatriz Sánchez-Cano

Beatriz Sánchez-Cano

School of Physics and Astronomy, University of Leicester, Leicester, UK

Contribution: Methodology, Validation, Formal analysis, Writing - review & editing

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Olivier Witasse

Olivier Witasse

European Space Research and Technology Centre, ESA-ESTEC, Noordwijk, The Netherlands

Contribution: Formal analysis, Writing - review & editing

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Colin Wilson

Colin Wilson

European Space Research and Technology Centre, ESA-ESTEC, Noordwijk, The Netherlands

Contribution: Writing - review & editing

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Ingo Müller-Wodarg

Ingo Müller-Wodarg

Imperial College London, London, UK

Contribution: Methodology, Validation, Formal analysis, Resources, Writing - review & editing, Supervision, Project administration, Funding acquisition

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First published: 06 June 2025

Abstract

This study presents a comprehensive analysis of the Martian ionosphere using Mutual Radio Occultation (RO) observations between Mars Express and Trace Gas Orbiter, featuring 71 full vertical profiles out of a total of 124 measurements. Among these, 35 measurements were taken from regions with Solar Zenith Angles lower than 40°. The profiles also represent the largest data set for the lower M1 ionospheric layer during the midday ever measured. This paper has also been submitted with a comprehensive data set, which marks the first time MEX-TGO RO data has been made available to the community. Additionally, neutral temperature profiles have been extracted from the measurements. We find unexpected features in the lower thermosphere temperature behavior which we conclude is likely due to the effects of local circulation and associated dynamical heating rather than solar-controlled.

Key Points

  • Many low-SZA ionospheric profiles have been gathered

  • All data sets for MEX-TGO Mutual Radio Occultation have now been made available to the community

  • Temperature trends around 120 km do not follow the expected Solar Zenith Angles trend with direct solar heating

Plain Language Summary

This article shows the results of 71 Martian mutual radio occultation (RO) measurements. This new measurement technique is similar to conventional RO, where a radio signal is sent from a satellite orbiting another planet to a ground station on earth. As this signal passes through the planetary atmosphere, it bends slightly due to refraction and we can look at this amount of bending to infer things such as temperature and electron density. Mutual RO (sometimes called crosslink or inter-satellite RO) is when we do not send the signal back to Earth, but we send the radio signal between two satellites orbiting the same planet. Mutual RO has a large advantage over conventional spacecraft-to-Earth RO because we can measure local times close to midday. This article uses these data sets from this new measuring technique to explore the trends of the ionosphere with varying amounts of irradiance from the sun. This article also uses ionospheric readings to predict the temperature around 120 km altitude and then finds that it is more controlled by dynamics (the transport of the air, like winds) instead of the direct heating from the sun.

1 Introduction

A radio occultation (RO) observation occurs when a radio transmitter and receiver are obscured from each other by a planetary atmosphere. Just before the signal is lost, the line of sight between the two antennas grazes the planet's limb, progressively penetrating deeper into the atmosphere until reaching a medium of sufficient opacity; be that a planetary surface for terrestrial planets, or a dense atmosphere on the gas giants. During this process, the signal traverses different atmospheric layers, each possessing varying refractive properties, resulting in a slight frequency shift. After accounting for the Doppler shift caused by the relative motion of the two spacecraft, this frequency shift can be analyzed to determine the refractive properties of the atmosphere. These properties can then be used to estimate the neutral atmosphere's density and the electron density of the ionosphere (e.g., Fjeldbo et al., 1971; A. Kliore et al., 2004; Withers, 2020). Traditionally, RO observations for planets other than Earth involve a spacecraft orbiting the planet and a ground station on Earth. However, this technique can also be performed between two spacecraft orbiting the same planet, a method known as mutual RO or Crosslink Occultation (Ao et al., 2015).

Since 1 November 2020, mutual RO observations have been conducted at Mars between ESA's Mars Express (MEX) and the ExoMars Trace Gas Orbiter (TGO) spacecraft, offering significant advancements in the study of the Martian atmosphere. A key advantage of mutual RO is its ability to provide a substantially broader spatial distribution of measurement coordinates and a wider range of Solar Zenith Angles (SZA). SZA is the value from the surface normal to direction of sun, so a SZA of 0° is at midday, directly under the sun, whereas 90° is at the sunset/sunrise terminator as seen from the surface of the planet. This expanded coverage is crucial for understanding atmospheric conditions across different regions of Mars. For instance, the primary factor influencing Martian ionospheric densities is the SZA, with the Radio Occultation Science Experiment (ROSE) on the Mars Atmosphere and Volatile EvolutioN mission (MAVEN) achieving their lowest SZA measurement at 45° (Withers et al., 2024). Such angles are exceedingly rare, with our SPICE simulations indicating that only 0.1% occur below 70°, resulting in a lack of critical data for midday martian conditions. While lower SZA RO measurements can be found in the Mariner 9 (A. J. Kliore et al., 1972) and Viking 1 (Fjeldbo et al., 1977) archives, these only extend down to 47° and 53°, respectively (Vogt et al., 2016).

Although other instruments, such as mass spectroscopy and radar sounders, have explored regions near noon, RO provides a unique advantage by offering a complete cross-section of the atmosphere. This capability is particularly important for studying features like the M1 layer of the ionosphere (around 90–110 km), which remains largely unexplored in low SZA regions.

The first RO experiment beyond Earth was conducted at Mars by Mariner IV in 1965, which established a surface pressure of 5–9 mb (Kliore, 1974). The Martian ionosphere was first observed by the Mariner 9 spacecraft, which collected 114 profiles (Vogt et al., 2016; Withers et al., 2015) Further exploration of the ionosphere via RO was carried out in 1976 by the Viking orbiters (Hanson et al., 1977), which identified the subsolar peak electron density at an altitude of 120 km with a scale height of 10 km (Hantsch & Bauer, 1990). Over the following three decades, RO was employed to investigate the martian ionosphere using Mars Global Surveyor (MGS), Mars Express, and MAVEN (Hinson et al., 1999, Pätzold et al., 2004; Withers et al., 2020, respectively). This technique was also demonstrated by the Mars Cube One (MarCO-A) CubeSat in 2018 (Oudrhiri et al., 2020); however, due to pointing errors and the absence of an Ultra-Stable Oscillator, the ionosphere was not detected, particularly as the probe was focused on the nightside of Mars. The feasibility of conducting RO between two spacecraft at the same planet has also been explored, with an engineering demonstration of mutual RO performed between Mars Reconnaissance Orbiter and Mars Odyssey in 2007, resulting in three quality ionospheric soundings (Ao et al., 2015).

A more systematic exploration of MEX-TGO mutual RO has been conducted by Parrott et al. (2024), including the planning of occultation opportunities, the processing chain, initial results, and engineering recommendations for future missions. The extensive data sets, ranging from Level-1 to 4, generated by these measurements have been made available through the European Space Agency's Planetary Service Archive (Parrott, 2024).

This paper will elucidate the scientific implications of these measurements, focusing specifically on the sources of variability observed in the M2 (120–150 km) and M1 (90–110 km) peak densities and altitudes, as well as the inferred thermospheric temperatures. Through this analysis, we aim to enhance our understanding of the Martian atmosphere and its dynamic processes.

2 The Martian Ionosphere

The martian atmosphere, akin to other planetary atmospheres within the solar system, exhibits a radial structure characterized by a decrease in neutral density from the surface up to the interplanetary medium. The embedded ionosphere, located within the mesosphere and thermosphere, results from a balance of processes such as photoionization (and its secondaries) and recombination (Schunk & Nagy, 2009). The density of the dayside martian ionosphere is notably influenced by photoionization from sunlight, and impact ionization caused by photoelectrons and their secondaries. On the nightside, some ionization persists due to electron precipitation (Fox et al., 1993).

The structure of the martian ionosphere is primarily governed by photochemical processes as photochemical timescales are smaller than transport timescales (Fox et al., 2017; Matta et al., 2013). Consequently, the ionospheric layers generally conform to an alpha-Chapman profile. This profile arises from the interaction between the exponential increase in neutral density with decreasing altitude and the optical depth of radiation at specific wavelengths, as described in the equation for the two superimposed ionospheric layers.
N e ( z , χ ) = l = M 2 M 1 exp 1 2 1 z z l H l exp z z l H l sec χ ${N}_{e}(z,\chi )=\sum\limits _{l=M2}^{M1}\mathrm{exp}\left\{\left[\frac{1}{2}\left(1-\frac{z-{z}_{l}}{{H}_{l}}-\mathrm{exp}\left(-\frac{z-{z}_{l}}{{H}_{l}}\right)\mathrm{sec}\,\chi \right)\right]\right\}$ (1)

The topside of the Chapman profile reflects the e-folding nature of neutral atmospheres, while the bottom side is shaped by reduced radiation penetration at lower altitudes. The Martian ionosphere typically consists of two such layers: the primary M2 layer, located at approximately 120–150 km, and the secondary M1 layer, found at around 90–110 km. The M2 layer primarily forms due to the photoionization of CO2 by extreme ultraviolet (EUV) radiation, peaking where the optical depth for this wavelength reaches unity. Below this altitude, the M1 layer's height is determined by the penetration depth of soft X-rays, where its formation is largely driven by photoionization and then secondary ionizations from photoelectrons generated by these higher-energy soft X-ray photons (Fox, 2004; Martinis et al., 2003). Research has shown that internal factors like Mars's crustal magnetic field can also significantly influence the Martian ionosphere (Andrews et al., 2023; Langlais et al., 2019; Lillis et al., 2008; Majeed et al., 2025; Matta et al., 2015). Finally, there are also known effects of dust storms where the dust loading increases infra-red absorption and heats the lower atmosphere. This causes the atmosphere to thermally expand, leading to an increase in peak density altitudes (Felici et al., 2020; Girazian et al., 2020; Peter et al., 2023).

Due to conventional RO only exploring regions near the terminator, there has been considerable work on the difference between the dawn and dusk ionospheric dynamics. Segale et al. (2024) used MAVEN ROSE data to show that dawn regions have a significantly higher M2 altitude and density during perihelion, as opposed to dusk, which varies less with solar distance. Whilst investigating the systematic difference between MAVEN ROSE and LPW measurements, Felici et al. (2022) postulated that the dawn ionosphere exhibits higher variability in general than the dusk regions. Pilinski et al. (2019) suggested this dawn/dusk asymmetry is due to diurnal variations in coupling between the ionosphere and the neutral atmosphere. The neutral atmosphere (between 150 and 300 km) is known to be at its highest density and temperatures at dusk, instead of the middle of the day (Gupta et al., 2019). This would infer a higher molecular collisionallity at dusk, therefore effecting the coupling in the ionosphere-thermosphere system.

Although not the primary focus of this work, the nightside ionosphere is also of interest, where it has an irregular morphology and is sustained by electron impact ionization (Girazian et al., 2017a, 2017b). Observations have revealed density structures in the ionosphere, with electron densities peaking at around 5 × 1 0 3 $5\times 1{0}^{3}$ c m 3 ${\mathrm{c}\mathrm{m}}^{-3}$ on the nightside (Withers et al., 2022). Additionally, the ionosphere exhibits irregularities similar to those found in Earth's equatorial E region, particularly in areas where the magnetic field is parallel to the surface (Tian et al., 2022).

3 The Data

At the time of writing, the MEX-TGO mutual RO campaign is still ongoing, with a cadence of roughly two per week. So far, we have conducted 124 measurements across the full range of latitudes and local times, as illustrated in Figure 1. Of these, 71 successfully yielded day-side vertical electron density profiles. The measurements span SZA values from as low as 5.2° close to the sub-solar point to 171° near the anti-solar point. Notably, 35 of these observations were conducted below the minimum SZA of 46.8° typically achievable by the ROSE MAVEN experiment, highlighting our ability to comprehensively study for the first time the near-noon dayside ionosphere. Additionally, 18 readings were obtained from the nightside; however, only the day-side vertical profiles and their corresponding specifications are presented in this article. Numerous other mutual RO measurements have been discarded due to reasons listed in Parrott et al. (2024). In brief, these reasons include synchronization errors between MEX and TGO, large spectral artifacts due to Electra antenna faults and MELACOM broadcasting a HAIL sequence which included regular silent periods (making carrier tone extraction impossible). The main purpose of these profiles is to study the photochemical region of the ionosphere (less than 200 km). The electron densities in the diffusion region higher up are considered too low to be considered reliable with the current noise floor of the RO measurements. These specifications are detailed in Table 1, and the corresponding profiles are displayed in Figures 2 and 3. One may notice the occasional profile having missing values (e.g., the 01/02/23 profile in panel I of Figure 2), this is due to omission of portions of signal due to of spectral artifacts in the readings from the receiving antenna (called Electra).

Details are in the caption following the image

Distribution of 124 mutual radio occultations with latitude on the y-axis and local solar time on the x-axis. Histograms placed on the axis to show the even spread, with 19 bins for the ± $\pm $ 90° latitude y-axis (9.5° per bin) and 19 bins for the 24 hr local time x-axis (75 min per bin).

Table 1. Specification Table for All Mutual Radio Occultation Measurements
Date UTC start UTC of occultation SZA (°) Lat (°N) Lon (°E) Local time Max altitude (km) Scheme Solar distance (AU) F10.7 Ly-a (mWm−2)
02/04/21 15:09:00 15:18:16 14 13 144 11:04 399 Ingress 1.62 71 1.44
06/04/21 03:30:00 03:38:49 34 43 352 11:01 415 Ingress 1.62 71 1.45
14/04/21 23:32:00 23:33:09 82 43 61 05:55 394 Egress 1.63 75 1.47
18/05/21 07:07:00 07:08:32 63 80 346 11:18 368 Egress 1.65 79 1.49
25/05/21 00:08:00 00:09:05 36 54 153 11:07 321 Egress 1.65 79 1.45
22/07/21 00:06:00 00:07:20 32 −8 6 12:18 374 Egress 1.67 91 1.49
06/04/22 02:14:21 02:23:47 62 4 224 07:55 387 Ingress 1.42 117 1.72
27/04/22 13:52:20 13:52:55 50 −17 13 15:28 326 Egress 1.42 117 1.66
18/05/22 05:00:27 05:09:23 39 −56 276 10:52 343 Ingress 1.42 117 1.64
27/05/22 13:21:22 13:22:00 41 18 246 10:59 407 Egress 1.39 121 1.79
01/06/22 11:01:00 11:09:50 69 −35 263 06:46 347 Ingress 1.39 121 1.74
13/06/22 03:18:23 03:28:08 73 −14 288 17:07 350 Ingress 1.39 121 1.73
30/06/22 14:06:29 14:15:16 39 −47 261 14:41 379 Ingress 1.38 99 1.75
08/07/22 10:46:11 10:55:28 32 −47 17 13:57 379 Ingress 1.38 135 1.75
19/07/22 19:49:30 19:58:45 5 −30 322 11:56 380 Ingress 1.39 146 1.82
25/08/22 09:02:31 09:03:14 59 21 164 14:37 397 Egress 1.41 118 1.67
30/08/22 14:49:09 14:49:57 51 23 112 13:30 391 Egress 1.41 120 1.72
17/09/22 04:50:41 04:51:41 59 −59 346 07:44 371 Egress 1.43 137 1.72
19/09/22 06:00:57 06:01:21 58 −54 350 07:49 379 Egress 1.43 136 1.69
28/09/22 14:05:55 14:06:52 66 −46 307 07:03 373 Egress 1.44 136 1.71
13/10/22 15:14:55 15:14:54 70 −51 227 17:08 334 Egress 1.44 136 1.69
22/10/22 01:41:59 01:42:40 69 −52 149 16:57 378 Egress 1.47 103 1.67
27/10/22 20:43:17 20:52:23 68 47 240 14:28 425 Ingress 1.48 126 1.76
31/10/22 09:34:47 09:35:14 21 −33 46 11:58 367 Egress 1.49 129 1.79
11/11/22 04:36:05 04:36:43 67 29 168 08:11 399 Egress 1.50 135 1.73
24/11/22 07:47:32 07:56:41 75 −82 289 11:12 379 Ingress 1.52 104 1.85
07/12/22 14:38:51 14:39:33 80 24 45 17:09 403 Egress 1.53 142 1.81
14/12/22 06:03:10 06:04:38 77 65 209 15:17 409 Egress 1.54 157 1.74
19/12/22 19:33:50 19:34:17 53 42 45 14:15 418 Egress 1.55 152 1.73
21/12/22 22:19:24 22:28:18 41 −40 4 13:05 380 Ingress 1.55 136 1.75
22/12/22 16:28:43 16:29:09 60 59 97 12:49 377 Egress 1.55 131 1.78
27/12/22 04:07:52 04:16:36 33 −33 312 12:07 380 Ingress 1.56 152 1.86
04/01/23 08:44:08 08:53:03 27 −8 294 10:18 353 Ingress 1.57 150 1.85
09/01/23 05:10:05 05:18:19 80 48 138 17:14 369 Ingress 1.57 182 1.75
27/01/23 01:14:13 01:23:28 74 12 214 07:02 384 Ingress 1.59 140 1.79
01/02/23 03:27:34 03:37:18 81 83 227 06:52 397 Ingress 1.60 131 1.86
09/02/23 00:07:25 00:16:29 76 77 5 07:42 407 Ingress 1.61 203 1.87
15/02/23 17:21:54 17:31:12 63 73 231 11:44 391 Ingress 1.61 171 1.81
23/02/23 14:03:27 14:12:27 54 64 339 10:40 368 Ingress 1.62 147 1.87
26/02/23 18:39:46 18:48:46 59 62 275 08:58 365 Ingress 1.62 156 1.87
10/03/23 03:53:34 04:02:40 32 45 299 12:31 359 Ingress 1.63 170 2.01
20/03/23 15:17:13 15:26:23 54 69 212 11:26 434 Ingress 1.64 157 1.96
17/04/23 14:21:09 14:22:09 77 −58 151 12:33 381 Egress 1.66 175 1.88
01/05/23 20:57:44 21:06:43 26 28 206 13:50 410 Ingress 1.66 156 2.05
08/05/23 06:20:01 06:29:18 29 42 123 13:37 416 Ingress 1.66 164 1.94
15/05/23 05:34:23 05:43:25 53 62 230 15:32 429 Ingress 1.66 139 1.86
27/06/23 23:05:49 23:05:49 13 36 326 11:23 389 Egress 1.66 158 1.98
20/07/23 15:21:38 15:21:32 48 57 259 08:39 404 Egress 1.65 188 1.90
24/07/23 23:20:47 23:20:41 63 88 246 12:59 328 Egress 1.65 188 1.92
19/08/23 20:15:50 20:16:14 83 54 278 19:29 433 Egress 1.63 156 2.03
24/08/23 05:52:15 05:52:51 37 −13 64 12:01 325 Egress 1.63 156 1.86
28/08/23 08:38:51 08:48:02 47 70 45 11:04 345 Ingress 1.63 156 1.97
12/09/23 10:09:36 10:10:26 51 73 193 12:38 431 Egress 1.61 157 2.01
19/09/23 03:03:29 03:03:46 46 30 304 08:39 404 Egress 1.61 162 1.96
27/09/23 13:32:12 13:32:44 63 44 206 07:11 414 Egress 1.60 156 1.99
10/10/23 08:46:55 08:56:12 60 38 176 16:23 388 Ingress 1.58 160 2.04
16/10/23 12:08:14 12:18:07 31 36 146 13:51 417 Ingress 1.58 145 1.96
24/10/23 20:49:55 20:50:36 44 −26 83 12:51 351 Egress 1.58 145 1.93
29/10/23 12:52:15 12:52:39 49 −33 244 12:37 316 Egress 1.58 145 1.92
07/12/23 07:17:15 07:18:04 73 24 45 17:01 385 Egress 1.51 129 1.98
11/12/23 09:36:40 09:37:20 64 36 38 16:14 401 Egress 1.51 120 1.94
20/12/23 09:42:17 09:42:34 39 22 96 14:24 399 Egress 1.50 189 1.88
26/03/24 09:19:01 09:28:16 79 17 207 07:08 397 Ingress 1.39 150 1.89
31/03/24 00:17:09 00:17:02 66 −5 168 16:23 376 Egress 1.39 132 1.95
10/04/24 03:42:05 03:41:57 26 −45 157 12:28 305 Egress 1.39 132 2.03
19/04/24 19:44:20 19:45:00 8 −18 11 12:30 377 Egress 1.38 220 1.88
26/04/24 15:08:14 15:08:42 56 34 145 12:25 393 Egress 1.38 169 1.87
08/05/24 03:54:39 03:55:34 36 −22 21 09:24 381 Egress 1.38 208 1.88
15/05/24 08:37:11 08:37:56 54 −70 10 08:39 313 Egress 1.38 216 1.96
31/05/24 17:01:35 17:10:44 57 9 139 15:05 327 Ingress 1.39 184 1.83
17/06/24 19:41:19 19:42:16 35 8 212 11:21 362 Egress 1.39 180 2.17
Details are in the caption following the image

Vertical electron density profiles that have been acquired via mutual radio occultation between Mars Express and Trace Gas Orbiter between 02/04/21 and 01/02/23. As well as the Solar Zenith Angle, the legend for each plot informs when the measurement took place such that it can be checked in Table 1.

Details are in the caption following the image

More vertical electron density profiles that have been acquired via mutual radio occultation between Mars Express and Trace Gas Orbiter between 09/02/23 and 17/06/24.

The profiles are organized chronologically and depict the Martian ionosphere and lower neutral atmosphere under a variety of conditions. The profiles have been shown in order of date as this is inline with changing solar activity. Between 02/04/21 and 27/06/23, the solar cycle was ramping up to maximum. Figure 3 in Withers et al. (2023) also shows vertical profiles with the purpose of comparing solar minimum MAVEN ROSE profiles with solar maximum MGS profiles. So, Figures 2 and 3 can be used in conjunction with this to complete the solar cycle from solar minimum to solar maximum.

With these figures, we are immediately able to determine the behavior of the M2 peak density and altitude with changing SZA and find a clear correlation with increasing SZA, which agrees well with previous work (Fallows et al., 2015; Fox & Weber, 2012; Mendillo et al., 2013; Němec et al., 2011; Sánchez-Cano et al., 2013; Segale et al., 2024). For instance, Panel G of Figure 3 demonstrates the M2 peak altitude rising and its density decreasing as the SZA increases. A more detailed analysis of these profiles will be provided in Section 5.

To validate the profiles before further analysis can take place, a case study for two of these profiles is presented in Figure 4. This figure illustrates the vertical electron densities obtained from measurements conducted on 07/12/22 and 27/06/23, corresponding to panels A and B, respectively. The profile in panel A was selected for its high SZA of 80°, allowing for a direct comparison with conventional RO data. As such, this profile can be compared with both models and instruments. This comparison includes a profile from a MAVEN ROSE measurement taken under similar conditions, specifically on 07/11/22 at 18:11:18 UT, with a latitude of 44° and an SZA of 80°. Additionally, panel A features a comparison with in-situ electron density measurements from MAVEN's Langmuir Probe and Waves instrument (Andersson et al., 2015), specifically those obtained during Deep-Dip campaign 4 at 08/09/15. This date is very different to the mutual RO data set as MAVEN's orbital parameters mean that it only passes through the low altitude atmosphere during rare deep-dip campaigns. These campaigns have only gone to a low enough altitude around the terminator, so only high SZA comparisons can be made. Unfortunately, this is why such a comparison is not possible for the profile in panel B, as MAVEN has not conducted a deep-dip to the required sub-150 km altitude whilst also having a low SZA.

Details are in the caption following the image

Vertical electron density profiles acquired via mutual Radio Occultation (RO) (black) for the dates of 07/12/22 (Panel A) and 27/06/23 (Panel B). Both profiles are compared with three models: Mars Climate Database, NeMars and Mars Initial Reference Ionosphere. The inputs for all the models are given in 0. Panel B has a measurement from a low solar zenith angle of 13°, and panel A is from a higher angle of 80°, which is more comparable with conventional RO. As such, it has been compared with a MAVEN Radio Occultation Science Experiment measurement. Panel A also includes local measurements from MAVEN's Langmuir Probe and Waves instrument.

However, the profile in panel B from 27/06/23 is from such a low SZA (13°) that there are no instruments that it can be compared with and can only be shown against models. These have been included to further provide validity to the mutual RO results and the inputs to these models, such as SZA and irradiance, can be found in Table 1. The Mars Climate Database (MCD) Global Circulation Model (MCD) provides the most comprehensive prediction due to its inclusion of atmospheric and heliophysical dynamics (Forget et al., 1999; González-Galindo et al., 2013; Millour et al., 2022), although it is constrained by resolution limitations and the absence of an M1 layer. Whilst the MCD profiles might seem sparse, the specific values for M2 altitude and peak density should be considered the most accurate among the other two models. The NeMars model is an empirical model derived from data collected by MEX's Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS) experiment, as well as conventional RO data from the MGS (Sánchez-Cano et al., 2013). The Mars Initial Reference Ionosphere (MIRI) model (Mendillo et al., 2013), which primarily relies on MARSIS data and incorporates some conventional RO data from MGS, also serves as a comparative framework. Additionally, the MIRI model includes data from the Mars Express Radio Science (MaRS) experiment (Pätzold et al., 2004). As a semi-empirical model, MIRI's numerical parameterizations are informed by well-established physical principles governing ionospheric behavior.

4 Results

The SZA trends in altitude and peak density for the M1 and M2 ionospheric layers are illustrated in Figure 5, derived from the profiles presented in Figures 2 and 3. As noted by Withers et al. (2024), the lowest SZA RO profiles obtained on Mars occur at 45°, indicated by a purple demarcation in the figure. This highlights the advantage of this mutual RO method, revealing 34 measurements that would be unattainable using conventional RO techniques. The error bars represent 1 standard deviation, and have been calculated in the same way as those in Parrott et al. (2024), in that each data set was processed 100 times with a 5% of the max amplitude input as stochastic noise. Error bars are not visible for panel C and D as altitude readings in our technique are very accurate. Height-error is a combination of spatial error from the SPICE framework ( $\ll $ 1 km) and the Electra/MELACOM on/off commanding time ( < ${< } $ 1 s).

Details are in the caption following the image

The variability of four key ionospheric parameters with increasing Solar Zenith Angles. Panel (a) indicates the M2 electron density, blue stars shows the density if the time and location for each measurement were input into a Mars Climate Database Global Circulation Model, the black lines are the empirical fits (explained in the text), the green line is the trend found in Němec et al. (2011), the red line is that of the NeMars model (Sánchez-Cano et al., 2013) and the purple is the fit from Fallows et al. (2015).

Each of the four panels is compared with the NeMars model, with the inputs listed in Table 1. An alternative empirical fit for these M2 trends is also provided by Němec et al. (2011), based on MARSIS data. They observed that the M2 density is better represented by an inverse exponential decay rather than the conventional flattened cosine function. Both of these models focused on the entire ionospheric structure, but Fallows et al. (2015) specifically focused on the M1 trend (found through MGS conventional RO profiles), so their trend can also be found in Figure 5.

Additionally, the MCD is utilized for comparison. The inputs for this are detailed in Table 1, include date, time, and coordinates, enabling the calculation of SZA, solar distance, season, solar activity, and atmospheric state; so this model should be regarded as the most accurate for M2 peak densities. However, it does not include a representation of the M1 layer and suffers from low vertical resolution. Consequently, it is not employed in panel B, which examines M2 altitude, as the model restricts the M2 peak altitude to only four discrete altitudes.

Having outlined the models, we now turn to the panel descriptions in descending order. Panel A of Figure 5 depicts the M2 density trend as a function of SZA, following the empirically fit relation of 1.6 × 1 0 5 × cos SZA 0.25 $1.6\times 1{0}^{5}\times \cos {\text{SZA}}^{-0.25}$ . All models used here, except the model of Němec et al. (2011), have trends that follow a similar flattened cosine morphology, although the MCD exhibits a narrower spread, suggesting that peak densities are modulated by factors not accounted for in the MCD. However, both the mutual RO and MCD data shows some amount of spread. A key reason for this could be the dawn/dusk symmetry mentioned earlier in this article.

Panel B illustrates the same trend for the M1 layer. An initial conclusion can be made about the presence of the M1 ionospheric layer, which was expected to not exist during the midday (Mayyasi & Mendillo, 2015), but was predicted recently by Segale et al. (2024). A notable anomaly occurs when SZA is 53°, with a density of 1.51 × 1 0 11 $1.51\times 1{0}^{11}$   m 3 ${\mathrm{m}}^{-3}$ , recorded at 08:37 on 15/05/24, shortly after a solar flare and during a coronal mass ejection disturbance. This significant result is outside the scope of this publication and merits a dedicated publication. This panel is particularly significant as it represents the first examination of the M1 layer in low-SZA regions.

Panel C presents the M2 altitude trend, with both models predicting a slight growth with SZA, which only begins to rise substantially around 70° SZA.

Lastly, panel D focuses on M1 altitude, which exhibits the greatest variability among these trends and shows minimal correlation with SZA. The highest M1 altitude is observed at 82°, while the lowest is at 15°, which agrees with theory (Fallows et al., 2015; Fox & Weber, 2012; Mendillo et al., 2013; Němec et al., 2011; Sánchez-Cano et al., 2013; Segale et al., 2024). This wide spread around the theoretical trend has reduced the value of showing any empirical fit. The model in Němec et al. (2011) does not provide a fit for M1 altitudes and the NeMars models are expected to perform poorly in predicting this variable for low SZA, as they are partially based on MARSIS data, which, due to its radar sounder nature, cannot penetrate below the higher M2 layer. They also assimilate MGS RO data, but is confined to high SZA, making the low SZA predictions speculative.

5 Discussion

5.1 Solar Driven Ionospheric Variability

Numerous studies have analyzed how martian ionospheric layers vary with SZA (Hantsch & Bauer, 1990; Morgan et al., 2008; Němec et al., 2011; Zhang et al., 1990). However, the mutualRO data set marks a significant shift from focusing solely on high SZA values, necessitating an update to the empirical formulas to ensure their validity in low SZA regions. The following density formulas for the M1 and M2 ionospheric layers are presented, with irradiance represented by either F 10.7 ${F}_{10.7}$ or F EUV ${F}_{\mathit{EUV}}$ , measured in solar flux units and mWm−2, respectively. The latter is preferred due to its higher accuracy, as it uses a frequency band more relevant to ionospheric formation. These irradiance levels, derived from the 43 and 59.5 nm bands of the FISM2 model (Chamberlin et al., 2020), were chosen because they closely match the ionization cross-sections of CO2 (as shown in Figure 10 of Lollo et al., 2012). On the other hand, F 10.7 ${F}_{10.7}$ is included for comparability with previous empirical fits, even though it is measured for Earth at a different radio frequency band. Below are the empirical fits for the M1 and M2 electron densities, expressed in terms of F EUV ${F}_{\mathit{EUV}}$ or F 10.7 ${F}_{10.7}$ .
N M 2 = 1.6 × 1 0 11 cos ( SZA ) 0.25 + 4.3 × 1 0 8 F 10.7 ${N}_{M2}=1.6\times 1{0}^{11}\,\cos {(\text{SZA})}^{-0.25}+4.3\times 1{0}^{8}{F}_{10.7}$ (2)
= 1.6 × 1 0 11 cos ( SZA ) 0.25 + 5.3 × 1 0 10 F EUV ${=}1.6\times 1{0}^{11}\,\cos {(\text{SZA})}^{-0.25}+5.3\times 1{0}^{10}{F}_{\mathit{EUV}}$ (3)
N M 1 = 7.3 × 1 0 10 cos ( SZA ) 0.34 + 2.5 × 1 0 8 F 10.7 ${N}_{M1}=7.3\times 1{0}^{10}\,\cos {(\text{SZA})}^{-0.34}+2.5\times 1{0}^{8}{F}_{10.7}$ (4)
= 7.3 × 1 0 10 cos ( SZA ) 0.34 + 3.1 × 1 0 10 F EUV ${=}7.3\times 1{0}^{10}\,\cos {(\text{SZA})}^{-0.34}+3.1\times 1{0}^{10}{F}_{\mathit{EUV}}$ (5)

Equations 2 and 4 were derived using the same methodology as Němec et al. (2011), where the largest factor (SZA) was determined first, followed by the calculation of the Spearman rank coefficient on the residuals for subsequent minor parameters until the correlation fell below 0.2. This analysis yielded a surprising result: solar distance played a negligible role in influencing electron densities, with correlations of −0.16 for M2 and −0.01 for M1. This is evident in Figure 6, where the effects of solar distance (shown in the panel C) show no resemblance to the sub-solar peak density values. In contrast, increasing solar activity (indicated by F 10.7 ${F}_{10.7}$ and FISM-2 data) is correlated with rising sub-solar values. The low correlations observed are likely due to the limited sample size.

Details are in the caption following the image

Sub-Solar M2 Peak Electron Densities [corrected using 1.6 × 1 0 11 cos ( SZA ) 0.25 $1.6\times 1{0}^{11}\,\cos {(\text{SZA})}^{-0.25}$ ] compared with three major driving forces. Panel (b) shows the F 10.7 ${F}_{10.7}$ irradiance levels measured at Earth. Panel (c) is the martian solar distance measured in AU. Panel is irradiance levels simulated using the FISM-2 Model to 1AU.

As described in Section 2, the M1 layer is primarily driven by impact soft X-ray photoionization. Therefore, it may be more appropriate to examine the correlation with weaker soft X-ray irradiance levels. Instead of using the aforementioned EUV bands, the average of the 0.225, 0.6, 1.3, and 2.5 nm bands was utilized. This led to a coefficient of 2.27 × 1 0 11 $2.27\times 1{0}^{11}$ with a correlation of 0.61, which is a slight improvement over F EUV ${F}_{\mathit{EUV}}$ , which had a correlation of 0.58.

The SZA coefficient found here is notably lower than those reported in previous studies. The value of −0.25 produces a much flatter SZA trend for M2 densities. Hantsch and Bauer (1990), using Viking Lander and Mariner 4 data, predicted a coefficient of −0.57. Fox and Yeager (2006), using MGS occultation data, found a coefficient of −0.49 for periods of high solar activity. Morgan et al. (2008) refined the coefficient to −0.476 using a large data set from MARSIS AIS, which populated the low-SZA region. The lower coefficients obtained from mutual RO are likely because previous estimates have been primarily based on conventional RO, which lacks data for low-SZA regions and requires extrapolation to these lower SZA values. The only substantial data for midday comes from MARSIS AIS, which systematically produces higher topside density readings. Consequently, the inclusion of radar sounding data leads to an overestimation of midday density values and, overall, a steeper cosine trend with a larger SZA coefficient.

The M1 layer has been less extensively studied. However, Fox and Yeager (2006) used MGS conventional RO measurements from high-SZA regions and found a cosine exponent of −0.55 for low solar activity and −0.53 for high solar activity. The fact that the M1 SZA coefficient is larger than that of M2 is noteworthy. This is likely due to the greater penetration depth of soft X-rays, meaning the ionization occurs at altitudes where the neutral atmosphere is denser. As the slant angle increases during the day, moving away from the sub-solar point, the integral density rises at a faster rate than if the flux were at the same angle at a higher altitude. This steeper rate of ionization results in a larger SZA cosine coefficient.

Estimates of the sub-solar M2 peak density value lie in the middle range of previous estimates. The most accurate estimates are obtained via MARSIS radar sounding instruments, which consistently access low-SZA regions and do not require extrapolation from near the terminator. However, estimates by different authors using the same instrument vary widely due to the period at which their measurements were taken, including 2.1 × 1 0 11 $2.1\times 1{0}^{11}$ , 2.0 × 1 0 11 $2.0\times 1{0}^{11}$ , 1.8 × 1 0 11 $1.8\times 1{0}^{11}$ , and 1.6 × 1 0 11 $1.6\times 1{0}^{11}$   m 3 ${\mathrm{m}}^{-3}$ from Safaeinili et al. (2007), Gurnett et al. (2008), Nielsen et al. (2006), and Morgan et al. (2008), respectively. Only the last estimate agrees with the value obtained via mutual RO, as radar sounding tends to predict higher electron densities than RO.

Empirical fits were also determined for the altitudes of both ionospheric layers. The small sample size significantly limited the confidence levels, as indicated by the low correlation levels and the spread around the fits in Figure 5. Consequently, the fitted model was kept relatively simple, with SZA being the only significant factor. The first equation describing the altitudes of the M2 ionospheric layer was developed by Hantsch and Bauer (1990) and follows the form h m = h 0 + H ln ( sec ( SZA ) ) ${h}_{m}={h}_{0}+H\,\ln(\mathrm{sec}(\text{SZA}))$ , where h 0 ${h}_{0}$ is the sub-solar altitude and H $H$ is the scale height. The empirical fits are as follows:
h M 2 = 125.9 + 5.9 ln ( sec ( SZA ) ) ${h}_{M2}=125.9+5.9\,\ln(\mathrm{sec}(\text{SZA}))$ (6)
h M 1 = 106.2 + 5.3 ln ( sec ( SZA ) ) ${h}_{M1}=106.2+5.3\,\ln(\mathrm{sec}(\text{SZA}))$ (7)

5.2 Neutral Temperature Trend

As described in Appendix A2, the neutral temperatures can be inferred by the scale height of the M2 ionospheric peak. With this, a trend for the neutral temperature around the M2 ionospheric peak with increasing SZA can be found in Figure 7, which shows a temperature gradient of around 0.46 K per degree of SZA.

Details are in the caption following the image

Temperature trend with solar zenith angle. Blue stars are the from the same empirical Chapman fit method described in Appendix A2, but applied to the profiles found via the Mars Climate Database Global Circulation Model. The red line is the same method applied but for profiles derived from the NeMars model.

Similar to the approach used for Figure 5, error bars have been calculated in the same way, and the same MCD has been employed for comparison. The inputs for this are derived from the time and coordinates of each mutual RO measurement, ensuring consistency in SZA, solar activity, and solar distance, with variations in season and atmospheric circulation. Although the NeMars model was not originally intended to provide insights into neutral temperatures, it has been included here due to its ability to explicitly output ionospheric scale height, which can then be utilized in Equation A2.1 to estimate neutral temperatures.

Both the data and the two models have been normalized by bringing the initial value to 0 K, recognizing that these models rely heavily on MARSIS data for low SZA regions, as it represents the most extensive data set for these midday local times (Vogt et al., 2016). However, due to the fundamentally different measurement techniques and processing, the values needed to be normalized with a temperature offset of 202 K, 139 K, and 236 K for our measurements, the MCD, and NeMars, respectively.

The results depicted in Figure 7 may initially seem counter-intuitive, given that conventional understanding suggests a decrease in temperature with an increase in SZA due to reduced insolation. The increased slant angle causes solar flux to penetrate less deeply, resulting in a reduced deposition of thermal energy in the atmosphere around the M2 peak.

One might also hypothesize that, given the M2 altitudes are situated within the lower thermosphere, temperatures would be expected to rise with altitude. Furthermore, as Figure 5 illustrates, atmospheric layers are anticipated to ascend with increasing SZA. Despite this, an analysis of the 71 available profiles revealed no correlation between M2 peak altitude and temperature.

A comparable trend was observed by Jain et al. (2023), using data from MAVEN's Imaging Ultraviolet Spectrograph instrument (McClintock et al., 2015), although at a considerably higher altitude of 170–180 km. They proposed that temperature increases steadily throughout the Martian day, with heat only dissipating beyond the dusk terminator.

The temperature dynamics in this region have previously been explored through simulations by Bougher and Shinagawa (1998) using the Mars Thermosphere General Circulation Model (MTGCM), where their simulation results showed an increase in temperature with SZA. However, their study did not provide a detailed explanation for why this temperature trend occurred.

Using the more advanced and modern MCD, we have simulated transport processes at various altitudes. The outcomes of these simulations are presented in Figure 8. The MCD was used for the Martian spring equinox (Solar Longitude = 0°) with the meridian set to local time 18:00, placing the sub-solar point (12:00) at approximately 90° longitude.

Details are in the caption following the image

Mars Climate Database simulation results of the global thermospheric temperatures and wind at altitudes 120–200 km. Local times seem to be in reverse order, this is to match latitude with local times and to account for the direction of rotation of Mars. The dusk terminator is leading up to 18:00, and can be seen by the downwelling in the wind map and the warmer region in the temperature map.

The left column of Figure 8 displays temperature, and it shows the warmest regions are observed near the poles and the terminator around 18:00. This temperature distribution can be employed to validate the results obtained via mutual RO in Figure 7, which showed that the temperature should increase as we get further away from the subsolar point at 12:00. Please note, the local times appear to be counting backwards across the x-axis, this is to account for the rotational direction of Mars' spin. This complex dynamic has also been depicted in Figure 9 to aid understanding. The right column depicts the magnitude and direction of horizontal winds as a quiver map, superimposed on a map showing the scalar value of downward wind. At an altitude of 200 km, the simulation reveals divergent winds originating from approximately 19:00 local time. The divergence does not originate at the sub-solar point due to the time lag required for the low-density atmosphere to warm. These divergent winds accelerate toward the poles, becoming transpolar, crossing over to the night side, and converging on the other side of the planet. The MTGCM also found these high-altitude transpolar winds in 1998 (Bougher & Shinagawa, 1998). The convergent winds gather around 08:00 leading to downwelling. This, in turn, causes divergent winds at lower altitudes near this antisolar point. Overall, the simulation illustrates divergent winds on the night side around 120 km due to downwelling near the anti-solar point, as well as divergent winds on the day side resulting from solar heating. These dynamics result in winds converging near the terminator, accompanied by further downwelling. The observed higher temperatures are attributed to the adiabatic heating of air as it descends to lower altitudes.

Details are in the caption following the image

A cartoon showing the cause of the increasing temperature as the Solar Zenith Angle increases near the equator. This is due to high altitude trans-polar winds causing divergent nightside winds around 120 km. The subsolar point is intentionally 50° of the divergent region, to account for the time required for solar heating.

In summary, this MCD simulation explains why there are divergent winds originating from the antisolar point. When these winds coming from the nightside collide with winds from the dayside (driven by solar heating), they are diverted downwards and warm-up as the air parcels are compressed as the pressure increases with decreasing altitude.

6 Conclusions

This study presents a detailed analysis of the martian ionosphere using mutual RO observations, showcasing 71 full vertical profiles out of a total of 124 measurements. Notably, 35 of these measurements were conducted in SZA regions lower than previously explored, offering new insights into the martian ionosphere. This expanded SZA coverage is a distinct advantage of mutual RO over conventional RO, and unlike radar sounders it includes whole vertical profile of the ionosphere, allowing for a more comprehensive understanding of atmospheric and ionospheric dynamics.

This article has also explored the trends of the peak electron densities and altitudes of both the M2 and M2 ionospheric layers. Finding similar cosine trends to previous studies, but finding that the M2 peak density should change less dramatically during the day. This was inferred by the cosine coefficient −0.25, which is about half the predictions in other works. This is likely due to our midday data sets which previous authors have not had access to. Empirical fits for altitudes where also provided, but the spread around this trend is significant as it is likely held back by the small data set size. For both fits, irradiance has been factored in as F 10.7 ${F}_{10.7}$ and F EUV ${F}_{\mathit{EUV}}$ . The former to align with previous works, and the latter due to the ionospheres sensitivity to this specific frequency band.

Additionally, this study extracted neutral temperature values from the derived vertical profiles. This revealed a thermospheric temperature increasing with SZA. This counter-intuitive result was explored with MCD simulations to reveal the dynamics are circulation driven, instead of being due to solar heating.

In conclusion, this research not only advances our understanding of the Martian ionosphere but also demonstrates the value of mutual RO as a powerful tool for thermospheric studies. The findings may have important implications for future missions and research, providing a solid foundation for further exploration of Mars and potentially other planetary bodies with similar observational techniques.

Acknowledgments

J.P acknowledges his UK Science and Technology Facilities Council (STFC) Ph.D. Bursary ST/T506151/1 and the ongoing support of the ESA Science Operations Centre and Mission Operations Centre teams. He also thanks Kingdom Parrott for their creation of Figure 9. IMW is grateful for the support from UK-STFC grant ST/S000364/1. B.S.-C. acknowledges support through UK-STFC Ernest Rutherford Fellowship ST/V004115/1.

    Appendix A

    A1 Processing Chain Amendment

    Several techniques have been implemented to extract valuable information from the raw data sets collected by TGO's Electra antenna. However, a significant enhancement has been introduced to improve the reliability of the final vertical electron density profiles. Specifically, Steps 4 and 5 in the Processing section of Parrott et al. (2024) outlined two procedures designed to account for variable frequency drift caused by the unstable oscillator. The initial step involves fitting a polynomial of variable order to the “vacuum portion” of the residuum, ensuring it closely approximates the data and intersects at the point where the ionosphere and neutral atmosphere counteract, producing a gradient of 0 $0$   H z s 1 $\mathrm{H}\mathrm{z}{\mathrm{s}}^{-1}$ . The subsequent step entails iteratively applying an increasing linear frequency bias during the inverse Abel transform until the electron density in the 70–80 km region of the resultant vertical profile is minimized to near zero.

    However, this linear bias introduced errors, as its magnitude increased over time, leading to significant discrepancies toward the end of the measurement. These errors often manifested as artificially high electron densities in the lower neutral atmosphere, sometimes exceeding the M2 peak density.

    To address this issue, the two steps have been consolidated into a single process, thereby eliminating the need for the linear bias stage. The polynomial detrend's effectiveness is now validated by minimizing the electron density in the 70–80 km region after the Abel inversion. The revised approach involves adjusting the polynomial detrend to account for the oscillator drift in the “vacuum portion” of the residuum, while allowing for a small offset from the 0 $0$   H z s 1 $\mathrm{H}\mathrm{z}{\mathrm{s}}^{-1}$ point—up to ± $\pm $ 0.5 Hz. This offset is determined through an optimization algorithm that iteratively adjusts the value until the same physically realistic low electron density is achieved in the 70–80 km region.

    A2 Finding Neutral Temperatures Near the M2 Layer

    Neutral temperatures at M2 altitudes can be determined through the analysis of the scale height in vertical electron density profiles. This method is valid because this region of the atmosphere is at photochemical equilibrium, where the timescales for transport are significantly longer than those for photochemical production and loss processes (Withers, 2009). The underlying logic is as follows: as the neutral atmosphere warms, it expands, causing the optical depth of unity to be reached at higher altitudes by the incident solar flux. This results in peak photoionization occurring at elevated heights. However, since the solar flux itself remains constant, the peak electron density does not change. Consequently, the ionospheric layers exhibit an increased scale height H $H$ , which can be readily determined.

    The process begins by parametrically fitting Equation 1 to the M2 peak, following the approach outlined by Sánchez-Cano et al. (2016). However, regions significantly above the M2 peak are no longer in photochemical equilibrium due to the dominance of transport dynamics, and regions below the M2 peak coincide with the M1 ionospheric layer. Therefore for this analysis, the parametric fit is performed within a range of −20 to +50 km around the M2 peak, ensuring a reliable estimation of the scale height H $H$ .

    The scale height H $H$ can then be used to calculate the neutral temperature T n ${T}_{n}$ using the following equation:
    T n = H g m k ${T}_{n}=\frac{Hgm}{k}$ (A2.1)
    where m $m$ is the molecular mass of CO2, k $k$ is the Boltzmann constant, and gravity g $g$ is dependent on altitude, calculated as:
    g = G M r m h 2 $g=G\frac{M}{{\left({r}_{m}-h\right)}^{2}}$ (A2.2)

    Here, G $G$ represents the Martian gravitational acceleration of 6.67 × 1 0 11 $6.67\times 1{0}^{-11}$ m 3 k g 1 s 2 ${\mathrm{m}}^{3}{\mathrm{k}\mathrm{g}}^{-1}{\mathrm{s}}^{-2}$ , r m ${r}_{m}$ is the mean Martian radius of 3.338 × 1 0 6 $3.338\times 1{0}^{6}$ m $\mathrm{m}$ , and h $h$ corresponds to the M2 altitude.

    Data Availability Statement

    All data required has been provided in the ESA Guest Storage Facility (Parrott, 2024). This includes the data for Table 1, and the data products for multiple steps along the processing chain to acquire the vertical electron density profiles. A data product guide has been provided to assist. The products exist for each of the mutual RO measurements shown, and they are:
    1. Beginning with the In-phase and Quadrature representation of the waveform received at TGO's Electra antenna.

    2. The net Doppler shift in the signal.

    3. A simulation with SPICE for the Doppler shift produced by the relative motion of the two spacecraft.

    4. The difference between the net Doppler shift and the SPICE simulation. This is the frequency shift due to the Martian atmosphere, modulated by the effects of the Electra unstable oscillator.

    5. The residuum, this is the frequency shift due to the atmosphere once the instabilities have been correct for.

    6. Vertical refractivity profile acquired via the inverse-Abel transform.

    7. Vertical electron density profile.